Aug 2026· Engineering Research Express· Vol 8· 0 citations· 35 references
Physics
TL;DR
An enhanced sand cat swarm algorithm (ESC-SCSA) is developed and comprehensively evaluated through sensitivity analysis, ablation studies, convergence analysis, and statistical significance tests, demonstrating its effectiveness and potential generalization capability across both continuous and discrete optimization problems.
Abstract
Population-based metaheuristic algorithms are widely applied to both continuous and discrete optimization problems; however, their performance is often constrained by limitations in population initialization quality and the coordination between exploration and exploitation, particularly in complex and high-dimensional optimization landscapes. In many existing approaches, uniform random initialization leads to uneven spatial coverage in continuous domains and insufficient solution diversity, while single-mechanism search strategies often fail to provide an effective transition between global exploration and local exploitation. These structural limitations reduce search robustness and increase the risk of premature convergence, especially in multimodal, hybrid, and composition optimization problems. To address these challenges, this study proposes a coordinated enhancement framework that jointly improves population initialization and search coordination. The proposed framework integrates a hybrid dual-population initialization strategy with a threshold-based multi-operator search mechanism. During initialization, uniform random sampling and hyperbolic transformation are combined with superiority-based selection to generate a high-quality and diverse initial population. Throughout the optimization process, cosine contraction, sinusoidal perturbation operator, and the original SCSA search operator are coordinated using an iteration-regulated search-strength coefficient with predefined threshold intervals, enabling a structured transition between exploration and exploitation. Based on this framework, an enhanced sand cat swarm algorithm (ESC-SCSA) is developed and comprehensively evaluated through sensitivity analysis, ablation studies, convergence analysis, and statistical significance tests on the CEC2017 and CEC2022 benchmark suites, followed by validation on flexible job shop scheduling problem instances. Experimental results demonstrate that ESC-SCSA consistently improves the original SCSA and exhibits competitive performance compared with several state-of-the-art metaheuristic algorithms across the CEC2017 and CEC2022 benchmark suites. Sensitivity analysis identifies effective parameter settings for the proposed framework, while the ablation study confirms that the hybrid initialization strategy and threshold-based multi-operator coordination each contribute substantially to the observed performance improvements. Convergence analysis further reveals faster and more stable search behaviour throughout the optimization process. Moreover, ESC-SCSA achieved the lowest mean makespan on nine of the ten Brandimarte benchmark instances, indicating its effectiveness and potential generalization capability across both continuous and discrete optimization problems.
Complex engineering optimization problems are often characterized by multimodality, high dimensionality, and nonlinear constraints, posing significant challenges for efficient and reliable computation. To address these challenges, this paper develops a hybrid crossover-based optimization framework that enhances population interaction and improves search efficiency. The proposed framework integrates two complementary mechanisms, namely a Levy long jump crossover strategy for global exploration and a horizontal-vertical crossover strategy for effective information exchange and local refinement, thereby improving convergence behavior and robustness. To support scalable computation, the method is implemented within a unified multi-backend computational framework based on FEALPy, enabling consistent and efficient execution across heterogeneous platforms, including NumPy and PyTorch on both CPU and GPU. This design enhances portability, reproducibility, and computational efficiency in large-scale optimization tasks. Extensive experiments on the IEEE CEC2022 benchmark suite demonstrate that the proposed framework achieves competitive or superior performance compared with several representative metaheuristic algorithms, as validated by Wilcoxon rank-sum and Friedman statistical tests. In addition, the method shows strong performance on constrained engineering design problems. Finally, the proposed framework is applied to UAV path planning, formulated as a constrained optimization problem, demonstrating its effectiveness and scalability in complex engineering scenarios.
Complex nonlinear problems are typically solved by optimization methods, and metaheuristic algorithms have attracted significant attention because of their ability to solve complex optimization problems. Most of the available approaches, however, have weaknesses, including premature convergence, a lack of balance between exploration and exploitation and slow convergence within high-dimensional spaces. To overcome these shortcomings, in this paper, the hybridization of the sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) and the hybrid sine cosine-butterfly optimization algorithm (SCA-BOA), which have the global exploration power of the sine cosine algorithm and the high local exploitation power of the butterfly optimization algorithm, are suggested. The suggested solution works in two phases. In the first step, the sine cosine mechanism improves the diversity in the population and conducts a global search with sinusoidal operators. At a later stage, the butterfly optimization strategy increases the search near promising regions, enhancing local refinement. This hybrid design permits a more balanced trade-off between exploration and exploitation as well as improved convergence stability. The proposed algorithm was evaluated using classical benchmark functions and the IEEE CEC 2022 benchmark suite under identical experimental settings. Ten standard benchmark functions were tested using the algorithm and compared to nine existing metaheuristic algorithms under the same experimental conditions. The findings show that the SCA-BOA has better performance in terms of fitness values, convergence speed, and stability of the solution. The experimental results demonstrate that the proposed hybrid SCA-BOA achieved the best overall average ranking score (2.3) among the compared optimization algorithms and produced competitive mean fitness and standard deviation values across diverse benchmark landscapes. Furthermore, the proposed algorithm was validated using the IEEE CEC 2022 benchmark suite, where convergence analysis demonstrated improved convergence stability and adaptive search behavior on unimodal, multimodal, hybrid, and composition benchmark functions. In addition, population diversity analysis quantitatively confirmed the balanced exploration–exploitation capability of the proposed hybrid algorithm and its effectiveness in avoiding premature convergence during optimization. These results demonstrate the effectiveness of the proposed algorithm and its ability to address complex continuous optimization problems in the field.
In Multi-objective particle swarm optimization (MOPSO), the external archive largely determines how well convergence and diversity are balanced. Ineffective archive maintenance may lead to uneven solution distributions, inaccurate convergence, and premature trapping in local regions.To overcome these limitations, this paper proposes TAMOPSO, a Two-stage Archive Maintenance-based Multi-Objective Particle Swarm Optimization algorithm. In the first stage, adaptive grids with dynamic boundary expansion are used to locate high-density regions. In the second stage, solutions in these regions are evaluated by integrating angle-based diversity assessment and a dual-distance convergence metric, with selection preferences adaptively adjusted according to the evolutionary stage, thereby improving the distribution and Pareto-front coverage of the obtained solution set while controlling archive size. To further enhance particle guidance, a bounded auxiliary archive is introduced to reuse historical high-quality non-dominated solutions discarded during archive maintenance and assist personal best updates. In addition, a stagnation detection-based particle reconstruction strategy is designed, using sparsely distributed elite solutions from the external archive as reconstruction templates to guide stagnant particles back to promising search regions and enhance global exploration. Tests on representative benchmark suites indicate that TAMOPSO produces higher-quality approximation sets than the compared mainstream algorithms in most cases.
Jing Zhang, Yanmin Liu, Yuci Li et al.· Scientific Reports· 0 citations
Particle swarm optimization (PSO) is a classical metaheuristic algorithm that has been widely used to solve continuous optimization problems. However, it still suffers from inherent drawbacks, such as being prone to premature convergence and an imbalance between exploration and exploitation. To address these problems, a Multi-swarm Collaborative Particle Swarm Optimization with Adaptive Learning Strategy (MCPSO-ALS) is proposed in this paper. Firstly, an Adaptive Population Division Strategy (APDS) is designed to realize effective information interaction among particles. At each iteration, the overall population is dynamically divided and reorganized, based on the fitness values of all the particles. Specifically, particles with high fitness form an elite population focusing on local search; particles with low fitness form a poor population focusing on global search; and ordinary particles form a general population aiming to achieve a balance between exploration and exploitation. Secondly, an Adaptive Learning Mechanism (ALM) is introduced. In this mechanism, particles with different roles adopt distinct updating strategies, which productively guarantees the dynamic equilibrium between exploration and exploitation. To validate the outstanding performance of the proposed algorithm, comprehensive experiments are conducted on CEC2013 and CEC2017. The experimental results demonstrate that the proposed method exhibits significant advantages in convergence speed, solving accuracy, and comprehensive optimization capabilities compared with several state-of-the-art algorithms.
Zhi-Y. Gao, Xu Yang· Mathematics· 0 citations
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