A two-stage evolutionary algorithm for large-scale sparse multiobjective optimization problems

There is evidence that many real-world applications can be characterized as sparse multiobjective problems (SMOPs), where most variables of their Pareto optimal solutions are zero. Existing multiobjective evolutionary algorithms (MOEAs) have shown their competitiveness on conventional SMOPs. However, they may encounter difficulties when tackling large-scale SMOPs (LSMOPs). This paper thereby proposes a two-stage MOEA tailored to LSMOPs, named TS-SparseEA. TS-SparseEA integrates the prior information into the evolution and enables the population to spread over the Pareto front by two stages. In the first stage, TS-SparseEA adopts a new binary weight optimization framework, transforming the original large-scale optimization problem into a low-dimensional one via a set of low-dimensional binary weights. In the second stage, TS-SparseEA employs an improved evolutionary algorithm, including a hybrid encoding and a specialized matching strategy, where each solution is reproduced by a conditional combination between two types of variables. To summarize, the proposed binary weight optimization can better address large-scale sparse variables by generating a high-quality initial population, whereas the new hybrid encoding can facilitate the offspring evolution. Extensive experiments have verified the effectiveness of TS-SparseEA on LSMOPs, by comparing it with several state-of-the-art MOEAs on both benchmark problems and real-world applications.