New Approaches To The Problems Of Continuous Minimax Optimizations

Continuous optimization problems are widespread in the research fields and ap-plications such as mathematics, computer science, economics, engineering, etc. Gener-ally, an optimization problem is, for an objective function f(x), finding the minimum or maximum over the variable x from all feasible solutions. However, the continuous minimax optimization problem, is a special kind of optimizations, its optimal solution is the minimum over s of the maximum over y on an objective function f(x, y). To put it simply, minimax is a minimizing problem which contains another maximizing problem.Despite the importance of the minimax problem, how to approach it is still a dif-ficult and open problem. The significance of this dissertation is the proposed new ap-proaches can solve continuous minimax problem more effectively and efficiently.In this paper, depending on whether or not satisfying the symmetry condition, minimax problems could be considered either symmetric or asymmetric. Our works mainly focused on, firstly, proposing an efficient and stable two-population coevolu-tionary PSO(particle swarm optimization) algorithm for symmetric problems. In this algorithm, we use a two-way alpha-beta pruning evaluation method for reducing the redundant computation thus improve the efficiency. Besides, considering the inherent problem of CEAs, we present a simulated-annealing based update(replacement) strat-egy. Secondly, we introduce a relaxation method based PSO called RelaxPSO, we transformed the original problem into a series of constrained optimizations via relax-ation. Comparative experimental results show that, our SACPP and RelaxPSO perform well on these problems.In addition, we applied SACPP and RelaxPSO to some applications, including con-strained optimization problems and robust control problems, the experiments demon-strate that our methods could find out the global optima, and possess higher execution efficiency in terms of function evaluations and CPU time.