multiple-constrained knapsack problem, multidimensional knapsack problem. It consists in selecting a subset of given objects (or items) in such a way that the total profit of the selected objects is maximized while a set of knapsack constraints are satisfied. As in the KP, the utility uij of the selected elements should be maximized formalized by the objective function U (1). The NP-hard 01 multidimensional knapsack problem is a generalisation of the 0-1 simple knapsack problem. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature. The knapsack problem is one of the most studied problems in combinatorial optimization. The Multiple-choice Multidimensional Knapsack Problem (MMKP) is a variant of the knapsack problem (KP). Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. For the multidimensional knapsack problem with a large number of items and knapsack constraints, a two-level formulation is presented to take advantage of the. In the Neurogenetic approach, we show that the Neural and Genetic iterations, when interleaved appropriately, can complement each other and provide better solutions than either the Neural or the Genetic approach alone. Multidimensional Knapsack problem (MKP) will be used as a benchmark. In the Genetic Algorithms approach we propose a new way of generating initial population. sign of efficient evolutionary algorithms for combinatorial optimization problems. Measures such as fitness distance correlation and autocorrelation are applied to examine the landscapes associated with the tested genetic encodings. Common mutation operators, such as bit-flip mutation, are employed to generate fitness landscapes. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. Five representations are investigated for the multidimensional knapsack problem. The goal of a Multidimensional Knapsack Problem (MKP) is to boost. In this study, we propose a Neural approach, a Genetic Algorithms approach and a Neurogenetic approach, which is a hybrid of the Neural and the Genetic Algorithms approach. Keyword: Multidimensional knapsack problem exact algorithms heuristic. As a result, various approximate solution approaches, such as the relaxation approaches, heuristic and metaheuristic approaches have been developed and applied effectively to this problem. The problem’s NP-Hard nature prevents the successful application of exact procedures such as branch and bound, implicit enumeration and dynamic programming for larger problems. The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences.
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