Convergence Analysis of Quantum Genetic Algorithm

It is an important and a complicated task to investigate the convergence of a new genetic algorithm based on quantum mechanics concepts including qubits and superposition of states, namely Quantum Genetic Algorithm, in the field of evolutionary computation. This paper analyzes convergence property of quantum genetic algorithm which uses its special quantum operator instead of canonical operators of classical genetic algorithms, such as crossover and mutation operators and even selection techniques. The Markov chain is a considerable part of the probability theory and stochastic processes; and one of its important applications is to model some classical evolutionary algorithms and to analyze their convergence property. In reality, inasmuch as modeling of the evolutionary algorithms in usual methods is very difficult, the finite Markov chain is used to formalize them. In here, the quantum genetic algorithm is modeled as a finite Markov chain and is shown by means of Markov chain analysis that the algorithm with preservation of the best solution in the population, will converge to the global optimum.