Dynamic Economic–Environmental Dispatch with Generator Priority: A Machine Learning–Optimization Framework

Abstract

The efficient management of power systems requires balancing electricity generation costs with associated environmental emissions under dynamically varying demand. This paper proposes a two-stage approach that combines machine learning (ML) with a metaheuristic optimization algorithm to address the dynamic economic–environmental load dispatch (DEELD) challenge. In the first stage, electricity consumption data are enriched with temporal features to capture demand patterns and enable accurate forecasting. In the second stage, the daily scheduling horizon is divided into multiple periods, and dispatch solutions are generated sequentially while enforcing ramp-rate constraints. To enhance operational realism, a priority-based generator scheduling mechanism is explicitly introduced, enforcing hierarchical unit commitment and reflecting practical dispatch policies. Rather than focusing on a single optimal solution, the proposed framework generates multiple feasible dispatch solutions and evaluates them using economic, environmental, and operational performance indicators. These solutions are then ranked according to predefined decision profiles, enabling system operators to select dispatch strategies that align with specific priorities. This transforms the dispatch process into a flexible decision-support tool capable of addressing diverse real-world requirements.

1. Introduction

The growing global demand for energy, coupled with increasing concerns about environmental degradation, has placed significant pressure on power systems to operate both efficiently and sustainably. Thermal power plants continue to supply a large share of the world’s electricity; however, their operation is associated with high fuel consumption and the emission of harmful pollutants, such as NO_x, SO₂, and CO₂ [1]. From an operational standpoint, power-system dispatch decisions must, therefore, balance economic efficiency with environmental responsibility under complex regulatory and operational constraints.

In the early stages of power-system optimization research, attention was mainly focused on the economic load dispatch problem, where the sole objective was to minimize total fuel cost while satisfying power balance and generator operating limits. Classical optimization techniques, such as linear programming, parametric, and pattern search methods, were widely applied due to their analytical simplicity and deterministic convergence properties [2,3,4]. These approaches were effective for small-scale and convex systems; however, their performance deteriorated when faced with nonlinearity, non-convex cost functions, and complex operational constraints typical of large interconnected power systems.

As awareness of environmental impacts increased and emission regulations became more complex, it became evident that fuel cost minimization alone was insufficient for sustainable power-system operation. Generating units operating at minimum cost do not necessarily produce minimum emissions, leading to an inherent conflict between economic and environmental objectives. To address this issue, researchers introduced the Combined Economic Emission Dispatch (CEED) problem, which simultaneously minimizes fuel cost and pollutant emissions subject to system and operational constraints, providing a more environmentally conscious dispatch framework [5].

Early CEED studies extended classical economic emission dispatch formulations to account for conflicting objectives and operational constraints. For instance, evolutionary programming combined with a fuzzy satisfying method was used to solve dynamic economic emission dispatch problems, effectively handling trade-offs between fuel cost and emissions under ramp-rate constraints [6]. Similarly, analytical modeling approaches were proposed to transform the multi-objective economic and emission dispatch problem into a single equivalent objective function, although such methods may face limitations in handling complex nonlinear characteristics [7]. To overcome these limitations, advanced metaheuristic optimization techniques were introduced to better handle nonlinear and multi-objective characteristics. For example, the non-dominated sorting genetic algorithm-II (NSGA-II) was applied to combine heat and power economic emission dispatch problems, demonstrating strong capability in generating well-distributed Pareto-optimal solutions [8]. Similarly, a multi-objective particle swarm optimization (MOPSO) approach was developed to improve solution diversity and convergence by redefining the global and local best solutions in a multi-objective context [9].

Artificial intelligence–based swarm methods were further explored to enhance performance. An artificial bee colony algorithm with dynamic population size was proposed to reduce parameter dependency while maintaining competitive performance in CEED problems [10]. In parallel, a multi-objective whale optimization algorithm with enhanced exploration and constraint-handling mechanisms showed improved convergence and diversity compared to conventional approaches [11]. Other nature-inspired algorithms were also introduced to improve solution quality. A multi-objective harmony search algorithm incorporated Pareto ranking and crowding distance to maintain solution diversity and outperform classical NSGA-II [12]. Likewise, an enhanced bat algorithm with advanced constraint handling and Lévy-flight-based search demonstrated better cost and emission optimization on standard test systems [13]. In addition, human-inspired learning strategies were applied, where a multi-objective human learning algorithm improved solution diversity and avoided premature convergence through learning-based phases and Pareto-based filtering mechanisms [14]. These developments highlight the trend toward more adaptive and intelligent optimization strategies for CEED problems.

To further improve convergence and global search capability, hybrid optimization frameworks were proposed. A hybrid chaotic particle swarm optimization combined with sequential quadratic programming was introduced to refine solutions and handle valve-point effects effectively [15]. Similarly, a hybrid gray wolf optimizer and particle swarm optimization approach demonstrated improved convergence speed and solution quality through combined exploration and exploitation mechanisms [16]. Enhancements to particle swarm optimization continued with the development of a new global PSO variant that improved global search ability and avoided local optima through modified position update rules and normalization techniques [17]. In parallel, a modified NSGA-II incorporating dynamic crowding distance and controlled elitism addressed diversity issues and improved Pareto front quality [18]. More recent developments include the introduction of Harris Hawks optimization, a nature-inspired algorithm based on cooperative hunting behavior, which demonstrated strong performance across benchmark and real-world optimization problems [19]. Additionally, hybrid PSO–GSA approaches combined swarm intelligence with gravitational search mechanisms to effectively handle complex CEED problems with multiple practical constraints [20].

Although ramp-rate constraints and time-dependent limits have been incorporated into some CEED models [21,22], most formulations remain limited in capturing the full complexity of real-world operation. Generator-priority mechanisms, sequential utilization logic, and coordinated multi-period operation are rarely modeled explicitly, despite their importance in practical dispatch environments. In addition, a large portion of the existing literature [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] primarily focuses on obtaining a single optimal or near-optimal solution for a given formulation. While these approaches demonstrate strong optimization capability, they often provide limited insight into the diversity of feasible solutions and the range of trade-offs available between competing objectives, although some studies [28] have begun to explore the use of metaheuristics as solution generators rather than purely optimizers. In real-world operation, system operators are rarely constrained to a single decision, and alternative solutions may be preferred depending on economic, environmental, or operational considerations.

To address these limitations, this paper proposes a dynamic CEED framework that integrates machine learning–based load forecasting with sequential metaheuristic optimization under realistic constraints. Hourly demand is first predicted, and the operating horizon is divided into multiple time periods to capture load variation. The problem is then solved sequentially, using each period’s optimal solution to initialize the next, ensuring temporal continuity. Ramp-rate constraints are explicitly enforced to maintain smooth inter-period transitions.

An explicit generator-priority constraint is further introduced to reflect practical dispatch policies. Units are assigned predefined priority levels such that higher-priority generators are dispatched first and must reach their maximum output before lower-priority units are activated. This hierarchical mechanism prevents unrealistic simultaneous utilization and yields dispatch schedules that better represent actual system operation.

Beyond conventional approaches that focus on identifying a single optimal solution, this work adopts the perspective that metaheuristic methods should be viewed as solution generators rather than mere optimizers. Relying solely on a single optimal solution may overlook valuable alternative solutions that offer different trade-offs in practice. In this context, multiple feasible dispatch solutions are generated and evaluated through a set of features. A three-profile decision is then introduced to rank these solutions according to different operational priorities, enabling decision-makers to select the most suitable dispatch strategy based on their objectives.

The main contributions of this work are summarized as follows:

• A two-stage dynamic CEED framework integrating machine learning–based load forecasting with sequential metaheuristic optimization is proposed to address time-varying power demand conditions.
• Ramp-rate constraints and a priority-based generator dispatch mechanism are incorporated to improve operational realism and enforce hierarchical generator utilization during sequential scheduling.
• Multiple feasible dispatch solutions are generated and evaluated using economic, environmental, and operational performance indicators. A profile-based ranking mechanism is then applied to support decision-making under different operational preferences, enabling flexible selection of dispatch strategies according to stakeholder priorities.
• Unlike many existing CEED studies that focus on isolated optimization objectives or simplified operating conditions, the proposed framework integrates demand forecasting, sequential optimization, ramp-rate limitations, generator-priority rules, and multi-profile solution evaluation within a unified decision-support framework aimed at practical power-system operation.

The remainder of the paper is organized as follows: Section 2 formulates the dynamic CEED problem; Section 3 presents the proposed two-stage forecasting optimization framework; Section 4 discusses the results; and Section 5 concludes the study.

2. Economic–Environmental Problem Formulation

2.1. Problem Overview

The economic–environmental load dispatch problem seeks to simultaneously minimize generation costs and emissions while satisfying system constraints. Electricity demand varies over time due to daily, weekly, and seasonal patterns, making the problem inherently dynamic. Therefore, the formulation must capture both the economic–environmental objectives and the time-varying nature of load demand within a unified optimization framework.

2.2. Electricity Consumption Variations

Conventional CEED formulations rely on static optimization, where scheduling is based on average or forecasted demand over extended intervals. Such approaches fail to capture the time-varying nature of electricity consumption, which changes across hours, weekdays, and seasons. These variations require a dynamic formulation capable of adapting generation schedules to evolving demand patterns.

2.3. Mathematical Formulation

The current problem determines the optimal generation schedule that minimizes the total fuel cost and emissions while satisfying operational constraints. It is formulated as a multi-objective optimization problem subject to power balance, generation limits, ramp-rate constraints, and a generator-priority constraint. Unlike conventional CEED models that allow simultaneous participation of all units within capacity limits, the proposed formulation enforces hierarchical dispatch; higher-priority units must reach their allowable limits before lower-priority units are activated.

2.3.1. Fuel Cost Minimization

The overall fuel cost ($/h) for the system is obtained by summing the quadratic fuel cost functions of each generator. It is expressed as:

$$FC(P^t)=\sum _{i=1}^n(a_i+b_i{P}_i^t+c_i{(P_i^t)}^2)$$

(1)

where $FC(P^t)$ is the total fuel cost; n is the total number of generators; $P_i^t$ is the power output of unit i at time t; and $a_i$, $b_i$, and $c_i$ are cost coefficients.

However, practical thermal generating units exhibit the valve-point effect, which refers to the rippling and non-convex behavior of the fuel cost curve caused by the sequential opening of steam admission valves. This mechanical phenomenon introduces non-smoothness into the cost function, making the conventional quadratic model insufficient.

To capture this behavior, a sinusoidal term is added to the quadratic function:

$$FC(P^t)=\sum _{i=1}^n(a_i+b_i{P}_i^t+c_i{(P_i^t)}^2+\mid d_i\cdot sin(e_i\cdot (P_{i,min}-P_i^t))\mid )$$

(2)

where $d_i$ and $e_i$ are the coefficients representing the ripple magnitude and frequency.

2.3.2. Emission Minimization

The overall emissions (ton/h) for the system are obtained by summing a quadratic and an exponential function. The total emission function is defined as:

$$E(P^t)={\displaystyle \sum _{i=1}^n} ({\alpha }_i+{\beta }_i{P}_i^t+{\gamma }_i{(P_i^t)}^2+{\eta }_i{e}^{{\delta }_i{P}_i^t})$$

(3)

where ${\alpha }_i$, ${\beta }_i$, ${\gamma }_i$, ${\eta }_i$, and ${\delta }_i$ are emission coefficients of generator i.

2.3.3. Constraints

The problem is subject to several constraints to ensure feasible power generation:

Power Balance

At each time t, total generation must satisfy demand and transmission losses:

$$\sum _{i=1}^n{P}_i^t = P_d^t + P_L(P^t)$$

(4)

where $P_d$ is the total power demand, and $P_L$ is the transmission power loss, which is calculated using the B-coefficients method:

$$P_L^t={\displaystyle \sum _{i=1}^n} {\displaystyle \sum _{j=1}^n} P_i^t{B}_{ij}{P}_j^t+{\displaystyle \sum _{i=1}^n} B_{0i}{P}_i^t+B_{00}$$

(5)

where $B_{ij}$, $B_{i0}$, and $B_{00}$ are loss coefficients.

Generator Limits

Each unit operates within its minimum and maximum limits. This inequality constraint is given by:

$$P_{i,min} \le P_i^t \le P_{i,max}$$

(6)

where $P_{i,min}$ and $P_{i,max}$ are the minimum and maximum generation limit for unit i.

Generation Priority

Generators are classified into three priority levels:

• Type 1: Highest priority—always activated;
• Type 2: Activated only after all Type 1 units are at their maximum output;
• Type 3: Activated only after all Type 1 and Type 2 units are fully utilized.

To enforce hierarchical dispatch, lower-priority units can only generate when all higher-priority units are operating at their maximum limits:

$$\left(\sum _{i\in G_r} P_i^t = \sum _{i\in G_r} P_{i,max}\right) \Rightarrow \sum _{i\in G_{r+1}} P_i^t \ge 0$$

(7)

where $G_r$ denotes the set of generators in priority level r.

This ensures that lower-priority generators are dispatched only when higher-priority ones are already producing at full capacity.

2.3.4. Weighted Sum Method

In current multi-objective optimization problems, fuel costs and emissions represent conflicting objectives measured in different units ($/h and ton/h, respectively), and therefore cannot be directly combined. To handle this, the current study employs the Weighted Sum Method (WSM), a technique used for converting multi-objective formulations into a single-objective one. This method enables the combination of the economic and environmental objectives, with each measured in different units, into a single-objective function. By assigning appropriate weights, the WSM allows for simultaneous optimization of the two aspects while balancing their relative importance based on the weight factor w. Similar formulations that integrate weight and penalty factors have been widely adopted in earlier CEED studies [17,23]. The equation is expressed as:

$$F(P^t)=w·FC(P^t)+(1 - w)·pf·E(P^t)$$

(8)

where w can be from 0 to 1; and pf ($/ton) is the price penalty factor, which can be calculated as:

$$pf={\displaystyle \frac{FC(P_{max})}{E(P_{max})}}$$

(9)

The closer w is to 1, the more importance is given to the cost objective, while values closer to 0 prioritize emissions. In this work, the cost and emissions are equally important, so w is set to 0.5. This choice reflects the objective of the present study to treat economic and environmental aspects with equal importance, rather than prioritizing one objective over the other. Therefore, the weighting factor was selected based on the intended decision perspective of the framework, rather than through performance-oriented tuning. Substituting w = 0.5 into (8) yields $F(P^t)=0.5FC(P^t)+0.5pfE(P^t)$. Since multiplying an objective function by a positive constant does not affect the location of the optimum, the equivalent form in (10) is adopted for simplicity:

$$F(P^t)=FC(P^t)+pf·E(P^t)$$

(10)

The price-penalty factor is introduced to convert the emission objective into an economic-equivalent scale, allowing both objectives to be combined consistently within the same optimization function. Using the ratio evaluated at maximum generation provides a system-dependent normalization reference that preserves the relative magnitude between the fuel cost and emissions while avoiding dominance of one objective due solely to unit differences.

Although the exact value of the penalty factor may vary across different systems and operating conditions, the adopted formulation remains widely used in CEED studies as a practical normalization mechanism for combined economic–environmental optimization.

2.4. Dynamic Considerations

The economic–environmental dispatch problem is inherently dynamic due to time-varying electricity demand. Instead of a single, static optimization, the scheduling horizon is divided into successive time intervals and solved sequentially.

The optimal solution of period t is used to initialize period t + 1:

$$P_{i,init}^{(t+1)} = P_i^{(t)}$$

(11)

This inter-period linkage preserves scheduling continuity and enables enforcement of ramp-rate constraints.

In practice, power generators cannot adjust their output instantaneously due to mechanical and thermal limitations. The change in power generation over a specific time interval is constrained by ramp-rate limits [22,24]. These limits ensure that the generator’s output changes gradually between time periods. The ramp-rate constraints are expressed as:

$$P_i^{t-1} - {DR}_i \times \mathsf{\Delta }t \le P_i^t \le P_i^{t-1} + {UR}_i \times \mathsf{\Delta }t$$

(12)

where ${UR}_i$ and ${DR}_i$ are the ramp-up and ramp-down limits, and $\mathsf{\Delta }t$ is the time interval.

Considering both capacity and ramp-rate constraints, the feasible operating range from Equations (6) and (12) becomes:

$$\mathrm{max }(P_{i,min}, P_i^{t-1}- {DR}_i \times \mathsf{\Delta }t)\le \mathrm{m}\mathrm{i}\mathrm{n}\mathrm{ }(P_{i,max}, P_i^t \le P_i^{t-1}+{UR}_i \times \mathsf{\Delta }t)$$

(13)

The overall objective over the scheduling horizon is the sum of the period-wise objective functions:

$$F^{\prime }(P)={\displaystyle \sum _{t=1}^T} F(P^t)$$

(14)

3. Methodology

3.1. Proposed Approach

A two-stage learning–optimization framework is proposed to solve the dynamic economic–environmental load dispatch problem. The approach captures temporal demand variations and performs sequential daily generation scheduling.

In the first stage, hourly electricity consumption data are enriched with temporal features to support forecasting. A feature importance analysis identifies the most influential temporal factors, which are then used to develop a machine learning–based demand prediction model. The resulting forecasting model generates hourly demand estimates, representing the expected load profile over the scheduling horizon.

In the second stage, the predicted hourly demand values produced by the forecasting model are aggregated within four consecutive 6 h periods and used as the load requirements for the optimization process. These aggregated demands are sequentially supplied to a metaheuristic optimizer to determine the generation dispatch schedule for each period. The problem is solved iteratively across periods, where the optimal dispatch solution obtained for one period is used to initialize the subsequent period, thereby preserving temporal continuity and enabling dynamic scheduling behavior.

Operational realism is maintained by incorporating ramp-rate constraints and priority-based dispatch. Ramp limits restrict inter-period output variations, while priority rules enforce hierarchical generator activation. These constraints guide the optimization toward feasible and practically implementable dispatch schedules.

Infeasible operating conditions are handled through a penalty-based constraint management strategy integrated within the objective function. As illustrated in Algorithm 1, candidate solutions are first adjusted according to ramp-aware feasible operating bounds, after which the generator-priority hierarchy is enforced sequentially. Remaining violations related to power balance, ramp-rate limits, or priority constraints are penalized through large penalty terms added to the combined objective function, reducing the likelihood of selecting infeasible dispatch solutions during the optimization process.

Algorithm 1. Joint enforcement of ramp-rate and priority constraints during candidate solution evaluation.
Input	Candidate power outputs, current period, previous period solution
1.	Step 1: Compute ramp-aware feasible range for each unit
2.	For each generating unit i:
3.	Compute lower ramp bound: $\max (P_{i,min}, P_i^{t-1}-{DR}_i x \mathsf{\Delta }t)$
4.	Compute upper ramp bound: $\min (P_{i,max}, P_i^{t-1}+{UR}_i x \mathsf{\Delta }t)$
5.	End For
6.	Step 2: Clip candidate outputs to ramp-aware bounds
7.	For each generating unit i:
8.	If candidate > upper bound: set candidate to upper bound
9.	If candidate < lower bound: set candidate to lower bound
10.	End For
11.	Step 3: Enforce priority hierarchy
12.	For each priority level k:
13.	Check whether all generators with higher priority have reached their admissible maximum outputs (upper bound computed in Step 1)
14.	If not satisfied:
15.	Force generators of lower priority level k toward their admissible minimum outputs (lower bound computed in Step 1)
16.	End For
17.	Compute power balance mismatch penalty
18.	Compute ramp-rate violation penalty
19.	Compute generator-priority violation penalty
20.	Add all penalties to the combined objective function
Output Feasible dispatch

Rather than restricting the optimization process to a single dispatch outcome, the proposed framework is designed to generate multiple feasible operating strategies that satisfy the considered system constraints. This enables the exploration of alternative trade-offs between economic cost, environmental impact, and operational behavior. The resulting solution diversity enhances the practical applicability of the framework by allowing system operators to select dispatch strategies according to different operational preferences and decision profiles.

3.2. Machine Learning for Load Pattern Analysis

Understanding the underlying patterns in electricity consumption is essential for effective forecasting. Load pattern analysis using machine learning facilitates the identification of key demand drivers and enables more informed and accurate predictions.

3.2.1. Data

This study uses the PJM Interconnection PJME dataset, which contains hourly electricity consumption data for the eastern region of the PJM system. The dataset includes timestamps and corresponding load values (MW) spanning 2002–2018.

3.2.2. Electricity Consumption Pattern Analysis

Historical load data are analyzed by extracting temporal features from the timestamps, including the hour of day, the day of the week, the month, and the season. These features capture recurring demand structures and improve forecasting performance.

Feature importance is evaluated using the eXtreme Gradient Boosting (XGBoost) algorithm (version 3.2.0), developed by Chen and Guestrin [29]. XGBoost is a scalable gradient-boosting method that constructs decision trees sequentially, with each tree reducing the residual errors of the previous ones. Feature importance scores are computed based on each variable’s contribution to error reduction across the ensemble, identifying the most influential drivers of electricity demand.

3.2.3. Power Demand Prediction

Accurate demand forecasting is essential for generation scheduling and cost optimization. After identifying the most influential temporal features, electricity demand for each defined period is predicted using the Light Gradient Boosting Machine (LightGBM) algorithm.

LightGBM is a gradient-boosting framework optimized for large-scale data. It employs histogram-based splitting and leaf-wise tree growth to enhance computational efficiency and predictive performance. In this study, a LightGBM regressor is used to model nonlinear relationships in temporal load data [30]. The formula is:

$$\mathcal{L}(\mathsf{\varphi })={\displaystyle \sum _{i=1}^n} l(y_i,{\hat{y}}_i^{(t)})+{\displaystyle \sum _{k=1}^t} \mathsf{\Omega }(f_k)$$

(15)

where $l(y_i,{\hat{y}}_i^{(t)})$ is the loss function; and $\mathsf{\Omega }(f_k)$ is the regularization term of tree $f_k$.

Model performance is evaluated using Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE), and the dataset is divided into 75% for training and 25% for testing.

3.3. Optimization Using Hippopotamus Algorithm

The Hippopotamus Optimization Algorithm (HOA), proposed by Amiri et al. [31], is a population-based metaheuristic inspired by the collective and defensive behaviors of hippopotamuses. Candidate solutions are represented as position vectors in a D-dimensional search space and iteratively updated to balance exploration and exploitation.

The initial population is generated within the decision variable bounds as:

$$x_{i,j}={ll}_j+r\cdot ({ul}_j- {ll}_j)$$

(16)

where ll_j and ul_j denote the lower and upper bounds of variable j, and r ∈ [0, 1].

Position updating is performed according to:

$$x_{i,j} = x_{i,j}+\mathrm{y}\cdot (D_{hippo}- {I\cdot x}_{i,j})$$

(17)

where $D_{hippo}$ represents the dominant hippopotamus (best solution); y ∈ = [0, 1] is a random number; and I ∈ {0, 1}. This updating mechanism guides individuals toward promising regions while maintaining search diversity.

Since HOA is largely parameter-free, the present implementation follows the original formulation reported in [31]. The only user-defined settings are the population size and maximum number of iterations, which were selected to ensure stable convergence.

3.4. Dynamic Optimization Framework

Electricity demand varies significantly throughout the day, and incorporating this temporal variability is essential for realistic and efficient load dispatch. To ensure the framework aligns with real consumption behavior, the scheduling horizon is segmented based on temporal patterns in electricity usage. As will be demonstrated in the Results Section, the hour of the day is identified as the most influential factor affecting consumption; thus, the day is divided into four consecutive six-hour periods:

• Period 1—Night: 00:00–06:00;
• Period 2—Morning: 06:00–12:00;
• Period 3—Afternoon: 12:00–18:00;
• Period 4—Evening: 18:00–24:00.

Each period is treated as a dedicated optimization window while remaining sequentially dependent through generator ramp-rate constraints. This segmentation enables the optimization model to adapt to realistic temporal demand patterns while maintaining operational feasibility across successive periods.

The framework workflow is (in Figure 1):

While the above workflow outlines the overall framework structure, the optimization step involves a more detailed constraint-handling mechanism. Specifically, when ramp-rate bounds and priority rules are active simultaneously, their interaction must be carefully resolved at the level of each candidate solution evaluation. The Algorithm 1 details this joint constraint enforcement procedure.

To enhance the practical relevance of the proposed framework, a multi-solution evaluation layer is incorporated at the final stage of the workflow. Instead of relying on a single optimal solution, the HOA is executed multiple times to generate a diverse set of feasible dispatch solutions. Each solution is then evaluated using a set of performance indicators that capture economic, environmental, and operational characteristics, namely: daily cost, daily emissions, daily power loss, total ramp effort, maximum single-unit ramp, and maximum ramp utilization ratio. Based on these indicators, three decision-oriented profiles are defined to reflect different operational priorities:

• Economic: This profile prioritizes cost minimization while still accounting for environmental impact and operational constraints;
• Environmental: This profile prioritizes emission reduction while still accounting for economic cost and operational constraints;
• Operational: This profile emphasizes system flexibility and stability by prioritizing ramp-related metrics, ensuring smoother transitions between generation levels and improved operational feasibility.

Each profile is implemented through a weighted aggregation of the evaluation metrics. The weights, summarized in

Table 1. Weights assigned to features under different profiles.

Feature	Economic	Environmental	Operational
Daily cost	0.50	0.15	0.10
Daily emissions	0.15	0.50	0.10
Daily power loss	0.10	0.15	0.10
Total ramp effort	0.10	0.05	0.25
Maximum single-unit ramp	0.10	0.05	0.25
Maximum ramp utilization ratio	0.05	0.10	0.10

, were selected to represent three common decision-making perspectives. In each profile, the primary objective receives the largest weight (0.50), reflecting its dominant importance in the ranking process. The remaining weights are distributed among the other indicators according to their perceived relative importance to the corresponding decision perspective, ensuring that secondary economic, environmental, and operational considerations remain represented in the evaluation. Different weight assignments may lead to different ranking outcomes; therefore, the selected values should be interpreted as representative decision preferences rather than a universal weighting scheme.

3.5. Multi-Criteria Decision-Making

Each candidate schedule is evaluated using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique. The decision matrix $X\in {\mathbb{R}}^{20\times 6}$ contains the six daily features for all 20 runs. Normalization is performed using the Euclidean norm for each criterion:

$$r_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\sum }_k x_{kj}^2}}}$$

(18)

The weighted normalized matrix is then computed as $v_{ij}= w_i r_{ij}$, where $w_i$ represents the weight associated with each criterion, defined according to the selected decision profile. Since all criteria are minimization objectives, the positive ideal solution is defined as $A^{+}=\left\{\underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}} v_{ij}\right\}$ and the negative ideal solution as $A^{-}=\left\{\underset{i}{\mathrm{m}\mathrm{i}\mathrm{n}} v_{ij}\right\}$. The separation distances from the ideal and negative-ideal solutions are calculated using Euclidean distances $S_i^{+}$ and $S_i^{-}$. Finally, the closeness coefficient is computed as:

$$C_i={\displaystyle \frac{S_i^{-}}{S_i^{+}+S_i^{-}}}$$

(19)

4. Results and Discussion

This section presents the results and analysis of the proposed two-stage framework. First, the performance of the machine learning models in identifying key consumption patterns and predicting demand is evaluated. Next, the optimization framework is assessed under dynamic operational constraints, including ramp-rate limits and priority-based dispatch. The analysis considers multiple feasible solutions generated across independent runs. These solutions are evaluated using economic, environmental, and operational indicators and further analyzed through a profile-based ranking approach to highlight trade-offs and support decision-making.

4.1. Influential Features and Model Performance

Results for the machine learning phase are presented in this sub-section, focusing on the identification of key temporal drivers of electricity consumption and the evaluation of forecasting model performance.

4.1.1. Feature Importance Analysis

Understanding which temporal factors most influence electricity consumption is essential for building accurate and interpretable forecasting models. To identify these factors, an XGBoost regressor was applied to the enriched dataset containing temporal features. The Figure 2 shows the feature importance ranking:

As shown in the figure, the hour of the day emerged as the most influential feature, outperforming other features in terms of its impact on consumption variability. This finding aligns with practical expectations, as electricity usage typically fluctuates in predictable patterns across daily routines (e.g., morning peaks, mid-day lows, and evening surges). Season and month also showed substantial contributions, indicating broader shifts in electricity usage across different times of the year, as demand patterns in summer often differ notably from those in spring, for instance, driven by changes in temperature, daylight duration, and typical activity levels. In contrast, the day of the month feature showed limited influence.

4.1.2. Consumption Forecasting

Accurate forecasting of electricity consumption is critical for efficient power-system planning and cost-effective generation scheduling. After selecting the most relevant temporal features based on the feature importance analysis, a supervised learning model is trained to predict electricity demand. The model is designed to learn the relationship between selected temporal features and electricity usage, enabling accurate demand predictions that support the optimization process.

The results in

Table 2. Forecasting model performance.

Algorithm	RMSE (%)		MAPE (%)
	Train	Test	Train	Test
LightGBM	8.89	11	6.42	9.4

indicate that the model performs very well in capturing electricity demand patterns. Training errors remain well below 10%, demonstrating the model’s strong ability to learn underlying relationships in the data. Test errors also remain in the range of 9.4% (MAPE) and 11% (RMSE), showing that the model generalizes effectively to unseen observations.

To further assess the model’s reliability, Figure 3 presents a comparison between actual and predicted electricity demand on the selected test set.

As shown in the figure, the predicted values closely follow the trend of the actual consumption data, demonstrating the model’s ability to generalize well across unseen data. Minor deviations are observed during peak load hours, which may be attributed to sudden usage spikes not fully captured by temporal features alone.

4.2. Optimization Algorithm Validation

To ensure correct implementation of the HOA for the current problem, the algorithm was tested on standard static IEEE 6-unit and 10-unit benchmark systems. The obtained results were compared with published values to verify consistency before applying HOA within the proposed dynamic framework.

For the 6-unit system only, the emission equation is different from Equation (3), which is expressed as:

$$E(P^t)={\displaystyle \sum _{i=1}^n} (0.01\cdot ({\alpha }_i+{\beta }_i{P}_i^t+{\gamma }_i{(P_i^t)}^2)+{\eta }_i{e}^{{\delta }_i{P}_i^t})$$

(20)

4.2.1. IEEE 6-Unit Test System

The 6-unit case is based on the IEEE 30-bus system, where six thermal generators supply a total demand of 2.834 p.u. on a 100 MVA base. Generator limits and coefficients are shown in

Table 3. Generator parameters for 6-unit system.

System	Pi,min	Pi,max	ai	bi	ci	di	ei	αi	βi	γi	ηi	δi	Ramp-Up	Ramp-Down	Priority
6 units	0.05	0.5	10	200	100	0	0	4.091	−5.554	6.49	0.0002	2.857	0.125	0.225	2
	0.05	0.6	10	150	120	0	0	2.543	−6.047	5.638	0.0005	3.333	0.15	0.27	2
	0.05	1	20	180	40	0	0	4.258	−5.094	4.586	0.000001	8	0.25	0.45	1
	0.05	1.2	10	100	60	0	0	5.326	−3.55	3.38	0.002	2	0.3	0.54	1
	0.05	1	20	180	40	0	0	4.258	−5.094	4.586	0.000001	8	0.25	0.45	3
	0.05	0.6	10	150	100	0	0	6.131	−5.555	5.151	0.00001	6.667	0.15	0.27	3

and loss data are taken from [17]. The obtained results are presented in

Table 4. Single-objective optimal solutions for 6-generator system: (i) fuel cost minimization and (ii) emission minimization.

Units	Cost ($/h)				Emissions (ton/h)
	NGPSO [17]	MOEA/D [25]	NSGAII-D CD-CE [18]	HOA	NGPSO [17]	MOEA/D [25]	NSGAII DCD-CE [18]	HOA
1	0.120969	0.1792	0.114481	0.1209117788	0.410925	0.4056	0.410092	0.4109207656
2	0.286312	0.3712	0.305732	0.2862958914	0.463667	0.4594	0.461018	0.4636699208
3	0.583557	0.6939	0.598400	0.5836401425	0.544419	0.5502	0.552875	0.5443709407
4	0.992854	0.5905	0.980202	0.9930130259	0.390374	0.3852	0.389406	0.3903787809
5	0.523970	0.5889	0.515260	0.5238886761	0.544459	0.5453	0.544660	0.5444589809
6	0.351899	0.4354	0.354635	0.3518123192	0.515485	0.5181	0.508842	0.5155316619
PL	0.026	0.023	0.026	0.026	0.035	0.035	0.035	0.035
FC/E	605.99837	619.53	608.1247	605.99837	0.194179	0.1942	0.1942	0.194179

and

Table 5. Compromise cost–emission optimal solution for 6-generator system.

Units	NGPSO [17]	MOEA/D [25]	FSBF [26]	HOA
1	0.3062424	0.3185	0.320518	0.3268836603
2	0.40415941	0.4101	0.409661	0.4163454821
3	0.55773992	0.5623	0.553204	0.5547911791
4	0.58355217	0.5635	0.565322	0.5442954821
5	0.54952711	0.545	0.540641	0.5488706445
6	0.46099483	0.4631	0.473462	0.4721412524
FC	623.8705	625.69	625.9332	627.654219
E	0.1969727	0.1964	0.1964	0.195953
Combined	1489.3882	1488.8372	1488.8071	1488.691195

and are compared with results reported in the literature.

For the 6-generator case, HOA produced a minimum generation cost of 605.99837 $/h, matching the best value reported in the literature. The emission-only optimization obtained was identical to the best reported in the literature. For the combined economic–emission case, the obtained objective value was 1488.6912 $/h, outperforming the best reported value of 1488.8071 $/h.

4.2.2. IEEE 10-Unit Test System

The 10-unit system supplies a total demand of 2000 MW. Operational parameters and transmission loss data are taken from [17]. This case is also treated as a single-period (static) benchmark to further confirm implementation correctness. The results are compared with published benchmark values for verification, shown in

Table 6. Single-objective optimal solutions for 10-generator system: (i) fuel cost minimization and (ii) emission minimization.

Units	Cost ($/h)				Emissions (ton/h)
	NGPSO [17]	OWP-OMF [23]	QOTLBO [27]	HOA	NGPSO [17]	OWP-OMF [23]	QOTLBO [27]	HOA
1	55	55	55	55	55	55	55	55
2	80	80	79.9991	80	80	80	80	80
3	106.93994	106.8771	105.9616	106.94031	81.13417	80.9248	81.1261	81.12536
4	100.57627	100.7023	99.9321	100.57766	81.36374	81.1019	81.3640	81.41154
5	81.50172	81.5370	80.6424	81.49396	160	160	160	160
6	83.02089	82.9221	85.7878	83.02686	240	240	240	240
7	300	300	300	300	294.48506	294.5495	294.4790	294.71688
8	340	340	340	340	297.27010	297.6624	297.2439	297.47656
9	470	470	469.6979	470	396.76575	396.3406	396.8041	396.60583
10	470	470	469.9943	470	395.57633	396.0266	395.5788	395.25068
PL	87.038825	87.0386	87.01606	87.03880	81.59515	81.6057	81.59579	81.58685
FC/E	111,497.6308	111,497.6407	111,498	111,497.6308	3932.24327	3932.2538	3932.2	3932.24508

and

Table 7. Compromise fuel cost–emission optimal solution for 10-generator system.

Units	NGPSO [17]	QTTLBO [27]	GSA [32]	PDE [33]	HOA
1	55	55	54.9992	54.9853	55
2	80	80	79.9586	79.3803	80
3	81.23982334	83.9202	79.4341	83.9842	81.572584
4	80.83342958	82.8342	85	86.5942	80.968975
5	160	132.0131	142.1063	144.4386	160
6	235.00879098	173.9880	166.5670	165.7756	225.177663
7	289.35074508	299.7099	292.8749	283.2122	291.246131
8	297.45422963	317.9684	313.2387	312.7709	299.405383
9	401.50728395	427.0166	441.1775	440.1135	404.541342
10	401.42752424	431.3955	428.6306	432.6783	404.108616
FC	116,179.6487	113,460	113,492.04	113,506.49	115,841.39476
E	3939.2278	4110.2	4111.4	4111.4	3951.51920
Combined	216,170.54	217,791.14	217,853.68	217,867.20	216,144.01759

.

For this second case, HOA achieved a generation cost of 111,497.6308 $/h, matching the best-known result. The emission minimization yielded 3932.24508 ton/h, comparable to published values. Additionally, in the combined optimization, the obtained objective value was 216,144.01759 $/h, which is considered better than the best reported result (216,170.54 $/h).

The implemented HOA showed excellent performance in addressing the economic–emission dispatch problem. For the single-objective minimization cases, the obtained results were either equal or very close to the best reported values in the literature, while for the combined objective case, the proposed approach outperformed the compared methods.

4.3. Framework Simulation and Analysis

4.3.1. Simulation Process

To evaluate the DEELD framework, the system is simulated over one representative day. The hourly electricity demand is first predicted using the trained machine learning model. The 24 h horizon is divided into four six-hour periods, with hourly demand temporally aggregated into period-level load profiles for dispatch.

The predicted demand values are initially expressed in MW. To ensure compatibility with the IEEE 30-bus six-generator system, the demand is converted to per-unit (p.u.) using a 100 MVA base. A scaling factor of 1000 is then applied to place the demand within the feasible operating range of the benchmark system while maintaining the relative variation between periods. This normalization is applied only for simulation consistency and does not affect the dispatch structure (

Table 8. Periods and aggregated demands.

Period	Time Interval	Predicted PD (MW)	Predicted PD (p.u.)	Scaled PD (p.u.)
Night	00:00–06:00	185,860.46590	1858.6046590	1.8586046590
Morning	06:00–12:00	226,458.64963	2264.5864963	2.2645864963
Afternoon	12:00–18:00	223,880.68636	2238.8068636	2.2388068636
Evening	18:00–24:00	233,033.66177	2330.3366177	2.3303366177

).

Simulations are performed on the IEEE 30-bus system with six thermal generators. Their technical and economic characteristics, including generation limits, cost and emission coefficients, ramp rates, and priority levels, are given in the Table 3.

For each period, the algorithm is used to minimize generation costs and emissions while satisfying all operational constraints. The final population of one period is used as the initial population for the next period to ensure continuity in generator outputs.

Ramp-rate limits are defined on an hourly basis. Since each period represents six hours, the ramping interval is set to $\mathsf{\Delta }t=6$ when enforcing ramp constraints between periods.

The optimization process is executed over 20 runs to generate a set of feasible dispatch solutions for the entire scheduling horizon. Each solution is evaluated using economic, environmental, and operational performance indicators, including total cost, emissions, power loss, and ramping metrics. The solutions are then ranked using predefined decision profiles based on weighted performance criteria.

4.3.2. Optimization Solutions and Ranking

This section presents the generated dispatch solutions and their evaluation under different decision profiles. The optimization process is executed over 20 runs, producing a diverse set of feasible solutions. To illustrate the variability in solutions, the results of a single run are first presented for both scenarios, after which all solutions are ranked and analyzed.

The optimization is performed on the 6-unit system described in Table 4 under two operating scenarios. In the first scenario (without priority), all generators operate within their standard minimum and maximum limits, corresponding to conventional economic–environmental dispatch. In the second scenario, generators are dispatched according to predefined priority levels, where higher-priority units are fully utilized before lower-priority units are activated. To preserve flexibility within each priority group, the minimum generation limits are set to zero.

One run is selected without prior filtering from the set of runs to demonstrate the structure of the obtained solutions.

Table 9. Single representative run—without priority.

Feature	Night	Morning	Afternoon	Evening	Daily (Sum/Avg/Max)
Objective features
Fuel cost ($/h)	417.21240	501.93481	496.43070	516.01399	1931.59190
Emissions (ton/h)	0.20495	0.19912	0.19940	0.19845	0.80192
Combined ($/h)	1317.79550	1376.86963	1372.61301	1388.03789	5455.31603
Ramp features
Max single-unit ramp (p.u)	/	0.08536 G3	0.00553 G4	0.019262 G3	0.08536
Total ramp effort (p.u)	/	0.41170	0.02619	0.09296	0.53085
Max ramp utilization ratio	/	0.06636 G1	0.00264 G1	0.01501 G6	0.06636
Transmission features
Power loss (p.u)	0.01369	0.01940	0.01899	0.02042	0.07249
Loss fraction (%)	0.73%	0.85%	0.84%	0.87%	0.82%

and

Table 10. Single representative run—with priority.

Feature	Night	Morning	Afternoon	Evening	Daily (Sum/Avg/Max)
Objective features
Fuel cost ($/h)	429.62212	521.68974	515.93122	532.71198	1999.95506
Emissions (ton/h)	0.27069	0.28812	0.28946	0.28489	1.13316
Combined ($/h)	1619.06662	1787.71284	1787.82447	1784.54579	6979.14972
Ramp features
Max single-unit ramp (p.u)	/	0.24693 G4	0.03911 G1	0.05987 G2	0.24693
Total ramp effort (p.u)	/	0.41162	0.05272	0.09186	0.55619
Max ramp utilization ratio	/	0.13718 G4	0.02897 G1	0.06652 G2	0.13718
Transmission features
Power loss (p.u)	0.01589	0.02151	0.02179	0.02212	0.08130
Loss fraction (%)	0.85%	0.94%	0.96%	0.94%	0.92%

present the results for both scenarios.

When priority constraint is not considered, the dispatch results exhibit relatively balanced performance across economic, environmental, and operational indicators. The total daily generation cost reaches 1931.59 $/h, with emissions of 0.8019 ton/h, reflecting an efficient trade-off between cost and environmental impact. Across periods, cost follows the expected demand pattern, increasing from 417.21 $/h during the night to 516.01 $/h in the evening. The combined objective further confirms this balanced performance, with a total value of 5455.32 $/h, following a consistent trend across periods. This indicates that the optimizer is able to simultaneously manage cost and emissions efficiently without favoring one objective excessively.

Transmission performance remains stable, with a total power loss of 0.07249 p.u. and an average loss fraction of 0.8225%, indicating moderate network loading. The variation across periods is limited, suggesting that the optimizer distributes generation in a way that avoids excessive congestion.

From an operational perspective, ramping requirements are relatively low. The total ramp effort is 0.5308 p.u, and the maximum single-unit ramp reaches 0.0854 p.u, occurring between the afternoon and evening periods. Similarly, the maximum ramp utilization ratio remains modest at 0.0664, indicating that generator transitions stay well within allowable limits. This reflects a flexible dispatch strategy where generation adjustments are smoothly distributed among units.

When priority constraint is enforced, a noticeable shift in system behavior occurs. The total generation cost increases to 1999.96 $/h, accompanied by a significant rise in emissions to 1.1332 ton/h, indicating a degradation in both economic and environmental performance. This increase is consistent across all periods, with the evening cost reaching 532.71 $/h, higher than its counterpart in the first case. This degradation is also reflected in the combined objective, indicating a clear loss in overall optimization performance when both cost and emissions are considered simultaneously.

Transmission losses also increase, with the total power loss rising to 0.08130 p.u. and the average loss fraction reaching 0.92%. For example, during the afternoon period, the loss fraction climbs to 0.96%, suggesting that the imposed dispatch structure leads to less efficient power flow distribution.

Operationally, the system experiences higher stress. The maximum single-unit ramp increases significantly to 0.2469 p.u., nearly three times higher than in the first scenario. This indicates that certain units are required to compensate more aggressively for demand changes. The maximum ramp utilization ratio also rises to 0.1372, confirming that generators operate closer to their ramping limits. Although the total ramp effort remains comparable, the concentration of ramping on fewer units leads to less balanced operation.

In addition to the solution discussed previously, statistical results over the 20 runs are presented to illustrate the diversity of feasible dispatch alternatives available to decision-makers. Since the proposed approach is designed not only to identify a single optimal solution but also to generate multiple competitive operating strategies, analyzing the distribution of results across several runs becomes essential.

Table 11. Statistical results over the 20 runs—without priority.

Period	Objective	Best	Average	Worst	Std Deviation
Night	Fuel Cost	417.16763	417.19242	417.21240	0.0142258
	Emissions	0.2049528	0.2049574	0.2049630	0.0000032
	Combined	1317.79547	1317.79551	1317.79560	0.0000362
	Power Loss	0.0136715	0.0136845	0.0136897	0.0000042
Morning	Fuel Cost	501.87451	501.92940	501.96772	0.0251125
	Emissions	0.1991083	0.1991170	0.1991296	0.0000057
	Combined	1376.86932	1376.86942	1376.86965	0.0001062
	Power Loss	0.0193627	0.0193853	0.0194055	0.0000103
Afternoon	Fuel Cost	496.41847	496.43660	496.44892	0.0066137
	Emissions	0.1993956	0.1993984	0.1994025	0.0000015
	Combined	1372.61298	1372.61300	1372.61308	0.0000229
	Power Loss	0.0189837	0.0189893	0.0189933	0.0000021
Evening	Fuel Cost	516.00566	516.03579	516.06908	0.0139907
	Emissions	0.1984408	0.1984484	0.1984553	0.0000032
	Combined	1388.03782	1388.03790	1388.03802	0.0000486
	Power Loss	0.0204117	0.0204188	0.0204303	0.0000052

and

Table 12. Statistical results over the 20 runs—with priority.

Period	Objective	Best	Average	Worst	Std Deviation
Night	Fuel Cost	429.60339	429.63399	429.67373	0.0192367
	Emissions	0.2706797	0.2706886	0.2706957	0.0000044
	Combined	1619.06653	1619.06671	1619.06723	0.0002004
	Power Loss	0.0158770	0.0158804	0.0158849	0.0000021
Morning	Fuel Cost	521.68973	521.68973	521.68973	3.5 × 10−9
	Emissions	0.2881189	0.2881189	0.2881189	1.2 × 10−12
	Combined	1787.71284	1787.71284	1787.71284	1.6 × 10−9
	Power Loss	0.0215142	0.0215142	0.0215142	0.1 × 10−12
Afternoon	Fuel Cost	515.93039	516.20239	517.01516	0.4691436
	Emissions	0.2894546	0.2894597	0.2894746	0.0000086
	Combined	1787.82391	1788.11731	1788.99543	0.5068355
	Power Loss	0.0214642	0.0217093	0.0217916	0.0001415
Evening	Fuel Cost	532.67318	533.47945	533.98663	0.6184252
	Emissions	0.2848417	0.2848605	0.2848991	0.0000224
	Combined	1784.54579	1785.18482	1785.61342	0.5211431
	Power Loss	0.0218130	0.0219323	0.0221468	0.0001461

summarize the best, average, worst, and standard deviation values of fuel cost, emissions, and combined objectives for each period.

The statistical results obtained confirm the stability and consistency, per objective, of the proposed framework for both scenarios.

In the first case, the low standard deviation values across all periods indicate that the optimizer consistently converges toward competitive solutions while still maintaining slight variability between runs, allowing the generation of multiple feasible dispatch alternatives for different decision profiles. When priority constraint is enforced, a similar stability behavior is observed, with even lower variability during certain periods. In particular, the morning period exhibits nearly identical values across most runs, showing that the hierarchical generator-priority mechanism significantly reduces the feasible search space. This demonstrates that enforcing generator priorities limits operational flexibility and constrains the optimizer toward a smaller set of dispatch solutions. This effect is more pronounced in the considered 6-unit system, where the priority mechanism may restrict dispatch to only a limited number of active generators during certain periods. In larger-scale systems, a greater number of simultaneously active units would provide a richer feasible search space and potentially improve solution diversity.

To further analyze the variability in the generated solutions, a ranking heatmap is constructed based on the three decision-maker profiles using TOPSIS. Each run is assigned a rank under the economic, environmental, and operational profiles, where a rank of 1 indicates the most preferred solution. The resulting heatmap provides a visual representation of how solution preference varies across different decision criteria. Figure 4 presents the ranking heatmap for all 20 runs under both scenarios.

In the absence of priority constraints, the ranking distribution shows moderate variability across the three profiles, indicating the presence of multiple competitive solutions. For the economic profile, run 3 achieves the top rank, followed by runs 1 and 12, reflecting small but meaningful differences in cost-driven performance. In contrast, the environmental profile identifies run 1 as the best solution, with a score of 0.826, while runs 15 and 14 also rank highly due to slightly improved emission characteristics.

From an operational perspective, run 3 again emerges as the top-ranked solution, followed by runs 2 and 1, suggesting that certain solutions simultaneously achieve favorable ramping behavior and competitive cost. This overlap between economic and operational rankings indicates that, in the absence of restrictive constraints, the optimizer is able to identify solutions that balance multiple objectives effectively.

However, the heatmap also reveals that some runs exhibit strong trade-offs. For example, run 4, despite having relatively stable operational characteristics, ranks 19th in the economic profile and 20th in the operational profile, indicating poor overall performance. Similarly, run 11 ranks 20th economically, despite having comparable cost values, highlighting the sensitivity of the ranking process to combined feature effects.

Overall, the ranking pattern suggests that the no-priority system maintains a relatively smooth solution space, where several runs remain competitive across multiple profiles, enabling flexible decision-making.

When priority constraint is introduced, the ranking distribution becomes more polarized, with a clearer separation between high-performing and low-performing solutions. Notably, run 11 achieves the top rank across all three profiles, indicating a dominant solution under the constrained search space. Similarly, runs 5, 4, and 20 consistently rank within the top five across all profiles, forming a cluster of high-quality solutions.

This concentration of top-performing runs suggests that the priority constraint significantly reduces the diversity of competitive solutions. Unlike the without-priority case, where rankings are more dispersed, the constrained system favors a limited subset of solutions that comply effectively with the hierarchical dispatch structure.

At the lower end of the ranking spectrum, runs such as 13, 8, and 7 consistently rank poorly across all profiles. For instance, run 13 is ranked 20th in both the environmental and operational profiles, indicating that certain dispatch configurations are heavily penalized under the imposed constraints.

Figure 5 presents the parallel coordinates of the normalized feature values for each run, complementing the ranking results by showing how every solution performs across all metrics simultaneously. Rather than focusing only on which run is ranked best under a given profile, the figure allows the decision-maker to visually assess the trade-offs between criteria. A solution that appears optimal for one objective (e.g., achieving the best normalized value in cost) may perform poorly in another (such as emissions or ramping), making it less attractive overall. This representation, therefore, supports a more informed selection process, where the decision-maker can identify the solution that best aligns with their preferences by balancing performance across economic, environmental, and operational criteria, rather than relying solely on individual rankings. It should also be noted that, in some cases, multiple decision profiles select the same run as the best-performing solution, causing the corresponding colored lines to overlap in the figure.

As a general outcome of the obtained results, the following observations can be drawn regarding the individual contribution of each component to the overall system behavior and optimization performance:

• The forecasting stage improves adaptation to temporal demand variations;
• Sequential optimization enhances inter-period continuity;
• The incorporation of generator-priority and ramp-rate constraints improves the operational realism of the proposed framework and better reflects practical power-system operation.

5. Conclusions

This paper presented an integrated framework combining machine learning and optimization to address the economic–environmental dispatch problem under realistic operating conditions. The proposed approach leverages ML models to capture demand patterns and support more informed optimization, improving the adaptability of the dispatch process. In addition, the formulation explicitly accounts for system dynamicity by incorporating inter-period ramp constraints, ensuring smooth and feasible transitions between periods rather than treating each period independently.

A priority-based dispatch mechanism was also introduced to reflect practical operational preferences. While this approach successfully guides the optimization toward structured and consistent solutions, the results have shown that it can limit flexibility by restricting the participation of certain units. This effect becomes more pronounced in smaller systems, where fewer generators reduce the available degrees of freedom. Future work will, therefore, focus on extending the framework to larger-scale systems, where the increased diversity of units is expected to mitigate these limitations and enhance solution flexibility. Future work may also investigate the influence of different computational settings, such as population size and iteration budget, particularly when applied to larger-scale power systems.

From a practical perspective, a key limitation of the proposed framework lies in the dependence on coordinated data linking forecasting and optimization stages, which may not always be readily available in real-world systems. In addition, the sequential multi-period optimization introduces additional computational overhead due to repeated solution of the optimization problem across time intervals, and the overall performance remains influenced by forecasting accuracy, as prediction errors may propagate into the dispatch decisions.

Finally, the study highlights that, in practical decision-making contexts, identifying a single ‘best’ solution is often insufficient. Different stakeholders may prioritize objectives differently. To address this, multiple solutions were generated, evaluated, and ranked using a multi-criteria decision-making technique, followed by detailed analysis and visualization. This enables decision-makers to select solutions that best align with their specific preferences, providing a more realistic and applicable decision-support framework.

The superiority of the proposed framework arises from its integrated structure, where forecasting, sequential optimization, and operational constraints are tightly coupled within a unified decision pipeline. Unlike conventional single-stage approaches, it explicitly captures temporal demand evolution and enforces inter-period consistency, while also ensuring operational feasibility through ramp-rate and priority constraints, leading to solutions that are both realistic and practically implementable.