This paper focuses on the target Q-coverage and sensor deployment problem, where the coverage requirement of each target is different. Previous studies in the literature solved the Q-coverage optimization as a single-objective problem considering random sensor deployment. In this work, Q-coverage problem in directional sensor network is solved as a multi-objective optimization problem, where objectives are the maximization of the overall target coverage and the minimization of the number of active sensors. Maintaining their generic structures the same, three existing and well-known multi-objective genetic algorithms (MOGAs): strength Pareto evolutionary algorithm 2 (SPEA2), nondominated sorting genetic algorithm II (NSGA-II), and multi-objective evolutionary algorithm based on decomposition (MOEA/D) are modified to solve the proposed multi-objective Q-coverage problem. Since the sensor positions can significantly improve the overall coverage, two different sensor deployment algorithms are proposed to find the suitable positions of sensors, one is heuristic, and the other is based on particle swarm optimization. The MOGAs determine the optimal orientations of the sensors. For the implementation of the modified MOGAs, a new mutation operator, compatible for implementing the problem, has been designed. The impact of five different network parameters: the number of targets, the number of sensors, the number of orientations, the sensing radius values, and the coverage requirement, on the two objectives are analyzed. The performances of the three modified MOGAs are compared based on three performance metrics, hypervolume (HV), inverted generational distance (IGD), and spread. To analyze the robustness of the modified MOGAs, the sensitivity analysis is performed. In addition, the performances of the three modified MOGAs are compared with a genetic algorithm and a greedy algorithm, existing in the literature. Experimental results show that the modified MOGAs need, on an average, 16.28% fewer sensors than the existing genetic algorithm and 2.9% fewer sensors than the existing greedy algorithm, while achieving 7.8% and 1.18% higher target coverage, respectively. To show the scalability and effectiveness of the proposed MOGAs, they are executed on both a large scale network and a real network. Finally, the results are validated using the Wilcoxon signed rank test based on the performance metrics.

Multi-objective optimization (MOO) plays a critical role in mechanical and industrial engineering, where conflicting design goals must be balanced under complex constraints. In this study, we introduce the Multi-Objective Giant Trevally Optimizer (MOGTO), a novel extension of the Giant Trevally Optimizer inspired by predatory foraging dynamics. MOGTO integrates predation-regime switching into a Pareto-based framework, enhanced with feasibility-aware archiving, knee-biased selection, and adaptive constraint handling. We benchmark MOGTO against established algorithms—NSGA-II, SPEA2, MOEA/D, and ParetoSearch—using synthetic test suites (ZDT1–3, DTLZ2) and classical engineering problems (welded beam, spring, and pressure vessel). Performance was assessed with Hypervolume (HV), Inverted Generational Distance (IGD), Spacing, and coverage metrics across 30 independent runs. The results demonstrate that MOGTO consistently achieves competitive or superior HV and IGD, maintains more uniform spacing, and generates larger feasible archives than the baselines. Particularly on constrained engineering problems, MOGTO yields more feasible non-dominated solutions, confirming its robustness and industrial applicability. These findings establish MOGTO as a reliable and general-purpose metaheuristic for multi-objective optimization in engineering design.

Supply-chain scheduling in modern production systems faces significant challenges due to the complexity of balancing cost efficiency, delivery lead times, and order variability—especially under stochastic demand and uncertain transportation conditions. Conventional metaheuristic approaches, such as the standard Non-dominated Sorting Genetic Algorithm II (NSGA-II), often struggle with premature convergence, limited population diversity, and rigid parameter settings that hinder adaptability in dynamic environments. To address these limitations, this study proposes a novel Hybrid Adaptive NSGA-II (HA-NSGA-II) framework, enhanced by two key innovations: (1) a Global-Intensity Mutation Operator (GIMO) that strengthens population diversity by dynamically adjusting mutation intensity across the entire solution space; and (2) an Adaptive Parameter Self-Tuning (APST) module based on reinforcement learning, which intelligently regulates crossover and mutation rates in response to evolutionary progress and environmental changes. A tri-objective optimization model is formulated to simultaneously minimize total supply chain cost, order quantity variance (mitigating the bullwhip effect), and customer delivery delays. The proposed HA-NSGA-II demonstrates superior convergence and diversity performance compared to traditional NSGA-II, offering a more robust and adaptive solution for complex, real-world supply chain scheduling under uncertainty. The model is tested on a simulated supply chain with 5 factories, 15 warehouses, and 50 customers facing random demand and Gaussian-distributed lead times. The new HA-NSGA-II is compared with traditional NSGA-II, SPEA2, and MOEA/D based on Hypervolume (HV), Inverted Generational Distance (IGD), Spread (Δ), Total Inventory Cost, Bullwhip Index (BI), and Robustness Index (RI). Results of 50 simulation runs demonstrate that HA-NSGA-II surpasses all the baseline algorithms with 12.9% enhancement in HV, 41.1% improvement in IGD, and 13.7% reduction in convergence time. In addition, it delivers a 14.6% supply chain cost reduction, a 20.4% bullwhip effect suppression, and 25% accelerated times of fulfillment. The research concludes that the HA-NSGA-II provides a scalable and effective scheduling approach applicable for real-time Industry 4.0 supply chains. Work in the future involves expanding the framework towards multi-period dynamic environments using IoT and blockchain-based visibility.

Hybrid Flow Shop Scheduling (HFS) has garnered significant interest in terms of problem formulation and solution approaches. This work introduces an optimization approach for a case study on a hybrid flow shop scheduling problem. The objective is to minimize the makespan, energy consumption, and idle machines in manufacturing shop. The HFS consists of many concurrent production lines, each containing several machines, operating in one or more stages. A case study was conducted using fourteen jobs across three stages, which utilized lathe, milling, and deburring machines. The EE-HFS was optimized using Multi-Objective Tiki Taka Optimization (MOTTA). The study considered machine idle time as a key factor influencing energy efficiency, incorporating it into the scheduling evaluation. The optimization result was compared to established algorithms, such as the Non-dominated Sorting Genetic Algorithm-II, the Multi Objectives Evolutionary Algorithm Based on Decomposition, the Multi Objectives Particle Swarm Optimization, and the recent algorithm Multi Objectives Grey Wolf Optimizer. The metrics used for comparison include Error Ratio (ER), Pareto Percentage (%), Spacing, Maximum Spread, computational speed, Hyper Volume, Inverted Generational Distance (IGD), and Generational Distance (GD). The results indicate that MOTTA exhibits superior performance with 78.42% best overall and 100% better in the convergence and domination of the case study solution (ER, ND, GD, and IGD). Overall, the findings have important implications for Hybrid flow shop scheduling in terms of the energy utilization model, reducing idle machine time, and the promising potential of MOTTA for application in other combinatorial scheduling challenges. This case study provides substantial advantages to the organization by effectively decreasing its daily energy consumption, equipment usage, and enhancing resource management.

Coal blending in thermal power plants is a complex multi-objective challenge involving economic, operational and environmental considerations. This study presents a Q-learning-enhanced NSGA-II (QLNSGA-II) algorithm that integrates the adaptive policy optimization of Q-learning with the elitist selection of NSGA-II to dynamically adjust crossover and mutation rates based on real-time performance metrics. A physics-based objective function takes into account the thermodynamics of ash fusion and the kinetics of pollutant emission, ensuring compliance with combustion efficiency and NOx limits. Benchmark tests on the Walking Fish Group (WFG) and Unconstrained Function (UF) suites show that QLNSGA-II achieves a 12.7% improvement in Inverted Generational Distance (IGD) and a 9.3% improvement in Hypervolume (HV) compared to prevailing algorithms. Industrial validation at the Huaneng Yingkou power plant confirms a 14.7% reduction in fuel cost and a 41% reduction in slagging incidence over conventional blending methods, backed by 12 months of operational data. Other benefits include a 24.8% reduction in sulphur content, a 6.9% increase in the plant’s net heat rate and annual savings of RMB 12.3 million, 2,150 tonnes of limestone and 38,500 tonnes of CO2-equivalent emissions. These results highlight QLNSGA-II as a scalable, robust solution for multi-objective coal blending, offering a promising way to improve the efficiency and sustainability of coal-fired power generation.

Power batteries are one of the important components of electric vehicles, but the manufacturing process of vehicle power batteries is complex and diverse. Traditional scheduling methods face challenges such as low production efficiency and inadequate quality control in complex production environments. To address these issues, a multi-objective optimization model with makespan, total machine load, and processing quality as the established objectives, and a Multi-objective Particle Swarm Energy Valley Optimization (MPSEVO) is proposed to solve the problem. MPSEVO integrates the advantages of Multi-objective Particle Swarm Optimization (MOPSO) and Energy Valley Optimization (EVO). In this algorithm, the particle stability level is combined in MOPSO, and different update strategies are used for particles of different stability to enhance both the convergence and diversity of the solutions. Furthermore, a local search strategy is designed to further enhance the algorithm to avoid the local optimal solutions. The Hypervolume (HV) and Inverted Generational Distance (IGD) indicators are often used to evaluate the convergence and diversity of multi-objective algorithms. The experimental results show that MPSEVO’s HV and IGD indicators are better than other algorithms in 10 computational experiments, which verifies the effectiveness of the proposed strategy and algorithm. The proposed method is also applied to solve the actual battery workshop scheduling problem. Compared with MOPSO, MPSEVO reduces the total machine load by 7 units and the defect rate by 0.05%. In addition, the effectiveness of each part of the improved algorithm was analyzed by ablation experiments. This paper provides some ideas for improving the solution performance of MOPSO, and also provides a theoretical reference for enhancing the production efficiency of the vehicle power battery manufacturing workshop.

This paper presents a novel approach to address the challenges of complex terrain, dynamic wind fields, and multi-objective constraints in multi-UAV collaborative path planning for forest firefighting missions. An extensible algorithm, termed Parallel Vectorized Differential Evolution-based Multi-Objective Jellyfish Search (PVDE-MOJS), is proposed to enhance path planning performance. A comprehensive multi-objective cost function is formulated, incorporating path length, threat avoidance, altitude constraints, path smoothness, and wind effects. Forest-specific constraints are modeled using cylindrical threat zones and segmented wind fields. The conventional jellyfish search algorithm is then enhanced through multi-core parallel fitness evaluation, vectorized non-dominated sorting, and differential evolution-based mutation. These improvements substantially boost convergence efficiency and solution quality in high-dimensional optimization scenarios. Simulation results on the Phillip Archipelago Forest Farm digital elevation model (DEM) in Australia demonstrate that PVDE-MOJS outperforms the original MOJS algorithm in terms of inverted generational distance (IGD) across benchmark functions UF1–UF10. The proposed method achieves effective obstacle avoidance, altitude optimization, and wind adaptation, producing uniformly distributed Pareto fronts. This work offers a viable solution for emergency UAV path planning in forest fire rescue scenarios, with future extensions aimed at dynamic environments and large-scale UAV swarms.

To enhance the safety of children in frontal collisions of school buses, this study conducts the design optimization for a pre-inflation airbag under mixed conditions involving two child age groups (6 and 12 years old), three sitting postures, and two crash pulses. A coupling model integrating the school bus restraint system and the pre-inflation airbag is developed. Based on non-dominated sorting genetic algorithm III (NSGA-III), an improved variant called NSGA-III-SAA is proposed. This variant incorporates the symmetric Latin hypercube design method, adopts adaptive crossover and mutation rates, and modifies the environmental selection mechanism using an adaptive niche strategy. An experimental comparison between NSGA-III-SAA and five state-of-the-art multi-objective evolutionary algorithms (MOEAs) is conducted using Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suites. Based on the inverted generational distance (IGD) and hypervolume (HV), the performance scores of NSGA-III-SAA and the five other MOEAs are 1.06, 1.40, 2.00, 2.80, 2.85, and 3.81, respectively, lower scores signify better performance, indicating that NSGA-III-SAA outperforms the others. Additionally, it demonstrates clear advantages in computational efficiency and constraint handling. Through NSGA-III-SAA, the optimal configuration of the airbag design variables is as follows: upper strap length of 0.2645 m, installation height of 0.4092 m, opening pressure of 1.161 × 10 5 Pa, and opening degree of 1.99. Compared to pre-optimization results, the head injury criterion ( HIC 15 ), thorax injury values ( T 3ms and THPC ), and weighted injury criteria ( WICC 6 and WICC 12 ) for children under twelve conditions show significant reductions. Specifically, the weighted injury criteria decrease by 41.38%, 43.13%, 34.20%, 30.21%, 34.08%, 27.09%, 25.38%, 30.80%, 28.91%, 19.45%, 26.86%, and 22.75%, respectively.

To address the modeling complexity and multi-objective collaborative optimization challenges in multi-depot and multiple unmanned aerial vehicle (UAV) delivery task planning, this paper proposes a bi-layer planning framework, which comprehensively considers resource constraints, multi-depot coordination, and the coupling characteristics of path execution. The novelty of this work lies in the seamless integration of an enhanced genetic algorithm and tailored swarm optimization within a unified two-tier architecture. The upper layer tackles the task assignment problem by formulating a multi-objective optimization model aimed at minimizing economic costs, delivery delays, and the number of UAVs deployed. The Enhanced Non-Dominated Sorting Genetic Algorithm II (ENSGA-II) is developed, incorporating heuristic initialization, goal-oriented search operators, an adaptive mutation mechanism, and a staged evolution control strategy to improve solution feasibility and distribution quality. The main contributions are threefold: (1) a novel ENSGA-II design for efficient and well-distributed task allocation; (2) an improved PSO-based path planner with chaotic initialization and adaptive parameters; and (3) comprehensive validation demonstrating substantial gains over baseline methods. The lower layer addresses the path planning problem by establishing a multi-objective model that considers path length, flight risk, and altitude variation. An improved particle swarm optimization (PSO) algorithm is proposed by integrating chaotic initialization, linearly adjusted acceleration coefficients and maximum velocity, a stochastic disturbance-based position update mechanism, and an adaptively tuned inertia weight to enhance algorithmic performance and path generation quality. Simulation results under typical task scenarios demonstrate that the proposed model achieves an average reduction of 47.8% in economic costs and 71.4% in UAV deployment quantity while significantly reducing delivery window violations. The framework exhibits excellent capability in multi-objective collaborative optimization. The ENSGA-II algorithm outperforms baseline algorithms significantly across performance metrics, achieving a hypervolume (HV) value of 1.0771 (improving by 72.35% to 109.82%) and an average inverted generational distance (IGD) of 0.0295, markedly better than those of comparison algorithms (ranging from 0.0893 to 0.2714). The algorithm also demonstrates overwhelming superiority in the C-metric, indicating outstanding global optimization capability in terms of distribution, convergence, and the diversity of the solution set. Moreover, the proposed framework and algorithm are both effective and feasible, offering a novel approach to low-altitude urban logistics delivery problems.

Multimodal Medical Image Fusion is a key evolution in medical imaging. It contributes to improving diagnosis, providing better treatment, and reducing risk. Multimodal medical image fusion is a multi-objective due to the need of balancing factors like the weights of the fusion rules and the speed of the fusion process. While multi-objective particle swarm optimization has already been applied to solve this problem, it suffers from premature. It has been shown that the Darwinian Particle Swarm Optimization performs better than the classical Particle Swarm optimization by escaping the local optima. Therefore, this paper proposes a new approach based on the combination of variable-order fractional-order with multi-objective Darwinian Particle Swarm Optimization. Variable-order fractional-order improves the convergence rate of multi-objective Darwinian Particle Swarm Optimization by adjusting the particle velocity and position dynamically. Moreover, the new approach uses the gradient compass in the spatial domain to generate detailed images, further enhancing fusion quality. The proposed method is used to optimize both the fusion process weights and processing time. Experiments using the fusion of computed tomography along with magnetic resonance imaging show that the proposed technique outperforms existing techniques. Both the Inverted Generational Distance (IGD) and the Hyper-Volume (HV) metrics of the proposed multi-objective problem solution surpass the state-of-the-art showing the optimality of the provided solution. Additionally, the proposed solution image visual demonstrated high visual quality, efficient edge preservation, and the absence of noisy artefacts. Furthermore, our proposed fusion approach showed its suitability for real-time application, with a processing time not exceeding 0.085 seconds, outperforming other methods.

Cloud resource brokerage is a fundamental challenge in cloud computing, requiring the efficient selection and allocation of services from multiple providers to optimize performance, sustainability, and cost-effectiveness. Traditional approaches often struggle with balancing conflicting objectives, such as minimizing the response time, reducing energy consumption, and maximizing broker profits. This paper presents NSGA-III-GKM++, an advanced multi-objective optimization model that integrates the NSGA-III evolutionary algorithm with an enhanced K-means++ clustering technique to improve the convergence speed, solution diversity, and computational efficiency. The proposed framework is extensively evaluated using Deb–Thiele–Laumanns–Zitzler (DTLZ) and Unconstrained Function (UF) benchmark problems and real-world cloud brokerage scenarios. Comparative analysis against NSGA-II, MOPSO, and NSGA-III-GKM demonstrates the superiority of NSGA-III-GKM++ in achieving high-quality tradeoffs between performance and cost. The results indicate a 20% reduction in the response time, 15% lower energy consumption, and a 25% increase in the broker’s profit, validating its effectiveness in real-world deployments. Statistical significance tests further confirm the robustness of the proposed model, particularly in terms of hypervolume and Inverted Generational Distance (IGD) metrics. By leveraging intelligent clustering and evolutionary computation, NSGA-III-GKM++ serves as a powerful decision support tool for cloud brokerage, facilitating optimal service selection while ensuring sustainability and economic feasibility.

Engineering frequently deals with multi-objective optimization problems. In the scheduling of combined heat and power systems, the competing goals of economic cost and pollutant emission are challenging for conventional single-objective algorithms to handle, necessitating the use of effective multi-objective optimization algorithms. The research design improves the multi-objective differential evolution algorithm, which is constructed by making the scaling factor and crossover probability change adaptively, adopting non-dominated sorting, combining the congestion distance calculation to deal with multi-objectives, adding elite populations and quadratic mutation links, and so on. Based on this algorithm, the dynamic economic emission dispatch model of combined heat and power system is constructed to optimize the economic and environmental benefits of the system. The results revealed that the improved multi-objective differential evolution algorithm in Zitzler-Deb-Thiele 1 function test had generational distance of 0.0513, inverted generational distance of 0.3265, and hyper volume metric of 0.1301. Its Pareto optimal frontier fitted the standard curve better and was uniformly distributed, giving better performance. It was applied to solving dynamic economic emission dispatch model for combined heat and power system and compared with time-varying multi-objective PSO algorithm and others. Based on the ieee 30-node system deployment, it contained two cogeneration units, seven generator units, and one heating unit. The improved multi-objective differential evolution algorithm optimized the fuel cost as low as $2300590 and the pollution emission as low as 200285 kg. Its Pareto optimal frontier distribution was better, and it performed better in the hyper volume metric and inverted generational distance metrics. The research demonstrates that the improved multi-objective differential evolution algorithm can effectively balance operational cost and performance, achieving reduced fuel cost and pollution emissions. Furthermore, it exhibits strong adaptability and optimization capabilities in practical engineering applications, enhancing system operation efficiency and reducing pollution.

As early detection of voice disorders can significantly improve patients’ situation, the automated detection using Artificial Intelligence techniques can be crucial in various applications in this scope. This paper introduces a multi-objective bio-inspired, AI-based optimization approach for the automated detection of voice disorders. Different multi-objective evolutionary algorithms (the Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA-II), and the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D)) have been compared to detect voice disorders by optimizing two conflicting objectives: error rate and the number of features. The optimization problem has been formulated as a wrapper-based algorithm for feature selection and multi-objective optimization relying on four machine learning algorithms: K-Nearest Neighbour algorithm (KNN), Random Forest (RF), Multilayer Perceptron (MLP), and Support Vector Machine (SVM). Three publicly available voice disorder datasets have been utilized, and results have been compared based on Inverted-Generational Distance, Hypervolume, spacing, and spread. The results reveal that NSGA-II with the MLP algorithm attained the best convergence and performance. Further, the conformal prediction is leveraged to quantify uncertainty in the feature-selected models, ensuring statistically valid confidence intervals for predictions.

The remanufacturing of end-of-life products is an effective approach to alleviating resource shortages, environmental pollution, and global warming. As the initial step in the remanufacturing process, the quality and efficiency of disassembly have a decisive impact on the entire workflow. However, the complexity of product structures poses numerous challenges to practical disassembly operations. These challenges include not only conventional precedence constraints among disassembly tasks but also sequential dependencies, where interference between tasks due to their execution order can prolong operation times and complicate the formulation of disassembly plans. Additionally, the inherent uncertainties in the disassembly process further affect the practical applicability of disassembly plans. Therefore, developing reliable disassembly plans must fully consider both sequential dependencies and uncertainties. To this end, this paper employs a chance-constrained programming model to characterise uncertain information and constructs a multi-objective sequence-dependent disassembly line balancing (MO-SDDLB) problem model under uncertain environments. The model aims to minimise the hazard index, workstation time variance, and energy consumption, achieving a multi-dimensional optimisation of the disassembly process. To efficiently solve this problem, this paper designs an innovative multi-objective adaptive large neighbourhood search (MO-ALNS) algorithm. The algorithm integrates three destruction and repair operators, combined with simulated annealing, roulette wheel selection, and local search strategies, significantly enhancing solution efficiency and quality. Practical disassembly experiments on a lithium-ion battery validate the effectiveness of the proposed model and algorithm. Moreover, the proposed MO-ALNS demonstrated a superior performance compared to other state-of-the-art methods. On average, against the best competitor results, MO-ALNS improved the number of Pareto solutions (NPS) by approximately 21%, reduced the inverted generational distance (IGD) by about 21%, and increased the hypervolume (HV) by nearly 8%. Furthermore, MO-ALNS exhibited a superior stability, providing a practical and feasible solution for disassembly optimisation.

To address the multi-objective flexible job shop scheduling problem in rolling production mode (FJSP-RPM), this study proposes a Multi Objective Improved of Salp Swarm Algorithm (MISSA) that simultaneously optimizes equipment utilization and total tardiness. The MISSA generates initial population through various heuristic strategies to improve the initial population quality. The exploitation capability of the algorithm is enhanced through the global crossover strategy and variety of local search strategies. In terms of improvement strategies, the MISSA (using all three strategies) outperforms other incomplete variant algorithms (using only two strategies) in three metrics: Generational Distance (GD), Inverted Generational Distance (IGD), and diversity metric, achieving superior results in 9 test cases, 8 test cases, and 4 test cases respectively. When compared with NSGA2, NSGA3, and SPEA2 algorithms, the MISSA demonstrates advantages in 8 test cases for GD, 8 test cases for IGD, and 7 test cases for the diversity metric. Additionally, the distribution of the obtained solution sets is significantly better than that of the comparative algorithms, which validats the effectiveness of the MISSA in solving FJSP-RPM.

This paper introduces an improved multi-objective grey wolf optimizer (IMOGWO) and demonstrates its application to the aerodynamic optimization of an axial cooling fan. Building upon the traditional multi-objective grey wolf optimizer (MOGWO), several improvement strategies were adopted to enhance its performance. Firstly, the IMOGWO started population initialization based on the Bloch coordinates of qubits to ensure a high-quality initial population. Additionally, it employed a nonlinear convergence factor to facilitate global exploration and integrated the inspiration of Manta Ray Foraging to enhance the information exchange between populations. Finally, associative learning was leveraged for archive updating, allowing for perturbative mutation of solutions in crowded regions of the archive to increase solution diversity and improve the algorithm’s search capability. The proposed IMOGWO was applied to five multi-objective benchmark functions, comprising three two-objective and two three-objective problems, and experimental results were compared with three well-known multi-objective algorithms: the non-dominated sorting genetic algorithm II (NSGA II), MOGWO, and the multi-objective multi-verse optimizer (MOMVO). It is demonstrated that the proposed algorithm had advantages in convergence accuracy and diversity of solutions, which were quantified by the performance metrics (generational distance (GD), inverted generational distance (IGD), Spacing (SP), and Hypervolume (HV)). Furthermore, a multi-objective optimization process coupled with the IMOGWO algorithm and Computational Fluid Dynamics (CFD) was proposed. By optimizing the design parameters of an axial cooling fan, a set of non-dominated solutions was obtained within limited iteration steps. Consequently, the IMOGWO also presented an effective and practical approach for addressing multi-objective optimization challenges with respect to engineering problems.

This research presents an advancement of the Elk Herd Optimization targeting specific real-world multi-objective optimization problems, this algorithm is stated as the multi-objective Elk Herd Optimization (MOEHO). MOEHO exploits reproductive behaviour among elk herds for balancing exploration and exploitation within the optimization procedure toward diversification and convergence. The algorithm performed better over the set of small-to-medium scale structural design problems thus is widely applicable in engineering design. Further, when compared with eight benchmark truss structures against five well-established algorithms the MOEHO has outperformed them in the perspective of performance parameters like Spacing (SP), Hypervolume (HV) and Inverted Generational Distance (IGD). More concrete statistical analysis through Friedman rank test also ascertains the robustness and efficiency of the algorithm, especially at high complexities in optimization. The research attracts attention to the ability of such an algorithm which maintains a balance between the exploration and exploitation. Computational efficiency of MOEHO and qualitatively diversifying solutions along Pareto front, makes it especially applicable in complex engineering applications. Further research into extension of MOEHO with applicability on more dimensional problems, applied even in energy systems optimization.

ABSTRACT With the rise of low-cost launches, miniaturized space technology, and commercialization, the cost of space missions has dropped, leading to a surge in flexible Earth observation satellites. This increased demand for complex and diverse imaging products requires addressing multi-objective optimization in practice. To this end, we propose a multi-objective agile Earth observation satellite scheduling problem (MOAEOSSP) model and introduce a reinforcement learning-based multi-objective grey wolf optimization (RLMOGWO) algorithm. It aims to maximize observation efficiency while minimizing energy consumption. During population initialization, the algorithm uses chaos mapping and opposition-based learning to enhance diversity and global search, reducing the risk of local optima. It integrates Q-learning into an improved multi-objective grey wolf optimization framework, designing state-action combinations that balance exploration and exploitation. Dynamic parameter adjustments guide position updates, boosting adaptability across different optimization stages. Moreover, the algorithm introduces a reward mechanism based on the crowding distance and inverted generational distance (IGD) to maintain Pareto front diversity and distribution, ensuring a strong multi-objective optimization performance. The experimental results show that the algorithm excels at solving the MOAEOSSP, outperforming competing algorithms across several metrics and demonstrating its effectiveness for complex optimization problems.

Multi-Objective Feature Selection Algorithm using Beluga Whale Optimization

This study presents a comprehensive comparative analysis of three leading evolutionary algorithms—NSGA-II, MOEA/D, and SPEA2—within a fuzzy multi-objective optimization framework. The primary goal is to evaluate their performance in solving complex optimization problems under uncertainty, where objectives and constraints are represented through fuzzy sets. Benchmark problems from the ZDT and DTLZ families were employed to assess each algorithm’s efficiency based on convergence, diversity, and robustness metrics such as Hypervolume (HV), Generational Distance (GD), Inverted GD (IGD), Spread, and Spacing. Experimental results reveal that the integration of fuzzy modeling significantly enhances optimization performance by providing flexibility and robustness against imprecise or uncertain data. Among the algorithms compared, the fuzzy-enhanced NSGA-II demonstrated superior convergence to the Pareto front, higher diversity, and improved stability, followed by MOEA/D, while SPEA2 showed comparatively lower performance. Statistical tests confirmed the significance of these results, establishing that fuzzy-based multi-objective optimization can yield more realistic and reliable decision outcomes in uncertain environments.