Abstract
A number of decomposition-based algorithms have been proposed for many-objective problems using a set of uniformly distributed weight vectors in the literature. In those algorithms, a many-objective problem is decomposed into single-objective problems. Each single-objective problem is optimized in a cooperative manner with other single-objective problems. Their performance strongly depends on the Pareto front shape of a test problem. This is because weight vectors are generated using a triangular simplex lattice structure. It is easy for decomposition-based algorithms to obtain uniformly distributed solutions on triangular Pareto fronts. However, it is not easy for them to handle non-triangular Pareto fronts such as inverted-triangular and disconnected Pareto fronts. In our former study, we examined the performance of MOEA/D when the triangular simplex lattice structure was replaced with the inverted triangular structure for generating weight vectors. The use of those weight vectors deteriorated the performance of MOEA/D for almost all test problems including those with inverted triangular Pareto fronts. In this paper, we examine the use of the inverted triangular simplex lattice structure in two variants of MOEA/D (MOEA/D-DE and MOEA/D-STM) and other four decomposition-based algorithms (NSGA-III, θ-DEA, MOEA/DD, and Global WASF-GA). Their performance is reported for many-objective problems with triangular and inverted triangular Pareto fronts.
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Doi, K., Imada, R., Nojima, Y., Ishibuchi, H. (2017). Use of Inverted Triangular Weight Vectors in Decomposition-Based Many-Objective Algorithms. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_27
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DOI: https://doi.org/10.1007/978-3-319-68759-9_27
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