On the use of hypervolume for diversity measurement of Pareto front approximations

In multiobjective optimization, a good quality indicator is of great importance to the performance assessment of algorithms. This paper investigates the effectiveness of the widely-used hypervolume indicator, which is the only one found so far to strictly comply with the Pareto dominance. While hypervolume is of undisputed success to assess the quality of an approximation, it is sensitive to misleading cases, particularly for diversity assessment. To address this issue, this paper presents a modified hypervolume indicator based on linear projection for diversity evaluation. In addition to experimental studies to demonstrate the effectiveness of the proposed indicator, the indicator is introduced into the environmental selecction of an indicator-based multiobjective optimization evolutionary algorithm. Experiments show that the proposed indicator yields more evenly-distributed approximations than the original hypervolume indicator.