Theoretical analysis of dynamic selection of switching auxiliary objectives on XdivK problem

Abstract

Subject of Research. The paper deals with analysis of the EA+RL method inefficiency reasons on XdivK optimization problem with switching auxiliary objectives. It is proposed to modify the EA+RL method. The EA+RL method increases efficiency of an evolutionary algorithm by introducing auxiliary objectives. The XdivK problem is characterized by a large number of local optima. Switching objectives help to escape from local optima on some stages of optimization while being obstructive on the other stages. Method. To perform theoretical analysis of the EA+RL method and its proposed modification, the corresponding optimization process was modeled by Markov chains. The number of fitness function evaluations needed to reach the optimum was estimated based on the analysis of transition probabilities. Main Results. The EA+RL method and its proposed modification were theoretically analyzed on the XdivK problem with switching auxiliary objectives. It was proved that the proposed modification ignores obstructive objectives contrary to the EA+RL method. The lower and upper bounds on the running time of the proposed modification were obtained. Practical Relevance. The proposed modification increases the efficiency of EA+RL method, successfully used to solve NP-hard optimization problems, such as the test case generation problem.