<p>A weighted optimization framework based on problem transformation is an effective method for solving large-scale multi-objective optimization problems (LSMOPs). The problem transformation approach searches an area that is close to the reference solutions by using transformation functions to ensure rapid population convergence. Clustering-based methods can help identify critical regions or representative sets of solutions in the solution space, and can be used to select reference solutions. Accordingly, a clustering-based weighted optimization algorithm is proposed in this paper to solve LSMOPs. First, a combination of hierarchical clustering and partitional clustering is used to select reference solutions from the current population. The clustering selection method makes the selected solutions more diverse, and the reference solutions are used to guide the search direction for performing weighted optimization. Second, a power value transformation method is designed during the problem transformation stage. The transformation can alter the method for mapping the decision variables and effectively reduce the original decision space. Finally, an adaptive method for allocating the number of fitness evaluations is proposed to reasonably distribute computing resources throughout the evolutionary process. The proposed algorithm is tested on two benchmark large-scale multi-objective optimization test problem suites, and seven competitive multi-objective optimization algorithms are compared with it. The experimental results show that the proposed algorithm has advantages over the state-of-the-art algorithms in terms of search performance and convergence speed.</p>

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A clustering-based weighted optimization algorithm for large-scale multi-objective optimization problems

  • Hao Wang,
  • Shuwei Zhu,
  • Wei Fang

摘要

A weighted optimization framework based on problem transformation is an effective method for solving large-scale multi-objective optimization problems (LSMOPs). The problem transformation approach searches an area that is close to the reference solutions by using transformation functions to ensure rapid population convergence. Clustering-based methods can help identify critical regions or representative sets of solutions in the solution space, and can be used to select reference solutions. Accordingly, a clustering-based weighted optimization algorithm is proposed in this paper to solve LSMOPs. First, a combination of hierarchical clustering and partitional clustering is used to select reference solutions from the current population. The clustering selection method makes the selected solutions more diverse, and the reference solutions are used to guide the search direction for performing weighted optimization. Second, a power value transformation method is designed during the problem transformation stage. The transformation can alter the method for mapping the decision variables and effectively reduce the original decision space. Finally, an adaptive method for allocating the number of fitness evaluations is proposed to reasonably distribute computing resources throughout the evolutionary process. The proposed algorithm is tested on two benchmark large-scale multi-objective optimization test problem suites, and seven competitive multi-objective optimization algorithms are compared with it. The experimental results show that the proposed algorithm has advantages over the state-of-the-art algorithms in terms of search performance and convergence speed.