Abstract
Quantum-inspired genetic algorithm (QGA) is applied to simulated annealing (SA) to develop a class of quantum-inspired simulated annealing genetic algorithm (QSAGA) for combinatorial optimization. With the condition of preserving QGA advantages, QSAGA takes advantage of the SA algorithm so as to avoid premature convergence. To demonstrate its effectiveness and applicability, experiments are carried out on the knapsack problem. The results show that QSAGA performs well, without premature convergence as compared to QGA.
Introduction
Quantum computing is based on the concepts of qubits and superposition of states of quantum mechanics. So far, many efforts on quantum computing have progressed actively due to its superiority to the traditional optimization method on various specialized problems. Recently, some QGA can represent a linear superposition of solutions due to its probabilistic representation. However, the performance of QGA is easy to be trapped in local optimal so as to be of premature convergence. This paper proposes a novel QSAGA evolutionary algorithm. With the condition of preserving QGA advantages, QSAGA takes advantage of SA so as to avoid premature convergence.
The Description of QSAGA
Like the QGA, QSAGA is also characterized by the representation of the individual, the evaluation function, and the population dynamics. Initially, QSAGA can represent diverse individuals probabilistically. As the probability of each Q-bit approaches either 1 or 0 by the Q-gate, the Q-bit individual converges to a single state and the diversity property disappears gradually.
Experiment
To demonstrate its effectiveness and applicability, experiments are carried out on the knapsack problem. The results show that QSAGA performs better than QGA and GA in terms of the convergence rate and final results. Initially, QSAGA shows a slower convergence rate than QGA, but the QSAGA final results are better than QGA and GA in 1000 generations. The tendency of the convergence rate can be shown clearly in the results of the mean of average profits of population. In the beginning, convergence rates of all the algorithms increase. But GA maintains a nearly constant profit due to its premature convergence, while QGA approaches towards the neighborhood of global optimal with a constant convergence rate. Especially, QSAGA have a faster convergence rate to find out the global optimal.
Conclusions
The experimental results demonstrate the effectiveness and the applicability of QSAGA and shows excellent global search ability and superiority of convergence ability of QSAGA.