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    A new many-objective evolutionary algorithm (MaOEA) uses Minkowski distance for better convergence estimation in complex optimization problems. This approach dynamically adjusts to Pareto front shapes, improving selection pressure and solution quality compared to existing methods.

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    Area of Science:

    • Optimization Algorithms
    • Computational Intelligence
    • Evolutionary Computation

    Background:

    • Traditional evolutionary algorithms (EAs) struggle with many-objective optimization problems (MaOPs) due to an exponential increase in nondominated solutions, reducing selection pressure.
    • Existing many-objective EAs (MaOEAs) often use Euclidean or Manhattan distances for convergence estimation, which are limited cases of Minkowski distance.
    • The varying shapes of Pareto fronts (PFs) in MaOPs necessitate a more flexible approach to convergence estimation.

    Purpose of the Study:

    • To propose a novel many-objective evolutionary algorithm (MaOEA) that effectively addresses the challenges of MaOPs.
    • To introduce a dynamic estimation of the Pareto front's concavity-convexity degree (P) for adaptive convergence estimation.
    • To enhance the selection process by incorporating both convergence and diversity metrics.

    Main Methods:

    • A Minkowski distance-based evolutionary algorithm is developed for solving MaOPs.
    • The algorithm dynamically estimates the order P of the Minkowski distance based on the approximate Pareto front's shape.
    • Convergence is estimated using the Minkowski distance of the determined order P, followed by selection based on convergence and diversity.

    Main Results:

    • The proposed algorithm demonstrates competitive performance against five state-of-the-art MaOEAs on benchmark MaOPs.
    • Modified versions of two compared algorithms, incorporating the P-estimation and Minkowski distance, showed improved effectiveness.
    • The dynamic estimation of P and the use of Minkowski distance enhance the algorithm's ability to handle diverse Pareto front shapes.

    Conclusions:

    • The proposed Minkowski distance-based EA is a competitive and effective approach for solving many-objective optimization problems.
    • Dynamically adapting the Minkowski distance order (P) improves convergence estimation and selection pressure in MaOEAs.
    • Integrating the proposed P-estimation method and Minkowski distance into existing algorithms enhances their performance on MaOPs.