Adaptive control of acceleration coefficients for particle swarm optimization based on clustering analysis

Research into setting the values of the acceleration coefficients c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> in Particle Swarm Optimization (PSO) is one of the most significant and promising areas in evolutionary computation. Parameters c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> in PSO indicate the “self-cognitive” and “social-influence” components which are important for the ability to explore and converge respectively. Instead of using fixed value of c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> with 2.0, this paper presents the use of clustering analysis to adaptively adjust the value of these two parameters in PSO. By applying the K-means algorithm, distribution of the population in the search space is clustered in each generation. An adaptive system which is based on considering the relative size of the cluster containing the best particle and the one containing the worst particle is used to adjust the values of c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> . The proposed method has been applied to optimize multidimensional mathematical functions, and the simulation results demonstrate that the proposed method performs with a faster convergence rate and better solutions when compared with the methods with fixed values of c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and c <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> .