Exploring cluster-dependent isomorphism in multi-objective evolutionary optimization

In this paper, a Two-Round learning-based Algorithm for Continuous box-constrained multi-objective Evolutionary optimization (TRACE) under the decomposition framework is proposed, in which the isomorphism relationship between the clustered Pareto Front and Pareto solution set is explored and a new time-varying adaptive crossover operator is developed. The learning process involves two stages. In the first stage, the $K$-means is applied to cluster the population of objective vectors. By exploring the property of cluster-dependent isomorphism between the objective space and the decision space, a parent individual for each individual is selected from the corresponding clusters in the decision space. The time-varying adaptive crossover operator is then used together with the classical polynomial mutation operator to generate a new solution based on the selected parent individuals. As part of the environmental selection process, the $K$-means is applied again to the combination of parent and offspring individuals in the objective space to assist in the selection of suitable solutions for each decomposed subspace. TRACE is compared with 11 state-of-the-art multi-objective evolutionary algorithms on totally 43 difficult problems with different characteristics. Furthermore, TRACE is compared with three promising multi-objective evolutionary algorithms for community detection in attribute networks. Extensive experiments show that TRACE significantly outperforms the compared algorithms in most instances.