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.
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Notes
- 1.
In practice, this requires isolating fronts from each environment before computing hypervolumes, since the reference point of a given environment may intersect with the next environment.
- 2.
One could argue that an application may require a custom importance distribution for the different stages of the run. This can be achieved through the weighted hypervolume measure, as proposed in [17].
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Oliveira, S., Wanner, E.F., de Souza, S.R., Bezerra, L.C.T., Stützle, T. (2019). The Hypervolume Indicator as a Performance Measure in Dynamic Optimization. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_26
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