An effective combination of mechanisms for particle swarm optimization-based ensemble strategy

A high-quality ensemble strategy can effectively integrate several coefficients, mechanisms, and algorithms into a single framework. The adaptability, timing of intervention, and complementarity are the key factors to consider for the selected coefficients, mechanisms, and algorithms. In this study, two complementary variants based on Particle Swarm Optimization (PSO), namely Modified PSO (MPSO) and Social Learning PSO (SLPSO), were selected, forming IMPSO and ISLPSO after improvements. IMPSO excels at exploration, while ISLPSO excels at exploitation. The Improved Novel Ratio Adaptation Scheme (INRAS) is employed as a selection strategy and provides the ability to abandon less-optimal particles. The Modified Nonlinear Population Size Reduction (MNLPSR) enables the extension of generations, allowing for more sufficient evolution in later stages. Due to the use of MNLPSR, an improved inertia weight and adaptive acceleration coefficients are introduced to ensure compatibility with the proposed algorithm. Additionally, an improved dynamic differential mutation strategy is designed not only to be compatible with the proposed algorithm but also to enhance particle diversity. Both the Improved Sine Cosine Algorithm (ISCA) and Sequential Quadratic Programming (SQP), which focus on searching near the global best particles, are incorporated into the proposed ensemble strategy. This PSO-based variant is named the Effective Combination of Mechanisms for a PSO-based Ensemble Strategy (ECM-PSOES). Ablation experiments demonstrated the effectiveness of the individual coefficients and mechanisms. The novel PSO-based variant was evaluated on the CEC2017 benchmarks and compared with 14 state-of-the-art PSO-based variants and 11 non-PSO algorithms. Additionally, to evaluate the flexible and robust capability of the proposed algorithm, three real-world applications for long-term Transmission Network Expansion Planning (TNEP), Planetary Gear Train Design (PGTD), and Robot Gripper Design (RGD) were tested. The experimental results illustrate that the proposed algorithm displays superior performance compared to recently proposed PSO-based variants and most non-PSO algorithms. However, the proposed algorithm falls short of outperforming Differential Evolution (DE)-based algorithms and still requires time to match the performance of top-tier metaheuristics. The source code of ECM-PSOES is provided at https://github.com/microhard1999/CODES.