A quartile-based hyper-heuristic for solving the 0/1 knapsack problem

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.