基于贝叶斯统计推断的离散分布估计算法

Discrete Distribution Estimation Algorithm Based on Bayesian Statistical Inference

将贝叶斯统计推断理论引入分布估计算法概率模型中,提出一种基于贝叶斯统计推断的离散分布估计算法。根据离散优化问题中解的分布规律建立先验概率模型,将优势群体的概率模型和二元边缘分布算法中森林结构的概率模型相结合,得出条件概率模型,利用贝叶斯统计推断,并结合上述2种概率模型建立后验概率模型,以指导新群体的产生。仿真结果表明,该算法求解gr21旅行商问题的收敛速度大于EDAs1算法,在种群规模、最大运行代数等参数固定的情况下,分别分析结合速率和学习速率对算法性能的影响,得出当其值取0.2时,算法性能最稳定。

Bayesian statistical inference theory is added in the process of building the probability model of estimation of distribution algorithm.This paper proposes a discrete distribution estimation algorithm based on Bayesian statistical inference.A model of a priori probability is built according to the distributing regularity of the problem’s solution.The model of conditional probability is constructed through combining the probability model of advantage groups with forest structure of Bivariate Marginal Distribution Algorithm（BMDA）.The model of posterior probability is given by combining the above mentioned probability model to guide new population generating.Simulation results show that the algorithm convergence rate is greater than the EDAs1 when solving the gr21 Traveling Salesman Problem（TSP）.Analyzing the effect of combining speed and learning rate for this algorithm under the condition that parameters are fixed,such as population size and maximum running algebra etc.The results show when their values are 0.2,the algorithm performance is the most stable.