Resetting Weight Vectors in MOEAD for Multi objective Optimization Problems With Discontinuous Pareto Front
Abstract : When a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is applied to solve problems with discontinuous Pareto front (PF), a set of evenly distributed weight vectors may lead to many solutions assembling in boundaries of the discontinuous PF. To overcome this limitation, this article proposes a mechanism of resetting weight vectors (RWVs) for MOEA/D. When the RWV mechanism is triggered, a classic data clustering algorithm DBSCAN is used to categorize current solutions into several parts. A classic statistical method called principal component analysis (PCA) is used to determine the ideal number of solutions in each part of PF. Thereafter, PCA is used again for each part of PF separately and virtual targeted solutions are generated by linear interpolation methods. Then, the new weight vectors are reset according to the interrelationship between the optimal solutions and the weight vectors under the Tchebycheff decomposition framework. Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method. Numerical experiments show that the proposed MOEA/D-RWV can achieve good results for bi-objective and tri-objective optimization problems with discontinuous PF. In addition, the test on a recently proposed MaF benchmark suite demonstrates that MOEA/D-RWV also works for some problems with other complicated characteristics.
? In many existing studies, the weight vectors are predefined and distributed uniformly in a unit simplex.
? Then a weight vector deletion operation is used to remove existing unpromising weight vectors or/and weight vectors associated with the crowded solutions in the population.
? Adaptation of the weight vectors during the optimisation process provides a viable approach to enhance existing decomposition-based EMO.
? There may exist a big difference of distance between adjacent Pareto optimal solutions (obtained by adjacent weight vectors) in different parts of the Pareto front.
? It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization.
? The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions.
? MOEA/D decomposes the target MOP into a number of scalar optimization problems and then applies the EA to optimize these subproblems simultaneously.
? Dealing with these subproblems simultaneously will be a waste of computing efforts, as it contributes nothing to the performance of the algorithm.
• This study proposed a model of multi-objective optimization for reservoir operation (MORO) with the objectives of maximizing water diversion and power generation.
• In this study, MOEA/D-AWA was adopted to the MORO problem with the proposed operation model, and the monthly water level values of the reservoir were selected as the decision variables.
• Under certain constraints, the quality of the solutions is evaluated according to the proposed objective functions.
• The proposed reservoir operation model is effective and reasonable in theory, and can be used to improve the comprehensive benefits of the reservoir.
? The new weight vector initialization method can significantly improve the performance of MOEA/D in general.
? At first, the classical ZDT and DTLZ problems are investigated. Performances of MOEA/D-AWA on MOPs with complex PFs are studied afterwards.
? We can conclude from the above results that the weight vector initialization method in MOEA/D-AWA significantly improves the performance of MOEA/D on tri-objective MOPs with simple PF.
? The AWA strategy is designed to enhance the performance of MOEA/D on the MOPs with complex PFs.
? MOEA/D-AWA combines the new weight vector initialization method and the AWA strategy together, so the best performances in terms of both coverage and uniformity are achieved.
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