Constrained multi-objective optimization based on Lasso double machine learning

Abstract

Constrained multi-objective optimization requires a delicate balance between objective improvement and constraint satisfaction throughout the search process. While existing stage-wise methods utilize infeasible solutions, they rely on rigid heuristic rules and fail to quantify the actual utility of these solutions. To address this limitation, we propose a novel approach leveraging double machine learning to dynamically assess the value of infeasible solutions. Specifically, we formulate a causal framework where the lagged infeasible-solution ratio serves as the treatment, and the subsequent fixed-reference online hypervolume improvement is the outcome. By employing historical-only time-block cross-fitting with Lasso regularization and double residualization, our method derives an orthogonal policy score that accurately estimates the causal effect of this treatment. This score is then converted into a bounded replacement ratio, stabilized by hypervolume feedback, and integrated into both decomposition- and dominance-based evolutionary algorithms. Extensive experiments on constrained multi-objective optimization benchmarks and synthetic temporal designs demonstrate that our approach achieves superior optimization performance. Furthermore, it yields calibrated score estimates and correct directional control, proving robust against temporal placebos and score noise.