Optimization based on nonlinear transformation in decision space

Abstract

When dealing with black box optimization problem, the nature of the problem cannot be completely mastered and the position where the optimal solution appears cannot be determined. A sufficient search of all feasible regions is the necessary way to obtain the global optimal solution. As a kind of method based on search with population, evolutionary computing has attracted much attention in the field of optimization. Compared with the traditional search method, the population is expected to expand the search area, but in many instances, the solutions of the evolutionary algorithms cannot explore wide area continuously and effectively. Specifically, after several iterations, the general optimizer focuses the solutions near a small region and output one promising solution. In the limited range, population lose the advantage of searching several regions meanwhile. In this article, a new framework called optimization based on nonlinear transformation in decision space (ONTD) is proposed, in which a problem population is generated by converting a given problem. And each converted problem (subproblem) has its own interesting area with high calculation weight on the decision space. The optimizers combining differential evolution operator and ONTD are instantiated for comparison. And an adaptive ONTD strategy (AONTD) is proposed to adjust high calculation region of each converted problem. Through dealing with the different converted problems at the same time, on the test and trap problems, several optima can be retained with the optimizers based on ONTD. And on the benchmark problems, the optimizers based on ONTD also have competitive performance.