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.
Highlights
Knapsack problem is a well known discrete combinatorial optimization problem [1], which has numerous applications in resource allocation [2], decision support [3], project selection [4]
In this paper, a binary version of multi-scale quantum harmonic oscillator algorithm (BMQHOA) with genetic operator is proposed for solving KP01
The key point of the population based binary multi-scale quantum harmonic oscillator algorithm (BMQHOA) is that by defining the number of different bits between solutions as the distance of solutions in binary search space, the continuous search space is mapped into binary search space
Summary
Knapsack problem is a well known discrete combinatorial optimization problem [1], which has numerous applications in resource allocation [2], decision support [3], project selection [4]. Y. Huang et al.: BMQHOA for 0-1 Knapsack Problem With Genetic Operator the earliest and popular metaheuristic optimization algorithm. These three phases are the three nested loops of conventional MQHOA In this step, the algorithm generates new solutions based on current sampling points. When the difference of adjacent variances is less than the current scale, it is believed that sampling points are in a stable state at the current energy level This step is the basic operation of MQHOA and occupies most of the computation time of MQHOA. The current worst sampling point is eliminated, and the newly generated sampling point introduces new information into the current system This step makes the diversity of sampling areas increase, and is consistent with the physical model of MQHOA.
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