A genetic algorithm combined with mathematical programming to solve generalised quadratic multiple knapsack problem

Yassine Adouani

International Journal of Mathematics in Operational Research, 2025, vol. 32, issue 2, 199-213

Abstract: In this paper, the generalised quadratic multiple knapsack problem (GQMKP) is tackled with an efficient hybrid approach, called GA&IP, which combines a binary genetic algorithm (GA) with integer programming (IP) to solve the GQMKP problem. In the GA&IP approach, a linearisation technique is used to transform the GQMKP into a linear problem called LGQMKP. After that, the LGQMKP is transformed into several dependent classical knapsack problems using a GA. Finally, an IP algorithm is applied to optimally solve each knapsack problem. The effectiveness of the GA&IP approach is demonstrated through experimentation on 96 diverse benchmark instances that are commonly used in the field. Experimental results show the effectiveness of the proposed GA&IP in solving the GQMKP problem and the hybridisation with integer programming can enhance the genetic algorithm.

Keywords: generalised quadratic knapsack problem; genetic algorithm; integer programming. (search for similar items in EconPapers)
Date: 2025
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