Co-evolutionary competitive swarm optimizer with three-phase for large-scale complex optimization problem

Practical optimization problems often involve a large number of variables, and solving them in a reasonable amount of time becomes a challenge. Competitive swarm optimizer (CSO) is an efficient variant of particle swarm optimization (PSO) algorithm and has been applied extensively to deal with a variety of practical large-scale optimization problems. In this article, a novel co-evolutionary method with three-phase, namely TPCSO, is developed by incorporating a novel multi-phase cooperative evolutionary technique to enhance the convergence and the search ability of CSO. In the modified CSO, the population is evenly decomposed into two sub-populations, then the update strategy of each sub-population is adjusted by the requirements of the diversity and convergence during the evolution process. In the first phase, the diversity is paid more attention in order to explore more regions. And in the second phase, the promising area in two sub-populations are exploited by introducing excellent particles of two sub-populations. The third phase focuses on the convergence by learning from the global best solution. Finally, the performance of TPCSO is evaluated and proved by large-scale benchmark functions selected from CEC’2010 and CEC’2013. The experimental and statistical results show that TPCSO can effectively solve these large-scale problems and fast obtain the optimal results with higher accuracy by comparing with several algorithms.