A coordinated hybrid initialization and multi-operator framework for swarm-based optimization

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.