An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
On the convergence of cross decomposition
Mathematical Programming: Series A and B
Can AI planners solve practical problems?
Computational Intelligence
Temporal planning with continuous change
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Fast planning through planning graph analysis
Artificial Intelligence
Artificial Intelligence - Special issue on heuristic search in artificial intelligence
Local search characteristics of incomplete SAT procedures
Artificial Intelligence
A Discrete Lagrangian-Based Global-SearchMethod for Solving Satisfiability Problems
Journal of Global Optimization
Unifying SAT-based and Graph-based Planning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Simulated Annealing with Asymptotic Convergence for Nonlinear Constrained Global Optimization
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
The Theory of Discrete Lagrange Multipliers for Nonlinear Discrete Optimization
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
TALplanner: An Empirical Investigation of a Temporal Logic-based Forward Chaining Planner
TIME '99 Proceedings of the Sixth International Workshop on Temporal Representation and Reasoning
The theory and applications of discrete constrained optimization using lagrange multipliers
The theory and applications of discrete constrained optimization using lagrange multipliers
Partitioning of Temporal Planning Problems in Mixed Space Using the Theory of Extended Saddle Points
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
Combining linear programming and satisfiability solving for resource planning
The Knowledge Engineering Review
Integer optimization models of AI planning problems
The Knowledge Engineering Review
The FF planning system: fast plan generation through heuristic search
Journal of Artificial Intelligence Research
PDDL2.1: an extension to PDDL for expressing temporal planning domains
Journal of Artificial Intelligence Research
Efficient implementation of the plan graph in STAN
Journal of Artificial Intelligence Research
Total-order planning with partially ordered subtasks
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Pushing the envelope: planning, propositional logic, and stochastic search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Decomposition of planning problems
AI Communications
Simulated annealing with asymptotic convergence for nonlinear constrained optimization
Journal of Global Optimization
Effective method for constrained minimum - reverse bridge theorem
Computers & Mathematics with Applications
Constrained optimization for validation-guided conditional random field learning
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Cost-optimal external planning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Temporal planning using subgoal partitioning and resolution in SGPlan
Journal of Artificial Intelligence Research
Long-distance mutual exclusion for propositional planning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Hi-index | 0.00 |
In this paper, we study the partitioning of constraints in temporal planning problems formulated as mixed-integer nonlinear programming (MINLP) problems. Constraint partitioning is attractive because it leads to much easier subproblems, where each is a significant relaxation of the original problem. Moreover, each subproblem is very similar to the original problem and can be solved by any existing solver with little or no modification. Constraint partitioning, however, introduces global constraints that may be violated when subproblems are evaluated independently. To reduce the overhead in resolving such global constraints, we develop in this paper new conditions and algorithms for limiting the search space to be backtracked in each subproblem. Using a penalty formulation of a MINLP where the constraint functions of the MINLP are transformed into non-negative functions, we present a necessary and sufficient extended saddle-point condition (ESPC) for constrained local minimization. When the penalties are larger than some thresholds, our theory shows a one-to-one correspondence between a constrained local minimum of the MINLP and an extended saddle point of the penalty function. Hence, one way to find a constrained local minimum is to increase gradually the penalties of those violated constraints and to look for a local minimum of the penalty function using any existing algorithm until a solution to the constrained model is found. Next, we extend the ESPC to constraint-partitioned MINLPs and propose a partition-and-resolve strategy for resolving violated global constraints across subproblems. Using the discrete-space ASPEN and the mixed-space MIPS planners to solve subproblems, we show significant improvements on some planning benchmarks, both in terms of the quality of the plans generated and the execution times to find them.