GPU-Accelerated Tensorized Flexible Differential Evolution for Large-Scale Constrained Multi-Objective Optimization

Large-scale constrained multi-objective optimization problems (LCMOPs) pose significant challenges due to the curse of dimensionality, complex constraint landscapes, and high computational overhead. In time-sensitive scenarios, existing large-scale constrained multi-objective evolutionary algorithms (LCMOEAs) often incur high computational costs and therefore struggle to meet efficiency requirements. This paper proposes a GPU-accelerated tensorized flexible differential evolution algorithm (TFDEMO) for LCMOPs. To address the curse of dimensionality and complex constraint landscapes in LCMOPs while maintaining GPU-level parallel efficiency, a tensorized flexible differential evolution operator (FlexDE) is developed. It utilizes a Bernoulli masking mechanism to switch between guided and random mutation modes in parallel on the GPU. The guidance probability is adaptively adjusted based on historical performance and the evolutionary state. Furthermore, a dual-population collaborative neighborhood selection mechanism is designed. For the main population, a Boolean mask tensor method is proposed, which constructs four Boolean mask tensors in parallel to encode feasibility states and dominance relations across all subproblems and their neighborhoods, and aggregates them via bitwise operations to produce the dominance tensor in a single pass. The auxiliary population performs constraint-ignoring neighborhood selection and shares its offspring with the main population to assist the main population in crossing large infeasible regions. The experimental results on the LIRCMOP and ZXH_CF benchmark suites with decision variable dimensions ranging from 100 to 800 demonstrate that TFDEMO achieves the best overall performance among the compared algorithms under both fixed-time and fixed function-evaluation settings. Additionally, a portfolio rebalancing problem with three objectives, five constraints, and scalable dimensions is designed to evaluate the performance of the proposed algorithm in time-sensitive application scenarios.