EFFECTIVE SOLVING OF MULTIMODAL OPTIMIZATION PROBLEMS

Abstract

In this work, we consider multimodal optimization problems. Such problems contain many local extrema. We can say that most practical problems are multimodal. In particular, discrete optimization problems with Boolean and integer variables can easily be transformed into multimodal problems with continuous variables. Multimodal optimization problems can be of small or large dimensions in which the number of variables to be determined is hundreds or thousands of variables. Libraries of test and applied problems have been created to test the effectiveness of new global optimization methods. The author suggests separating problems with unknown optimal solutions in these tests. Then the best method for solving multimodal optimization problems will be the one that will allow obtaining better solutions in most such problems. Currently, this criterion is satisfied only by the exact quadratic regularization method developed by the author. This is confirmed by significant computational experiments on existing tests and applied multimodal optimization problems.