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A Memetic Algorithm Based on Probability Learning for Solving the Multidimensional Knapsack Problem.

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    This study introduces a novel memetic algorithm with probability learning (MA/PL) to solve the multidimensional knapsack problem (MKP). The new approach effectively utilizes problem-specific heuristics and probability distributions, demonstrating strong performance on benchmark instances.

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    Area of Science:

    • Operations Research
    • Computer Science
    • Artificial Intelligence

    Background:

    • The multidimensional knapsack problem (MKP) is a significant combinatorial optimization challenge with broad practical applications.
    • Existing methods for MKP often require complex heuristics or lack efficient ways to leverage problem-specific knowledge.

    Purpose of the Study:

    • To propose a novel memetic algorithm based on probability learning (MA/PL) for effectively solving the multidimensional knapsack problem (MKP).
    • To introduce problem-dependent heuristics and a new MA/PL framework that incorporates item dependencies.

    Main Methods:

    • Development of two logarithmic utility functions (LUFs) to guide repair and local search operators, considering item profit and weight.
    • Introduction of a novel MA/PL framework utilizing marginal probability distributions (MPD) and joint probability distributions (JPD) for MKP.
    • Integration of learning rules inspired by competitive learning and binary Markov chains for MPD and JPD.

    Main Results:

    • The proposed MA/PL algorithm demonstrated effectiveness in solving 179 benchmark MKP instances.
    • Experimental results confirmed the practical value and efficiency of the MA/PL approach on a real-life case study.
    • The integration of LUFs and probability distributions significantly improved the algorithm's performance.

    Conclusions:

    • The developed MA/PL algorithm offers a powerful and effective solution for the multidimensional knapsack problem.
    • The novel framework successfully extracts and utilizes problem-specific knowledge, outperforming existing methods.
    • This research contributes a valuable tool for addressing complex optimization problems in various domains.