Adaptive Neighbor Multi-Objective Evolutionary Algorithm Based on Hypervolume Indicator

There are two key factors in designing multi-objective evolutionary algorithms (MOEAs). One is how to ensure the evolutionary procedure approaches to the Pareto optimal solutions set, and the other is how to obtain well distributed solutions set. A tree neighbor containing the relation which represents the close degree of individuals is defined. Along with the Pareto dominance relationship, a density estimation metric—neighbor tree density is proposed to assign the fitness. In order to save the computational cost, a novel algorithm to calculate the exclusive hypervolume indicator is proposed. It is enough to calculate once (similar methods normally need to calculate twice) when evaluating an individuals contribution to total hypervolume. Moreover, if the size of external population exceeds the predefined threshold, the individual which contributes least to the exclusive hypervolume indicator will be eliminated. Based on all of these, an adaptive neighbor multi-objective evolutionary algorithm based on Hypervolume indicator (ANMOEA/HI) is proposed. In order to verify the efficiency of our proposed algorithm, it is tested with other 3 state-of-the-art MOEAs on 7 test problems. Four different kinds of metrics are used to give a fair judgment on their performances. Experimental results demonstrate that the proposed ANMOEA/HI obtains good performance in both convergence and distribution.