Neural, Genetic, And Neurogenetic Approaches For Solving The 0-1 Multidimensional Knapsack Problem

Abstract

The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences. 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. 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. 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. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. In the Genetic Algorithms approach we propose a new way of generating initial population. 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. Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature.