Abstract
The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a popular algorithm for solving Multi-Objective Problems (MOPs). The main component of MOEA/D is to decompose a MOP into easier sub-problems using a set of weight vectors. The choice of the number of weight vectors significantly impacts the performance of MOEA/D. However, the right choice for this number varies, given different MOPs and search stages. We adaptively change the number of vectors by removing unnecessary vectors and adding new ones in empty areas of the objective space. Our MOEA/D variant uses the Consolidation Ratio to decide when to change the number of vectors and to decide where to add or remove these weighted vectors. We investigate the effects of this adaptive MOEA/D against MOEA/D with a poorly chosen set of vectors, a MOEA/D with fine-tuned vectors and MOEA/D with Adaptive Weight Adjustment on two commonly used benchmark functions. We analyse the algorithms in terms of hypervolume, IGD and entropy performance. Our results show that the proposed method is equivalent to MOEA/D with fine-tuned vectors and superior to MOEA/D with poorly defined vectors. Thus, our adaptive mechanism mitigates problems related to the choice of the number of weight vectors in MOEA/D, increasing the final performance of MOEA/D by filling empty areas of the objective space and avoiding premature stagnation of the search progress.
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Notes
- 1.
In the case of discontinuous PF case, there is no need to cover the discontinuity area.
- 2.
- 3.
For the HV calculation, we use the reference point set to (1 + 1/H,1 + 1/H) for two objective problems and (1 + 1/H, 1 + 1/H, 1 + 1/H) for three objective problems.
- 4.
We initialize the weight vectors using the Simplex-lattice Design (SLD) method, causing the number to slightly change between MOPs with 2 and 3 objectives.
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Lavinas, Y., Teru, A.M., Kobayashi, Y., Aranha, C. (2021). MOEA/D with Adaptative Number of Weight Vectors. In: Aranha, C., Martín-Vide, C., Vega-Rodríguez, M.A. (eds) Theory and Practice of Natural Computing. TPNC 2021. Lecture Notes in Computer Science(), vol 13082. Springer, Cham. https://doi.org/10.1007/978-3-030-90425-8_7
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