Analysis of the Quantum-inspired Evolutionary Algorithm Using the Markov Chains Abstract A Markov chain is stochastic process with property that given the values of the process from time zero up through the current time, and one of its important applications is to model some evolutionary algorithms and to analyze their convergence property, with considering the matrix of transition probabilities. Evolutionary Algorithms are common algorithms in computer science to search irregular and poorly understood spaces; Quantum-inspired Evolutionary Algorithm is a new type of these algorithms based on quantum mechanics concepts which uses its special quantum operator. In this paper, the quantum-inspired evolutionary algorithm is modeled as a finite Markov chain and is shown that this algorithm always preserves the best solution in the population for oncoming generations will converge to the global optimum. Keywords Finite Markov Chain, Global Convergence, Quantum-inspired Evolutionary Algorithm 1. Introduction In applied probability, a stochastic process is a Markovian process [1][2], if the probability of any state of the system characterized by this process in the future, depends only on its state in the present and is independent of how the system reached the present. Markovian processes and Markov chains are special and important subjects in the theory of stochastic process. This is due to the fact the behavior of many engineering systems and algorithms can be modeled using this kind of processes. So, these mathematical equipments are employed to solve many practically important engineering problems. One of the engineering problems in computer science is the convergence analysis of the algorithms, and between these algorithms, convergence investigation of the heuristic and evolutionary algorithms is more complicated and important. Mehrshad Khosraviani Dept. of Computer Engineering & IT Amirkabir University of Technology Tehran, Iran khosraviani@aut.ac.ir Saadat Pour Mozafari Dept. of Computer Engineering & IT Amirkabir University of Technology Tehran, Iran saadat@aut.ac.ir Mohammad Mehdi Ebadzadeh Dept. of Computer Engineering & IT Amirkabir University of Technology Tehran, Iran ebadzadeh@aut.ac.ir Proceedings of The Third International Conference on Mathematical Sciences- ICM 2008 1006