This chapter introduces a new problem-solving approach within the framework of cooperative coevolution that incorporates the additional mechanism of meta-modelling. We first provide a general introduction to the conceptual problem-solving approach used in cooperative coevolution that employs a Divide-and-Conquer strategy to address high-dimensional optimization problems through decomposition into multiple low-dimensional subproblems as subcomponents that are then tackled separately. In the next section, we provide an analysis to highlight one major issue associated with such a cooperative coevolutionary problem solving for nonseparable high-dimensional optimization problems. This issue can be formulated as a dimensionality mismatch between the original problem and subproblems that makes it challenging to precisely evaluate the quality of a candidate solution to a subcomponent so that selection can operate on it correctly. Crucially, the analysis has identified a scope for evaluation and selection of these subcomponent candidate solutions through approximate ranks. As such in the next section, we propose the Self-Evaluation Evolution framework that employs meta-models as surrogate functions to provide such approximate rankings in searching a good solution to a subproblem. In essence, the framework turns the original, high-dimensional optimization problems into a computationally expensive problem that are more tractable. The following section presents our computational study to demonstrate the advantages of this framework in comparison with 4 representative algorithms as problem size is increased on a large scale global optimization benchmark (CEC’2010). We close the chapter with a discussion that highlights situations where the framework is not appropriate for use.

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High-Dimensional Optimization as Computationally Expensive Optimization

  • Xin Yao,
  • Siang Yew Chong

摘要

This chapter introduces a new problem-solving approach within the framework of cooperative coevolution that incorporates the additional mechanism of meta-modelling. We first provide a general introduction to the conceptual problem-solving approach used in cooperative coevolution that employs a Divide-and-Conquer strategy to address high-dimensional optimization problems through decomposition into multiple low-dimensional subproblems as subcomponents that are then tackled separately. In the next section, we provide an analysis to highlight one major issue associated with such a cooperative coevolutionary problem solving for nonseparable high-dimensional optimization problems. This issue can be formulated as a dimensionality mismatch between the original problem and subproblems that makes it challenging to precisely evaluate the quality of a candidate solution to a subcomponent so that selection can operate on it correctly. Crucially, the analysis has identified a scope for evaluation and selection of these subcomponent candidate solutions through approximate ranks. As such in the next section, we propose the Self-Evaluation Evolution framework that employs meta-models as surrogate functions to provide such approximate rankings in searching a good solution to a subproblem. In essence, the framework turns the original, high-dimensional optimization problems into a computationally expensive problem that are more tractable. The following section presents our computational study to demonstrate the advantages of this framework in comparison with 4 representative algorithms as problem size is increased on a large scale global optimization benchmark (CEC’2010). We close the chapter with a discussion that highlights situations where the framework is not appropriate for use.