A Binary Multi-Scale Quantum Harmonic Oscillator Algorithm for 0–1 Knapsack Problem With Genetic Operator

Abstract

The 0-1 knapsack problem is a typical discrete combinatorial optimization problem with numerous applications. In this paper, a binary multi-scale quantum harmonic oscillator algorithm (BMQHOA) with genetic operator is proposed for solving 0-1 knapsack problem. The framework of BMQHOA is consisted of three nested phases including energy level stablization, energy level decline and scale adjustment. In BMQHOA, the number of different bits between solutions is defined as the distance between solutions to map the continuous search space into the discrete search space. Repair operator with greedy strategy is adopted in BMQHOA to guarantee the knapsack capacity constraint. The current best solution is used to perform a random mutation with the origin solutions, making solutions evolve towards the current optimal solution. The performance of BMQHOA is evaluated on two low-dimensional and three high-dimensional KP01 data sets, and computational results are compared with several state-of-art 0-1 knapsack algorithms. Experimental results demonstrate that the proposed BMQHOA can get the best solutions of most knapsack data sets, and performs well on convergence and stability.

Keywords

• Evolutionary computation
• knapsack problem
• binary multi-scale quantum harmonic oscillator algorithm
• genetic operator