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arXiv · 1903.03494

Genetic Algorithm for a class of Knapsack Problems

Shalin Shah
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Abstract

The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly. There are also the core branch and bound algorithms that can solve large randomly generated instances in a very short amount of time. However, as the correlation between the variables is increased, the difficulty of the problem increases. Recently a new class of knapsack problems was introduced by D. Pisinger called the spanner knapsack instances. These instances are unsolvable by the core branch and bound instances; and as the size of the coefficients and the capacity constraint increase, the spanner instances are unsolvable even by dynamic programming based algorithms. In this paper, a genetic algorithm is presented for spanner knapsack instances. Results show that the algorithm is capable of delivering optimum solutions within a reasonable amount of computational duration.

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Shalin Shah. 2019-02-15. Genetic Algorithm for a class of Knapsack Problems. https://arxiv.org/abs/1903.03494

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