Sparse Large-Scale Multiobjective Optimization by Identifying Nonzero Decision Variables

Sparse large-scale evolutionary multiobjective optimization has garnered substantial interest over the past years due to its significant practical implications. These optimization problems are characterized by a predominance of zero-valued decision variables in the Pareto optimal solutions. Most existing algorithms focus on exploiting the sparsity of solutions by starting with initializing all decision variables with a nonzero value. Opposite to the existing approaches, we propose to initialize all decision variables to zero, then progressively identify and optimize the nonzero ones. The proposed framework consists of two stages. In the first stage of evolutionary optimization, a clustering method is applied at a predefined period of generations to identify nonzero decision variables according to the statistics of each variable's current and historical values. Once a new nonzero decision variable is identified, it is randomly initialized within one of the two intervals, one defined by its lower quartile and lower bound, and the other by its upper quartile and upper bound. In the second stage, the clustering method is also periodically employed to distinguish between zero and nonzero decision variables. Different to the first stage, the zero decision variables will be set to zero straight, and the nonzero decision variables will be mutated at a higher probability. The performance of the proposed framework is empirically examined against state-of-the-art evolutionary algorithms on both sparse and nonsparse benchmarks and real-world problems, demonstrating its superior performance on different classes of problems.