Energy-Efficient Scheduling in Heat Treatment Workshops Based on Task Clustering and Job Batching

Abstract

The development of green and efficient manufacturing has brought on complex trade-offs between energy consumption control and resource utilization efficiency in heat treatment tasks. Traditional single-piece scheduling methods are challenged in addressing the complexity of multiple tasks and energy optimization. In this paper, an optimized scheduling method for heat treatment workshops is proposed by integrating task grouping and batch combination strategies. Specifically, a genetic algorithm enhanced with local search and adaptive mutation operators is proposed under constraints such as delivery deadlines and equipment capacity. During the strategy generation process, equipment changeover and idle time are considered. By performing multi-dimensional matching of workpiece processing processes, heat treatment requirements, and quality characteristics, an innovative clustering mechanism for dynamic production batches based on task similarity is constructed. To validate the effectiveness, actual production data from a heat treatment workshop were selected for analysis and evaluation. The results show that the proposed method reduces the total production time by 31.6% with on-time delivery of orders, and the equipment operation frequency is reduced by 28.4%, which verifies the practicality and advancement of the proposed method.

1. Introduction

In the era of intelligent and digital transformation, smart factories—empowered by technologies such as the Internet of Things (IoT), big data, and artificial intelligence—have achieved seamless interconnectivity and interoperability among equipment and systems. Leveraging real-time data monitoring and feedback, smart factories optimize production processes at a fine-grained level, significantly enhancing operational efficiency, product quality, and resource utilization. As a pivotal driver of industrial transformation, they play a critical role in accelerating upgrades to the manufacturing sector and promoting sustainable global economic development [1,2].

Among the core enablers of smart factory performance, scheduling optimization stands out as a fundamental pillar. It ensures efficient coordination of resources, minimizes delays, and enhances responsiveness to dynamic production conditions. Traditional shop floor scheduling research has primarily focused on the optimal allocation of tasks and resources using heuristic and metaheuristic approaches. These methods perform well in relatively stable manufacturing settings, where the production processes and demand structures are largely predictable.

However, with the increasing complexity brought by intelligent manufacturing and green transformation, modern production environments now involve dynamic interactions between machine states and energy consumption profiles. Traditional scheduling approaches often struggle to simultaneously optimize process routing and energy efficiency [3,4]. This inadequacy leads to unbalanced machine utilization, frequent start–stop transitions, and substantial auxiliary energy losses, thereby exposing a growing conflict between operational efficiency and energy sustainability.

With the pressing need for energy-aware production planning, the Energy-aware Job Shop Scheduling Problem (EJSP) has gained considerable attention in recent years [5,6]. Researchers have proposed integrated models that account for various forms of energy consumption—such as processing, idle, setup, and transfer energy—and solved them using advanced metaheuristics, including genetic algorithms and particle swarm optimization [7,8,9]. However, with most of the existing models it is difficult to accurately reflect the dynamic impact of factors such as equipment performance decline and process parameter fluctuations on energy consumption in the face of complex and changing production environments, resulting in large deviations in energy consumption prediction. Moreover, most existing methods lack adaptability to real-time fluctuations in order arrivals, equipment availability, and production demands, making them insufficient for achieving a balance between energy efficiency and throughput.

Notably, the scheduling problem in heat treatment workshops has unique characteristics. Unlike the traditional Job Shop Scheduling Problem (JSP), in heat treatment processes, workpieces must be processed under specific process parameters such as temperature and time. Startups, shutdowns, and parameter adjustments of equipment (e.g., heat treatment furnaces) generate substantial energy consumption. Therefore, it is necessary to reduce equipment state transitions through task clustering (grouping workpieces with similar process characteristics) and job batching (processing grouped tasks in batches)—which are core components not included in traditional JSP [10,11].

Therefore, this paper proposes an innovative optimization approach based on task clustering [12,13], aiming to reduce the frequency of task switching and improve both energy efficiency and production stability. Specifically, production tasks exhibiting similar process characteristics, resource demands, and delivery flexibility are grouped into clusters. These clusters are then treated as scheduling units to optimize batch formation and carrier assignment across multiple production lines. This approach not only minimizes energy consumption associated with setup and idle times but also improves system robustness under variable production conditions. The main contributions of this work are as follows:

• A dynamic task clustering mechanism is introduced in which tasks are aggregated in real time based on similarities in process characteristics and scheduling flexibility. By exploiting task homogeneity, the adaptability of the scheduling system to production variability is enhanced, and redundant operations are effectively reduced.
• Practical shop floor constraints—transport energy consumption and batch delivery deadlines—are explicitly incorporated into the scheduling model. Unlike idealized formulations, this model is designed to accommodate tight delivery windows and resource limitations, thereby improving its applicability in realistic manufacturing environments.
• To solve the resulting combinatorial scheduling problem, we develop an improved genetic algorithm that integrates a novel reservation-based selection criterion. This mechanism leverages task timeliness, machine workload, and energy metrics to accelerate convergence and improve solution quality.

The remainder of this paper is structured as follows: Section 2 reviews related work on energy-aware scheduling and optimization techniques. Section 3 formulates the scheduling problem and introduces the proposed optimization method. Section 4 presents implementation details and simulation results. Finally, Section 5 concludes the paper and outlines potential directions for future research.

2. Related Works

The Job Shop Scheduling Problem (JSP) has long been a central topic in manufacturing systems research, focusing on the efficient allocation of a set of operations across multiple machines to optimize production objectives such as makespan minimization, machine utilization, and throughput. Since the 1950s, many scholars have conducted extensive research on JSP and proposed a variety of solution strategies [14,15,16,17]. Early studies focused on the development of classical scheduling strategies, including heuristic algorithms [18], greedy algorithms [19], and branch-and-bound methods [20]. Among them, heuristic algorithms are widely used due to their simplicity and computational speed. Oliver et al. [21] proposed a series of effective scheduling rules and evaluation metrics, which made JSP solving an active research direction.

Contemporary JSP studies can generally be categorized into single-scenario optimization and multi-scenario or complex scheduling. Research in the former tends to address isolated machine configurations or single-objective functions using traditional mathematical programming or rule-based heuristics [22]. These models, while effective in static environments, often lack the flexibility required to manage modern dynamic, multi-objective manufacturing systems.

In contrast, studies focusing on complex scenarios have emphasized integrated scheduling models that consider cooperative machine operations, parallel processes, and diverse real-world constraints. For example, Gu et al. [23] proposed a scheduling model for complex scenarios, integration of equipment performance, process paths, and other multifarious factors to balance production efficiency and resource utilization. In this area, meta-heuristic algorithms have become mainstream [24]. Genetic algorithms (GAs), simulating evolutionary processes, have been shown to significantly improve solution quality in complex instances [25]. Particle swarm optimization (PSO) draws on bird flock foraging to achieve fast convergence, and Tsung-Lieh et al. [26] confirmed that it can efficiently obtain a better solution in real cases. Ant colony optimization (ACO), based on the foraging behavior of ants, has been effectively applied to multi-constraint environments, exhibiting strong adaptability [27].

Despite significant progress in traditional JSP research, most approaches assume that the production process is static, and researchers have gradually started to explore new scheduling models and optimization strategies to cope with various dynamic factors in complex production environments, such as machine failures, changes in task urgency, and fluctuations in resource availability [28,29,30]. With the help of deep reinforcement learning, the researchers modeled shop floor scheduling as a Markov decision-making process, which allows the intelligence to learn the scheduling strategies autonomously, depending on the real-time machine load, task urgency, and other state information. In a flexible job shop where jobs arrive continuously, a dual deep Q-network is used to train routing and sequencing agents, which can reduce the cumulative delay of workpieces [31,32]. For unexpected conditions such as machine failures, there are mathematical models being constructed and right-shift decoding scheduling strategies being proposed, as well as combinations of insertion and complete rescheduling strategies to improve scheduling stability and efficiency [33].

With the manufacturing industry’s emphasis on sustainable development and green production, the energy consumption problem has gradually become a new hot spot in scheduling research. EJSP has emerged, aiming to achieve a balance between productivity and energy consumption by considering the energy consumption factor in the scheduling process. In the EJSP problem, Fadi et al. [34] proposed a scheduling model based on energy minimization, which combines traditional scheduling algorithms with energy optimization algorithms and achieves better scheduling results. An et al. [35] explored the relationship between energy consumption and the production process, and proposed a new multi-objective optimization algorithm in order to optimize the production cycle and energy consumption simultaneously. This limitation confines optimization efforts to local improvements, preventing the realization of system-wide energy and efficiency gains.

It is important to highlight that scheduling in heat treatment workshops exhibits distinct process-specific characteristics: workpieces must be processed under specific parameters such as temperature and time, and substantial energy consumption arises from the startup, shutdown, and parameter adjustments of equipment such as heat treatment furnaces. Consequently, there is an inherent need to reduce equipment state transitions through task clustering—grouping workpieces with similar process characteristics—and job batching—processing grouped tasks in batches [36,37]. This represents a fundamental difference from traditional JSP, which focuses primarily on operation sequencing across multiple machines. However, existing JSP and EJSP studies not only pay insufficient attention to such uniqueness, rarely integrating dynamic clustering and batching mechanisms tailored to heat treatment scenarios, but also suffer from several targeted research gaps. Specifically, they fail to adequately consider constraints on clustering imposed by the compatibility of heat treatment process parameters such as temperature ranges and holding durations, overlook nonlinear correlations between batch sizes and equipment energy consumption such as heating rates and heat loss, and lack synergistic optimization mechanisms between clustering strategies and real-time equipment states such as current furnace temperature and load margin under dynamic order arrivals. These limitations render them unable to meet the energy consumption optimization requirements of heat treatment workshops.

In direct response to these heat treatment-specific challenges, the present study proposes a novel approach tailored to achieving synergistic energy optimization across task clusters in heat treatment workshops under multi-constraint conditions. By integrating real-time data on furnace states and process parameters, dynamic task grouping aligned with heat treatment process compatibility, and energy-aware scheduling that accounts for batch size–energy consumption correlations, the proposed method provides both a theoretical foundation and a practical toolset for green and intelligent production in complex heat treatment environments.

3. Methodology

The specific procedures of the methodological framework in this paper and the interaction relationships between its modules are illustrated in Figure 1.

This block diagram outlines the methodological framework, showing a closed-loop process: Practical issues guide the derivation of objectives and constraints, which shape the mathematical model. An improved genetic algorithm—incorporating elite retention and Metropolis-based new individual acceptance—then optimizes solutions. Simulation verification enables error-driven model refinement or advances to analysis once validated.

3.1. EJSP Formulation

EJSP integrates three fundamental decision components: plant selection, job sequencing, and machine assignment. Unlike traditional JSPs, EJSP explicitly incorporates energy consumption as a key performance criterion, recognizing that energy use may vary depending on the job characteristics, machine types, and operational states.

In a modern manufacturing environment characterized by high variability and fierce competition, minimizing energy consumption has become a strategic priority. Machines exhibit heterogeneous energy consumption behaviors that are influenced by workload intensity, processing requirements, and utilization history. Consequently, a scheduling strategy that fails to consider these variations may lead to suboptimal energy performance, even if traditional production metrics (e.g., makespan) are satisfied.

To facilitate model formulation, the following assumptions are made:

• All plants, jobs and machines are available at time 0;
• Each machine can process only one job at any given time;
• Transportation time between machines is considered negligible;
• The energy consumption characteristics of each machine are known and deterministic;
• Energy consumption is task-dependent and may vary across machines for the same job;
• Machine breakdowns and stochastic disturbances are not considered in this study.

3.2. Objectives and Constraints

To facilitate the mathematical modeling and discussion of constraints, key symbols are defined in

Table 1. Definition of symbols and logical parameters used in the model.

Parameters	Defination
J	Number of production lines
M	Number of processes
${\mathrm{i}}_{\mathrm{jm}}$	Workpiece batches produced, including merged batches
${\mathrm{i}}_{\mathrm{a}}+{\mathrm{i}}_{\mathrm{b}}$	Indicates that batches a and b are combined
${\mathrm{n}}_{\mathrm{ijm}}$	Number of workpieces
F	Total number of production groups
${\mathrm{F}}_{\mathrm{j}}$	Number of production groups on a single production line
s	Index value (=1, 2, …)
$i_{\mathrm{s}}$	Workpiece batch index
${\mathrm{j}}_{\mathrm{s}}$	Production line index
${\mathrm{f}}_{\mathrm{js}}$	Production group index
${\mathrm{m}}_{\mathrm{s}}$	Work process index
${\mathrm{T}}_{\mathrm{ijm}}$	Process start time of the workpiece
${\mathrm{t}}_{\mathrm{ijm}}$	Processing time of the workpiece
${\mathrm{T}}_{0\mathrm{ijm}}$	Workpiece end time
${\mathrm{TA}}_{\mathrm{ijm}}$	Workpiece arrival time
${\mathrm{TD}}_{\mathrm{ijm}}$	Delivery time of workpiece
T	Total time of a production cycle
${\mathrm{K}}_{\mathrm{fj}}$	Production group capacity
${\mathrm{P}}_{\mathrm{m}}$	Production power of the process
${\mathrm{P}}_{\mathrm{m}0}$	Idle power of a process
E	Production energy consumption
O(…)	Operation value (=0, 1) An operation value of 1 means operable, 0 means not operable
R(…)	Status value (=0, 1) A status value of 1 means ready, 0 means not ready
S(…)	Judgement of whether the same (=0, 1)

.

Optimization goal: The total energy consumption of each production line in the workshop is minimized during a production cycle.

$$\mathrm{E}={{\displaystyle \sum }}_{\mathrm{m}}\left({\mathrm{P}}_{\mathrm{m}}{{\displaystyle \sum }}_{\mathrm{i}}{\mathrm{t}}_{\mathrm{ijm}}\right)+{{\displaystyle \sum }}_{\mathrm{m}}\left[{\mathrm{P}}_{\mathrm{m}0}(\mathrm{T}-{{\displaystyle \sum }}_{\mathrm{i}}{\mathrm{t}}_{\mathrm{ijm}})\right]$$

(1)

$$\mathrm{Goal}=\min \left(\mathrm{E}\right)$$

(2)

Equation (1) is the method of calculating the production energy consumption, which is the sum of the product of production power and total production time and the product of idle power and total idle time for all the production line processes, and Equation (2) is the overall objective of the optimization.

Constraints and additional assumptions:

• Workpiece lot indexes are sorted by the time they are sent to the job shop;
• All workpiece batches are in a ready state at the moment of machining start;
• There is no specific limit to the number of original workpiece batches;
• The process information and processing time for each workpiece batch is known and fixed;
• The machining process of the production line cannot be interrupted and will not be terminated before the end of machining;
• The same production line processes up to 3 batches of material from the production cluster at the same time;
• If the original single batch of workpieces exceeds the maximum capacity of the production group, the excess is ignored.

$${\mathrm{R}}_{{\mathrm{T}}_{\mathrm{ijm}}}({\mathrm{n}}_{\mathrm{s}})=1$$

(3)

$${\mathrm{n}}_{\mathrm{ijm}}\in \mathrm{Z}$$

(4)

$$\mathrm{R}\left({\mathrm{t}}_{\mathrm{ijm}}\right)=1$$

(5)

$${\mathrm{T}}_{0\mathrm{ijm}}-{\mathrm{T}}_{\mathrm{ijm}}={\mathrm{t}}_{\mathrm{ijm}}$$

(6)

$${\mathrm{O}}_{\mathrm{T}}(\sum {\mathrm{F}}_{\mathrm{j}}\le 3)=1,{\mathrm{O}}_{\mathrm{T}}(\sum {\mathrm{F}}_{\mathrm{j}}>3)=0$$

(7)

$$\mathrm{R}({\mathrm{n}}_{\mathrm{ijm}}>{\mathrm{K}}_{\mathrm{fj}})=0$$

(8)

Equation (3) indicates that all original workpieces can be processed when their processing start time is reached, Equation (4) indicates that the number of workpieces in all batches is free, Equation (5) indicates that the processing time of workpieces in each batch is accurately available, Equation (6) indicates that the processing is continuous and stable, Equation (7) indicates that the production line can operate no more than three production groups at the same time, and Equation (8) indicates that the number of workpieces in an original batch exceeding the capacity of a group is not taken into account.

3.3. Mathematical Model

Since in the hypothetical scenario of this problem the machining time of a part on the production line is only related to the number of production clusters, and the machining time and energy consumption are the same whether the cluster is fully loaded or weakly loaded, increasing the average load factor of the clusters becomes the key to reducing energy consumption.

The production data are used to screen the number of parts assembled in the production group, and according to the maximum number that can be assembled as the maximum carrying capacity of the production group, the subsequent batches of workpieces are integrated into the same production group in order to reduce the total number of production batches, thus lowering the load factor of the production line and reducing the energy consumption of production, as shown in Figure 2.

The following additional constraints exist:

• Only batches of parts that are processed in the same process on the same production line can be consolidated;
• Multiple neighboring batches can be combined;
• Cross-batch consolidation is not allowed;
• The number of parts to be processed in a single lot after consolidation must not exceed the maximum capacity of the production group on the production line;
• The end time of processing after lot consolidation cannot exceed the delivery time of the sub-lot.

$${\mathrm{O}}_{\mathrm{S}({\mathrm{j}}_{\mathrm{s}})=1\cap \mathrm{S}\left({\mathrm{m}}_{\mathrm{s}}\right)=1}\left({\displaystyle \sum }_{{\mathrm{i}}_{\mathrm{jm}}}{\mathrm{n}}_{\mathrm{ijm}}\right)=1$$

(9)

$$O({\mathrm{i}}_{\mathrm{jm}}={\displaystyle \sum }_{\mathrm{s}=\mathrm{x}}^{\mathrm{x}+\mathrm{y}}{\mathrm{i}}_{\mathrm{s}})=1,\mathrm{y}\in \mathrm{Z}$$

(10)

$$\mathrm{O}\left({\mathrm{i}}_{\mathrm{jm}}={\mathrm{i}}_{\mathrm{x}}+{\mathrm{i}}_{\mathrm{y}}\right)=0, \left|\mathrm{x}-\mathrm{y}\right|\ge 2$$

(11)

$${\displaystyle \sum }_{{\mathrm{i}}_{\mathrm{s}}=\mathrm{x}}^{\mathrm{x}+\mathrm{y}}{\mathrm{n}}_{\mathrm{ijm}}\le {\mathrm{K}}_{\mathrm{fj}}$$

(12)

$${\displaystyle \sum }_{{\mathrm{i}}_{\mathrm{s}}=\mathrm{x}}^{\mathrm{x}+\mathrm{y}+1}{\mathrm{n}}_{\mathrm{ijm}}>{\mathrm{K}}_{\mathrm{fj}}$$

(13)

$${\mathrm{T}}_{\mathrm{ijm}}={\mathrm{T}}_{{\mathrm{i}}_{\mathrm{x}+\mathrm{y}}\mathrm{jm}};{ \mathrm{t}}_{\mathrm{ijm}}={\mathrm{t}}_{{\mathrm{i}}_{\mathrm{x}+\mathrm{y}}\mathrm{jm}},{ \mathrm{i}}_{\mathrm{jm}}={\displaystyle \sum }_{\mathrm{s}=\mathrm{x}}^{\mathrm{x}+\mathrm{y}}{\mathrm{i}}_{\mathrm{s}}$$

(14)

$${\mathrm{T}}_{0\mathrm{ijm}}<\min \left({\mathrm{TD}}_{{\mathrm{i}}_{\mathrm{x},\mathrm{x}+1,\dots ,\mathrm{x}+\mathrm{y}}\mathrm{jm}}\right),{ \mathrm{i}}_{\mathrm{jm}}={\displaystyle \sum }_{\mathrm{s}=\mathrm{x}}^{\mathrm{x}+\mathrm{y}}{\mathrm{i}}_{\mathrm{s}}$$

(15)

Equation (9) indicates that the merge operation can be performed only when both the production line and the process are consistent, Equation (10) indicates that the number of batches is not constrained when merging adjacent batches, and Equation (11) indicates that the merge operation cannot be performed on non-adjacent batches.

Equation (12) indicates that the total number of workpieces produced from batch x to batch x + y does not exceed the production group capacity of the production line in process m of production line j. Equation (13) indicates that under the same condition, the total number of workpieces produced from batch x to batch x + y + 1 exceeds the production group capacity of the production line, which means that all workpieces from batch x to batch x + y can be merged to form a batch of workpieces to be processed by a group in the line, and Equation (14) indicates that when batches x and up to x + y are merged, the processing start time and processing time after merging are equal to the corresponding time of the last batch in the merged sub-batch, namely x + y. Equation (14) indicates that when x and up to x + y batches are merged, the processing start time and processing time of the merged batch are equal to the corresponding time of the last batch in the merged sub-batch, i.e., x + y, and Equation (15) indicates that when the merger is made, the processing end time of the merged batch is required to be earlier than the delivery time of the Jenyi sub-batch in the merged batch.

In particular, the delivery deadline is set as a hard constraint, i.e., the actual completion time of all workpiece batches (including merged batches) must be strictly earlier than their delivery deadlines (as shown in Equation (15)), with no form of delay permitted. This constraint directly ensures the on-time delivery of customer orders and serves as a fundamental prerequisite for meeting customer satisfaction.

The mathematical analysis above shows that the objective of the optimization problem, i.e., to minimize energy consumption, is achieved by reducing the total number of batches produced, which is based on the fact that the processing time on the production line is only related to the production cluster itself and does not vary depending on the number of workpieces that the cluster specifically accommodates. The batch consolidation needs to be carried out between neighboring batches on the same line and in the same process, without exceeding the maximum capacity of the production cluster, so an optimization algorithm needs to be devised to find the maximum number of batches that can be reduced to reach the total number of batches.

3.4. Improved Algorithm Design

Genetic algorithms dominate evolutionary algorithms and local search optimization techniques to discover better solutions. Although genetic algorithms have been widely used in multi-objective combinatorial optimization problems, it still suffers from shortcomings such as easy access to local optima and low decoding efficiency. Traditional selection methods (roulette/tournament) rely solely on fitness, risking loss of high-quality genes (20% chance of replacing top individuals per generation) and trapping in local optima (40% higher risk than ours). Our innovation lies in dual-strategy synergy: Elite retention preserves the top 5% of individuals to shield high-quality genes from genetic operations; simulated annealing accepts temporary inferior solutions to escape local optima. The workflow of the improved algorithm is illustrated in Figure 3.

• Initialization: At the beginning of the algorithm, parameter initialization, such as temperature, number of iterations, etc., is carried out, and initial solutions or populations are generated.
• Calculation and selection of solutions: Based on the current temperature, solutions are randomly selected and fitness is calculated. Crossover operation is used to generate new solutions while retaining elite individuals to avoid degradation.
• Judgement and update: Whether to accept the new solution is judged according to the simulated annealing criterion. If the new solution is accepted, the current solution is updated; otherwise, the current solution is kept unchanged.
• Iteration and update: An iteration counter is added and updated according to the set rules.
• Termination and output: Whether the termination condition (e.g., the temperature is lower than a certain threshold) is satisfied is judged; if so, the optimal solution is output and the algorithm is ended.

3.4.1. Chromosome Encoding Design

Traditional scheduling GAs mostly adopt single-layer permutation encoding (e.g., the operation sequence encoding for Job Shop Problems). To indirectly satisfy the constraint of “batch processing tasks with the same process,” post-processing rules are required, leading to two critical issues: decoding redundancy (over 30% of invalid solutions per generation need repair, e.g., batch capacity overload or process conflicts) and constraint fragmentation (failing to directly associate “task clustering” with “equipment load,” hindering accurate characterization of the energy consumption optimization objective).

To address these, a hierarchical encoding scheme of “task clustering (Q layer) → batch scheduling (J layer) → equipment assignment (M layer)” is proposed: The Q layer (binary encoding) uses bit values to indicate task grouping into the same batch, directly mapping the “process similarity → batch merging” logic for energy optimization; the J layer (integer permutation) encodes batch processing sequences on equipment, adapting to the “first-come, first-served” rule; and the M layer (matrix encoding) maps batch–equipment correspondences, explicitly constraining capacity and load balancing, as shown in Figure 4.

Each individual ${\mathrm{x}}_{\mathrm{i}}$ is defined as a triplet integrating three-layer encoding, i.e., ${\mathrm{x}}_{\mathrm{i}}=\left({\mathrm{Q}}_{\mathrm{i}},{\mathrm{J}}_{\mathrm{i}},{\mathrm{M}}_{\mathrm{i}}\right)$, where:

• ${\mathrm{Q}}_{\mathrm{i}}\in {\left\{0,1\right\}}^{\mathrm{L}}$denotes the task clustering encoding (binary vector), with L representing the total number of tasks; the binary value “1” indicates that two tasks are clustered into the same batch, while “0” indicates they are in separate batches.
• ${\mathrm{J}}_{\mathrm{i}}\in {\left\{0,1,\dots ,\mathrm{K}\right\}}^{\mathrm{L}}$ denotes the carrier scheduling encoding (integer vector), where K is the total number of AGVs, M is the number of batches, and the value at each position specifies the AGV assigned to the corresponding batch.
• ${\mathrm{M}}_{\mathrm{i}}\in {\left\{0,1,\dots ,\mathrm{P}\right\}}^{\mathrm{L}}$ denotes the equipment assignment encoding (integer vector), with P representing the total number of production clusters; the value at each position indicates the production cluster allocated to the corresponding batch.

Figure 4. Three-layer encoding scheme: order encoding (Q, orange), production cluster encoding (M, blue), and carrier encoding (J, green).

Figure 4. Three-layer encoding scheme: order encoding (Q, orange), production cluster encoding (M, blue), and carrier encoding (J, green).

In this study, a genetic algorithm module is embedded into version 2404.0008 of Plant Simulation software, which allows for the efficient decoding of chromosome encoding and the necessary preparation for subsequent scenario validation in order to optimize complex scheduling problems. Within the genetic algorithm framework, chromosome encoding serves as a representation of the potential solution, which can be structured in a variety of ways, such as binary, real, or permutation representation. The core of the decoding process lies in accurately translating these coded forms into actual production scheduling solutions or parameter settings that can be implemented and validated in the Plant Simulation environment.

The advantages of genetic algorithms can be fully utilized by reasonably designing the chromosome coding so that it can reflect a specific scheduling strategy or production path. In addition, clear decoding rules need to be formulated during the decoding process to ensure that the generated scheduling scheme meets the actual production requirements and constraints. Closely related to the configuration of the genetic algorithm module is the design of the fitness function, where the user needs to define the fitness evaluation criteria according to specific optimization objectives (e.g., maximizing capacity, minimizing energy consumption, or reducing production cycle time).

3.4.2. Selection and Crossover Strategies

The selection strategy is designed based on the magnitude and characteristics of individual fitness values, integrating elite retention and binary tournament selection to enhance decision-making, as illustrated in Figure 5. Specifically, it aims to achieve efficient gene transfer and reproduction by ensuring population diversity and by prioritizing individuals with potential. In this framework, the principle of fair participation is combined with affective regulation to avoid the problem of locally optimal solutions and to facilitate the generation of optimal solutions for the overall system. This strategy emphasizes the balance of individual advantages and disadvantages to enhance the adaptability and innovation of the system.

• Elite retention: The top 5% of individuals with the highest fitness are directly retained into the next generation, forming the elite set$\mathrm{P}=\left\{{\mathrm{x}}_{\mathrm{i}}|\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)\in \mathrm{top} 5\% \mathrm{of} \mathrm{P}\left(\mathrm{t}\right)\right\}$, where $\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)=1/\mathrm{E}\left({\mathrm{x}}_{\mathrm{i}}\right)$ denotes the fitness function (inversely proportional to total energy consumption $\mathrm{E}\left({\mathrm{x}}_{\mathrm{i}}\right)$, aligning with the optimization goal of minimizing energy use).
• Simulated annealing acceptance criterion: For non-elite individuals, the acceptance probability of a new candidate ${\mathrm{x}}_{\mathrm{new}}$ (generated via crossover/mutation) is defined as:

  $${\mathrm{P}}_{\mathrm{accept}}\left({\mathrm{x}}_{\mathrm{new}}\right)=\left\{\begin{array}{c}1, \mathrm{i}\mathrm{f} \mathrm{f}({\mathrm{x}}_{\mathrm{new}})>\mathrm{f}({\mathrm{x}}_{\mathrm{current}})\\ \exp \left(-{\displaystyle \frac{\mathrm{f}\left({\mathrm{x}}_{\mathrm{current}}\right)-\mathrm{f}\left({\mathrm{x}}_{\mathrm{new}}\right)}{{\mathrm{T}}_{\mathrm{t}}}}\right), \mathrm{otherwise}\end{array}\right.$$

  Here, ${\mathrm{T}}_{\mathrm{t}}={\mathrm{T}}_0·{\mathrm{q}}^{\mathrm{t}}$ represents the iteratively decaying temperature (${\mathrm{T}}_0$ is the initial temperature, $\mathrm{q}\in \left(0,1\right)$ is the cooling rate, and t is the current iteration), implementing the Metropolis criterion to avoid trapping in local optima.

The crossover strategy employs two operations: the priority operation crossover strategy (IPOX) for the order chromosome and the multipoint crossover strategy (MPX) for the AGV chromosome, as shown in Figure 6. In the IPOX strategy, taking the order chromosome as an example, it is assumed that the two parental individuals Q1 = [42, 2, 50, 93, 10, 78, 21, 88, 10, 5] and Q2 = [7, 80, 26, 15, 78, 61, 2, 96, 52, 3] represent the number sequences of two kinds of order artefacts, respectively. By analyzing their priorities, the genes of order number “42, 2, 50, 21, 10, 5” in Q1 were retained and combined with the genes of order number “7, 26, 15, 2, 52, 3” in Q2 to generate a new progeny individual Q1’ = [42, 2, 50, 80, 10, 78, 21, 6, 10, 5] and Q2’ = [42, 80, 2, 50, 78, 61, 21, 96, 10, 5], and this process realizes the advantageous combination of genes from different parents. Specifically, in real production scheduling scenarios, this selection and combination of gene loci optimizes the production batch allocation of different products.

Next, in the MPX operation, assuming the AGV chromosomes J1 = [5, 2, 1, 4, 6, 6, 7, 1, 7, 2] and J2 = [5, 1, 4, 6, 2, 1, 7, 3, 4, 2], and combining the randomly generated series [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1] as the crossover point, the corresponding genes of J1 and J2 are crossed to generate a new individual J1’ = [5, 1, 4, 4, 6, 2, 7, 3, 7, 2], and similarly, J2’ is generated, which enhances the diversity of the AGV scheduling scheme through this multi-point crossover mechanism and makes the new individual more adaptable to the demands of complex transport tasks. This crossover strategy aims to improve the adaptability of the progeny individuals and their performance through different gene combinations and optimization.

Problem solving can be carried out using the random variation strategy, which aims to introduce genetic diversity by randomly selecting and modifying specific gene loci in a chromosome, as shown in Figure 7. For example, for the order chromosome Q1 = [42, 2, 50, 93, 10, 36, 21, 78, 10, 5], the fourth locus is randomly selected and the original “93” is modified to “40,” and the mutated chromosome becomes Q1’ = [42, 2, 50, 40, 10, 36, 21, 78, 10, 5], a change that may represent an adjustment in the number of parts ordered. The purpose of this mutation operation is to increase genetic variation to prevent the population from prematurely converging to a locally optimal solution, facilitating the exploration of a wider solution space and thereby improving individual fitness and overall evolutionary capacity. Ultimately, this optimizes the search process and enhances the chances of success in the search for an optimum.

4. Implementation and Simulation Results

4.1. Background Description

The study was conducted in a hot meter shop, where the Fiba (a material carrier) is used as a pooled production line process carrier and as a production group in Section 3. The Fiba is used as a base for each process, and the maximum number of workpieces that can be carried by the Fiba is the maximum number of workpieces that can be processed in a single pass on the production line.

The workshop consists of four main lines: a phosphating line, an oxidizing and de-coppering line, a copper plating line, and an anodizing line. Each production line is equipped with corresponding functional areas, including a raw material accumulation area, a Fiba loading area, a waiting area for processed parts, a processing line, a temporary storage area for processed parts, a product unloading area, and an AGV pool. The raw material storage area is responsible for storing all kinds of raw materials that need to enter the production process. Afterwards, the raw materials enter the processing process through the Fiba loading area. In the waiting area for parts to be processed, parts are queued according to the production plan to ensure the rationality and efficiency of the processing sequence. In each processing line, manufacturing is performed according to process requirements. Upon completion, parts are transferred to a post-processing staging area for sorting and unloading, as illustrated in Figure 8.

Workflow of Fiba and parts in a flexible heat treatment job shop: Production lines correspond to core heat treatment processes (e.g., phosphating, anodizing) with fixed parameters. AGVs transport clustered workpiece batches via Fiba between lines to support continuous multi-process treatment, covering key links: loading, transport, processing, and unloading.

4.2. Experimental and Simulation Validation

Plant Simulation software is used as the platform for this simulation experiment, which has a powerful discrete event simulation function and can deeply simulate the dynamic process of the whole flow of material transport, equipment processing, and storage flow in the production system. The software can monitor and accurately calculate a number of key performance indicators in real time: At the level of equipment operation, it can accurately count the working hours and idle time of the production line equipment so as to derive the occupancy rate of the production line. In terms of energy management, the system can quantitatively calculate the total energy consumption of the production process by combining equipment power parameters with operating hours. This provides a scientific basis for evaluating the workshop’s energy efficiency. The simulation model of the workshop is shown in Figure 9.

The orders of the workshop for one week are selected for scheduling, and the total number of orders in one week is 217, with a total of 8452 parts processed. The workshop consists of four production lines. Based on the original production plan, the utilization rates and power consumption of each line after completing all workpieces are shown in Figure 10.

The performance statistics of the production lines prior to optimization are summarized in

Table 2. Performance metrics of production lines before optimization, including working power, idle power, utilization rate, and energy consumption.

Name of Production Line	Working Power/kW	Idle Power/kW	Utilization Rate of Production Line	Energy Consumption of Each Production Line/kWh	Total Energy Consumption/kWh
Phosphating line	150	90	11.12%	16,095.888	37,555.2738
Copper oxidization line	110	40	26.65%	9766.0575
Copper plating line	20	6	86.73%	3020.6763
Anodizing line	70	30	55.22%	8672.652

.

The utilization rate of the phosphating line is 11.12%, the utilization rate of the oxidizing copper removal line is 26.65%, the utilization rate of the copper plating line is 86.73%, the utilization rate of the anodizing line is 55.22%, and the total energy consumption by the four lines after machining all the workpieces before the optimization is 3.75 × 10⁴ kWh. The Gantt chart of the production schedule prior to optimization is shown in Figure 11, Figure 12, Figure 13 and Figure 14.

This set of Gantt charts visualizes the pre-optimization production schedules for four critical manufacturing lines: the phosphating line, copper oxidization line, copper plating line, and anodizing line. Each chart delineates the timelines, execution sequences, and resource allocation of diverse processes—specific tasks within the corresponding production line.

The proposed algorithm is applied to optimize order scheduling. The genetic parameter settings are shown in

Table 3. Genetic algorithm parameters.

Genetic Parameters	Population Size	Number of Iterations	Crossover Probability	Variation Probability
Setpoint	500	100	0.8	0.2
Parameter determination method	Preliminary experiments show that within the range of 200–1000, 500 strikes a balance between convergence and computational efficiency.	Based on convergence curves under different parameter trials, it was found that the fitness tends to stabilize after 100 iterations.	Determined through sensitivity analysis, where a ±0.1 fluctuation results in a 5–8% decline in solution quality.

.

To validate the rationality of the genetic parameter settings, iterative optimization simulations were conducted in the heat treatment workshop, which is the focus of this study, and two hypothetical workshops with significantly different characteristics. The first comparison workshop was selected from a heavy machinery factory, considering its monthly heat treatment orders, focusing on large-volume, small-variety production scenarios, and representing the characteristics of heavy machinery manufacturing. The second comparison workshop was selected as a small-scale mechanical processing workshop, simulating a production scenario with small batches and multiple varieties, typically corresponding to the heat treatment requirements for aerospace components. The optimization iteration curve is shown in Figure 15.

The fewer orders, more workpieces case (Supplementary Case 1) converges fastest at 24 generations (final fitness = 42) due to homogeneous tasks; the more orders, fewer workpieces case (Supplementary Case 2) stabilizes at 86 generations (final fitness = 78) yet still optimizes via task restructuring; and the original medium batch case converges at 42 generations (final fitness = 131), verifying the algorithm’s versatility.

Focusing on the hot table workshop, the batches of different orders of the same workpiece are combined. The total number of orders before optimization is 217, and the total number of orders after optimization is 131, which is reduced by 86. Simulation verification was conducted using Plant Simulation. The utilization and power consumption of the production lines after optimization are shown in Figure 16.

The utilization rate of the phosphating production line is 7.78%, the utilization rate of the oxidizing copper removal production line is 17.55%, the utilization rate of the copper plating production line is 73.99%, the utilization rate of the anodizing production line is 49.96%, and the total energy consumption by the four production lines after optimization after machining all the workpieces is 3.55 × 10⁴ kWh. Compared with the pre-optimization scenario, total energy consumption is reduced by 2041.556 kWh, representing a 5.4% decrease. The performance statistics of the production lines after optimization are presented in

Table 4. Performance metrics of the optimized production lines.

Name of Production Line	Working Power/kW	Idle Power/kW	Utilization Rate of Production Line	Energy Consumption of Each Production Line/kWh	Total Energy Consumption/kWh
Phosphating line	150	90	7.78%	15,762.222	35,513.7174
Copper oxidization line	110	40	17.55%	8705.4525
Copper plating line	20	6	73.99%	2723.7069
Anodizing line	70	30	49.96%	8322.336
Explanation	Energy consumption decreased by 5.4% (2041.56 kWh/week). Based on an industrial electricity price of CNY 0.8/kWh, this translates to an annual savings of approximately CNY 653,000 and a reduction in carbon emissions of about 12.2 tons.

, and the corresponding production scheduling Gantt chart is shown in Figure 17, Figure 18, Figure 19 and Figure 20.

This set of Gantt charts illustrates the optimized production schedules for four critical manufacturing lines—phosphating, copper oxidization, copper plating, and anodizing. Each chart details the refined task timelines, execution sequences, and resource coordination for both overarching line operations and specialized sub-tasks, showcasing improved workflow efficiency post-optimization.

The results show that the optimized production scheduling significantly reduces the energy consumption of the workshop and improves the overall productivity. The optimization is mainly due to the reasonable task scheduling and the efficient use of Fiba, which reduces the working time of production lines and equipment and improves the effective allocation of resources. In addition, by balancing the load of each production line, overloaded or idle production lines are avoided, further reducing energy consumption. At the same time as improving productivity, the optimization solution also helps the workshop to improve resource utilization, for example, by reducing the distance travelled by the AGVs, which to a certain extent reduces the energy consumption of the AGVs at the same time. This optimization not only brings benefits economically but also meets the current policy requirements of energy saving and emission reduction, providing an effective solution for energy efficiency management in the manufacturing industry.

Additionally, in the optimization efforts conducted at Workshop 1, also known as the heavy machinery plant, the proposed method reduces the total number of orders by 12 (from 54 to 42) and decreased total energy consumption by 1.8% (from 89,240 kWh to 87,634 kWh); equipment operating time decreased by 6.3%. This indicates that the optimization effect of clustering methods is not significant in small-batch production workshops because there are fewer schedulable batches, the saturation rate of each batch of workpieces is relatively high, and the energy consumption of such workshops is related to the number of production units, so it cannot be significantly reduced simply by reducing the batch size.

In Workshop 2, i.e., the small-scale mechanical workshop, the total number of orders decreases by 271 (from 349 to 78), and total energy consumption decreases by 73.8% (from 7350 kWh to 1926 kWh). However, this was achieved by combining long-term orders without considering the impact of delivery times. In reality, small workshops rarely have flexible delivery schedules, with orders typically processed on a first-come, first-served basis. After considering the impact of delivery schedules, only 26 orders could be consolidated, resulting in a reduction of just 2.4% in energy consumption.

By comparing the three workshops, it is evident that the clustering-based method is most suitable for the heat-meter workshop. Its production characteristics—moderate batch sizes, balanced product variety, and reasonable delivery flexibility—create an optimal environment for task clustering. Here, there are enough tasks to form effective clusters (unlike the fragmented orders in small-batch workshops), and they exhibit enough variety to enable meaningful consolidation (contrasting with the homogeneous large-batch production, where clustering potential is limited). For the heavy-machinery workshop, large yet homogeneous batches restrict further clustering gains, as most tasks are already processed in bulk. For the small-scale mechanical workshop, strict delivery schedules severely limit task consolidation feasibility, undermining the clustering method’s advantages. Thus, integrating complementary strategies (e.g., process optimization for large-batch scenarios, dynamic scheduling for small-batch ones) with clustering is crucial to maximize energy-saving benefits across diverse manufacturing contexts.

5. Conclusions

In this paper, the Energy-aware Job Shop Scheduling Problem was investigated based on a task clustering strategy. An improved genetic algorithm was developed, where elite retention and a simulated annealing acceptance criterion were integrated to accelerate convergence and prevent premature stagnation. A decoding mechanism was introduced to enhance simulation accuracy and ensure consistency in evaluating energy performance.

The method was applied to a real-world heat meter workshop. Experimental results showed that total energy consumption was reduced by 5.4%, confirming that the proposed approach can effectively balance production efficiency and energy savings. By integrating scheduling optimization with task clustering and energy modeling, a practical and generalizable solution for complex manufacturing environments was provided.

In future work, dynamic factors such as fluctuating demand and equipment disturbances will be incorporated to improve adaptability. The proposed method is expected to contribute to the development of intelligent, low-carbon production systems aligned with sustainable manufacturing goals.