Engineering Applications of Artificial Intelligence 92 (2020) 103684 Contents lists available at ScienceDirect Engineering Applications of Artificial Intelligence journal homepage: www.elsevier.com/locate/engappai A novel approach to solve AI planning problems in graph transformations Einollah Pira Faculty of Information Technology and Computer Engineering, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran ARTICLE INFO Keywords: Bayesian Optimization Algorithm AI planning Graph transformation system Bayesian network Refinement ABSTRACT 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. 1. Introduction Planning is a branch of artificial intelligence that concerns about solving the special problems in intelligent systems like agents, au- tonomous robots, and unmanned vehicles. Planning tries to select a sequence of actions that cause the considered system to transform from the initial state to the goal state. The aim is to find paths (also called plans) with the least actions to reach a specific goal in the shortest time (Russell and Norvig, 2016). Every planning problem includes some components such as actions, states and goals. The way these compo- nents are represented is called the planning language. STRIPS is one of the well-known planning languages used in the more general Planning Domain Definition Language (PDDL) (Aeronautiques et al., 1998). In STRIPS problems, a plan is defined by a set of propositional atoms that are meaningful in the problem. In this context, many planners such as Fast-Forward (FF) (Hoffmann and Nebel, 2001), LAMA (Richter and Westphal, 2010), and k-Best-first width-search (k-BFWS) (Lipovetzky and Geffner, 2017) have been proposed. Since the creation and deletion of objects are not allowed in PDDL, developing a planning system to work directly on graph transformation system (GTS) has recently been taken into consideration. GTS based planning systems usually use domain-independent heuristics in directing the search (Edelkamp et al., 2006; Snippe, 2011; Ziegert, 2014). E-mail address: pira@azaruniv.ac.ir. In this paper, we propose a novel approach based on a refinement technique and Bayesian Optimization Algorithm (BOA) to solve plan- ning problems in GTS based planning systems. In GTS based systems, the nodes of a state can be grouped due to their type. Therefore, the refinement technique deletes the predefined percent (also called refPerc) of nodes from each group of the specific goal state to make a refined goal state. BOA is an Estimation of Distribution Algorithm (EDA) in which Bayesian networks (BNs) are employed to evolve the solution populations (Pelikan et al., 2003). After producing the refined goal state, the proposed approach uses the BOA algorithm to solve the planning problem for this goal. Solving the planning problem for the refined goal state confirms that the last BN learned in BOA has the exact knowledge about dependencies between applied rules, because one of the solutions sampled from this network has led to an optimum solution. The proposed approach employs the last BN to solve the planning problem for the main goal state. To evaluate the effectiveness of the proposed approach, we use the model checker GROOVE as a planning system and implement the approach in it. GROOVE is an open source toolset to design and model checking graph transformation systems (Kastenberg and Rensink, 2006). The main contributions of the proposed approach are as follows: (1) it extracts the knowledge through solving the refined planning problem and then uses this knowledge to solve the main problem. (2) It employs https://doi.org/10.1016/j.engappai.2020.103684 Received 30 December 2019; Received in revised form 25 March 2020; Accepted 28 April 2020 Available online 7 May 2020 0952-1976/© 2020 Elsevier Ltd. All rights reserved.