(A) coevolutionary numerical solver for minimax problems

Abstract

Traditional numerical solvers for minimax problems were calculus based. In this paper, to overcome the disadvantages of calculus based methods we propose an evolutionary computation based numerical solver for minimax problems. Evolutionary computation is a stochastic optimization techique which can outperform conventional optimization methods. We can view the minimax problem as a game between two players with different objectives. One player trying to minimize the cost and the other trying to maximize it where strategies can be expressed as populations. The strategies from each players are matched and scored. Only the best strategies will survive for each players. The surviving strategies will make offsprings for the next generation. This process is iterated until pre-assigned terminal conditions are satisfied. We also consider the relative evaluation method for faster convergence and find an optimal matching number of the game. The proposed technique is applied to a missile acceleration control problem for verification.