An improved group theory-based optimization algorithm for discounted 0-1 knapsack problem

Abstract

Discounted 0-1 knapsack problem (D0-1KP) has been proved to be NP-hard, thus a lot of researches focus on designing non-deterministic algorithms to solve it. Group theory-based optimization algorithm (GTOA), as a recently proposed evolutionary algorithm (EA), can provide satisfactory results to D0-1KP. GTOA introduces important theories of algebra, i.e., group theory, to describe combinatorial optimization problems, and applies the classic operations in group theory to design operators for EA. In order to generate a better solution according to a set of existing solutions during each evolutionary iteration, an important operator called random linear combination operator (RLCO) is designed. However, the practical meaning of applying the operations in group theory is hard to explain, and the proposed RLCO is lack of interpretability, causing difficulties in analyzing and improving the algorithm. In this paper, to improve the interpretability and further enhance the performance, we propose a new operator named random xor operator (RXO), and interpret it from the view point of bitwise operation. By replacing RLCO with RXO, a new GTOA algorithm is realized for D0-1KP. Experimental results demonstrate that it can provide very competitive performance.