A global optimization technique with an adaptive order of checking for constraints

A new approach to solving multimodal problems with nonconvex constraints is proposed. A specific feature of this approach, which does not rely on the penalty function method, is a separate consideration of every constraint. The sequential checking for constraints performed at every iteration point is stopped as soon as the first violation is discovered. In a modified algorithm proposed and investigated in this paper as applied to the one-dimensional case is that the order of checking for constraints is adaptively determined at each iteration step. This makes it possible to begin checking for constraints with the one that is most likely to be violated at the current point. Thus, the iteration step can be completed at a lower cost. Sufficient conditions for convergence of the method are formulated. The results obtained by comparing algorithms with a fixed and adaptive order of checking for constraints are presented. The comparison was carried out by applying both methods to compute hundreds of randomly generated multimodal test problems with nonconvex constraints.