For this, we must ignore the others and solve a knapsack problem, and finally, we must somehow fit the solution to satisfy the constraints that are ignored.įor multiple cases of resource allocation problems that have some specific constraints, the problem can be solved in a way that is similar to the Knapsack problem.
Multiple knapsack problem crack#
One general approach to crack difficult problems is to identify the most restrictive constraint. The Knapsack problem is an instance of a Combinatorial Optimization problem. Keywords: knapsack problems setup matheuristic variable neighbourhood descent VND integer programming.Įuropean Journal of Industrial Engineering, 2020 Vol.14 No.5, pp.When given a set of items, where each item has a weight and a value, we need to determine a subset of items that are to be included in a collection in such a way that the total weight aggregates up to be lower than or equal to a given limit and the total value could be as big as possible. Computational experiments on randomly generated instances show the efficiency of our matheuristic in comparison to the direct use of a commercial solver. We consider local search techniques to assign classes to knapsacks and apply the IP to select the items in each knapsack. We then propose a matheuristic that combines variable neighbourhood descent (VND) with integer programming (IP). First, we provide mathematical formulations of GMKPS and MKPS and provide an upper bound expression for the knapsack problem. We refer to the particular case where items from the same class cannot be processed in more than one period as the multiple knapsack problem with setup (MKPS). GMKPS originates from industrial production problems where the items are divided into classes and processed in multiple periods.
We refer to it as the generalised multiple knapsack problem with setup (GMKPS). Title: Efficient matheuristic for the generalised multiple knapsack problem with setupĪuthors: Yassine Adouani Bassem Jarboui Malek MasmoudiĪddresses: Laboratory of Modeling and Optimization for Decisional, Industrial and Logistic Systems Laboratory, Faculty of Economics and Management Sciences, University of Sfax, Sfax, Tunisia ' Higher Colleges of Technology, Abu Dhabi, UAE ' Faculty of Sciences and Techniques, University of Lyon, University Jean Monnet Saint-Etienne, 42000 Saint-Etienne, FranceĪbstract: This paper introduces a new variant of the knapsack problem with setup (KPS).
Article: Efficient matheuristic for the generalised multiple knapsack problem with setup Journal: European Journal of Industrial Engineering (EJIE) 2020 Vol.14 No.5 pp.715 - 741 Abstract: This paper introduces a new variant of the knapsack problem with setup (KPS).
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