Push and Pull Framework with Integrated Evolutionary Learning to Solve Expensive Constrained Multi-Objective Optimization Problems

Expensive constrained multi-objective optimization problems (ECMOPs) are widely encountered in practical applications, where the evaluation of objective functions and constraints typically involve high computational costs, requiring extensive time-consuming or expensive numerical simulations or physical experiments. To effectively address such problems, this study integrates the Push and Pull Search (PPS) framework with surrogate-assisted learning-based optimization and proposes a Learning-Evolution integrated PPS framework (LE-PPS) to solve ECMOPs. Specifically, in the Push stage, constraints are ignored, and surrogate models are constructed for the objectives. Then, a neural network is trained to learn the mapping between arbitrary weight vectors in the objective space and their corresponding optimal solutions using the surrogate models, enabling rapid prediction of optimal solutions for diverse objective preferences. In the pull stage, a surrogate-assisted evolutionary algorithm is integrated with learning-based optimization, accelerating the convergence performance of the algorithm and avoiding local optima. To validate the effectiveness of the proposed LE-PPS, comparative experiments are conducted against six state-of-the-art algorithms on a set of benchmarking problems. The experimental results demonstrate that the LE-PPS algorithm achieves significant advantages in both convergence and diversity.