Causal Inference-Based Large-Scale Multiobjective Optimization

Abstract

Large-scale multiobjective optimization problems (LSMOPs), characterized by a substantial number of decision variables, pose significant challenges for many existing evolutionary algorithms. However, the search efficiency of these algorithms is not yet satisfactory. This is mainly because that the search efficiency of these algorithms may deteriorate dramatically since the search space increases exponentially with the number of decision variables. Having this in mind, we proposed a large-Scale multiobjective optimization framework named causal inference-based competitive swarm optimizer (CI-CSO). Specifically, a causal-information-(CI)-based operator is designed for competitive swarm optimizers. First, a causal inference technique named information geometric causal inference (IGCI) is introduced to adequately explore the CI between decision variables and fitness values. To further distinguish the positive or negative impacts of these critical variables on solution quality, a CI processing module is designed, facilitating targeted optimization. To enhance search efficiency, CI-based offspring generator are employed, leveraging the variance of causal effects to dynamically adjust the search step size and sampling range. To evaluate its performance, the proposed CI-based operator is embedded into two multiobjective evolutionary algorithms (MOEAs) (LSTPA and LMOCSO). To demonstrate the effectiveness of the proposed framework, experimental results are presented using the LSMOP test suite and five real-world problems, each involving up to 10 000 decision variables. In addition, six classic algorithms are included for comparison.