Abstract
Hungarian Differential Evolution (HDE) is a Multi-Objective Evolutionary Algorithm that transforms its selection process into a Linear Assignment Problem (LAP). In a LAP, we want to assign n agents to n tasks, where assigning an agent to a task corresponds to a cost. Thus, the aim is to minimize the overall assignment cost. It has been shown that HDE is competitive with respect to state-of-the-art algorithms. However, in this work, we identify two drawbacks in its selection process: it sometimes selects duplicated solutions and occasionally prefers weakly-dominated solutions over non-dominated ones. In this work, we propose an algorithm that tries to fix these drawbacks using the hypervolume indicator. However, since the computation of the hypervolume indicator is expensive, we adopted an approximation that uses a polar coordinates transformation. The resulting algorithm is called “Multi-Objective Evolutionary Algorithm Based on the Linear Assignment Problem and the Hypervolume Approximation using Polar Coordinates (MOEA-LAPCO).” Our experimental results show that our proposed MOEA-LAPCO outperforms the original HDE, and it is competitive with state-of-the-art algorithms.
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Notes
- 1.
A solution \(\boldsymbol{x}\) is said to weakly dominate \(\boldsymbol{y}\) (denoted as \(\boldsymbol{x} \preceq \boldsymbol{y}\)) if \(f_i(\boldsymbol{x}) \le f_i(\boldsymbol{y})\) for all \(i=1,\dots ,k\).
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The first author acknowledges support from CINVESTAV-IPN and CONACyT to pursue graduate studies in computer science. The second author acknowledges support from CONACyT grant no. 1920.
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Valencia-Rodríguez, D.C., Coello Coello, C.A. (2022). Multi-Objective Evolutionary Algorithm Based on the Linear Assignment Problem and the Hypervolume Approximation Using Polar Coordinates (MOEA-LAPCO). In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_16
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