Finding robust pareto-optimal solutions using geometric angle-based pruning algorithm

Abstract

Evolutionary multi-objective optimization algorithms have been developed to find a representative set of Pareto-optimal solutions in the past decades. However, researchers have pointed out that finding a representative set of Pareto-optimal solutions is not sufficient; the task of choosing a single preferred Pareto-optimal solution is also another important task which has received a widespread attention so far. In this paper, we propose an algorithm to help the decision maker (DM) choose the final preferred solution based on his/her preferred objectives. Our algorithm is called an adaptive angle based pruning algorithm with independent bias intensity tuning parameter (ADA-τ). The method begins by calculating the angle between a pair of solutions by using a simple arctangent function. The bias intensity parameter of each objective is introduced independently in order to approximate the portions of desirable solutions based on the DM's preferred objectives. We consider several benchmark problems including two and three-objective problems. The experimental results have shown that our pruning algorithm provides a robust sub-set of Pareto-optimal solutions for the benchmark problems. © 2014 Springer International Publishing Switzerland.