One of the useful knowledge representation tools, which can describe the joint probability distribution between some random variables with a graphical model and can be trained by a dataset, is the Bayesian network (BN). A BN is composed of a network structure and a conditional probability distribution table for each node. Discovering an optimal BN structure is an NP-hard optimization problem that various meta-heuristic algorithms are applied to solve this problem by researchers. The genetic algorithms, ant colony optimization, evolutionary programming, artificial bee colony, and bacterial foraging optimization are some of the meta-heuristic methods to solve this problem using a dataset. Most of these methods are applying a scoring metric to generate the best network structure from a set of candidates. A Fixed Structure Learning Automata-Based (FSLA-B) algorithm is presented in this paper to solve the structure learning problem of BNs. There is a fixed structure learning automaton for each pair of vertices in the BN's graph structure in the proposed algorithm. The action of this automaton determines the presence and direction of an edge between the vertices. The proposed algorithm performs a guided search procedure using the FSLA and escapes from local optimums. Several datasets are utilised in this paper to evaluate the performance of the proposed algorithm. By performing various experiments, multiple meta-heuristic algorithms are compared with the introduced new one. The obtained results represented that the proposed algorithm could produce competitive results and find the near-optimal solution for the BN structure learning problem.

中文翻译：

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一种基于固定结构学习自动机的贝叶斯网络结构学习优化算法

贝叶斯网络（BN）是一种有用的知识表示工具，它可以用图形模型描述一些随机变量之间的联合概率分布，并且可以通过数据集进行训练。BN由网络结构和每个节点的条件概率分布表组成。发现最优 BN 结构是一个 NP-hard 优化问题，研究人员应用各种元启发式算法来解决这个问题。遗传算法、蚁群优化、进化编程、人工蜂群和细菌觅食优化是使用数据集解决这个问题的一些元启发式方法。这些方法中的大多数都应用评分指标从一组候选中生成最佳网络结构。本文提出了一种基于固定结构学习自动机（FSLA-B）的算法来解决BN的结构学习问题。在所提出的算法中，BN的图结构中的每一对顶点都有一个固定结构的学习自动机。这个自动机的动作决定了顶点之间边的存在和方向。所提出的算法使用 FSLA 执行引导搜索过程并摆脱局部最优。本文使用了几个数据集来评估所提出算法的性能。通过执行各种实验，将多种元启发式算法与引入的新算法进行比较。获得的结果表明，所提出的算法可以产生有竞争力的结果，并为 BN 结构学习问题找到接近最优的解决方案。