Robust Multiobjective Competitive Swarm Optimization Based on Evolutionary Trend Prediction.

The competitive swarm optimizer (CSO) has been widely used for addressing multiobjective optimization problems owing to its diverse learning approach. However, the evolutionary process uncertainty within the algorithm weakens the optimization reliability. To deal with this concern, a robust multiobjective CSO with a predictive indicator (RMOCSO-PI), is proposed. This approach can reduce aimless and inefficient searches caused by the uncertainty to enhance algorithmic robustness. First, a predictive indicator is established based on the autoregressive model, which utilizes historical swarm distribution data to predict the evolutionary trends. Then, the particles are classified into winners and losers by evaluating their evolutionary potential, whose evolution would be guided differentially. Second, a space fusion-based competitive mechanism is designed to generate precise evolution directions for loser particles. The space fusion-based adaptive adjustment method integrates the learning cost metric in decision space with the learning worth metric in objective space for proper learning weight settings. Third, a dynamic cooperative mechanism is presented to purposefully guide the diversity exploration of particles. By estimating evolutionary states, three cooperative patterns are dynamically assigned to particles for purposeful diversity exploration. To provide theoretical support for the validity and reliability of RMOCSO-PI, a convergence analysis is given. Furthermore, experimental results verify that RMOCSO-PI has more stable and excellent optimization performance.