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Co-evolutionary particle swarm optimization to solve min-max problems

A co-evolutionary particle swarm optimization (PSO) to solve constrained optimization problems is proposed. First, we introduce the augmented Lagrangian to transform a constrained optimization to a min-max problem with the saddle-point solution. Next, a co-evolutionary PSO algorithm is developed with one PSO focusing on the minimum part of the min-max problem with the other PSO focusing on the maximum part of the min-max problem. The two PSOs are connected through the fitness function. In the fitness calculation of one PSO, the other PSO serves as the environment to that PSO. The new algorithm is tested on three benchmark functions. The simulation results illustrate the efficiency and effectiveness of the new co-evolutionary particle swarm algorithm.