Search Results (1,060)

The periodic vehicle routing problem (PVRP) is a well-known challenge in real-life logistics, requiring the planning of vehicle routes over multiple days while enforcing visitation frequency constraints. Although numerous metaheuristic and exact methods have tackled various PVRP extensions, real-world settings call for additional features such as depot configurations, tight visitation frequency constraints, and heterogeneous fleets. In this paper, we present a two-phase biased–randomized algorithm that addresses these complexities. In the first phase, a round-robin assignment quickly generates feasible and promising solutions, ensuring each customer’s frequency requirement is met across the multi-day horizon. The second phase refines these assignments via an iterative search procedure, improving route efficiency and reducing total operational costs. Extensive experimentation on standard PVRP benchmarks shows that our approach is able to generate solutions of comparable quality to established state-of-the-art algorithms in relatively low computational times and stands out in many instances, making it a practical choice for real life multi-day vehicle routing applications. Full article

The Set Coverage Problem (SCP) is an important combinatorial optimization problem known to be NP-complete. The use of metaheuristics to solve the SCP includes different algorithms. In particular, binarization techniques have been explored to adapt metaheuristics designed for continuous optimization problems to the binary domain of the SCP. In this work, we present a new approach to solve the SCP based on the Secretary Bird Optimization Algorithm (SBOA). This algorithm is inspired by the natural behavior of the secretary bird, known for its ability to hunt prey and evade predators in its environment. Since the SBOA was originally designed for optimization problems in continuous space and the SCP is a binary problem, this paper proposes the implementation of several binarization techniques to adapt the algorithm to the discrete domain. These techniques include eight transfer functions and five different discretization methods. Taken together, these combinations create multiple SBOA adaptations that effectively balance exploration and exploitation, promoting an adequate distribution in the search space. Experimental results applied to the SCP together with its variant Unicost SCP and compared to Grey Wolf Optimizer and Particle Swarm Optimization suggest that the binary version of SBOA is a robust algorithm capable of producing high quality solutions with low computational cost. Given the promising results obtained, it is proposed as future work to focus on complex and large-scale problems as well as to optimize their performance in terms of time and accuracy. Full article

Power system infrastructure is exposed to a range of threats, including both naturally occurring events and intentional attacks. Traditional vulnerability assessment models, typically based on the N-1 criterion, do not account for the intentionality of disruptive agents. This paper presents a game-theoretic approach to protecting power system infrastructure against deliberate attacks, taking into account the effects of demand response. The interaction between the disruptive agent and the system operator is modeled as a leader–follower Stackelberg game. The leader, positioned in the upper-level optimization problem, must decide which elements to render out of service, anticipating the reaction of the follower (the system operator), who occupies the lower-level problem. The Stackelberg game is reformulated as a bilevel optimization model and solved using a metaheuristic approach. To evaluate the applicability of the proposed method, a 24-bus test system was employed. The results demonstrate that integrating demand response significantly enhances system resilience, compelling the disruptive agent to adopt alternative attack strategies that lead to lower overall disruption. The proposed model serves as a valuable decision-support tool for system operators and planners seeking to improve the robustness and security of electrical networks against disruptive agents. Full article

A deterministic Mixed-Integer Nonlinear Programming (MINLP) model for the Integrated Generation and Transmission Expansion Planning (IGTEP) problem is presented. The proposed framework is distinguished by its foundation on the complete AC power flow formulation, which is solved to global optimality using BARON, a deterministic MINLP solver, which ensures the identification of truly optimal expansion strategies, overcoming the limitations of heuristic approaches that may converge to local optima. This approach is employed to establish a definitive, high-fidelity economic and technical benchmark, addressing the limitations of commonly used DC approximations and metaheuristic methods that often fail to capture the nonlinearities and interdependencies inherent in power system planning. The co-optimization model is formulated to simultaneously minimize the total annualized costs, which include investment in new generation and transmission assets, the operating costs of the entire generator fleet, and the cost of unsupplied energy. The model’s effectiveness is demonstrated on the IEEE 14-bus system under various dynamic load growth scenarios and planning horizons. A key finding is the model’s ability to identify the most economic expansion pathway; for shorter horizons, the optimal solution prioritizes strategic transmission reinforcements to unlock existing generation capacity, thereby deferring capital-intensive generation investments. However, over longer horizons with higher demand growth, the model correctly identifies the necessity for combined investments in both significant new generation capacity and further network expansion. These results underscore the value of an integrated, AC-based approach, demonstrating its capacity to reveal non-intuitive, economically superior expansion strategies that would be missed by decoupled or simplified models. The framework thus provides a crucial, high-fidelity benchmark for the validation of more scalable planning tools. Full article

This study aims to determine the model parameters of proton exchange membrane fuel cells (PEMFC) by employing the Sea Horse Optimization (SHO) algorithm, a novel metaheuristic approach inspired by natural behaviors. Although conventional algorithms in the literature have achieved considerable success in parametric modeling accuracy, many of them suffer from inherent drawbacks, such as premature convergence and entrapment in local minima. The SHO algorithm, with its adaptive and dynamic nature, is designed to overcome these limitations. To further evaluate its performance, a detailed parametric sensitivity analysis is conducted on SHO-specific control parameters. In this work, experimental polarization data from a Ballard Mark V PEMFC is used as a reference to estimate the equivalent circuit model parameters ${ϵ}_1$, ${ϵ}_2$, ${ϵ}_3$, ${ϵ}_4$, $\beta$, $\lambda$, $R_c$. The SHO algorithm achieved a mean absolute error (MAE) of 0.001079 and a coefficient of determination (R²) of 0.999791, with a model-to-experiment fit ratio of 99.92%. Compared to similar studies reported in the literature, the results indicate that the SHO algorithm offers competitive performance. Moreover, the average convergence time is recorded as 1.74 s for 5000 iteration, highlighting the algorithm’s rapid convergence and low computational cost. Overall, the SHO algorithm is demonstrated to be an efficient, robust, and promising alternative to conventional methods for parameter identification in PEMFC modeling. Full article

Renewable energy sources are being progressively incorporated into modern power grids to increase sustainability, stability, and resilience. To ensure that residential, commercial, and industrial customers have a dependable and efficient power supply, the transmission system must deliver electricity to end-users via the distribution network. To improve the performance of the distribution system, this study employs distributed generator (DG) units and focuses on determining their optimal placement, sizing, and power factor. A novel metaheuristic algorithm, referred to as Rüppell’s fox optimizer (RFO), is proposed to address this optimization problem under various scenarios. In the first scenario, where the DG operates at unity power factor, it is modeled as a photovoltaic system. In the second and third scenarios, the DG is modeled as a wind turbine system with fixed and optimal power factors, respectively. The performance of the proposed RFO algorithm is benchmarked against five well-known metaheuristic techniques to validate its effectiveness and competitiveness. Simulations are conducted on the IEEE 33-bus and IEEE 69-bus radial distribution test systems to demonstrate the applicability and robustness of the proposed approach. Full article

Metaheuristics are powerful optimization techniques that are well-suited for addressing complex combinatorial problems across diverse scientific and industrial domains. However, their application to computationally expensive problems remains challenging due to the high cost and significant number of fitness evaluations required during the search process. Surrogate modeling has recently emerged as an effective solution to reduce these computational demands by approximating the true, time-intensive fitness function. While surrogate-assisted metaheuristics have gained attention in recent years, their application to complex scheduling problems such as the Permutation Flowshop Scheduling Problem (PFSP) under learning, deterioration, and maintenance effects remains largely unexplored. To the best of our knowledge, this study is the first to investigate the integration of surrogate modeling within the artificial bee colony (ABC) framework specifically tailored to this problem context. We develop and evaluate two distinct strategies for integrating surrogate modeling into the optimization process, leveraging the ABC algorithm. The first strategy uses a Kriging model to dynamically guide the selection of the most effective search operator at each stage of the employed bee phase. The second strategy introduces three variants, each incorporating a Q-learning-based operator in the selection mechanism and a different evolution control mechanism, where the Kriging model is employed to approximate the fitness of generated offspring. Through extensive computational experiments and performance analysis, using Taillard’s well-known standard benchmarks, we assess solution quality, convergence, and the number of exact fitness evaluations, demonstrating that these approaches achieve competitive results. Full article

This paper presents a reinforcement learning (RL) approach for solving the team orienteering problem under both deterministic and dynamic travel time conditions. The proposed method builds on the transformer architecture and is trained to construct routes that adapt to real-time variations, such as traffic and environmental changes. A key contribution of this work is the model’s ability to generalize across problem instances with varying numbers of nodes and vehicles, eliminating the need for retraining when problem size changes. To assess performance, a comprehensive set of experiments involving 27,000 synthetic instances is conducted, comparing the RL model with a variable neighborhood search metaheuristic. The results indicate that the RL model achieves competitive solution quality while requiring significantly less computational time. Moreover, the RL approach consistently produces feasible solutions across all dynamic instances, demonstrating strong robustness in meeting time constraints. These findings suggest that learning-based methods can offer efficient, scalable, and adaptable solutions for routing problems in dynamic and uncertain environments. Full article

Precisely predicting photovoltaic (PV) output is crucial for reliable grid integration; so far, most models rely on site-specific sensor data or treat large meteorological datasets as black boxes. This study proposes an explainable machine-learning framework that simultaneously ranks the most informative weather parameters and reveals their physical relevance to PV generation. Starting from 27 local and plant-level variables recorded at 15 min resolution for a 1 MW array in Çanakkale region, Türkiye (1 August 2022–3 August 2024), we apply a three-stage feature-selection pipeline: (i) variance filtering, (ii) hierarchical correlation clustering with Ward linkage, and (iii) a meta-heuristic optimizer that maximizes a neural-network R² while penalizing poor or redundant inputs. The resulting subset, dominated by apparent temperature and diffuse, direct, global-tilted, and terrestrial irradiance, reduces dimensionality without significantly degrading accuracy. Feature importance is then quantified through two complementary aspects: (a) tree-based permutation scores extracted from a set of ensemble models and (b) information gain computed over random feature combinations. Both views converge on shortwave, direct, and global-tilted irradiance as the primary drivers of active power. Using only the selected features, the best model attains an average R² ≅ 0.91 on unseen data. By utilizing transparent feature-reduction techniques and explainable importance metrics, the proposed approach delivers compact, more generalized, and reliable PV forecasts that generalize to sites lacking embedded sensor networks, and it provides actionable insights for plant siting, sensor prioritization, and grid-operation strategies. Full article

Small- and medium-sized enterprises (SMEs) face dynamic and competitive environments where resilience and data-driven decision-making are critical. Despite the potential benefits of artificial intelligence (AI), machine learning (ML), and optimization techniques, SMEs often struggle to adopt these tools due to high costs, limited training, and restricted hardware access. This study reviews how SMEs can employ heuristics, metaheuristics, ML, and hybrid approaches to support strategic decisions under uncertainty and resource constraints. Using bibliometric mapping with UMAP and BERTopic, 82 key works are identified and clustered into 11 thematic areas. From this, the study develops a practical framework for implementing and evaluating optimization strategies tailored to SMEs’ limitations. The results highlight critical application areas, adoption barriers, and success factors, showing that heuristics and hybrid methods are especially effective for multi-objective optimization with lower computational demands. The study also outlines research gaps and proposes future directions to foster digital transformation in SMEs. Unlike prior reviews focused on specific industries or methods, this work offers a cross-sectoral perspective, emphasizing how these technologies can strengthen SME resilience and strategic planning. Full article

This paper proposes a novel integer-mixed probabilistic optimal power flow (IM-POPF) strategy for frequency regulation in islanded microgrids under uncertain operating conditions. Existing load-shedding approaches face critical limitations: continuous frameworks fail to reflect the discrete nature of actual load disconnections, while deterministic models inadequately capture the stochastic behavior of renewable generation and load variations. The proposed approach formulates load shedding as an integer optimization problem where variables are categorized as integer (load disconnection decisions at specific nodes) and continuous (voltages, power generation, and steady-state frequency), better reflecting practical power system operations. The key innovation combines integer load-shedding optimization with efficient uncertainty propagation through Unscented Transformation, eliminating the computational burden of Monte Carlo simulations while maintaining accuracy. Load and renewable uncertainties are modeled as normally distributed variables, and probabilistic constraints ensure operational limits compliance with predefined confidence levels. The methodology integrates Differential Evolution metaheuristics with Unscented Transformation for uncertainty propagation, requiring only 137 deterministic evaluations compared to 5000 for Monte Carlo methods. Validation on an IEEE 33-bus radial distribution system configured as an islanded microgrid demonstrates significant advantages over conventional approaches. Results show 36.5-fold computational efficiency improvement while achieving 95.28% confidence level compliance for frequency limits, compared to only 50% for deterministic methods. The integer formulation requires minimal additional load shedding (21.265%) compared to continuous approaches (20.682%), while better aligning with the discrete nature of real-world operational decisions. The proposed IM-POPF framework successfully minimizes total load shedding while maintaining frequency stability under uncertain conditions, providing a computationally efficient solution for real-time microgrid operation. Full article

Container terminals are facing significant challenges in meeting the increasing demands for volume and throughput, with limited space often presenting as a critical constraint. Key areas of concern at the quayside include the berth allocation problem, the quay crane assignment, and the scheduling problem. Effectively managing these issues is essential for optimizing port operations; failure to do so can lead to substantial operational and economic ramifications, ultimately affecting competitiveness within the global shipping industry. Optimization models, encompassing both mathematical frameworks and metaheuristic approaches, offer promising solutions. Additionally, the application of machine learning and reinforcement learning enables real-time solutions, while robust optimization and stochastic models present effective strategies, particularly in scenarios involving uncertainties. This study expands upon earlier foundational analyses of berth allocation, quay crane assignment, and scheduling issues, which have laid the groundwork for port optimization. Recent developments in uncertainty management, automation, real-time decision-making approaches, and environmentally sustainable objectives have prompted this review of the literature from 2015 to 2024, exploring emerging challenges and opportunities in container terminal operations. Recent research has increasingly shifted toward integrated approaches and the utilization of continuous berthing for better wharf utilization. Additionally, emerging trends, such as sustainability and green infrastructure in port operations, and policy trade-offs are gaining traction. In this review, we critically analyze and discuss various aspects, including spatial and temporal attributes, crane handling, sustainability, model formulation, policy trade-offs, solution approaches, and model performance evaluation, drawing on a review of 94 papers published between 2015 and 2024. Full article

Minimizing energy consumption remains a critical challenge in wireless sensor networks (WSNs) because of their reliance on nonrechargeable batteries. Clustering-based hierarchical communication has been widely adopted to address this issue by improving residual energy and balancing the network load. In this architecture, cluster heads (CHs) are responsible for data collection, aggregation, and forwarding, making their optimal selection essential for prolonging network lifetime. The effectiveness of CH selection is highly dependent on the choice of metaheuristic optimization method and the design of the fitness function. Although numerous studies have applied metaheuristic algorithms with suitably designed fitness functions to tackle the CH selection problem, many existing approaches fail to fully capture both the spatial distribution of nodes and dynamic energy conditions. To address these limitations, we propose the binary secretary bird optimization clustering (BSBOC) method. BSBOC introduces a binary variant of the secretary bird optimization algorithm (SBOA) to handle the discrete nature of CH selection. Additionally, it defines a novel multiobjective fitness function that, for the first time, considers the Voronoi diagram of CHs as an optimization objective, besides other well-known objectives. BSBOC was thoroughly assessed via comprehensive simulation experiments, benchmarked against two advanced methods (MOBGWO and WAOA), under both homogeneous and heterogeneous network models across two deployment scenarios. Findings from these simulations demonstrated that BSBOC notably decreased energy usage and prolonged network lifetime, highlighting its effectiveness as a reliable method for energy-aware clustering in WSNs. Full article

Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and struggle with interpretability, leading to insufficient predictive accuracy and engineering applicability under complex geological conditions. This study addresses these limitations by integrating Gaussian mixture modeling (GMM), manifold learning, and data augmentation to effectively capture multimodal hydrological data distributions and reveal their intrinsic symmetrical configurations and manifold structures, thereby reducing feature dimensionality. We then apply a whale optimization algorithm (WOA)-enhanced XGBoost model to forecast water inrush probabilities. Our model achieved an R² of 0.92, demonstrating a greater than 60% error reduction across various metrics. Validation at the Yangcheng Coal Mine confirmed that this balanced approach significantly enhances predictive accuracy, interpretability, and cross-scenario applicability. The synergy between high accuracy and transparency provides decision makers with reliable risk insights, enabling bidirectional validation with geological mechanisms and supporting the implementation of targeted, proactive safety measures. Full article

The performance of meta-heuristic algorithms on optimisation problems depend on the values of control parameters. These parameters greatly influence the behaviour of algorithms and affect the quality of the solutions. In order to optimise an algorithm for a specific problem set, a structured approach is followed to carefully select the appropriate control parameters. This approach is called control parameter tuning. Most existing tuning approaches focus on tuning an algorithm based on only one performance objective, such as accuracy or convergence speed. However, these objectives often work against each other, and improving the algorithm based on one objective can worsen the performance based on another objective. For example, obtaining a more accurate solution generally requires the algorithm to run for a longer time. The goal of this research is to develop a tuning approach that takes multiple performance objectives into account when tuning the control parameters of a meta-heuristic. The result of the tuning algorithm presents the experimenter with multiple values for control parameters, each representing different trade-offs between the various objectives. Experimental results demonstrate that M-race successfully discovered between 9 and 15 non-dominated parameter configurations across benchmark functions for both particle swarm optimisation (PSO) and differential evolution (DE) algorithms. These non-dominated parameter configurations represent balances among the tuning objectives used. Full article