Abstract
This research describes three novel heuristic-based approaches for solving the 0/1 knapsack problem. The knapsack problem, in its many variants, arises in many practical scenarios such as the selection of investment projects and budget control. As an NP-hard problem, it is not always possible to compute the optimal solution by using exact methods and, for this reason, the problem is usually solved by using heuristic-based strategies. In this document, we use information of the distributions of weight and profit of the items in the knapsack instances to design and implement new heuristic-based methods that solve those instances. The solution model proposed in this work is two-fold: the first part focuses on the generation of two new heuristics, while the second explores the combination of solving methods through a hyper-heuristic approach. The heuristics proposed, as well as the hyper-heuristic model, were tested on a heterogeneous set of knapsack problem instances and compared against four heuristics taken from the literature. One of the proposed heuristics proved to be highly competent with respect to heuristics available in the literature. By using the hyper-heuristic, a solver that dynamically selects heuristics based on the problem features, we improved the results obtained by the new heuristics proposed and, achieved the best results among all the methods tested in this investigation.
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Notes
- 1.
As the reader may have already noticed, GWR requires to know the optimal solution for the instances used for testing the methods. Given the sizes of the instances studied in this work, the optimal solution was found through dynamic programming. Unfortunately, this metric might not be useful for other instances, as for some of them it could be unfeasible to obtain the optimal solution.
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This research was supported in part by CONACyT Basic Science Projects under grant 241461 and ITESM Research Group with Strategic Focus in intelligent Systems.
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Gómez-Herrera, F., Ramirez-Valenzuela, R.A., Ortiz-Bayliss, J.C., Amaya, I., Terashima-Marín, H. (2018). A Quartile-Based Hyper-heuristic for Solving the 0/1 Knapsack Problem. In: Castro, F., Miranda-Jiménez, S., González-Mendoza, M. (eds) Advances in Soft Computing. MICAI 2017. Lecture Notes in Computer Science(), vol 10632. Springer, Cham. https://doi.org/10.1007/978-3-030-02837-4_10
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