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    This study introduces MFEA-DGD, a novel evolutionary multitasking algorithm that guarantees population convergence and explains knowledge transfer benefits. It outperforms existing methods in speed and solution quality for complex optimization problems.

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    Area of Science:

    • Computational Intelligence
    • Optimization Algorithms
    • Evolutionary Computation

    Background:

    • Multifactorial Evolutionary Algorithm (MFEA) is a popular Evolutionary Multitasking (EMT) approach.
    • MFEA enhances efficiency and solution quality through knowledge transfer but lacks theoretical convergence guarantees and explanations for performance gains.

    Purpose of the Study:

    • To propose a novel MFEA, MFEA-DGD, based on Diffusion Gradient Descent (DGD).
    • To provide theoretical convergence proofs for DGD in multitask scenarios.
    • To explain how knowledge transfer aids in escaping local optima.

    Main Methods:

    • Developed MFEA-DGD integrating DGD principles.
    • Proved DGD convergence for similar tasks, highlighting the role of local convexity in knowledge transfer.
    • Designed complementary crossover and mutation operators for MFEA-DGD.
    • Introduced a hyper-rectangular search strategy for enhanced exploration.

    Main Results:

    • MFEA-DGD demonstrates guaranteed population convergence, akin to DGD.
    • Theoretical analysis explains the performance benefits of knowledge transfer.
    • Experimental results show MFEA-DGD converges faster and achieves competitive solutions compared to state-of-the-art EMT algorithms.
    • The study links experimental outcomes to task convexity.

    Conclusions:

    • MFEA-DGD offers a theoretically grounded and empirically validated approach to Evolutionary Multitasking.
    • The algorithm ensures convergence and provides explainable knowledge transfer mechanisms.
    • MFEA-DGD represents a significant advancement in efficient and effective multitask optimization.