Meta-Learning-Assisted Constraint Relaxation for Constrained Black-Box Optimization

Abstract

Constraint handling is central to constrained black-box optimization (BBO), where objective improvement and feasibility restoration often provide conflicting search signals. Existing $\epsilon$-relaxation methods are simple and effective, but their relaxation schedules are usually fixed or manually designed for a limited range of problems. To address this limitation, this letter proposes MeCO, a meta-learning-assisted optimizer that learns an adaptive $\epsilon$-relaxation policy for constrained BBO. MeCO couples a SHADE optimizer with a Double Deep Q-Network controller. At each optimization step, the controller observes compact population and constraint features and selects a scalar action, which is decoded into a relaxation vector for the candidate comparison rule. The policy is trained across constrained BBO instances and then deployed on held-out problems without problem-specific tuning. Experiments on the CEC2017 constrained benchmark, 16 UAV path-planning tasks and eight real-world engineering problems provide evidence that MeCO transfers across held-out benchmark functions, higher dimensions, and an application-domain setting. Ablation and behavior analyses further clarify the roles of constraint-related state features, action scaling, reward shaping, and meta-training.