Dynamic decomposition and hyper-distance based many-objective evolutionary algorithm

Nowadays many algorithms have appeared to solve many-objective optimization problems (MaOPs), yet the balance between convergence and diversity is still an open issue. In this paper, we propose a dynamic decomposition and hyper-distance based many-objective evolutionary algorithm named DHEA. On one hand, to maximize the diversity of the population, we use dynamic decomposition to decompose the whole population into multiple clusters. Specifically, first find pivot solutions according to the distribution of the population through the max–min-angle strategy, and then, assign solutions into different clusters according to their distances to pivot solutions. On the other hand, to select solutions from each cluster with balanced convergence and diversity, we propose hyper-distance based angle penalized distance for fitness assignment. Specifically, first compute the distance of solutions to the hyperplane and to the pivot solution to measure convergence and diversity, respectively, and then select the solution with the smallest fitness value. Hyper-distance, as convergence-related component, alleviates the bias towards problems with concave PFs. Besides, to promote convergence, the concept of knee points is introduced to mating selection. Through comparison with nine algorithms on 27 test problems, DHEA is validated to be effective and competitive to deal with MaOPs with different types of Pareto fronts and stable on different numbers of objectives.