Solving large knapsack problems with a genetic algorithm

This paper develops a new approach to finding solutions to the subset sum problem. The subset sum problem is an important NP-complete problem in computer science which has applications in operations research, cryptography, and bin packing. A genetic algorithm is developed which easily solves this problem. The genetic algorithm begins with a randomly generated population of solutions and breeds a new population using the best elements of the previous population. Each generation of solutions produces better solutions to the subset-sum problem than the previous generation. It is shown that this approach will efficiently produce solutions to large (10,000 elements or more) subset sum problems. Various parameters of the algorithm are varied in order to improve its performance.

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