A Simple and Fast Hypervolume Indicator-Based Multiobjective Evolutionary Algorithm

Abstract

To find diversified solutions converging to true Pareto fronts (PFs), hypervolume (HV) indicator-based 
algorithms have been established as effective approaches in multiobjective evolutionary algorithms (MOEAs). 
However, the bottleneck of HV indicator-based MOEAs is the high time complexity for measuring the exact HV 
contributions of different solutions. To cope with this problem, in this paper, a simple and fast hypervolume 
indicator-based MOEA (FV-MOEA) is proposed to quickly update the exact HV contributions of different solutions. 
The core idea of FV-MOEA is that the HV contribution of a solution is only associated with partial solutions 
rather than the whole solution set. Thus, the time cost of FV-MOEA can be greatly reduced by deleting irrelevant 
solutions. Experimental studies on 44 benchmark multiobjective optimization problems with 2-5 objectives in 
platform jMetal demonstrate that FV-MOEA not only reports higher hypervolumes than the five classical MOEAs 
(nondominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm 2 (SPEA2), multiobjective 
evolutionary algorithm based on decomposition (MOEA/D), indicator-based evolutionary algorithm, and S-metric 
selection based evolutionary multiobjective optimization algorithm (SMS-EMOA)), but also obtains significant 
speedup compared to other HV indicator-based MOEAs.