Selective Pressure through Differential Evolution and Decomposition in Multi-Objective Simulated Annealing

Abstract

In the real world, optimization problems have multiple objectives that usually are in conflict. Traditionally the Pareto-based approach has been applied to Multi-Objective Optimization Problems (MOPs). But this strategy has a limitation: The increment in the number of objectives produces issues. Such as the deterioration of the searchability of the algorithm. It reduces the selective pressure on the Pareto Front (PF). To address this problem, we propose an algorithm called MOSA/D. MOSA/D is a Multi-Objective Simulated Annealing (MOSA) strategy based on Decomposition (D) and Differential Evolution (DE). Decomposition divides a MOP into sub-problems that can be optimized almost in a classical sense, like single-optimization problems. With this idea, in MOSA/D, each sub-problem is annealed to find its optimal solution. During this annealing process, Differential Evolution produces candidate solutions to be evaluated by aggregation and probability functions. Simulated Annealing adds exploration and exploitation to each sub-problem while decomposition strategy and differential evolution operators reduce the lack of selective pressure toward the PF. MOSA/D is compared to MOEA/D to prove the performance of the algorithm. The experimental design used the DTLZ benchmark. In particular, the problems DTLZ1, DTLZ2, and DTLZ3 with five objectives. Experimental results show that MOSA/D outperforms or performs similarly to MOEA/D. These results are in terms of the mean and standard deviation from Hypervolume (HV) and Inverted Generational Distance (IGD).