マルコフ解析に基づいた遺伝的アルゴリズムの性能評価

緩和時間による評価と実数値遺伝的アルゴリズムへの適用

抄録

Genetic algorithm (GA) is a probabilistic algorithm for solving optimization problems, which is modeled on a genetic evolution process in biology, and is focused as an effective algorithm to find the global optimal solutions for many types of problems. Most research results on GAs are related to the design for some specific GAs and the simulation-based study for their applicability. It has not been established yet how to evaluate the performance of specific GAs in a general framework. In this paper, we give two theoretical results on the performance evaluation of GAs by using the Markovian analysis. First, we discuss convergence properties of GAs, and derive an associated performance measure, called the relaxation time for the Markov chain. Secondly, we develop an alternative Markovian analysis with rewards for real-coded GAs having real-vector individuals.