A Study on Performance Evaluation Ability of a Modified Inverted Generational Distance Indicator

The inverted generational distance (IGD) has been frequently used as a performance indicator for many-objective problems where the use of the hypervolume is difficult. However, since IGD is not Pareto compliant, it is possible that misleading Pareto incompliant results are obtained. Recently, a simple modification of IGD was proposed by taking into account the Pareto dominance relation between a solution and a reference point when their distance is calculated. It was also shown that the modified indicator called IGD+ is weakly Pareto compliant. However, actual effects of the modification on performance comparison have not been examined. Moreover, IGD+ has not been compared with other distance-based weakly Pareto compliant indicators such as the additive epsilon indicator and the D1 indicator (i.e., IGD with the weighted achievement scalarizing function). In this paper, we examine the effect of the modification by comparing IGD+ with IGD for multiobjective and many-objective problems. In computational experiments, we generate a large number of ordered pairs of non-dominated solution sets where one is better than the other. Two solution sets in each pair are compared by the above-mentioned performance indicators. We examine whether each indicator can correctly say which solution set is better between them.