Optimal Linear Crossover for Mitigating Negative Transfer in Evolutionary Multitasking

Evolutionary multitasking algorithms use information exchange among individuals in a population to solve multiple optimization problems simultaneously. Negative transfer is a critical factor that affects the performance of evolutionary multitasking algorithms. In this study, we propose an innovative approach to mitigate negative transfer in evolutionary multitasking algorithms. The proposed approach is grounded in rigorous theoretical analysis, which provides valuable theoretical insights into the design of an optimal linear crossover operator for mitigating negative transfer. By identifying interpretable conditions, we establish a solid theoretical foundation to prevent negative transfer in diverse scenarios. Building upon these findings, we theoretically derive a closed-form expression for the optimal crossover operator and propose practical design methods based on approximations. Furthermore, we integrate the proposed optimal crossover operator into a fundamental evolutionary multitasking algorithm framework. The resultant algorithm is comparable or superior to other state-of-the-art methods. Empirical validation through comprehensive experiments confirms the effectiveness of our theoretical findings.