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    This study analyzes the running time of decomposition-based multiobjective evolutionary algorithms (MOEAs). Crossover in MOEA/D significantly reduces running time and simplifies weight vector settings compared to mutation-only approaches.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Optimization Algorithms

    Background:

    • Decomposition-based multiobjective evolutionary algorithms (MOEAs) are widely used for multiobjective optimization problems (MOPs).
    • Theoretical understanding of these algorithms, particularly MOEA/D, remains limited despite practical success.

    Purpose of the Study:

    • To provide a theoretical running time analysis of a MOEA/D variant incorporating crossover (MOEA/D-C).
    • To compare the efficiency and parameter setting requirements of MOEA/D-C against a mutation-only variant (MOEA/D-M).

    Main Methods:

    • Running time analysis of MOEA/D-C on five pseudo-Boolean functions.
    • Theoretical comparison of expected running time upper bounds and weight vector decomposition needs between MOEA/D-C and MOEA/D-M.

    Main Results:

    • MOEA/D-C demonstrates lower expected running time upper bounds for covering Pareto fronts compared to MOEA/D-M.
    • MOEA/D-C requires simpler weight vector settings, while MOEA/D-M needs a complex set of optimally decomposed weight vectors.

    Conclusions:

    • Incorporating crossover into decomposition-based MOEAs enhances efficiency and simplifies parameter tuning.
    • The findings offer insights into the effectiveness of MOEA/D and related algorithms in computational experiments.