A Fast Clustering Based Evolutionary Algorithm for Super-Large-Scale Sparse Multi-Objective Optimization

During the last three decades, evolutionary algorithms (EAs) have shown superiority in solving complex optimization problems, especially those with multiple objectives and non-differentiable landscapes. However, due to the stochastic search strategies, the performance of most EAs deteriorates drastically when handling a large number of decision variables. To tackle the curse of dimensionality, this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions. The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution, and provides a fast clustering method to highly reduce the dimensionality of the search space. More importantly, all the operations related to the decision variables only contain several matrix calculations, which can be directly accelerated by GPUs. While existing EAs are capable of handling fewer than 10 000 real variables, the proposed algorithm is verified to be effective in handling 1 000 000 real variables. Furthermore, since the proposed algorithm handles the large number of variables via accelerated matrix calculations, its runtime can be reduced to less than 10% of the runtime of existing EAs.