Solving the set-union knapsack problem by a novel hybrid Jaya algorithm

Abstract

The set-union knapsack problem (SUKP) is a variation of the 0–1 knapsack problem (KP) in which each item is a set of elements, each item has a nonnegative value, and each element has a nonnegative weight. The weight of one item is given by the total weight of the elements in the union of the items’ sets. The SUKP accommodates a number of real-life applications and is more complicated and computationally difficult than the 0–1 KP. In this paper, we propose a novel hybrid Jaya algorithm with double coding (DHJaya) to solve the SUKP. In the DHJaya, double coding is used to represent the individual, which includes the solutions for solving the SUKP by adopting a mapping function. The Jaya algorithm and differential evolution algorithm are combined to improve the exploration ability. To enhance the exploitation ability, the Cauchy mutation is performed on some individuals. Meanwhile, an improved repairing and optimization algorithm (MS-GROA) is proposed to repair the infeasible solutions and optimize the feasible solutions. We test the DHJaya using three sets of SUKP instances to demonstrate its efficiency, and the obtained results are compared with those in the previous study. Extensive experiments show a remarkable performance of the proposed approach.