Hidden Preference-based Multi-objective Evolutionary Algorithm Based on Chebyshev Distance

Abstract

As an important branch of multi-objective optimization,preference-based multi-objective evolutionary algorithms have been widely used in scientific researches and engineering practices,which have important research significance.In order to obtain the extreme solutions and the knee solution with the most compromised performance over each optimization objective in multi-objective optimization problems,a definition of knee solution based on Chebyshev distance and its geometric interpretation is presented.Based on the definition,a multi-objective evolutionary algorithm HP-NSGA-II aiming to search for the extreme solutions and the knee solution is proposed.The regional dynamic updating strategy of the proposed algorithm updates the target regions dynamically in each iteration,and finally converges to the target regions.The strategy of maintaining the balance between regions ensures the balance of the number of individuals in each region,so that the individuals could be distributed evenly in each region.Based on widely used test functions,sufficient experimental verification is carried out,and the experimental results indicate that HP-NSGA-II algorithm can achieve better performance in terms of convergence,regional balance and regional controllability in two-dimensional and three-dimensional test problems,and can accurately obtain the extreme solutions and knee solution.

Keywords

• evolutionary algorithm|multi-objective optimization|preference|chebyshev distance|knee solution|extreme solution