Weighted quantum genetic algorithm for one-dimensional bin packing problem

Genetic algorithms (GA) are one of the efficient methods for various NP-hard combinatorial optimization problems. And previous research has also proposed hybrid genetic algorithms (HGA) that combine first-fit decreasing (FFD) approximate solutions with GAs. However, as the advantages of quantum genetic algorithm (QGA) over GA have been demonstrated, several researchers have attempted to solve optimization problems using QGA. In this paper, we have proposed a new quantum approach to solve a bin packing problem (BPP), a typical NP-hard problem, using a weighted quantum genetic algorithm (WQGA), and experimentally verify that the BP problem based on a WQGA is superior to optimization method based on GA and HGA. Numerical experiments are designed to prove the efficiency of the WQGA. Our results show that the WQGA is superior to GA and HGA.