![]() In this article a reformulation of the MMKP as a set partitioning problem is proposed to allow for new insights into modelling the MMKP. The MMKP basically consists of finding a subset of objects that maximizes the total profit while observing some capacity restrictions. In this regard, an exact model that is able to provide high-quality feasible solutions for solving it or being partially included in algorithmic schemes is desirable. The Multiple-choice Multidimensional Knapsack Problem (MMKP) is a well-known ?-hard combinatorial optimization problem that has received a lot of attention from the research community as it can be easily translated to several real-world problems arising in areas such as allocating resources, reliability engineering, cognitive radio networks, cloud computing, etc. The results show that the approach outperforms other state-of-the-art methods described so far, providing the best known solution for a significant number of benchmark instances.Ī set partitioning reformulation for the multiple-choice multidimensional knapsack problem An extensive set of computational experiments is reported for benchmark instances from the literature and for a large set of hard instances generated randomly. A new strategy for defining the reduced problems is explored, together with a new family of cuts and a reformulation procedure that is used at each iteration to improve the performance of the heuristic. The solutions of these problems are used to update the global lower and upper bounds for the optimal solution value. The approach is based on the resolution of linear programming relaxations of the problem and reduced problems that are obtained by fixing some variables of the problem. A new hybrid heuristic is proposed that embeds several new procedures for this problem. Many real applications lead to very large scale multiple choice multidimensional knapsack problems that can hardly be addressed using exact algorithms. However, the multiple choice multidimensional knapsack problem appears to be more difficult to solve in part because of its choice constraints. The problem is a variant of the multidimensional knapsack problem where items are divided into classes, and exactly one item per class has to be chosen. In this article, a new solution approach for the multiple choice multidimensional knapsack problem is described. Mansi, Raïd Alves, Cláudio Valério de Carvalho, J. A hybrid heuristic for the multiple choice multidimensional knapsack problem
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