The Hypervolume Indicator as a Performance Measure in Dynamic Optimization

Sabrina M. Oliveira, Elizabeth F. Wanner, Sérgio Ricardo de Souza, Leonardo C. T. Bezerra, Thomas Stützle

Abstract: In many real world problems the quality of solutions needs to be evaluated at least according to a bi-objective non-dominated front, where the goal is to optimize solution quality using as little computational resources as possible. This is even more important in the context of dynamic optimization, where quickly addressing problem changes is critical. In this work, we relate approaches for the performance assessment of dynamic optimization algorithms to the existing literature on bi-objective optimization. In particular, we introduce and investigate the use of the hypervolume indicator to compare the performance of algorithms applied to dynamic optimization problems. As a case study, we compare variants of a state-of-the-art dynamic ant colony algorithm on the traveling salesman problem with dynamic demands (DDTSP). Results demonstrate that our proposed approach accurately measures the desirable characteristics one expects from a dynamic optimizer and provides more insights than existing alternatives.