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Efficient nonlinear correlation detection for decomposed search in evolutionary multi-objective optimization

The mapping relation between decision variables and objective functions is complicated in multi-objective optimization problems. Dimension reduction-based memetic optimization strategy was proposed to decompose a multi-objective optimization problem into several easier subproblems in decision subspaces by detecting the correlation between decision variables and objective functions. In this work, the process of optimizing the original problem by separately searching the decision space of the subproblems is termed decomposed search. We embed the decomposed search strategy in existing multi-objective evolutionary algorithms to improve their performance. However, it is highly time-consuming to detect the mapping relation and select solutions for decomposed search. To improve the computational efficiency of the strategy, we adopt nonlinear correlation information entropy to measure the correlation between the decision variables and objective functions and suggest a probabilistic similarity measurement to select solutions for the decomposed search, which is shown to be effective by experimental results. Finally, the correlation detection and solution selection strategies proposed in this paper are embedded in both Pareto- and non-Pareto-based multi-objective evolutionary algorithms to compare them with existing ones. Our experimental results demonstrate that the proposed strategies have significantly improved the computational efficiency at the expense of slightly degraded performance.