Abstract
We introduce a novel planner SCIPPlan for metric hybrid factored planning in nonlinear domains with general metric objectives, transcendental functions such as exponentials, and instantaneous continuous actions. Our key contribution is to leverage the spatial branch-and-bound solver of SCIP inside a nonlinear constraint generation framework where we iteratively check relaxed plans for temporal feasibility using a domain simulator, and repair the source of the infeasibility through a novel nonlinear constraint generation methodology. We experimentally evaluate SCIPPlan on a variety of domains, showing it is competitive with, or outperforms, ENHSP in terms of run time and makespan and handles general metric objectives. SCIPPlan is also competitive with a general metric-optimizing unconstrained Tensorflow-based planner (TF-Plan) in nonlinear domains with exponential transition functions and metric objectives. Overall, this work demonstrates the potential of combining nonlinear optimizers with constraint generation for planning in expressive metric nonlinear hybrid domains.
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- 1.
Relaxation refers to the omission of temporal constraints from the master problem.
- 2.
In this work, we focus on hybrid planning problems where duration \(\varDelta \) is completely controlled by the planner. When there are exogenous events or processes that can change the total duration of a time step, we need to define a continuous state variable \(\varDelta ' \in S^c\) as a function of \(\varvec{s}, \varvec{a}, \varDelta \) such that \(f(\varvec{s}, \varvec{a}, \varDelta ) = \varDelta '\) and transfer zero-crossing definitions onto \(\varDelta '\). In this work, we assume \(\varDelta = \varDelta '\) and omit \(\varDelta '\) for notational simplicity.
- 3.
The concept of a mode is analogous to its counterpart in the field of Hybrid Automata [8].
- 4.
Symbolic refers to the fact that Constraint (2) is a function of decision variables (i.e., \(\varvec{s}^{t},\varvec{a}^{t}, \varDelta ^t\)) whose values are decided at optimization time.
- 5.
We note that TF-Plan does not handle (i) discrete variables, (ii) global or goal constraints, or (iii) support dynamic time discretization, but can handle exponential transitions and complex metric objectives (e.g., NavigationMud).
References
Agarwal, Y., Balaji, B., Gupta, R., Lyles, J., Wei, M., Weng, T.: Occupancy-driven energy management for smart building automation. In: ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building, pp. 1–6 (2010)
Boutilier, C., Dean, T., Hanks, S.: Decision-theoretic planning: structural assumptions and computational leverage. JAIR 11(1), 1–94 (1999). http://dl.acm.org/citation.cfm?id=3013545.3013546
Bryce, D., Gao, S., Musliner, D., Goldman, R.: SMT-based nonlinear PDDL+ planning. In: 29th AAAI, pp. 3247–3253 (2015). http://dl.acm.org/citation.cfm?id=2888116.2888168
Cashmore, M., Fox, M., Long, D., Magazzeni, D.: A compilation of the full PDDL+ language into SMT. In: ICAPS, pp. 79–87 (2016). http://dl.acm.org/citation.cfm?id=3038594.3038605
Coles, A.J., Coles, A.I., Fox, M., Long, D.: COLIN: planning with continuous linear numeric change. JAIR 44, 1–96 (2012)
Fox, M., Long, D.: Modelling mixed discrete-continuous domains for planning. JAIR 27(1), 235–297 (2006). http://dl.acm.org/citation.cfm?id=1622572.1622580
Fox, M., Long, D., Magazzeni, D.: Plan-based policies for efficient multiple battery load management. CoRR abs/1401.5859 (2014). http://arxiv.org/abs/1401.5859
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, pp. 373–382. ACM, New York (1995). https://doi.org/10.1145/225058.225162, http://doi.acm.org/10.1145/225058.225162
Löhr, J., Eyerich, P., Keller, T., Nebel, B.: A planning based framework for controlling hybrid systems. In: ICAPS, pp. 164–171 (2012). http://www.aaai.org/ocs/index.php/ICAPS/ICAPS12/paper/view/4708
Maher, S.J., et al.: The SCIP optimization suite 4.0. Technical report 17-12, ZIB, Takustr. 7, 14195 Berlin (2017)
Mitten, L.G.M.: Branch-and-bound methods: general formulation and properties. Oper. Res. 18(1), 24–34 (1970). http://www.jstor.org/stable/168660
Penna, G.D., Magazzeni, D., Mercorio, F., Intrigila, B.: UPMurphi: a tool for universal planning on PDDL+ problems. In: ICAPS, pp. 106–113 (2009). http://dl.acm.org/citation.cfm?id=3037223.3037238
Piotrowski, W.M., Fox, M., Long, D., Magazzeni, D., Mercorio, F.: Heuristic planning for hybrid systems. In: AAAI, pp. 4254–4255 (2016). http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12394
Raghavan, A., Sanner, S., Tadepalli, P., Fern, A., Khardon, R.: Hindsight optimization for hybrid state and action MDPs. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI 2017), San Francisco, USA (2017)
Sanner, S.: Relational dynamic influence diagram language (RDDL): Language description (2010)
Say, B., Wu, G., Zhou, Y.Q., Sanner, S.: Nonlinear hybrid planning with deep net learned transition models and mixed-integer linear programming. In: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, pp. 750–756 (2017). https://doi.org/10.24963/ijcai.2017/104
Scala, E., Haslum, P., Thiébaux, S., Ramírez, M.: Interval-based relaxation for general numeric planning. In: ECAI, pp. 655–663 (2016). https://doi.org/10.3233/978-1-61499-672-9-655
Shin, J.A., Davis, E.: Processes and continuous change in a sat-based planner. Artif. Intell. 166(1–2), 194–253 (2005). https://doi.org/10.1016/j.artint.2005.04.001
Wu, G., Say, B., Sanner, S.: Scalable planning with tensorflow for hybrid nonlinear domains. In: Proceedings of the Thirty First Annual Conference on Advances in Neural Information Processing Systems (NIPS 2017), Long Beach, CA (2017)
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Say, B., Sanner, S. (2019). Metric Hybrid Factored Planning in Nonlinear Domains with Constraint Generation. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_33
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