Durham E-Theses Reasoning about Goal-Plan Trees in Autonomous Agents: Development of Petri net and Constraint-Based Approaches with Resulting Performance Comparisons SHAW, PATRICIA,H How to cite: SHAW, PATRICIA,H (2010) Reasoning about Goal-Plan Trees in Autonomous Agents: Development of Petri net and Constraint-Based Approaches with Resulting Performance Comparisons, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/125/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk 2 Reasoning about Goal-Plan Trees in Autonomous Agents: Development of Petri net and Constraint-Based Approaches with Resulting Performance Comparisons A thesis submitted to the University of Durham in partial fulfilment for the degree of Doctor of Philosophy 2010 By Patricia H. Shaw School of Engineering and Computing Sciences Abstract Multi-agent systems and autonomous agents are becoming increasingly important in current computing technology. In many applications, the agents are often asked to achieve multiple goals individually or within teams where the distribution of these goals may be negotiated among the agents. It is expected that agents should be capable of working towards achieving all its currently adopted goals concur- rently. However, in doing so, the goals can interact both constructively and de- structively with each other, so a rational agent must be able to reason about these interactions and any other constraints that may be imposed on them, such as the limited availability of resources that could affect their ability to achieve all adopted goals when pursuing them concurrently. Currently, agent development languages require the developer to manually identify and handle these circumstances. In this thesis, we develop two approaches for reasoning about the interactions between the goals of an individual agent. The first of these employs Petri nets to represent and reason about the goals, while the second uses constraint satisfaction techniques to find efficient ways of achieving the goals. Three types of reasoning are incorporated into these models: reasoning about consumable resources where the availability of the resources is limited; the constructive interaction of goals whereby a single plan can be used to achieve multiple goals; and the interleaving of steps for achieving different goals that could cause one or more goals to fail. Experimental evaluation of the two approaches under various different circum- stances highlights the benefits of the reasoning developed here whilst also identify- ing areas where one approach provides better results than the other. This can then be applied to suggest the underlying technique used to implement the reasoning that the agent may want to employ based on the goals it has been assigned. ii Declaration No part of the material presented in this thesis has pre- viously been submitted by the author in support of an application for another degree or qualification of this or any other university or other institute of learning. All the work presented here is the sole work of the author and no one else. This research has been documented, in part, within the following publications: • Shaw, P. and Bordini, R. 2007. Towards alterna- tive approaches to reasoning about goals. In Proc. 5th Int. Workshop on Declarative Agent Languages and Technologies. Springer. • Shaw, P., Farwer, B. and Bordini, R. H. 2008. The- oretical and experimental results on the goal-plan tree problem. In Proc. 7th Int. Conf. on Au- tonomous Agents and Multiagent Systems. iii Contents Abstract ii Declaration iii Acknowledgements xv 1 Introduction 1 2 Background 8 2.1 Introduction to Agents . 8 2.2 Reasoning about Goals . 13 2.2.1 Reasoning about Resources . 15 2.2.2 Reasoning about Positive Interaction . 18 2.2.3 Reasoning about Negative Interference . 19 2.3 Alternative Approaches to Decision Making . 23 2.3.1 Petri nets . 24 2.3.2 Planning . 25 2.3.3 Constraint Satisfaction Problem (CSP) . 29 2.4 Testing Performance . 32 3 Reasoning about Goals 35 3.1 Goal-Plan Tree . 35 3.2 Consumable Resources . 36 3.3 Positive Interaction . 40 3.4 Negative Interference . 44 3.5 Goal-Plan Tree Automated Generation . 46 iv 4 Petri net Model 49 4.1 Petri nets . 49 4.2 Modelling a Goal-Plan Tree Problem . 53 4.3 Modelling Consumable Resource Reasoning . 58 4.4 Modelling Positive Interaction Reasoning . 64 4.5 Modelling Negative Interference Reasoning . 66 4.6 Petri net Automated Generation . 68 5 Constraint-Based Model 75 5.1 Constraint Satisfaction Problem . 75 5.1.1 Constraint Logic Programming . 77 5.1.2 GNU Prolog . 78 5.1.3 GNU Prolog Notation . 81 5.2 Modelling the Goal-Plan Tree . 87 5.3 Modelling Consumable Resource Reasoning . 96 5.4 Modelling Positive Interaction Reasoning . 100 5.5 Modelling Negative Interference Reasoning . 103 5.6 Constraint Automated Generation . 105 6 Evaluation 107 6.1 Experimental set-up . 107 6.2 Deep Goal-Plan Trees . 115 6.2.1 Consumable Resources . 116 6.2.2 Positive Interaction . 126 6.2.3 Negative Interference . 132 6.2.4 Combined Reasoning . 140 6.2.5 Deep Goal-Plan Tree Conclusions . 145 6.3 Broad Goal-Plan Trees . 146 6.3.1 Consumable Resources . 147 6.3.2 Positive Interaction . 151 6.3.3 Negative Interference . 154 6.3.4 Combined Reasoning . 156 6.3.5 Broad Goal-Plan Tree Conclusions . 159 v 6.4 General Goal-Plan Tree . 160 6.4.1 Varying the Combined Reasoning Types . 161 6.4.2 General Goal-Plan Tree Conclusions . 171 6.5 Summary of Comparison of Tree Structures and Reasoning Models . 171 6.5.1 Reasoning about Consumable Resources . 172 6.5.2 Reasoning about Positive Interaction . 173 6.5.3 Reasoning about Negative Interference . 174 6.5.4 Combined Reasoning . 174 6.5.5 Conclusion . 175 7 Conclusions and Future Work 178 vi List of Tables 6.1 Settings considered in experiments for reasoning about resources . 112 6.2 Settings considered in experiments for reasoning about positive in- teraction . 113 6.3 Settings considered in experiments for reasoning about negative in- terference . 113 6.4 Settings considered in experiments for combined reasoning . 114 6.5 Plan requirements for the three sizes of deep tree used . 116 6.6 Load timings for setting: Medium sized deep tree, low resource availability, high goal interaction, varying number of goals and rea- soning about resources . 121 6.7 Memory usage for setting: Medium sized deep tree, low resource availability, high goal interaction, varying number of goals and rea- soning about resources . 122 6.8 Load timings for setting: Medium sized deep tree, high goal inter- action, 20 goals, varying resource availability and reasoning about resources . 125 6.9 Memory usage for setting: Medium sized deep tree, high goal inter- action, 20 goals, varying resource availability and reasoning about resources . 126 6.10 Load timings for setting: Deep tree, high level positive interaction, high goal interaction, 20 goals, varying tree size and reasoning about positive interaction . 128 6.11 Memory usage for setting: Deep tree, high level positive interaction, high goal interaction, 20 goals, varying tree size and reasoning about positive interaction . 129 vii 6.12 Load timings for setting: Medium sized deep tree, high goal interac- tion, 20 goals, varying positive interaction level and reasoning about positive interaction . 131 6.13 Memory usage for setting: Medium sized deep tree, high goal in- teraction, 20 goals, varying positive interaction level and reasoning about positive interaction . 132 6.14 Load timings for setting: Deep tree, long duration negative interfer- ence, high goal interaction, 20 goals, varying tree size and reasoning about negative interference . 135 6.15 Memory usage for setting: Deep tree, long duration negative in- terference, high goal interaction, 20 goals, varying tree size and reasoning about negative interference . 136 6.16 Load timings for setting: Medium sized deep tree, high goal inter- action, 20 goals, varying negative interference level and reasoning about negative interference . 138 6.17 Memory usage for setting: Medium sized deep tree, high goal inter- action, 20 goals, varying negative interference level and reasoning about negative interference . 138 6.18 Load timings for setting: Medium sized deep tree, long duration negative interference, 20 goals, varying goal interaction and reason- ing about negative interference . 140 6.19 Memory usage for setting: Medium sized deep tree, long duration negative interference, 20 goals, varying goal interaction and reason- ing about negative interference . 141 6.20 Load timings for setting: Medium sized deep tree, low resource availability, high level positive interaction, long duration negative interference, high goal interaction, 20 goals, varying reasoning com- bination . 144 6.21 Load timings for comparison results of medium sized deep tree, individual reasoning types . 144 viii 6.22 Memory usage for setting: Medium sized deep tree, low resource availability, high level positive interaction, long duration negative interference, high goal interaction, 20 goals, varying reasoning com- bination . 145 6.23 Memory usage for comparison results of medium sized deep tree, individual reasoning types . 145 6.24 Plan requirements for the three sizes of broad tree used .