This thesis proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, the evaluation function, and the population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator that drives the individuals toward better solutions. The termination condition of QEA is designed by defining a new measure on the convergence of Q-bit individuals. To analyze the characteristics of QEA, the theoretical analysis of the QEA algorithm as well as the effects of changing parameters of QEA are examined. In particular, some issues of QEA such as the analysis of changing the initial values of Q-bits, a novel variation operator $H_\epsilon$ gate, and a two-phase QEA (TPQEA) scheme are addressed to improve the performance of QEA. To demonstrate the effectiveness and applicability of QEA, experiments are carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small number of population, without premature convergence as compared to the conventional genetic algorithms. Moreover, through the experiments on numerical optimization problems, the superior performance of QEA is also verified. These results show that QEA can be applied to a class of numerical as well as combinatorial optimization problems.