Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems

In this paper an algorithm for pruning a set of non-dominated solutions is proposed. The algorithm is based on the crowding distance calculation used in the elitist non-dominated sorting genetic algorithm (NSGA-II). The time complexity class of the new algorithm is estimated and in most cases it is the same as for the original pruning algorithm. Numerical results also support this estimate. For used bi-objective test problems, the proposed pruning algorithm is demonstrated to provide better distribution compared to the original pruning algorithm of NSGA-II. However, with tri-objective test problems there is no improvement and this study reveals that crowding distance does not estimate crowdedness well in this case and presumably also in cases of more objectives.