Optimizing User Distributions in Open-Plan Offices for Communication and Their Implications for Energy Demand and Light Doses: A Living Lab Case Study

Abstract

Open-plan offices have established themselves as economically efficient working environments and promote communication. Zoned lighting concepts have proven to be particularly energy-efficient and are determined by the respective occupancy profile. Due to their size, open-plan offices usually have very different levels of daylight availability depending on their position in the room, which affects the light doses per workstation. It is unclear what influence the distribution of users in the room has on the respective target values. This study therefore examines the effects of a variation in the spatial distribution of users in a real open-plan office regarding the three target values of communication distances, daily light doses, and artificial light energy requirements. Statistical methods are used to examine how a user distribution optimized for one target variable affects the other target variables. Since optimizing user distribution is an NP-hard combinatorial problem, heuristic methods are used. The results show that optimized user distribution improves only one target variable. There are no consistently strong correlations between the optimization of communication distances, energy savings, and achievable daily light doses. The work thus contributes to the holistic design of sustainable, user-centered working environments. This research is an example of a living lab case study with optimization-based modeling, emphasizing its exploratory nature rather than controlled experimental inference.

1. Introduction

1.1. Behavioral Dynamics in Open-Plan Offices

Open-plan offices have established themselves as the dominant office type due to their economic advantages, including low construction and operating costs, high space efficiency, and greater flexibility compared to individual offices. Typologically, open-plan offices are characterized by open spatial structures with few physical boundaries, which generally allows for high daylight utilization when appropriate systems are used. However, the lack of spatial separation often leads to reduced comfort, including higher noise levels, increased acoustic and visual distractions, and a general loss of privacy, which can result in reduced user satisfaction [1,2].

To counteract these drawbacks, modern adaptations of open-plan offices increasingly utilize hybrid spatial typologies, ranging from team-oriented spaces to modular pods [3], with the goal of enabling a largely disruption-free collaboration between employees, especially in terms of communication.

Communication is considered a key factor in work productivity. Since effective collaboration requires physical proximity [3], employees are positioned in the room in such a way that communication channels are efficient and direct. Short distances in multi-person offices and few barriers increase the likelihood of informal interactions and promote the exchange of implicit knowledge [4,5], which can have a positive effect on productivity [6,7] and team spirit [2]. Targeted distribution of users can therefore be considered an important lever for increasing the effectiveness of open workspaces.

Meetings offer advantages in terms of innovation, critical reflection, problem solving, and idea generation, and have a positive effect on productivity [8,9]. Despite these advances, meetings also represent a significant resource-related burden. For example, managers today spend more time in meetings than ever before [10]. The duration and location of meetings vary considerably depending on an individual’s organizational role within the company [11]. This development not only affects the temporal organization of the workday but also has substantial implications for physical presence in office buildings, as meetings contribute significantly to a high degree of mobility within the building, particularly due to the preparation and follow-up of meetings. As a result of this mobility, complex occupancy patterns [10] emerge in office areas and workplaces. These patterns are further intensified by the increasing implementation of modern and employee-centered flexible work arrangements such as remote work and flextime, which reduce the amount of shared time available for productive on-site collaboration.

Overall, these developments illustrate that in modern work environments both organizational factors and individual work arrangements are not only integral to productive collaboration but also have a lasting impact on the physical use of workplaces. The resulting occupancy dynamics must therefore be adequately considered in both planning and organizational models, not only to meet the increasing demands on communication and productivity but also to ensure the overarching functionality and performance of building technologies and controls systems.

1.2. Lighting-Related Implications of Behavioral Dynamics

An essential basic idea of energy-efficient building operation is to provide energy is only where it is needed. In the context of artificial lighting system in open-plan offices, the implementation of zoned lighting concept has proven essential, and their energy-saving potential has already been demonstrated in previous studies [12,13]. To achieve a more energy-efficient system performance, occupancy-related information is collected using presence sensors, such as passive infrared sensors (PIR), which have proven essential for the demand-oriented provision of artificial light [14]. Compared to manual control, presence-based control promises energy savings of approximately 30% [15].

Moreover, zoned lighting concepts often show positive effects regarding comfort criteria and user satisfaction [12], as increased zoning can help prevent conflicts resulting from different lighting preferences [16]. Although the concept of zoning is closely tied to artificial lighting systems, it is transferable to other building systems as well.

In terms of energy demand in zoned lighting systems, the consumption of each lighting zone results from the logical OR-linkage of the individual user dynamics assigned to that zone. Additionally, since office applications are generally subject to the normative requirement of 500 lx at the workplace (see [17]), accounting for spatial and temporal variations in daylight is essential for determining the artificial lighting energy demand. These fluctuations can be dynamically monitored using illuminance sensors [18]. Considering these influencing factors, the most efficient use of such systems results when two key conditions are met: (1) users within a lighting zone exhibit a similar occupancy behavior during periods of insufficient daylight, and (2) zones with higher daylight availability are occupied by users with higher presence rates.

In addition to energy consumption, modern artificial lighting design is increasingly shaped by additional planning objectives. As a central comfort factor, lighting conditions significantly influence the subjective well-being of employees and, indirectly, their productivity [19]. Several studies also show that light can have a direct effect on mood and cognitive performance [20,21], thereby positively influencing work productivity at this level as well. These effects are generally considered short-term, acute effects of light, which are mainly addressed by lighting conditions with increased color temperatures and illuminance levels.

In addition, lighting is also a critical parameter on a long-term scale, as circadian rhythms are demonstrably influenced by a variety of light-related parameters. For example, higher daily light doses can have a stabilizing effect [22,23], which, in turn, can lead to improved sleep quality, increased overall well-being, and enhanced work productivity. Given that people today spend approximately 90% of their time indoors [24], artificial light plays a key role in achieving such non-image-forming effects of light, as daylight availability is often insufficient due to a variety of constraints, including, in particular, window size and orientation, the glazing material used, the properties and arrangement of interior and exterior surfaces and the integration of daylight guidance or limitation systems. These elements determine how much natural light reaches certain areas of the room [25,26]. In addition, glare protection and overheating protection must be ensured for user acceptance when using daylight.

Nevertheless, the prioritized use of daylight to achieve non-visually effective light doses proves beneficial not only from an energy perspective. Artificial lighting systems are generally designed to meet specific target values, which makes temporary increases in illuminance for optimizing daily light doses difficult. Since daylight is not subject to these limitations, well-lit areas in particular offer increased potential from a non-visual standpoint. However, the usability of this potential largely depends on users’ occupancy behavior and whether workspaces with sufficient daylight exposure are occupied by employees with higher presence rates.

1.3. Problem Definition

Although individual user dynamics and the resulting utilization of spatial zones have a significant impact on energy demand and achievable daily light doses, these aspects are currently not considered when assigning individuals to specific workplaces. One reason for this is that the primary intention of open office layouts is clearly focused on enhancing communication, collaboration, and knowledge exchange [2,3], which leads to a prioritization of short communication paths and, ideally, opportunities for direct coordination [4]. Another reason is that physical proximity between employees is considerably easier to quantify than non-visual light effects or energy consumption. However, there is still insufficient knowledge on whether such decisions are detrimental to lighting-related key performance indicators or whether synergetic effects exist between the various requirement domains, which could potentially be leveraged in future optimization strategies.

A deeper understanding of how employees are distributed in the room and how this distribution affects key performance indicators is therefore essential (not only for communication flows, but also space utilization efficiency, energy demand and comfort aspects) and central to understanding of the functional potential and limitations of open working environments. As already described, dependencies between multiple individuals (e.g., interaction intensity, behavioral pattern congruence) and the variety of spatial positioning options (e.g., distance between zones) must be considered. This makes the analysis of mutual influence a quadratic assignment problem, e.g., an NP-hard problem that cannot be solved in a reasonable time using brute force approaches, even with only a few users and zones, due to the factorial growth of possible assignments (n!). Consequently, suitable heuristic or approximate methods such as simulated annealing, Tabu Search or genetic algorithms are required to provide a suitable solution (see methods in [27]).

1.4. Purpose of This Study

The main objective of this study is to examine the influence of user distribution in the room on the target variables communication distances (representative of productivity), daily light doses, and artificial light energy requirements, and to quantify their potential mutual influences. To achieve this goal, new user distributions in the room are created based on real measurement data and various optimization algorithms, each optimizing a specific target variable. This allows us to examine how optimizing user distribution in the room regarding one of the three target variables affects the other two. Based on the derived results, the study aims to provide a solid basis for holistic recommendations for workplace design.

We hypothesized that the initial user distribution in the study object corresponds more to a communication-oriented optimum than a user distribution that is optimized in terms of energy demand or incidence of light. This is based on the assumption that informal and formal communication flows tend to be prioritized in practical space allocation decisions, especially in team-oriented office environments. Therefore, we expected that communication-optimized user distributions in the room may be accompanied by increased energy demand and suboptimal light incidence, leading to potential trade-offs. In this context, this paper investigates whether certain optimization strategies could provide additional benefits, for example, whether improvements in one target variable (e.g., communication distances) could lead to secondary benefits or at least acceptable trade-offs in the other target variables. The study uses statistical methods and real measurement data to investigate whether such trade-offs or synergies exist and to what extent they can be quantified. The aim is to support evidence-based decisions in spatial planning by providing a systematic understanding of the interactions of different optimization objectives in open working environments.

2. Related Work

2.1. Hot-Desking

A central assumption of open work concepts is that spatial proximity facilitates the exchange of information and improves work productivity [28]. In this context, hot-desking is becoming increasingly relevant, as it allows employees to use available workstations flexibly and thus facilitates dynamic group formation. Studies emphasize that hot-desking enables more intensive use of space, reduces costs, and can promote networking within organizations through flexible workplace selection [29,30].

At the same time, studies show that the flexible use of workplaces also favors informal interactions and knowledge sharing, for example, through chance encounters and the temporary proximity of people with similar tasks. These social contact opportunities can have a positive impact on a sense of community and group-based productivity [30].

However, hot-desking is also associated with social and organizational challenges, which also waste working time for setting up the workplace and have a disruptive effect [31], which could have a negative impact on satisfaction and thus on productivity. Therefore, overly dynamic user distributions should be avoided.

Despite this differentiated view, the influence of spatial proximity on communication and productivity remains a key issue. However, current studies still focus too little on dynamic user distributions according to commissioning, in particular targeted positioning according to thematic or project-related proximity, although this could in principle open up advantages for communication and productivity.

2.2. Computer-Aided Methods for User Distribution in the Room

An increasingly relevant strand of research is concerned with the data-based optimization of user distribution within a room. In this context, the work of Sood et al. describes the development and testing of the spacematch platform, which allocates flexible workspaces to occupants according to individual comfort preferences. Supported by a web-based mobile application, subjective comfort data on indoor environment quality (IEQ) parameters were correlated with objective sensor values in a field study and segmented into user-specific comfort profiles using unsupervised clustering. The aim was to identify stable preference patterns via longitudinal data collection in order to optimize space allocation as well as energy and area use. The results show the potential of dynamic, personalized space allocation, which can increase both user satisfaction and operational efficiency [32].

Berelson et al. also consider IEQ parameters for intelligent hot-desking. User preferences were collected via a survey and algorithmically compared with sensor data using a weighted distance function to assign suitable desks. A pilot test with students showed a significant increase in satisfaction among the majority of participants [33].

Hammes et al. considered individual occupancy patterns to optimize the distribution of users in the room for zoned lighting concepts with the objective of maximizing both energy efficiency and daily light doses [34]. The study showed that depending on user distribution, there are large ranges in both achievable light doses and the energy demand for artificial lighting. These result from the high variability in occupancy patterns and the spatially inhomogeneous availability of daylight. The study also demonstrated that there are clear trade-offs between optimizing light doses and optimizing energy efficiency. For example, users with high light doses often simultaneously have a high demand for artificial lighting, as their occupancy times also occur during periods of low daylight availability [34].

To the best of the authors’ knowledge, beyond these findings, aspects of communication and correlation analyses between the target values have not yet been sufficiently elaborated in the literature. The same applies to studies that go beyond optimizing physical office design and focus specifically on user distribution in the room to improve communication, energy consumption, and daily light doses. However, since these aspects are highly relevant for the application of user distribution optimization within office spaces, they should be investigated in greater depth.

3. Methodology

The study design is situated within the framework of a living lab case study with optimization-based modeling. The analyses are exploratory in nature and focus on understanding trade-offs in one specific real-world office environment. Consequently, the findings are considered context-specific and are not intended for direct generalization. Rather, they are intended to illustrate tendencies that arise under different optimization scenarios.

3.1. Study Object

This study is based on a long-term data collected during real operation in the former open-plan office of Bartenbach GmbH in Aldrans (Austria), which was designed as a Living Lab (see Figure 1). The open-plan office was divided into nine separate lighting zones, regularly accommodating 18 people and up to a maximum of 28 people. Although the five lighting zones on the south façade were designed for a maximum of four workstations each, two people are assigned to each of the nine lighting zones (see Figure 2). The study period was February 2022 to January 2023.

Each lighting zone can be controlled separately and is controlled in automatic mode by presence detection via passive infrared sensors (PIR, see Figure 3). This means that the logical OR combined occupancy profile of two people determines the artificial lighting energy demand of the respective lighting zone. This is because the requirement is that as soon as a person is within the lighting zone, the necessary artificial light for the work task must be provided. The occupancy sensors are designed for the respective workplace in the detection area. For each lighting zone, there are also illuminance sensors at the workstation, which measure the horizontal illuminance at the table and regulate the artificial light in the respective zone so that the normative 500 lx is guaranteed (according to EN12464-1 [17]). Since the actuator status and energy requirements of the luminaires are also logged, the proportion of artificial light can be calculated from the illuminance sensor and the energy requirements can be assigned to the respective user presences at the workplace. The artificial lighting and daylight system could be controlled individually for each zone, as the option of manual control is considered a key factor for user acceptance [35].

Due to the large south-facing façade and the presence of skylights (see Figure 1), a high proportion of daylight was available in the study object. Based on a Radiance simulation, an average daylight autonomy (DA) of 81.56% was determined using Radiance simulation (details in [36]), considering the normative illuminance level of 500 lx [17] and a reference period from 08:00 to 18:00. Depending on the spatial position within the room, significant differences in measurable daylight availability can be observed. This indicates a strong position-dependent influence on the achievable light doses (see Figure 4). Further details on the study object can be found in [12,37]. DA was calculated using Radiance to describe the study object. This allows the high daylight availability and its spatial distribution to be visualized. However, the study is based entirely on real measurement data.

The organizational framework for employees was a flextime working arrangement, with core working hours from Monday to Thursday from 09:00 to 12:00 and 14:00 to 17:00, and Fridays from 09:00 to 12:00. Employees also had the option to work from home. The job profile corresponded to that of a project manager in the field of research and development (R&D). The time studies by Panko et al. show that project managers generally spend around a quarter of their working time in meetings [38]. This picture also emerged in the open-plan office under consideration and resulted in highly dynamic occupancy patterns at the workplace.

As the communication style is strongly influenced by the office layout (cf. [7]), the focus is on avoiding barriers. In line with the study results of Boutellier et al., spontaneous, informal conversations occurred frequently in the studied object, leading to a more intensive exchange of knowledge and thus greater productivity. Employees communicated more directly and situationally, which made coordination processes more efficient. In particular, the reduced physical barriers between colleagues had a positive influence on their willingness to engage in conversations (cf. [7]). Within the R&D staff, there were individual areas of focus, meaning that some employees required more frequent exchange. However, their positioning had historically been random. Employees working on the same project or with similar skills have been placed close to each other, which theoretically leads to better communication and therefore greater productivity [39].

3.2. Data Acquisition and Processing

The building under investigation was equipped with a central building control system (Beckhoff, CX5140-0141, TwinCAT2), which enabled the collection of both occupancy and illuminance data. Occupancy information at the workstation level (PIR sensors; NodOn, PIR-2-1-01, positions in Figure 3) was recorded for status changes. This resulted in multiple detections per minute. The illuminance sensors (Thermokon, LDF 1000A, positions in Figure 3) record the measured values per minute, as do the energy meters (Eltako, FWZ12-16A). All data for the entire study period (February 2022–January 2023) were provided for analysis in a machine-readable file format (.csv). The study is based on real measurement data collected in the office building of Bartenbach GmbH with an ideal room occupancy of 18 people.

The core idea of the study is to derive new user distributions in the room in order to evaluate their impact on the target variables. To derive energy-optimized user distributions in the room, the energy consumption per zone is required, resulting from the various logically OR linked individual presences (153 different combinations of 2 out of 18 people). This can be determined from the available measurement data. The resulting energy demand per zone was calculated based on a target illuminance of 500 lx.

A position-dependent correction factor was used to determine the vertical illuminance at eye level. This factor was derived from Radiance simulations in order to realistically represent the spatial distribution of light in the room. The correction factor was determined for each workstation and calculated based on the measured horizontal illuminance values. This study did not apply explicit spectral weighting. The calculated vertical illuminance is combined with the respective occupancy data to determine the light dose per user at each position. These values form the basis for optimizing user distribution in the room using target daily light doses.

To evaluate the communicative aspects of workplace allocation, both the relevance of interaction between employees and the distance between workstations were considered. The relevance of interaction was retrospectively assessed by the R&D department’s management, as direct, self-reported employee feedback could not be collected for organizational reasons. The assessment was expressed as a percentage and represents a weighting between individual employees, including consideration of independent work (see

Table 1. Preference matrix: Interaction intensity between people, assessed by the managers in the study object. Not representative of the initial situation.

		Development											Research
		User A	User B	User C	User D	User E	User F	User G	User H	User I	User J	User K	User L	User M	User N	User O	User P	User Q	User R
Development	User A	32.50%	9.00%	20.00%	5.00%	5.00%	5.00%	3.00%	6.00%	2.00%	8.50%	2.50%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.50%
	User B	9.00%	41.50%	5.00%	5.50%	2.50%	8.50%	2.50%	7.50%	2.50%	7.50%	3.00%	0.00%	0.00%	0.00%	1.50%	0.00%	1.00%	2.50%
	User C	20.00%	5.00%	22.00%	10.00%	5.00%	4.50%	5.00%	6.00%	2.50%	11.00%	4.00%	2.50%	0.00%	0.00%	0.00%	0.00%	0.00%	2.50%
	User D	5.00%	5.50%	10.00%	27.50%	5.00%	4.00%	6.50%	10.00%	4.00%	10.00%	10.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	2.50%
	User E	5.00%	2.50%	5.00%	5.00%	49.00%	4.00%	5.00%	3.00%	3.50%	11.00%	4.00%	0.00%	0.00%	0.00%	0.00%	3.00%	0.00%	0.00%
	User F	5.00%	8.50%	4.50%	4.00%	4.00%	35.00%	6.50%	12.50%	4.00%	11.00%	2.50%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	2.50%
	User G	3.00%	2.50%	5.00%	6.50%	5.00%	6.50%	31.00%	15.50%	10.00%	7.50%	6.50%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.00%
	User H	6.00%	7.50%	6.00%	10.00%	3.00%	12.50%	15.50%	0.00%	12.50%	14.00%	10.00%	1.00%	0.00%	0.00%	0.00%	0.00%	1.00%	1.00%
	User I	2.00%	2.50%	2.50%	4.00%	3.50%	4.00%	10.00%	12.50%	39.50%	8.50%	6.00%	0.00%	0.00%	2.50%	0.00%	0.00%	0.00%	2.50%
	User J	8.50%	7.50%	11.00%	10.00%	11.00%	11.00%	7.50%	14.00%	8.50%	0.00%	8.00%	1.00%	0.00%	0.00%	0.00%	0.00%	0.50%	1.50%
	User K	2.50%	3.00%	4.00%	10.00%	4.00%	2.50%	6.50%	10.00%	6.00%	8.00%	39.50%	0.00%	0.00%	0.00%	1.00%	1.50%	1.00%	0.50%
Research	User L	0.00%	0.00%	2.50%	0.00%	0.00%	0.00%	0.00%	1.00%	0.00%	1.00%	0.00%	14.00%	25.00%	7.50%	10.00%	27.50%	6.50%	5.00%
	User M	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	25.00%	37.50%	0.00%	7.50%	30.00%	0.00%	0.00%
	User N	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	2.50%	0.00%	0.00%	7.50%	0.00%	60.00%	0.00%	0.00%	15.00%	15.00%
	User O	0.00%	1.50%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.00%	10.00%	7.50%	0.00%	67.50%	7.50%	0.00%	5.00%
	User P	0.00%	0.00%	0.00%	0.00%	3.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.50%	27.50%	30.00%	0.00%	7.50%	30.50%	0.00%	0.00%
	User Q	0.00%	1.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.00%	0.00%	0.50%	1.00%	6.50%	0.00%	15.00%	0.00%	0.00%	50.00%	25.00%
	User R	1.50%	2.50%	2.50%	2.50%	0.00%	2.50%	1.00%	1.00%	2.50%	1.50%	0.50%	5.00%	0.00%	15.00%	5.00%	0.00%	25.00%	32.00%

—Not representative of the initial situation). The distance between workstations was derived from floor plan documentation (see Figure 2) and recorded in meters (see

Table 2. Distance matrix: Spatial distance between the workplaces in meters (cf. Figure 2), assessed by the executive managers in the study object.

		Zone
		1_1	1_2	2_1	2_2	3_1	3_2	4_1	4_2	5_1	5_2	6_1	6_2	7_1	7_2	8_1	8_2	9_1	9_2
Zone	1_1	0.00	0.89	4.80	5.69	14.41	15.29	19.20	20.09	4.30	4.39	6.44	7.13	10.52	11.34	15.03	15.88	19.68	20.55
	1_2	0.89	0.00	3.91	4.80	13.52	14.40	18.31	19.20	4.39	4.30	5.88	6.44	9.72	10.52	14.18	15.03	18.81	19.68
	2_1	4.80	3.91	0.00	0.89	9.61	10.49	14.40	15.29	6.44	5.81	4.30	4.39	6.45	7.13	10.52	11.34	15.03	15.88
	2_2	5.69	4.80	0.89	0.00	8.72	9.60	13.51	14.40	7.13	6.44	4.39	4.30	5.82	6.44	9.71	10.52	14.18	15.03
	3_1	14.41	13.52	9.61	8.72	0.00	0.89	4.80	5.69	15.08	14.23	10.59	9.77	6.55	5.93	4.45	4.54	6.54	7.22
	3_2	15.29	14.40	10.49	9.60	0.89	0.00	3.91	4.80	15.92	15.07	11.40	10.58	7.22	6.55	4.54	4.45	5.92	6.55
	4_1	19.20	18.31	14.40	13.51	4.80	3.91	0.00	0.89	19.71	18.84	15.07	14.22	10.58	9.78	6.55	5.92	4.45	0.45
	4_2	20.09	19.20	15.29	14.40	5.69	4.80	0.89	0.00	20.58	19.71	15.92	15.07	11.39	10.58	7.22	6.55	4.54	4.45
	5_1	4.30	4.39	6.44	7.13	15.08	15.92	19.71	20.58	0.00	0.89	4.80	5.69	9.60	10.49	14.40	15.29	19.20	20.09
	5_2	4.39	4.3	5.81	6.44	14.23	15.07	18.84	19.71	0.89	0.00	3.91	4.80	8.72	9.60	13.51	14.40	18.31	19.20
	6_1	6.44	5.88	4.30	4.39	10.59	11.40	15.07	15.92	4.80	3.91	0.00	0.89	4.81	5.69	9.60	10.49	14.40	15.29
	6_2	7.13	6.44	4.39	4.30	9.77	10.58	14.22	15.07	5.69	4.80	0.89	0.00	3.92	4.80	8.71	9.60	13.51	14.40
	7_1	10.52	9.72	6.45	5.82	6.55	7.22	10.58	11.39	9.60	8.72	4.81	3.92	0.00	0.89	4.80	5.69	9.60	10.49
	7_2	11.34	10.52	7.13	6.44	5.93	6.55	9.78	10.58	10.49	9.60	5.69	4.80	0.89	0.00	3.91	4.80	8.71	9.60
	8_1	15.03	14.18	10.52	9.71	4.45	4.54	6.55	7.22	14.40	13.51	9.60	8.71	4.80	3.91	0.00	0.89	4.80	5.69
	8_2	15.88	15.03	11.34	10.52	4.54	4.45	5.92	6.55	15.29	14.40	10.49	9.60	5.69	4.80	0.89	0.00	3.91	4.80
	9_1	19.68	18.81	15.03	14.18	6.54	5.92	4.45	4.54	19.20	18.31	14.40	13.51	9.60	8.71	4.80	3.91	0.00	0.89
	9_2	20.55	19.68	15.88	15.03	7.22	6.55	0.45	4.45	20.09	19.20	15.29	14.40	10.49	9.60	5.69	4.80	0.89	0.00

). The preference-weighted communication distance for a user distribution in the room is calculated by matrix multiplication (preference matrix with distance matrix).

Regarding the assessment of collaboration between employees, two key aspects of work behavior in the examined open-plan office should be noted. First, most employees demonstrated a high degree of personal responsibility for their assigned project tasks, which helps to explain the frequently reported highly perceived independent work. Second, there was a minimal overlap between the thematic areas of development and research. The development team primarily focused on the design of optical components, whereas the research team concentrated on topics related to perceptual psychology and daylight studies. This distinction was also reflected in communication patterns, as relevance was primarily evaluated within individual groups, with limited cross-group communication.

All employees gave written informed consent to the use of their data before data collection. All data were processed in compliance with data protection regulations. The study was conducted outside the influence of COVID-19.

3.2.1. Deriving Optimized User Distributions Depending on Target Variables

There is a separate optimized user distribution in the room for each of the three optimization target variables (communication distances, light doses and artificial light energy consumption). Deriving these distributions represents a highly complex combinatorial problem. Since there are more than 1.25 × 10¹³ possible combinations of 18 seats, each allocated to nine zones of two people [40], a brute-force search is not productive. Brute-force solutions are no longer feasible within realistic computing times, thus rendering the problem NP-hard. To derive solutions, nevertheless, the problem is formally described as a multidimensional assignment problem. Therefore, heuristics and approximation methods are indispensable for determining optimized seating arrangements and obtaining the best possible solutions within an acceptable computing time. These methods can specifically identify, from the multitude of potential user arrangements, those that deliver minimum or maximum values depending on the target variable under consideration. This forms the basis for a methodically sound comparison of optimization approaches. Since different requirements exist for each target variable, separate optimization approaches are required for each one.

3.2.2. Algorithm Selection

Depending on the structure and complexity of the assignment problem, e.g., simple bipartite matching or a multidimensional assignment problem, different algorithmic approaches are required. The optimization of the user distribution in the room according to the target criteria of energy efficiency and daily light doses follows the methodology of Hammes et al. [34]. Due to a lack of references in the existing literature, multiple optimization algorithms were applied and compared to determine the optimal seating allocations for communicative aspects. Although the Blossom-Hungarian algorithm combination has proven successful in optimizing energy efficiency [34], a suitable algorithm must be found to derive a user distribution that minimizes communication distances.

The study compared eight different optimization algorithms for improving communication distances by deriving more suitable user distributions within the room. Iterated Local Search (ILS) achieved the best results in minimizing communication distances but took the longest to compute. Simulated Annealing (SA), on the other hand, was the fastest and still delivered good results. For this reason, SA was used to optimize the user distribution for the target variable, communication distance. Statistical tests confirmed significant differences in the performance and runtimes of the methods, although some methods did not differ significantly from each other. A detailed comparison of the algorithms is provided at the end of the article.

3.2.3. Synergy Effects Between the Target Criteria

While the selection of the algorithm remains constant, it is imperative to assess the potential synergistic effects between the diverse target criteria, including energy consumption, daily light dose, and communication distances. To this end, the seat assignments were optimized for each individual performance criterion, both for the best- and worst-case scenarios. Comparing these extremes reveals both trade-offs and potential synergies between the criteria. This makes it clear whether an improvement in one area simultaneously leads to advantages or disadvantages in others.

3.2.4. Outcome Measures

For each determined seating allocation, the following outcome measures were subsequently calculated. Regarding energy consumption, the energy demand was assessed at the zonal level in kilowatt-hours (kWh). The total energy consumption in this study refers to the sum of all energy demands per lighting zone over the study period. This includes the energy demands of nine zones from February 2022 to January 2023. The measurement intervals were not subdivided into interim intervals. Since this is partly determined by the degree of simultaneous work zone use by two employees (“same presences”), this factor was also calculated at the zonal level in minutes. Light doses were calculated at a zonal level. Communicative aspects were quantified at the level of user pairs as weighted distances in meters, calculated by multiplying the physical distance between workstations by a corresponding relevance factor. Additionally, for each employee, the weighted distance to their most relevant colleague was determined in meters.

3.2.5. Data Normalization

Since the aim of this study was to examine whether improvement on one target value also leads to an improvement in one or both of the other target values, analyses were conducted partially in relation to the relative shift in target values. However, as the three target variables were based on different initial conditions and thus exhibited different potentials for shifting, the data were normalized prior to analysis.

Normalization was performed for each target variable with respect to the optimized range, i.e., the minimum and maximum values resulting from the respective best-case and worst-case optimizations. For example, the weighted communication distances of users were normalized relative to the observed minimum and maximum communication distances (min: 1.56 m, max: 12.9 m). The resulting values were expressed as a percentage position within the identified range, where 0% corresponds to the minimum value and 100% to the maximum value. All reported percentage shifts are therefore to be understood as relative displacements with reference to the respective optimized ranges.

3.3. Statistical Analysis

Optimizations were performed for both the best and worst-cases for all three target criteria. The optimizations were applied to 18 users in nine zones. The evaluation unit was the user pairings and their positions in the room for each algorithm, based on real measurement data. In each optimization run, all 18 users were uniquely assigned to the nine available zones so that each user appeared exactly once. This guarantees that no user was present in more than one pair within the same optimized configuration. Consequently, the evaluation unit was the pairing of two different users at the zone level. Since different user distributions result for each target variable and optimization (e.g., user A and user B in zone 1 in the best-case and user A and user C in zone 2 in the worst-case), the user pairings are not identical between optimizations. By defining the zone as an independent unit, the statistical independence of the observations was ensured and dependencies between pairs were structurally avoided.

The present study is designed as a living lab case study with optimization-based modeling, rather than a controlled experiment with fixed group sizes. Consequently, all statistical analyses are conducted in an exploratory manner, with the primary objective of elucidating tendencies and trade-offs between communication, light doses, and lighting energy demand. Generalized linear mixed models (GLMMs) are employed to address the nested data structure, as users are paired within zones (applies to the case of the target value energy demand), and to appropriately handle non-normally distributed data. In this particular context, the utilization of GLMMs is particularly appropriate. These models are adept at incorporating dependencies within zones by including users or zones as random effects. Additionally, GLMMs possess the capacity to accommodate data that deviate from normality. Correlation analyses employing Pearson or Spearman coefficients are conducted to explore potential relationships. However, the results are not intended to establish confirmatory conclusions about generality.

The optimization strategies were compared using the GLMM. For the analysis of energy demand, the statistical unit of analysis was designated as the zone, with a sample size of n = 9. This designation was made due to the fact that energy consumption is the result of the combined occupancy profiles of two users per zone. For the purpose of analyzing communication distances and light doses, the statistical unit of analysis was defined as the individual user (n = 18). This methodological decision was made because these measures are determined by user-specific positions within the office and are therefore deemed to be independent at the individual level. To account for non-independence inherent in the data, random intercepts for zones or users were included. In this particular context, the utilization of GLMMs is particularly appropriate, as they possess the capacity to manage complex data structures that are nested and outcomes that deviate from normality.

Q-Q plots of the residuals were first examined to visually assess deviations from normality. The link function with the best fit was selected as the distributional assumption for the dependent variable. Model fit was then further evaluated through residual analyses, including, where appropriate, a Shapiro–Wilk test for normality of the residuals. If this was not the case, model diagnostics focused on the appropriateness of the assumed distribution and on overdispersion tests. The rationale behind this procedure is that deviations from normality or distributional assumptions directly impact the validity of the GLMM results. Therefore, diagnostic tests were necessary to ensure reliable inference. The optimization strategy was modeled as a fixed effect and the respective performance indicator as the dependent variable. This way of modeling shows the relationship between the cause (optimization strategy) and the effect (performance indicator). It also includes random effects to show how users or zones can make a difference.

To control pairwise comparisons between the optimization strategies, a post hoc test based on estimated marginal means (EMMs) with Bonferroni correction was performed. The number of pairwise comparisons corresponded to the number of optimization strategies (k) under investigation, resulting in k × (k − 1)/2 unadjusted p-values. In the present analyses with three strategies, this led to three pairwise comparisons and thus three initial p-values, which were adjusted using the Bonferroni correction.

The subsequent application of post hoc tests is contingent upon the identification of overall differences in the GLMM, thereby ensuring that any significant effect identified can be traced back to specific group contrasts. Q-Q plots were used to visually assess deviations from normality, while the Shapiro–Wilk test provided a formal test statistic. The number of residuals evaluated by Q-Q plots and the Shapiro–Wilk test corresponded to the number of observed values in each analysis (i.e., one value per user or per zone, depending on the model). These approaches were employed in a complementary manner.

The results of the GLMM are represented by the estimated effect, standard error (SE), z-value (effect/SE), and p-value. The p-values were estimated and based on two-sided approximate Wald tests to assess the significance of the fixed effects. The effect indicates the difference from the reference condition. Since the study is designed as an exploratory case study, the p-values serve only to illustrate trends within the optimization scenarios. Descriptive metrics such as means, standard deviations, and ranges are reported in addition to illustrate trade-offs between communication distances, light doses, and energy consumption. The intraclass correlation coefficient (ICC) was calculated to quantify the proportion of variance explained by random effects. The SE describes the accuracy of the estimate. The z-value quantifies the statistical significance relative to the null hypothesis. The p-value indicates the probability that the observed effect occurred by chance.

For the purpose of descriptive traceability, the means, standard deviations, and minimum and maximum values are provided for both the best- and worst-case scenarios. In the context of GLMMs, effect sizes were determined through the calculation of partial R² values (for fixed effects) and confidence intervals for the fixed-effect estimates, which quantify the proportion of the variance in the dependent variable explained by the optimization strategy and provide a measure of estimate precision. These values served to quantify the proportion of the variance in the dependent variable that was explained by the optimization strategy. The interpretation of partial R² values is guided by established conventions. Specifically, values ranging from approximately 0.01 to 0.06 are classified as small, those from 0.06 to 0.14 are considered medium, and values exceeding 0.14 are designated as large [41]. Furthermore, confidence intervals were reported for the estimated effects to document the precision of the estimates.

The energy demand was assessed at the zone level because it is derived from the combined presence profile of user pairs (logically OR-linked) and the required artificial lighting during presence times to ensure the normative minimum illuminance. Energy consumption analyses were conducted at the zone level, with a sample size of nine zones (n = 9). In contrast, distances and daily light doses were collected and evaluated per user and their position in the room, representing purely user-specific measures (n = 18). In order to facilitate comprehension when comparing the same target variable across different optimization scenarios, it is imperative to make a distinction in evaluation level. Correlation analyses, however, refer specifically to the user pairings within each zone, resulting in a sample size of nine (n = 9) for these analyses.

Data were statistically compared both between and within the individual optimization strategies. The analysis in relation to the differences between the optimization strategies is based on comparisons of the resulting distributions in the individual performance indicators. The statistical analyses were conducted with reference to the absolute values obtained.

The analyses within the individual optimization strategies targeted the identification of relationships between different performance indicators and were conducted using correlation analyses. The analyses used the normalized values, e.g., the relative displacements with reference to the respective optimized ranges. To facilitate a more comprehensive assessment of the correlations, both best-case and worst-case optimizations as well as the initial situation were included. All values were determined on a zonal level.

Pearson correlation coefficients were generally calculated to assess relationships. In cases where the assumptions of normality (assessed via the Shapiro–Wilk test) and homogeneity of variance (assessed via Levene’s test) were partially violated, the nonparametric Spearman rank correlation was applied. In correlation analyses, the Pearson or Spearman correlation coefficient is reported alongside its magnitude (|r| or |ρ|), the corresponding p-value. The exact p-value was calculated using the t-approximation [42]. The magnitude of the correlation coefficient indicates the strength of the relationship, regardless of direction. For the Pearson coefficient, |r| indicates the strength of the linear correlation, while for the Spearman coefficient, |ρ| indicates the strength of the monotonic relationship between the variables. Due to the limited sample size (n = 9 for zone-based analyses), these analyses are underpowered and serve only to identify trends.

For descriptive analyses, either the mean and standard deviation or, in the case of non-normally distributed data, the median along with the 25th and 75th percentiles (in parentheses) are reported in addition to the overall total. In case of a non-normal distribution in one of the optimizations (best-case or worst-case), central tendency and dispersion are reported as median and interquartile range (IQR) for both groups to ensure comparability. Correlation analyses are presented with regard to correlation coefficients and significance levels. For significant results, effect sizes are additionally provided. Figures show either box plots or correlation plots (scatterplots with regression lines).

All statistical analyses were conducted with JASP (version 0.18.3.0) at a two-sided significance level of 0.05. Further analyses were carried out using Python (Python 3.12). The main libraries used were pandas (version 2.2.3), numpy (2.1.3), scipy (version 1.15.1) and scikit_posthocs (version 0.11.14) for data analysis as well as matplotlib (version 3.9.3), seaborn (0.3.12) and plotly (version 6.0.1) for data visualization.

4. Results

4.1. Comparison of Performance Indicators Between Objective-Specific Optimization Strategies

4.1.1. Communication Distances

The initial user distribution in the room resulted in a cumulative preference-weighted communication distance of 100.87 m (total distance from each user to all others; calculated using matrix multiplication of Table 1 with Table 2). When optimizing for communication via Simulated Annealing (

Table 3. Cumulative preference-weighted communication distances, the corresponding user-related share in the median and the median of the user-related communication distances to the respective most important colleague (all values in m), each resulting from explicit best-case and worst-case optimizations to a specific target value.

		Best-Case Scenario	Worst-Case Scenario
Initial situation	Total in m:	100.87
	User-related in m:	5.5 (4.19–6.55)
	Preferred user in m:	5.31 (4.45–6.44)
Optimization of communication paths via Simulated Annealing	Total in m:	62.04	137.79
	User-related in m:	3.73 (2.39–4.11)	7.17 (5.56–9.78) *
	Preferred user in m:	2.49 (1.33–3.99) *	14.05 (12.42–17.09) *
Optimization of daily light doses via method of [34]	Total in m:	114.54	103.79
	User-related in m:	6.24 (5.05–7.94) *	5.71 (4.14–6.94) *
	Preferred user in m:	6.57 (4.47–14.14)	10.52 (5.75–14.65) *
Optimization of energy demand via method of [34]	Total in m:	106.25	114.15
	User-related in m:	5.37 (4.59–6.22)	6.39 (5.08–8.37) *
	Preferred user in m:	5.69 (1.64–10.3)	9.60 (4.8–14.40)

Note: Values show cumulative totals (in bold) and medians and IQR to ensure comparability. Normally distributed data are marked with *.

), this value dropped to 62.04 m in the best-case scenario, corresponding to a 38.5% reduction. This optimization also yielded the shortest distances to the most relevant colleagues of 2.49 m (1.33–3.99 m). Determined in each case by the sum of all weighted communication distances per user. In comparison, these are 5.31 m (4.45–6.44 m) in the initial situation. In addition, user-level distances varied widely (3.73 m (2.39–4.11 m)). In the worst-case scenario the optimization resulted in a total distance of 137.79 m, yielding a range of 75.75 m across users. Consequently, user-level distances increased from 5.50 m (4.19–6.55 m) in the initial situation to 7.17 m (5.56–9.78 m). The distances to the preferred user also deteriorated considerably (14.05 m (12.42–17.09 m)).

When optimizing for light dose (Table 3), communication distances increased in the best-case scenario to 114.54 m (+13.54%), with significant increases in both the distances to the most relevant colleagues (6.57 m (4.47–14.14 m)) and the user-level distances (6.24 m (5.05–7.94 m)). Contrarily, minimizing light doses in the worst-case scenario showed only a marginal effect on communication distances on both cumulative (103.79 m, +2.89%) and user-level (5.71 m (4.14–6.94 m)). The distances to the preferred users became significantly greater (10.52 m (5.75–14.65 m)).

In relation to energy efficiency optimization (Table 3), communication distances increased in the best-case scenario to 106.25 m (+5.32%). Both the distances to key colleagues (5.69 m (1.64–10.30 m)) and user-level distances (5.37 m (4.59–6.22 m)) remained comparatively high. Communication distances also increased in the worst-case scenario. This applies to the communication distance in total (114.15 m; +13.16%), as well as at user level 6.39 m (5.08–8.37 m) and to the preferred users (9.6 m (4.8–14.4 m).

A GLMM was used to investigate the effects of different optimization strategies on weighted communication distances. The optimization strategy was modeled as a fixed effect, the weighted communication distances is the dependent variable, and random intercepts for individual users (n = 18) were considered as random effects. The explicit optimization of communication distance served as the reference category.

For the best-case scenario, the GLMM showed significant differences between the strategies. Compared to the reference scenario, energy optimization increased communication distance by 2.46 m (SE = 0.46; z = 5.29; p = 1.22 × 10⁻⁷), while optimizing user distribution under the target daily light dose increased the distance by 2.92 m (SE = 0.46; z = 6.28; p =3.12 × 10⁻¹⁰). In the worst-case scenario, energy optimization reduced the distance by −1.31 m (SE = 0.49; z = −2.67; p = 0.01), and optimization of user distribution under the light dose target reduced the distance by −1.89 m (SE = 0.49; z = −3.85; p = 1.18 × 10⁻⁴). This means that the effects are contrary to the actual aims of the best- and worst-case scenarios. Q-Q plots of the residuals showed deviations from the theoretical line in the best-case scenario due to positive skewness and slight peaking (skewness: 0.95; kurtosis: 2.01 (cf. Figure 5a)). In the worst-case scenario, the residuals were almost on the line (skewness: 0.06; kurtosis: −0.45 (cf. Figure 5b)). These results were confirmed by the Shapiro–Wilk test (best-case: W = 0.95; p = 0.03; worst-case: W = 0.99; p = 0.86). The variance of the random intercepts revealed that individual users significantly influenced the results. In the best-case scenario, the variance was 1.44 (ICC = 0.43); in the worst-case scenario, the variance was 3.40 (ICC = 0.61). The EMMs revealed the following communication distances: 3.45 m for explicit optimization (worst-case: 7.66 m), 5.90 m for energy optimization (worst-case: 6.34 m), and 6.36 m for light dose optimization (worst-case: 5.77 m). Post hoc pairwise comparisons with Bonferroni correction revealed significant differences between nearly all strategies (all p < 0.001, see

Table 4. p-values of the post hoc pairwise comparisons with Bonferroni correction resulting from the comparison of the optimization procedures with different target variables under the target variable communication distance and distance to the preferred user.

Objective	Post Hoc Pairwise Comparisons (Bonferroni)	p-Value
		Best-Case Scenario	Worst-Case Scenario
Preference weighted communication distance	Optimization of communication distances vs. optimization of energy consumption	3.65 × 10−7	0.02
	Optimization of communication distances vs. optimization of daily light doses	9.96 × 10−10	3.53 × 10−4
	Optimization of energy consumption vs. optimization of daily light doses	0.96	0.72
Distance to preferred user	Optimization of communication distances vs. optimization of energy consumption	0.02	5.06 × 10−4
	Optimization of communication distances vs. optimization of daily light doses	1.67 × 10−4	2.03 × 10−3
	Optimization of energy consumption vs. optimization of daily light doses	0.57	1.00

), except for optimizing user distribution under the energy efficiency target and light dose optimization (p-values in Table 4). The fixed effects explained in best-case scenario a moderate proportion of the variance in the dependent variable, as indicated by a partial R² of 0.33 (worst-case: R² = 0.10).

Significant differences were also found in the distances to the preferred user. In the best-cases scenario, the distances to the preferred user increased due to energy optimization (4.02 m; SE = 1.48; z = 2.72; p = 0.01) and light dose optimization (5.96 m; SE = 1.48; z = 4.03; p = 5.58 × 10⁻⁵), and decreased in the worst-cases of energy optimization (−5.35 m; SE = 1.42; z = −3.76; p = 1.69 × 10⁻⁴) and light dose optimization (−4.83 m; SE = 1.42; z = −3.40; p = 6.76 × 10⁻⁴), respectively, compared to the reference. Thus, the results were contrary to the target objectives. Q-Q plots of the residuals showed deviations in the best-case (skewness: 0.81; kurtosis: 0.07 (cf. Figure 5c)) and approximate normality in the worst-case (skewness: 0.07; kurtosis: −0.62 (Figure 5d)). The Shapiro–Wilk test confirmed this, with W = 0.93 with p = 0.01 in the best-case and W = 0.97 with p = 0.11 in the worst-case. The variance of the random intercepts and the ICC were very small (variance, best-case: 1.5 × 10⁻³; worst-case: 0.02; ICC: best-case: 5.58 × 10⁻⁵; worst-case: 1.25 × 10⁻³). The EMMs were 2.89 m for the distances to the preferred user with the explicit optimization of communication distance (worst-case: 14.58 m), 6.91 m for energy optimization (worst-case: 9.23 m), and 8.85 m for lighting optimization (worst-case: 9.74 m). Post hoc comparisons showed significant differences between most strategies (p < 0.001, see Table 4), except between energy and light dose optimization (best-case: p = 0.57; worst-case: p = 1.00). The partial R² values for the fixed effects are 0.24 for the best-case and 0.25 for the worst-case.

4.1.2. Daily Light Doses

For the initial user distribution in the room, a daily light dose of 2723.27 ± 930.10 lxh (min: 1152.26 lxh, max: 4738.46 lxh) is obtained for all users (

Table 5. User-related daily light doses resulting from explicit best-case and worst-case optimizations to a specific target value.

		Best-Case Scenario	Worst-Case Scenario
Initial situation	mean ± std in lxh:	2723.27 ± 930.10
	min in lxh:	1152.26
	max in lxh:	4738.46
Optimization of communication paths via Simulated Annealing	mean ± std in lxh:	2645.26 ± 929.73	2659.9 ± 976.41
	min in lxh:	1314.74	1282.35
	max in lxh:	3945.05	4121.75
Optimization of daily light doses via method of [34]	mean ± std in lxh:	2909.31 ± 1221.09	2417.19 ± 532.42
	min in lxh:	889.31	1537.17
	max in lxh:	5146.58	3766.81
Optimization of energy demand via method of [34]	mean ± std in lxh:	2696.84 ± 983.96	2624.18 ± 904.27
	min in lxh:	1172.31	1165.06
	max in lxh:	4400.82	3955.43

Note: Values show mean and standard deviation (in bold) and minima and maxima to ensure comparability.

). The best-case optimization leads to an average daily light dose of 2909.31 ± 1221.09 lxh (+6.83%, min: 889.31 lxh, max: 5146.58 lxh). Contrarily, the worst-case scenario optimization showed a significant reduction compared to the initial situation (2417.19 ± 532.42, −11.24%, min: 1537.17 lxh, max: 3766.812 lxh).

Optimizing the communication paths with simulated annealing led to a slight deterioration in both the best-case (2645.26 ± 780.35 lxh, −2.86%, min: 1314.74 lxh, max: 3945.05 lxh) and worst-case (2659.9 ± 833.3 lxh, −2.33%, min: 1282.35 lxh, max: 4121.75 lxh) scenario. A similar outcome was observed in relation to the optimization of user distribution in the room under the energy efficiency target, where both the best-case (2696.83 ± 983.96 lxh, −0,97%, min: 1172.31 lxh, max: 4400.82 lxh) and worst-case (2624.18 ± 904.27 lxh, −3.64%, min: 1165.06 lxh, max: 3955.43 lxh) scenario showed a reduction in the daily achieved light doses.

A GLMM was calculated with the mean daily light dose as the dependent variable (for best-case and worst-case scenarios). The optimization strategy was modeled as a fixed effect (reference: explicit optimization), and random intercepts for users (n = 18) were considered to account for interindividual variance.

The analysis showed that, compared to the explicit optimization, neither the derived light doses resulting from the optimization of user distribution under the target criterion of energy efficiency (best-case: effect = −212.47 lxh; SE = 144.16; z = −1.47; p = 0.14; worst-case: effect = 206.99 lxh; SE = 139.17; z = 1.49; p = 0.14) nor the derived light doses resulting from the optimization of communication distances resulted in significant differences (best-case: effect = −264.05 lxh; SE = 144.16; z = −1.83; p = 0.07; worst-case: effect = 242.70 lxh; SE = 139.17; z = 1.74; p = 0.08). The Q-Q plots of the residuals showed no systematic deviations from the theoretical normal distribution (best-case: skewness = 0.19; kurtosis = –0.16 (Figure 6a); worst-case: skewness = 0.17; kurtosis = –0.55 (Figure 6b), which was confirmed by the Shapiro–Wilk test (best-case: W = 0.99; p = 0.81; worst-case: W = 0.98; p = 0.41). The estimated variance of the random intercepts was 778,871 (ICC = 0.81) in the best-case scenario and 390,959 (ICC = 0.69) in the worst-case scenario, indicating that a large proportion of the variance is explained by differences between users. The EMMs were 2909.31 lxh for the explicit optimization (worst-case: 2417.19 lxh), 2696.84 lxh for the energetic optimization (worst-case: 2624.18 lxh), and 2645.26 lxh for the communication distance optimization (worst-case: 2659.90 lxh). Post hoc comparisons with Bonferroni correction revealed no significant differences between the strategies for either the best or worst-case (all p > 0.05, see

Table 6. p-values of the post hoc pairwise comparisons with Bonferroni correction resulting from the comparison of the optimization procedures with different target variables under the target variable daily light doses.

Post Hoc Pairwise Comparisons (Bonferroni)	p-Value
	Best-Case	Worst-Case
Optimization of communication distances vs. optimization of energy consumption	0.42	0.41
Optimization of communication distances vs. optimization of daily light doses	0.20	0.24
Optimization of energy consumption vs. optimization of daily light doses	1.00	1.00

). The partial R² values for the fixed effects are 0.01 and 0.02 for the best- and worst-case scenarios, respectively.

4.1.3. Lighting Energy Demand

The initial situation shows an energy demand of 237.12 kWh with a zonal consumption of 26.35 ± 16.87 kWh (

Table 7. Lighting energy demand (in kWh) resulting from explicit best-case and worst-case optimizations to a specific target value (all data are normally distributed).

		Best-Case Scenario	Worst-Case Scenario
Initial situation	Total in kWh:	237.12
	Workplace-related in kWh:	26.35 ± 16.87
	Same presences in min:	15,952 ± 7532
Optimization of communication paths via Simulated Annealing	Total in kWh:	235.78	237.85
	Workplace-related in kWh:	26.2 ± 6.64	26.43 ± 4.51
	Same presences in min:	16,774 ± 7131	15,412 ± 5262
Optimization of daily light doses via method of [34]	Total in kWh:	227.18	247.82
	Workplace-related in kWh:	25.24 ± 10.08	27.54 ± 16.37
	Same presences in min:	18,210 ± 8593	18,687 ± 9343
Optimization of energy demand via method of [34]	Total in kWh:	178.32	268.60
	Workplace-related in kWh:	19.81 ± 4.70	29.84 ± 12.69
	Same presences in min:	19,076 ± 7.81	12,100 ± 4231

Note: Values show cumulative totals (in bold) and mean and standard deviation to ensure comparability.

). The best-case optimization achieves significant savings (178.32 kWh; −24.8%), which is also reflected at zone level (19.81 ± 4.70 kWh). The reduced energy demand results from an increase in same presences during the energy-relevant periods in the optimized arrangement (19,076 ± 7812 min) compared to the initial situation (15,952 ± 7532 min)). For the worst-case optimizations, the explicit energy maximization leads to a total energy demand of 268.60 kWh, which is 13.27% worse than the initial situation, resulting in an increased energy demand per zone of 29.84 ± 12.69 kWh. The higher energy demand can be explained by significantly lower same presences durations (12,100 ± 4231 min).

In contrast, the best-case optimization according to communication distances only leads to a small reduction in total lighting energy demand (235.78 kWh, −0.56%) with a zonal consumption of 26.2 ± 6.64 kWh. Similarly, the worst-case optimization did not lead to a meaningful change in energy demand regarding both the total (237.85 kWh, +0.31%) and zone-related (26.43 ± 4.51 kWh) level. The same presences differ only slightly between the best-case (16.774 ± 7.131 min) and worst-case scenarios (15,412 ± 5262 min).

The optimization under the target value of the daily light dose leads to moderate changes in the artificial light energy demand for both the best-case (227.18 kWh, −4.19%) and worst-case (247.82 kWh, +4.51%) scenarios. At zone level, this means 25.24 ± 10.08 kWh for the best-case optimization and 27.54 ± 16.37 kWh for the worst-case. There is almost no difference between the mean same presences in the best-case (18,210 ± 8593 min) and worst-case scenarios (18,687 ± 9343 min).

A GLMM was used to investigate the effects of optimization strategies (communication distances, light doses, and energy consumption) on energy consumption. The optimization strategies were modeled as fixed effects, energy consumption served as the dependent variable, and random intercepts for the work zone (n = 9) were considered as random effects. Explicit optimization of energy consumption was set as the reference category. The differences in sample size compared to previous evaluations are due to the fact that the evaluation is now carried out at the lighting zone level rather than at the user level. This is because the energy demand of a lighting zone is calculated from the combined occupancy profile of its assigned users (logical OR-linkage). Each of the nine lighting zones covers two workstations (cf. Figure 2).

The GLMM revealed significant differences between the optimization strategies. Compared to the reference condition, optimizing communication distances increased energy consumption by 6.39 kWh (SE = 2.99; z = 2.14; p = 0.03), while optimizing daily light doses showed a non-significant increase of 5.43 kWh (SE = 2.99; z = 1.82; p = 0.07). The variance of the random intercepts suggests that the zones contributed moderately to the variability of the results (9.62; ICC = 0.19). Q–Q plots of the residuals showed slight deviations from the theoretically expected distribution (skewness: −0.59; kurtosis: 0.58 (cf. Figure 7a); normal distribution confirmed by Shapiro–Wilk: W = 0.97; p = 0.60). In the best-case scenario the EMMs were 19.81 kWh for the explicit energy optimization, 26.20 kWh for the resulting energy consumption from optimizing user distribution in the room under the target criterion of communication distances, and 25.24 kWh for optimizing light doses. Post hoc pairwise comparisons with Bonferroni correction revealed no statistically significant differences between the strategies (all p > 0.05, see

Table 8. p-values of the post hoc pairwise comparisons with Bonferroni correction resulting from the comparison of the optimization procedures with different target variables under the target variable lighting energy demand and same presences.

Objective	Post Hoc Pairwise Comparisons (Bonferroni)	p-Value
		Best-Case Scenario	Worst-Case Scenario
Lighting energy demand	Optimization of communication distances vs. optimization of energy consumption	0.10	1.00
	Optimization of communication distances vs. optimization of daily light doses	0.21	1.00
	Optimization of energy consumption vs. optimization of daily light doses	1.00	1.00
Same Presences	Optimization of communication distances vs. optimization of energy consumption	1.00	2.21 × 10−3
	Optimization of communication distances vs. optimization of daily light doses	0.21	0.27
	Optimization of energy consumption vs. optimization of daily light doses	0.78	0.28

). The partial R² for the fixed effects was 0.14 in the best-case scenario. This indicates that the optimization strategy explained approximately 14% of the variance in the dependent variable.

No significant differences between the strategies were found in the worst-case scenario. Compared to the explicit optimization of energy consumption, the optimization of user distribution in the room under the target criterion of communication distances reduced energy consumption by −3.42 kWh (SE = 5.44; z = −0.63; p = 0.53), while the optimization of light doses reduced artificial energy consumption by −2.31 kWh (SE = 5.44; z = −0.42; p = 0.67). The variance of the random intercept was 2.12 × 10⁻⁷ (ICC = 1.59 × 10⁻⁹), indicating that there was no additional variability due to work packages. The residuals were approximately normally distributed (skewness: 0.14; kurtosis: −0.38 (cf. Figure 7b); confirmed by the Shapiro–Wilk test (W = 0.95; p = 0.22)). The worst-case EMMs were 29.84 kWh for the explicit optimization of artificial light energy demand, 26.43 kWh for the resulting energy demand from the energy optimization, and 27.54 kWh for the resulting energy demand from the user distribution for optimized light doses. Post hoc pairwise comparisons with Bonferroni correction confirmed that none of the pairwise differences reached statistical significance (all adjusted p = 1.00, see Table 8). The partial R² for the fixed effects was 0.02 in the worst-case scenario.

A GLMM was also used to investigate the effects of different optimization strategies on the number of same presences during energy-relevant times. The strategy was modeled as a fixed effect, the number of simultaneous presences as the dependent variable, and random intercepts for individual workstation zones (n = 9) were considered as random effects.

In the best-case scenario, the GLMM results showed no significant differences between the strategies, with the effects of the two non-explicit energy optimizations relative to the reference being −865.67 min (SE = 1273.56; z = −0.68; p = 0.50) and −2302.17 min (SE = 1273.56; z = −1.81; p = 0.07), respectively. The residuals were approximately normally distributed (skewness = 0.32, kurtosis = −0.71 (cf. Figure 7c); Shapiro–Wilk: W = 0.96; p = 0.34). The EMMs were 19,076 min for the explicit energetic optimization, 18,210.33 min for the optimization of user distribution under the target criterion of light doses, and 16,773.83 min for the communication distance optimization. The post hoc tests showed no significant pairwise differences (all p > 0.05, see Table 8). The partial R² for the fixed effects was low (0.02).

In the worst-case scenario, the optimization of light doses showed a significant increase in co-presence times by 6586.78 min (SE = 1951.31; z = 3.38; p = 0.001) compared to the reference, while this was not significant for the communication distance optimization (3312.48, SE = 1951.31; z = 1.70; p = 0.09). The residuals were normally distributed (skewness = 0.21; kurtosis = −0.32 (cf. Figure 7d); Shapiro–Wilk: W = 0.99; p = 0.95). The EMMs were 12,100 min for the explicit energetic optimization, 18,686.78 min for the lighting optimization, and 15,412.48 min for the communication distance optimization. Post hoc tests showed a significant difference (p = 0.002) only for the comparison between energetic and lighting optimization in the context of shared presence (see Table 8). The partial R² for the fixed effects was 0.16.

4.2. Correlation Analysis Within Objective-Specific Optimization Strategies

4.2.1. Correlation Analysis Within the Optimization of Communication Distances

Considering the primary optimization target communication distances and the secondary performance indicators, no significant correlations were observed. Figure 8 includes the derived user distribution in the room for the best-case, the worst-case and the initial situation. Each of the user distributions has different user pairings, which are distributed across the nine zones. No user appears more than once in a distribution. The Spearman correlation between communication distances and daily light doses (Figure 8a) was weak (ρ = 0.17; |ρ| = 0.17; n = 9) and not statistically significant (p = 0.41). This indicates that, in this dataset, communication distances and daily light doses show only a weak, statistically insignificant association. Similarly, the Spearman correlation between communication distances and energy demand (Figure 8b) was negligible (ρ = 0.15; |ρ| = 0.15; n = 9) and non-significant (p = 0.46). This finding indicates that communication distances and energy demand demonstrate only a negligible and statistically non-significant association within the specified dataset. With regard to the two secondary performance indicators daily light doses and energy demand (Figure 8c) a Spearman correlation analysis revealed a moderate and statistically significant association (ρ = 0.55; |ρ| = 0.55; n = 9; p = 0.003). This finding indicates a moderate to strong correlation between higher daily light exposure and increased energy demand at workstations.

4.2.2. Correlation Analysis Within the Optimization of Daily Light Doses

In relation to the primary optimization target daily light doses, a Pearson correlation showed a weak (r = 0.39; |r| = 0.39; n = 9) and significant (p = 0.04) correlation to communication paths (Figure 9a). This suggests that daily light exposure is weakly but significantly associated with communication distances in this dataset. To assess the association between daily light doses and energy consumption, a Pearson correlation was conducted. The results showed a moderate (r = 0.32; |r| = 0.32; n = 9) and non-significant (p = 0.10) relationship (Figure 9b). This finding indicates a monotone relationship, suggesting that an increase in daily light doses is moderately, but not significantly, correlated with an increase in energy consumption. Finally, a weak (r < −0.01; |r| < 0.01; n = 9) but non-significant (p = 1.00) relationship between the two second performance indicators energy consumption and communication distances was assessed by a Pearson correlation (Figure 9c). This finding suggests the absence of a monotone relationship between energy consumption and communication distances.

4.2.3. Correlation Analysis Within the Optimization of Lighting Energy Demand

Considering the primary optimization target energy demand and the secondary performance indicators, no significant correlations were observed. Again, the user pairings for the best-case, the worst-case, and the initial situation are used, all of which have different user pairings per zone (no multiple use of a user per distribution). The Pearson correlation between energy demand and communication distances (Figure 10a) was weak (r = −0.15; |r| = 0.15; n = 9) and not statistically significant (p = 0.46). This suggests that there is virtually no linear relationship between energy demand and communication distances. Similarly, the Pearson correlation between energy demand and daily light doses (Figure 10b) showed a moderate (r = 0.31; |r| = 0.31; n = 9) but non-significant (p = 0.12) relationship. While this suggests a positive trend, it is too weak and statistically insignificant to draw reliable conclusions. With regard to the two secondary performance indicators daily light doses and communication distances (Figure 10c) a Pearson correlation analysis revealed a weak and statistically not significant association (r = 0.19; |r| = 0.19; p = 0.35; n = 9). This confirms that there is only a very weak linear relationship between the two indicators.

5. Discussion

This study investigated how optimizing office seating arrangements for one of three key performance indicators (energy demand for artificial lighting, daily light dose, or proximity to colleagues) affects the others. By approaching these indicators as interconnected yet potentially competing objectives, the findings underscore both the complexity, and the trade-offs involved in occupant-centered spatial optimization.

The optimization process successfully demonstrated the potential for substantial improvements within individual target domains. Optimizing communication proximity led to a notable reduction in cumulative and individual communication distances, confirming the efficacy of this method for supporting team-oriented workplace layouts. The results specifically show a reduction in the distance to each employee’s most relevant colleague (cf. Table 3), which can be regarded as particularly valuable for facilitating informal and spontaneous exchanges in open office environments, as it supports face-to-face interaction, which has been shown to enhance collaboration, morale, and productivity [3,4,43].

Importantly, communication must be understood as a functionally oriented behavior within a formal and informal organizational context [44,45]. More communication does not inherently lead to better communication outcomes. Instead, effective communication depends on behavior that is aligned with task requirements and organizational goals [46]. In the present study, managerial consideration of interpersonal relevance preferences contributed to functional spatial arrangements that support efficient communication structures.

Similarly, optimizing for light dose modestly improved overall daylight exposure, while energy demand optimization resulted in clear savings in lighting energy consumption. In the presented study using real measurement data from February 2022 to January 2023, optimized user distributions led to artificial lighting energy savings of 24.8%. These improvements were achieved by grouping users in zones with favorable daylight conditions during energy-relevant periods (see [34] and Figure 4), supporting the rationale behind zoned lighting systems as a prerequisite for energy-efficient user placement [12]. Given that the building sector accounts for approximately one-third of global energy consumption and around 37% of CO₂ emissions [47,48], such strategies are essential not only to reduce operating costs, but also to meet international climate protection targets.

Moreover, the energetic optimization of user profiles within zones was found to coincide with increased space efficiency (see same presences in Table 7). Frequent co-presence in certain zones facilitates a more effective allocation of spatial resources. Concepts such as hot-desking and dynamic user distributions, particularly when informed by real-time occupancy data, are valuable tools for cost-effective space and resource use. These approaches are increasingly reflected in strategic corporate goals aimed at flexible workplace management and real estate efficiency [49,50]. Given that real estate represents a critical cost factor for many organizations, efficient and sustainable management through corporate real estate and facility strategies can yield essential advantages [51,52]. Dynamic workplace models, in particular, foster better alignment between spatial supply and organizational demand.

Despite the successes within individual domains, these benefits did not generalize across all performance indicators. Improvements in one domain frequently came at the expense of another. For example, minimizing communication distances often led to less favorable lighting conditions, while optimizing daylight exposure tended to increase distances between colleagues. Workstations with high daylight availability were not necessarily located near relevant colleagues or people with similar occupancy profiles during energy-relevant periods. This reveals a classic conflict of objectives. As with energy, daylight optimization using the Hungarian algorithm increased achievable daily light doses by approximately 7%, but this came with spatial compromises. Although daylight autonomy was generally high (81.56%), significant spatial differences led to fluctuations in light dose depending on occupancy schedules and daylight availability (see Figure 4). These differences can positively influence productivity, but they must be balanced against social and energetic criteria.

This interdependence was further explored through correlation analyses. Although certain trends between performance indicators were observable, such as moderate associations between light dose and energy demand (within the optimization of communication distances, cf. Figure 8c), these correlations were not consistent across optimization strategies and lacked statistical significance. As a result, no reliable interdependencies could be established between the measured variables. This reinforces the conclusion that optimizing one domain does not inherently lead to proportional improvements in others.

From a broader perspective, these findings highlight the limitations of single-objective optimization approaches in complex, multi-user office environments. The mutual dependencies and occasional tensions between social, energetic, and comfort criteria call for more integrative design strategies. Multi-objective optimization algorithms or adaptive spatial systems that respond to dynamic organizational and environmental demands may offer viable solutions. Furthermore, daylight utilization not only supports energy efficiency by reducing artificial lighting needs but also increases daily light doses, assuming that potential negative effects like glare or overheating are mitigated.

Finally, it must be noted that among the target variables, communication distances are likely the most intuitive and perceptible to building operators and decision makers. This can result in a tendency to prioritize communication optimization at the expense of less immediately tangible yet equally important criteria such as light exposure and energy efficiency. A holistic, data-driven framework is therefore required to navigate the complex interplay between organizational behavior, environmental sustainability, and human comfort and health in modern office design.

The results of this study should be interpreted as illustrative patterns within the context of the studied open-plan office, rather than as effects that can be generalized to other contexts. By explicitly framing the analyses as exploratory, the findings highlight trade-offs that emerge when optimizing user distributions for communication distances, lighting energy demand, and daily light doses. It is imperative to acknowledge that p-values and effect sizes are presented to indicate tendencies. However, they should not be interpreted as evidence of confirmatory statistical inference. The case study approach offers insights that are specific to the context of the study and may inform future applications in similar office environments, while avoiding overgeneralization beyond the studied setting.

Limitations

Several limitations should be noted. First, the study was based on a simulation framework with limited behavioral patterns and preference structures. The analysis of communication preferences was based exclusively on management ratings, as direct employee feedback could not be collected for organizational and data protection reasons. While this approach allows for an initial assessment of communication preferences and informal networks, it is associated with systematic biases. Management ratings do not necessarily reflect employees’ actual communication needs and only partially capture informal interactions. Numerous studies show that informal networks often do not correspond to formal hierarchies and therefore represent an additional resource by providing employees with access to knowledge, support and influence beyond formal structures, which promotes proactive and innovative behavior, especially under conditions of scarce resources [53,54]. Even if self-reported data or electronic communication analyses could provide additional perspectives, they would also not fully reflect the real situation, as deviations between predicted and actual behavior are inevitable. The results should therefore be interpreted against the backdrop of these limitations.

Second, communication paths were not optimized at the same time as the same presence times, as it is difficult to make a well-founded assessment of the influence of longer same presence times without corresponding studies. This is particularly true considering that high and largely homogeneous attendance times were found for all pairings.

Third, since the study refers to evaluation variables that exist in connection with occupancy patterns as well as the position-dependent daylight availability in the case of the use of artificial lighting and the daily achievable light doses, there are dependencies on building typology and organizational form. The building investigated has a high daylight availability (DA₅₀₀ = 81.56%) and high occupancy dynamics, which means that artificial lighting times are primarily in the morning and evening hours (see [36]). As these times have a higher occupancy dynamic, the influence of occupancy behavior could be overestimated. Due to the high proportion of daylight in the study object, more generally applicable statements require the methods to be applied to other building types with different daylight conditions.

Fourth, although the study was based on actual measurements, acceptance of optimized user distribution in rooms, particularly dynamic distribution, was not tested. Future studies should investigate this in detail.

A fifth limitation of the study is that daily light doses were derived from validated Radiance simulations, but spectrally resolved daylight measurements were not included (Details in [36]). Consequently, it was not possible to calculate melanotic equivalent daylight illuminance (MEDI) directly, and vertical illuminance was used as a proxy for non-image-forming (NIF) light exposure. This approach does not capture wavelength-dependent differences in circadian stimulation. Nevertheless, we consider this to be a reasonable approximation for two reasons: (1) under typical lighting conditions, higher overall illuminance generally correlates with stronger circadian-effective stimulation and (2) the time-resolved optimization across all users reduces the likelihood of substantial variations in correlated color temperature between workstations, thereby minimizing spectral biases. Thus, although deviations from precise MEDI values are possible, optimizing daily light doses can be regarded as a practical substitute for MEDI optimization under the given conditions. Future studies should include spectrally resolved measurements to refine these estimates and capture NIF-effective light exposure more accurately.

Finally, there is a risk of false detections due to the passive infrared sensors used. However, in comparison with alternative methods of presence detection, PIR detection at the individual workstation level has been shown to offer a high degree of measurement accuracy (approximately 90%) [55], which is further increased by placing the sensors in close proximity to the respective workstation (cf. Figure 3). The accuracy of PIR sensors increases with decreasing distance [14]. Furthermore, multiple measurements were taken per minute at each workstation. The study context has already measured the reduction in false-off rates by positioning them close to the workstation [56]. In order to empirically verify the accuracy of the system, a controlled laboratory study was conducted. In this study, PIR sensors were used in a manner analogous to the study object. These were also mounted beneath the table, thus restricting their detection area to the respective work area. To assess the system’s precision, a set of four common office activities (text input, sorting tasks, passive screen work, and absence) were replicated in a randomized sequence by multiple participants. Concurrently, task transitions were automatically indicated and documented. The ground-truth data were derived from both log files, enabling systematic validation. The study yielded an average recognition rate of 88.97% ± 7.54%. These results align with established literature values (cf. [55]), yet they also demonstrate context-dependent variability among workstations. A sensitivity analysis was conducted to determine the achievable improvement by optimizing the user distribution in the room, based on empirically determined error rates. The absolute value base is shifted, but the difference between the initial state and the optimization (savings) remains largely stable, since the same bias affects both scenarios. The probability of false presence detections remains unavoidable, albeit to a negligible extent. This finding serves to substantiate the study’s primary conclusions, affirming their resilience under the observed uncertainties.

6. Conclusions

In principle, open office layouts offer the potential to promote communication, cooperation and knowledge sharing. In practice, however, it is often the case that historically evolved, random user distributions within the room result in inefficient communication paths. Against this background, this study demonstrates that the targeted use of heuristic optimization methods can be used to design the distribution of users in the room in such a way that communication paths can be significantly minimized. Deriving the user distribution using simulated annealing leads to a 38.5% reduction in the total distance without placing an excessive burden on the computing time due to brute force methods.

As there are several target variables with regard to the distribution of users in the room, synergy effects were examined for isolated optimization on the other target variables. The correlation analyses conducted show that this optimization does not automatically have a positive impact on other spatial target variables. Within the optimization of user distribution regarding communication distances, a statistically significant correlation was found between the daily light doses and energy demand. In the algorithm comparison, this effect was not confirmed. In the context of the optimization of the daily light doses, there was a significant correlation between daily light doses and communication distances, indicating that higher daily light exposure in this dataset is weakly but significantly linked to communication paths. However, the direct algorithm comparison was unable to confirm this correlation. Finally, with regard to the optimization of energy efficiency, no synergies with the other target variables could be identified.

The distribution of users in the room can be optimized either in terms of communication, energy consumption or light-related comfort and health factors using suitable algorithms. There are no strong positive correlations between the optimizations. These conflicting objectives make it clear that the design of efficient working environments in open offices represents a multi-criteria optimization problem.

However, it should be noted that the building under study has a very high daylight autonomy. Therefore, the generalizability of the findings is limited to buildings with comparable conditions. Further studies in environments with lower daylight availability are necessary to establish broader validity. A further limitation of this study lies in the case study design, which uses statistical analyses exploratively to uncover trends and trade-offs rather than allowing for generalized conclusions. Although the GLMM provides a robust method for accounting for the nested data structure, the results should be interpreted within the specific living lab context and not generalized beyond it.

7. Outlook

Both positive and negative effects were found when optimizing individual target variables. Future research should therefore test algorithms for the complex multi-criteria optimization of user distribution in the room. An optimized user distribution in the room should bring employees with similar tasks together spatially, which can improve communication and thus productivity, and at the same time improve daily light doses and reduce the necessary use of artificial light energy. The development and validation of suitable optimization methods is crucial to resolve conflicting objectives and enable sustainable, productivity-enhancing working environments in terms of intelligent building design.

Future studies should include decision diagrams or trade-off analyses that clearly illustrate the interdependencies between different optimization targets to translate such numerical improvements into practical strategies. For instance, visualizations could demonstrate the impact of a 10% reduction in communication distance on the additional energy demand or achievable light doses in the room. These visualizations would make abstract numerical results more tangible and allow practitioners to quickly weigh the pros and cons of different seating strategies. Presenting these interrelations in a structured, transparent manner would equip facility managers and planners with actionable tools that support evidence-based decision-making and help balance competing objectives in real-world office environments.

Further, investigations into user satisfaction, perceived comfort, and long-term behavioral adaptation could complement the technical performance metrics and provide a more holistic picture of spatial effectiveness. Additionally, incorporating real-time sensor data and adaptive lighting control systems may bridge the gap between theoretical optimization and practical implementation in dynamic office environments.

8. Addendum: Algorithm Selection for Deriving User Distributions in the Room Under the Optimization Objective of Communication Distances

8.1. Algorithms

While algorithms for optimizing user distribution in space have already been identified in research under energy and lighting objectives, there was still no algorithm for optimizing user distribution in terms of communication distances. This addendum explains the selection of a suitable algorithm for the objective.

Beam Search selectively tracks only the most promising distributions to control the search efficiently. GRASP (Greedy Randomized Adaptive Search Procedure) initially generates random but structured user arrangements and iteratively improves them through local search. Iterated Local Search (ILS) uses targeted perturbations to break out of local optima and thereby explore more diverse distributions. Particle Swarm Optimization (PSO) models user positions as particles that move through the solution space and are controlled by individual and collective experience values. Stochastic single-path methods enable the step-by-step optimization of individual distributions by allowing suboptimal solutions through probabilistic transitions in order to minimize communication paths. Examples of this are simulated annealing and Tabu Search (see methods in [27]).

Differential evolution (DE) is a method of evolutionary optimization in which a population is gradually improved by repeated application of mutation, crossover and selection [57]. In this study, the algorithm is used to generate new spatial distributions of users by utilizing the differences between randomly selected, location-based user pairs. In addition, a genetic algorithm (GA) is used to optimize user distributions by mutation and crossover [58].

8.2. Evaluation Methodology

Several hyperparameters were tested for the optimization algorithms mentioned, and those with the best results in terms of outcomes and computation time were used for comparison. For the beam search algorithm, five promising solutions were explored in each iteration, and the search was conducted to a maximum depth of ten steps to efficiently limit the search space. The GRASP algorithm underwent 100 iterations. In each iteration, a restricted candidate list (RCL) containing the three most promising candidates (RCL size) was created. Then, a candidate was randomly selected from the RCL for local optimization. ILS was performed with 1000 iterations. Simulated annealing was performed with an initial temperature of 1000 and a cooling rate of 0.995. The search was performed for a maximum of 10,000 iterations to strike a balance between exploring the solution space and achieving convergence. PSO used 30 particles, which moved through the solution space over 200 iterations. Each particle’s position was influenced by the swarm’s individual and collective experience to find the optimal solution. The tabu search algorithm performed the search over a maximum of 1000 iterations. A tabu list of length 50 was used to temporarily block previously visited solutions and make the search more efficient by avoiding revisiting the same solutions. The Differential Evolution algorithm employed a population size of 20 individuals. Mutation occurred with a factor of 0.8, and crossover occurred with a probability of 0.9. Optimization was performed over 100 generations. The GA used a population size of 50 individuals. It performed the optimization over 100 generations using a mutation rate of 0.1.

All algorithms were either terminated after a maximum number of iterations or after a maximum number of iterations. Independent of the hyperparameters, the evaluation of the computing time was carried for each algorithm out for 100 to assess statistical deviations.

The preference-weighted communication distance for a user distribution in the room is calculated by matrix multiplication (preference matrix with distance matrix (see Table 1 and Table 2). Since two users always have the same preference for each other in the study setting, this results in a symmetric matrix along the main diagonal (see Table 1). Since the paths between the workstations are symmetrical anyway (Table 2), the resulting matrix of preference-weighted communication paths is also symmetric along the main diagonal. However, it cannot be ruled out that there is no symmetry in other applications (e.g., user A has a different preference for user B than user B has for user A). In this article, the total length from each user to all others is always determined, resulting in a total length of 100.87 m for the initial user distribution in the room.

A one-way ANOVA (Analysis of Variance) was performed to evaluate both the best-case and worst-case optimization. Nonparametric Kruskal–Wallis tests were applied for violations of the assumptions of normality (assessed with the Shapiro–Wilk test) or homogeneity of variance (assessed with the Levene test). Statistical analyses were performed using the obtained absolute values. Descriptive analyses report the mean with standard deviation if the data are normally distributed, or the median and the 25th and 75th percentiles in parentheses if the data deviate from the normal distribution. In addition, the total is always shown.

All results of the algorithms were statistically evaluated in order to assess their performance. The algorithm comparison was carried out on a Windows 11 workstation (version 10.0.22631) with Intel Core Ultra 7 155U, 1700 MHz, 12 cores and 14 logical processors as well as 32 GB and Python 3.12. A total of 100 runs were carried out for each algorithm to assess statistical deviations.

8.3. Resulting Communication Distances

All algorithms were able to identify distributions that improve communication distance (see Figure 11a). ILS achieved the best user allocation in terms of minimizing communication distance, with a total distance of 58.84 m. In relation to a percentage reduction compared to the existing seating arrangement, ILS (40.21% (40.21–41.67%) and GRASP (40.21% (39.93–40.49%)) performed best (see Figure 11a). The least favorable distributions in the best-case scenario were identified by PSO (24.17% (21.77–27.05%)). In the worst-case scenario, i.e., maximizing communication distances, ILS identifies the distributions that have the largest distances (−37.71% (−37.71–−37.71%), see Figure 11b).

As the assumptions of normality (Shapiro–Wilk test) for data analyses were violated, nonparametric statistical tests were used. A Kruskal–Wallis test revealed a significant difference between the algorithms with regard to the resulting communication distances (p < 0.001) for both minimizing (χ²(7) = 489.42; ε² = 0.61) and the maximizing (χ²(7) = 682.50; ε² = 0.85) the distances. The sample size n is in both cases is 800 (a total of eight algorithms were compared with 100 runs per algorithm).

In the minimization of communication distances, most pairwise comparisons in Dunn’s post hoc show highly significant differences (p < 0.05). Beam Search, Simulated Annealing and Tabu Search show no significant differences (p > 0.05), suggesting similar performance. A similar picture emerges when maximizing the distances. Dunn’s post hoc results show that Differential Evolution, Genetic Algorithm, ILS and PSO are significantly different from each other (p < 0.05). Simulated Annealing, GRASP and Tabu Search as well as Beam Search, on the other hand, do not differ significantly from each other (p > 0.05).

8.4. Resulting Runtimes

While ILS delivers the best results, this algorithm also has the longest calculation times for minimization and maximization (Min: 86.54 s (interquartile range (IQR), 25% and 75% quartiles: 52.61–97.65 s); Max: 116.10 s (55.82–134.03)). SA works the fastest (Min: 0.87 s (0.59–1.12 s); Max: 1.06 s (0.57–1.34 s). The comparison of the algorithms also showed no normal distribution in terms of runtime (see Figure 12). The Kruskal–Wallis test revealed significant differences with regard to the runtime of the algorithms both in the minimization (χ²(7) = 627.21; ε² = 0.78; p < 0.001) and in the maximization of the communication paths (χ²(7) = 617.36; ε² = 0.77; p < 0.001). The sample size here is again 800 (=100 × 8 algorithms). Since SA offered the fastest computing times and the third best results in distance minimization (39.47% (37.86–40.87%)), the results of this algorithm were used in the analysis.