Computational Complexity for Various Types of Stochastic Algorithms for Global Optimization

• Main Authors: Shih-shan Lin, 林詩珊
• Other Authors: Ruey-lin Sheu
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/42669643818873702280

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 96 === This thesis analyzes three stochastic algorithms for global optimization on continuous domain, including the Pure Random Search (PRS), the Pure Adaptive Search(PAS), and the Hesitant Adaptive Search(HAS). Let $overline{y}$ denote the given target value, and $N(overline{y})$ the number of iterations to achieve a value less than or equal to $overline{y}$. We are concerned with the expectation $E[N(overline{y})]$, a kind of measure for the computational complexity of an algorithm. We found that for PRS, $E[N(overline{y})]$ is inversely proportional to $p(overline{y})$ where $p(overline{y})$ is the probability to select a point with its objective function value at most $overline{y}$. For PAS, $E[N(overline{y})]$ is the logarithm of that for PRS. For HAS, the expected number is a function of $p(overline{y})$ and $b(overline{y})$ where $b(y)$ is the probability of choosing a point with the objective function value strictly less than $y$. When $b(overline{y})$ equals to one, the expected number coincides with that of PAS.