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yang xu
Last updated:
Tue, 03/09/2021 - 07:02
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In large-scale multi-objective optimization, as the decision space's dimensionality increases, evolutionary algorithms can easily fall into an optimal local state. Therefore, how to prevent the algorithm from falling into a local optimum and quickly converge to the Pareto front is a particularly challenging problem. In order to solve the problem, this paper proposes a grid-based fuzzy evolution large-scale multi-objective optimization framework, which divides the entire evolution process into two main stages: fuzzy evolution and precise evolution. In the first stage, many similar original solutions will be fuzzy into the same fuzzy solution. The purpose is to enhance the population's solutions so fuzzy evolution can prevent the algorithm from falling into the local optimum. The second stage aims to find a high-precision solution so that it is closer to the true Pareto front. This paper conducts experiments on various large-scale multi-objective problems with as many as 500 to 5000 decision variables. Experimental results show that in large-scale multi-objective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multi-objective optimization algorithms.

  • A fuzzy evolutionary sub-stages division method based on acceleration is proposed. This method divides the fuzzy evolution stage into multiple sub-stages, and the length of these sub-stages increases or decreases with a certain acceleration. In each sub-stage, the grid size is different, and the degree of blurring is also different. With the fuzzy evolution process's progress, the grid size is getting smaller and smaller, and the degree of blurring is getting lower and lower.
  • A membership function for fuzzy evolution is proposed. The algorithm as a whole is divided into two stages, namely the fuzzy evolution stage and the precise evolution stage. The fuzzy evolution stage includes multiple sub-stages, and each sub-stage blurs the individuals in the population according to different membership functions.
  • A meshing mechanism for fuzzy evolution is proposed. The grid division mechanism can ensure the distribution of the evolutionary population so that the individuals in the population are distributed as evenly as possible. The size of the grid is determined by the membership function, all individuals in the same grid will be fuzzified into one individual. After the population is fuzzified according to the grid, the individuals in the population have greater differences, so the offspring produced will have better diversity, which prevents the evolutionary algorithm from falling into the local optimum. The membership function can control the grid's size and adjust the search accuracy of the algorithm. As the number of iterations increases, the search accuracy of the algorithm becomes higher and higher.
  • In order to verify the effectiveness of the proposed GFE in solving MOPs, several representative MOEAs were embedded in the GFE and compared with the original algorithm on the multi-objective test suite DTLZ \cite{DTLZ}. Experimental results show that MOEAs embedded in the GFE were significantly better than the original algorithm in all test cases, and the possibility of using existing MOEAs to solve large-scale problems was realized. Furthermore, the competitive swarm optimizer (CSO) \cite{LMOCSO} was embedded in the GFE framework (GFECSO) and then compared with several state-of-the-art large-scale MOEAs on the large-scale multi-objective test suite LSMOP \cite{LSMOP}. Experimental results show that GFECSO was significantly better than other large-scale MOEAs in most test cases.

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