Adaptive online data-driven closed-loop parameter control strategy for swarm intelligence algorithm

Abstract

Parameter control is critical for the performance of any swarm intelligence algorithm. In this study, we propose an adaptive online data-driven closed-loop parameter control (CLPC) strategy for a swarm intelligence algorithm to solve both single-objective and multi-objective optimization problems with better performance. The proposed CLPC strategy involves three key parts: controller design, feedback selection, and reference determination. First, based on the control theory, we adopt a proportional integral derivative (PID) controller in the CLPC strategy, which can adaptively adjust the value of parameter according to the difference between reference and feedback. Second, to reflect and monitor the evolution state in real time, we use the mean shift clustering method and define the convergence entropy and the extension entropy to generate feedback. Finally, the reference should provide useful guidance for parameter control according to the features of optimization problems. Thus, in single-objective optimization, we propose a new lossless fitness landscape analysis method and design a decision tree to determine the reference; in multi-objective optimization, the range of the convergence entropy and the extension entropy are regarded as the reference. In addition, to illustrate the effectiveness of the CLPC strategy, two groups of experiments are performed based on the particle swarm optimization (PSO) algorithm in single-objective and multi-objective optimization. At the optimization algorithm level, we compare our proposed CLPC-PSO algorithm with three standard PSO algorithms, three decreasing inertia weight PSO algorithms, and two adaptive PSO algorithms. At the optimization problem level, we perform abundant experiments based on five single-objective benchmark functions, five multi-objective benchmark functions, and twelve scheduling instances. The statistical results show that the performance of the proposed CLPC-PSO algorithm is considerably better and more stable than those of the other eight PSO variants when faced with different problems having various features.