The aim of AI planning is to solve the problems with no exact solution available. These problems usually have a big search space, and planning may not find plans with the least actions and in the shortest time. Recent researches show that using suitable heuristics can help to find desired plans. In planning problems specified formally through graph transformation system (GTS), there are dependencies between applied rules (actions) in the search space. This fact motivates us to solve the planning problem for a small goal (instead of the main goal), extract dependencies from the searched space, and use these dependencies to solve the planning problem for the main goal. In GTS based systems, the nodes of a state (really is a graph) can be grouped due to their type. To create a small (refined) goal, we use a refinement technique to remove the predefined percent of nodes from each group of the main goal. Bayesian Optimization Algorithm (BOA) is then used to solve the planning problem for the refined goal. BOA is an Estimation of Distribution Algorithm (EDA) in which Bayesian networks are used to evolve the solution populations. Actually, a Bayesian network is learned from the current population, and then this network is employed to generate the next population. Since the last Bayesian network learned in BOA has the knowledge about dependencies between applied rules, this network can be used to solve the planning problem for the main goal. Experimental results on four well-known planning domains confirm that the proposed approach finds plans with the least actions and in the lower time compared with the state-of-the-art approaches.

AI规划的目的是在没有确切解决方案的情况下解决问题。这些问题通常具有很大的搜索空间，并且计划可能找不到行动最少，时间最短的计划。最近的研究表明，使用合适的启发式方法可以帮助找到所需的计划。在计划通过图转换系统（GTS）正式指定的问题时，搜索空间中所应用的规则（动作）之间存在依赖性。这个事实促使我们解决一个小目标（而不是主要目标）的规划问题，从搜索空间中提取依赖关系，并使用这些依赖关系来解决主要目标的规划问题。在基于GTS的系统中，状态的节点（实际上是图）可以根据其类型进行分组。要创建一个小的目标（精炼），我们使用一种优化技术从每个主要目标组中删除预定义的节点百分比。然后使用贝叶斯优化算法（BOA）来解决细化目标的计划问题。BOA是一种分配算法（EDA）的估计，其中使用贝叶斯网络来演化解决方案总体。实际上，贝叶斯网络是从当前种群中获知的，然后使用该网络来生成下一个种群。由于在BOA中学习的最后一个贝叶斯网络具有有关应用规则之间的依赖性的知识，因此该网络可用于解决主要目标的计划问题。在四个著名的计划领域的实验结果证实，与最新方法相比，该方法可以找到行动最少，时间更短的计划。