A two-stage evolutionary algorithm for uncertain constrained multi-objective problems with interval-valued objective

In real-world engineering applications, there exist numerous constrained multi-objective optimization problems (CMOPs) that exhibit uncertain characteristics.Among these CMOPs, problems involving interval uncertainty in the objective functions pose significant challenges in simultaneously achieving optimal interval performance and constraint satisfaction. To address these challenges, a novel two-stage evolutionary algorithm, termed TSICMOEA, is proposed to solve interval constrained multi-objective optimization problems (ICMOPs) with interval-valued objectives. In the first stage, the primary goal of evolution is to conduct a global search efficiently. To accomplish this, an enhanced convergence indicator and a two-level dominance ranking strategy are proposed. These improvements aim to increase environmental selection pressure and generate as many valuable elite individuals as possible for the subsequent stage. In the subsequent stage, an adaptive elite selection strategy is employed, consisting of two cooperative subprocesses. These subprocesses collaboratively accelerate the population's convergence toward the feasible region and improve the quality of feasible solutions. Compared to other representative algorithms on two distinct ICMOPs benchmark suits with interval-valued objectives, the proposed TS-ICMOEA demonstrates significantly superior results for balancing the feasibility, convergence, and diversity performance characteristics, especially in ICMOPs with high-dimensional objective.