Adaptive sparsity detection-based evolutionary algorithm for large-scale sparse multi-objective optimization problems

Large-scale sparse multi-objective optimization problems (LSSMOPs) widely exist in practical applications, which have large-scale decision variables and sparse Pareto optimal solutions. Existing algorithms have some shortcomings in dealing with LSSMOPs: (1) failing to make full use of the knowledge of the sparsity of the Pareto optimal solutions, leading to insufficient sparsity detection; (2) ignoring the connection between binary and real variables, leading to insufficient variables optimization. This paper proposes an adaptive sparsity detection-based evolutionary algorithm (ASD-MOEA) to address these issues, which is a two-stage algorithm. The first stage performs an adaptive sparsity detection strategy, which dynamically adjusts the probability of binary variables flipping and the fitness of decision variables according to the iteration ratio. Then, non-zero variables are mined based on fitness. The second stage performs a variable grouping-based optimization strategy, grouping decision variables according to their sparsity in the set of non-dominated solutions to reduce the search space, then performs genetic operations in the subspace. Finally, we compare ASD-MOEA with six mainstream algorithms. The results show that the proposed algorithm significantly outperforms the existing algorithms in dealing with LSSMOPs, and achieves a balance between sparsity maintenance and variable optimization.