Abstract
Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. At the core of many of these applications is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal feasible solution. In the arena of model-based autonomy, deep space probes have given way to more agile vehicles, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear as well as logical constraints.
This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, carried from the conflict-directed search algorithm in model-based reasoning. We introduce a novel algorithm called Generalized Conflict-Directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or sub-optimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. Evaluated empirically on a range of test problems of coordinated air vehicle control, GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm applied to either disjunctive linear programs or an equivalent binary integer programming encoding.
This research is funded by The Boeing Company grant MIT-BA-GTA-1 and by NASA grant NNA04CK91A.
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References
Stallman, R., Sussman, G.J.: Forward Reasoning and Dependency-Directed Backtracking in a System for Computer-Aided Circuit Analysis. J. of Artificial Intelligence 9, 135–196 (1977)
Gaschnig, J.: Experimental Case Studies of Backtrack vs. Waltz-type vs. New Algorithms for Satisfying Assignment Problems. In: Proceedings of The 2nd Canadian Conference on AI (1978)
Balas, E.: Disjunctive programming. Annals of Discrete Math. 5, 3–51 (1979)
Dechter, R., Pearl, J.: Generalized Best-first Search Strategies and the Optimality of A*. J. of ACM 32, 506–536 (1985)
de Kleer, J., Williams, B.: Diagnosis with Behavioral Modes. In: Proceedings of IJCAI (1989)
Dechter, R.: Enhancement Schemes for Constraint Processing: Backjumping, Learning and Cutset Decomposition. J. of Artificial Intelligence 41, 273–312 (1990)
Ginsberg, M.: Dynamic Backtracking. J. of Artificial Intelligence Research 1, 25–46 (1993)
Prosser, P.: Hybrid Algorithms for the Constraint Satisfaction Problem. J. of Computational Intelligence 9(3), 268–299 (1993)
Williams, B., Cagan, J.: Activity Analysis: The Qualitative Analysis of Stationary Points for Optimal Reasoning. In: Proceedings of AAAI (1994)
Williams, B., Nayak, P.: A Model-based Approach to Reactive Self-Configuring Systems. In: Proceedings of AAAI (1996)
Bertsimas, D., Tsitsiklis, J.N.: Introduction to Linear Optimization. Athena Scientific (1997)
Bayardo, R.J., Schrag, R.C.: Using CSP Look-back Techniques to Solve Real-world SAT Instances. In: Proceedings of AAAI (1997)
Hooker, J.N., Osorio, M.A.: Mixed Logical/Linear Programming. J. of Discrete Applied Math. 96-97, 395–442 (1999)
Kautz, H., Walser, J.P.: State space planning by integer optimization. In: Proceedings of AAAI (1999)
Vossen, T., Ball, M., Lotem, A., Nau, D.: On the Use of Integer Programming Models in AI Planning. In: Proceedings of IJCAI (1999)
Wolfman, S., Weld, D.: The LPSAT Engine & Its Application to Resource Planning. In: Proceedings of IJCAI (1999)
Schouwenaars, T., de Moor, B., Feron, E., How, J.: Mixed Integer Programming for Multi-Vehicle Path Planning. In: Proceedings of European Control Conference (2001)
Hooker, J.N.: Logic, Optimization and Constraint Programming. INFORMS J. on Computing 14, 295–321 (2002)
Katsirelos, G., Bacchus, F.: Unrestricted Nogood Recording in CSP Search. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 873–877. Springer, Heidelberg (2003)
Hofmann, A., Williams, B.: Safe Execution of Temporally Flexible Plans for Bipedal Walking Devices. In: Plan Execution Workshop of ICAPS (2005)
Li, H.: Generalized Conflict Learning for Hybrid Discrete Linear Optimization. Master’s Thesis, M.I.T. (2005)
Léauté, T., Williams, B.: Coordinating Agile Systems Through The Model-based Execution of Temporal Plans. In: Proceedings of AAAI (2005)
Williams, B., Ragno, R.: Conflict-directed A* and its Role in Model-based Embedded Systems. J. of Discrete Applied Math. (2005) (to appear)
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Li, H., Williams, B. (2005). Generalized Conflict Learning for Hybrid Discrete/Linear Optimization. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_32
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DOI: https://doi.org/10.1007/11564751_32
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