Residual Learning Inspired Crossover Operator and Strategy Enhancements for Evolutionary Multitasking

TL;DR

Evolutionary multitasking suffers from limited modeling of high-dimensional variable interactions and rigid task transfer. The authors propose MFEA-RL, which couples a Very Deep Super-Resolution (VDSR) residual crossover that expands $1 \times D$ individuals to a high-dimensional $I_h \in \mathbb{R}^{D \times D}$, a ResNet-based dynamic skill-factor allocator, and a random-mapping crossover to mitigate negative transfer, all underpinned by Johnson-Lindenstrauss-based theory. This approach yields a novel residual crossover operator and adaptive task assignment, with empirical wins on CEC2017-MTSO and WCCI2020-MTSO benchmarks and strong performance on real-world SCP problems. The results demonstrate improved convergence and robustness in complex, high-dimensional EMT settings, offering a scalable pathway to practical multitasking optimization.

Abstract

In evolutionary multitasking, strategies such as crossover operators and skill factor assignment are critical for effective knowledge transfer. Existing improvements to crossover operators primarily focus on low-dimensional variable combinations, such as arithmetic crossover or partially mapped crossover, which are insufficient for modeling complex high-dimensional interactions.Moreover, static or semi-dynamic crossover strategies fail to adapt to the dynamic dependencies among tasks. In addition, current Multifactorial Evolutionary Algorithm frameworks often rely on fixed skill factor assignment strategies, lacking flexibility. To address these limitations, this paper proposes the Multifactorial Evolutionary Algorithm-Residual Learning (MFEA-RL) method based on residual learning. The method employs a Very Deep Super-Resolution (VDSR) model to generate high-dimensional residual representations of individuals, enhancing the modeling of complex relationships within dimensions. A ResNet-based mechanism dynamically assigns skill factors to improve task adaptability, while a random mapping mechanism efficiently performs crossover operations and mitigates the risk of negative transfer. Theoretical analysis and experimental results show that MFEA-RL outperforms state-of-the-art multitasking algorithms. It excels in both convergence and adaptability on standard evolutionary multitasking benchmarks, including CEC2017-MTSO and WCCI2020-MTSO. Additionally, its effectiveness is validated through a real-world application scenario.

Figures (4)

• Figure 1: Architecture of MFEA-RL with residual learning and random mapping
• Figure 2: The convergence trends of the average objective value of MFEA-RL, AT-MFEA, MFEA, MFEA-II, MTEA-SaO, MTES, BLKT-DE and MFEA-AKT on CEC17-MTSO
• Figure 3: Convergence curves of the average objective value of VDSR-Res, VDSR and Res for representative tasks
• Figure 4: Convergence curves of algorithms on SCP problems