## State-space Planning by Integer Optimization (1999)

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Venue: | In Proceedings of the Sixteenth National Conference on Artificial Intelligence |

Citations: | 63 - 0 self |

### BibTeX

@INPROCEEDINGS{Kautz99state-spaceplanning,

author = {Henry Kautz and Joachim P. Walser},

title = {State-space Planning by Integer Optimization},

booktitle = {In Proceedings of the Sixteenth National Conference on Artificial Intelligence},

year = {1999},

pages = {526--533},

publisher = {AAAI Press}

}

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### Abstract

This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand -bound IP solvers and efficient new integer local search algorithms. ILP-PLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving state-space planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...

### Citations

1032 | Fast planning through planning graph analysis
- Blum, Furst
- 1997
(Show Context)
Citation Context ... parallel length of a solution, where several non-interfering actions may occur at each time step. This notion of optimality, which is also shared by the popular Graphplan system and its descendents (=-=Blum & Furst 1995-=-; Koehler et al. 1997), is an advance over planning frameworks that treat all feasible solutions indifferently: for many popular test domains finding a shortest solution is at least NP-hard, while fin... |

548 | Pushing the envelope: planning, propositional logic, and stochastic search
- Kautz, Selman
- 1996
(Show Context)
Citation Context ... other recent planning algorithms such as ASP and LRTA* (Bonet, Loerincs, & Geffner 1997). We will demonstrate that the known computational advantages of using local search on a state-based encoding (=-=Kautz & Selman 1996-=-) of this domain can be retained, while the integer local search framework allows us to find solutions of lower sequential cost. The ILP-PLAN approach improves on the best published solutions for this... |

447 | UCPOP: A sound, complete, partial order planner for ADL
- Penberthy, Weld
- 1992
(Show Context)
Citation Context ...y arbitrary linear inequalities over all the variables described above. Example: Resource Optimization Planning. We illustrate this translation with a a modified version of the airplane example from (=-=Penberthy & Weld 1992-=-) and (Koehler 1998). It simplifies the original example by ignoring timing aspects but extends it for optimization of passenger routings. The scenario is a plane that can fly between a number of diff... |

387 | AMPL: A Modeling Language for Mathematical Programming. The Scientific - Fourer, Gay, et al. - 1993 |

378 | Noise Strategies for Improving Local Search - Selman, Kautz, et al. - 1994 |

176 | Extending planning graphs to an ADL subset
- Koehler, Nebel, et al.
- 1997
(Show Context)
Citation Context ... a solution, where several non-interfering actions may occur at each time step. This notion of optimality, which is also shared by the popular Graphplan system and its descendents (Blum & Furst 1995; =-=Koehler et al. 1997-=-), is an advance over planning frameworks that treat all feasible solutions indifferently: for many popular test domains finding a shortest solution is at least NP-hard, while finding a feasible solut... |

158 | Encoding plans in propositional logic - Kautz, McAllester, et al. - 1996 |

157 | Learning by analogical reasoning in general problem solving
- Veloso
- 1992
(Show Context)
Citation Context ...sily. In both fields, there is increasing interest in finding near-optimal solutions to problems with a difficult feasibility aspect. Here, we consider a planning benchmark from the logistics domain (=-=Veloso 1992-=-) that also exhibits this characteristic. The scenario is the transportation of a set of packages that involves flights and truck-drives between locations. To model the problem, we use a variant of th... |

147 | Monotonic solution of the frame problem in the situation calculus; an efficient method for worlds with fully specified actions
- Schubert
- 1990
(Show Context)
Citation Context ...erties of STRIPS operators are encoded by the following kinds of axioms: (i) explanatory frame-axioms (if a state-change occurs, one action that could account for it must have taken place (Haas 1987; =-=Schubert 1989-=-; Kautz, McAllester, & Selman 1996)); (ii) an occurring action implies its effects and preconditions; (iii) exclusiveness of logically conflicting actions; and (iv) state invariant axioms in the style... |

145 | A robust and fast action selection mechanism for planning. Proc AAAI-97 - Bonet, Loerincs, et al. - 1997 |

129 | Automatic SAT-compilation of planning problems - Ernst, D, et al. - 1997 |

128 | BLACKBOX: A new approach to the application of theorem proving to problem solving - Kautz, Selman - 1998 |

128 |
Planning with sharable resource constraints
- Laborie, Ghallab
- 1995
(Show Context)
Citation Context ...lanners that extended nonlinear planning to include metric constraints in constraint programming type frameworks include O-PLAN (Tate 1996) and parcPLAN (El-Kholy & Richards 1996). The IxTeT planner (=-=Laborie & Ghallab 1995-=-) is a leastcommitment planner notable for using an efficient graphbased algorithm for detecting resource conflicts between parallel actions. Recent work by Vossen et al. (1999) describes an alternati... |

124 |
Complexity results for planning, in
- Bylander
- 1991
(Show Context)
Citation Context ...rameworks that treat all feasible solutions indifferently: for many popular test domains finding a shortest solution is at least NP-hard, while finding a feasible solution can be done in linear time (=-=Bylander 1991-=-). However, real world planning problems usually have more complex optimality criteria, that take into account e.g. different costs for different types of actions, minimization of resource usage, and ... |

95 | Planning under resource constraints
- Koehler
- 1998
(Show Context)
Citation Context ...ral, resources may be integer or real-valued. Every resource value has a global minimum and maximum value. Actions may be extended with resource preconditions and effects. Following the framework of (=-=Koehler 1998-=-), a resource precondition is a simple linear inequality that must hold in any states in which the action is applicable. The effect of an action may be to consume (decrease), produce (increase), or pr... |

81 | The role of domainspecific knowledge in the planning as satisfiability framework
- Kautz, Selman
- 1998
(Show Context)
Citation Context ... 1996), automatic generation of axioms from STRIPS operators (Ernst, Millstein, & Weld 1997; Kautz & Selman 1999), hierarchical task networks (Mali & Kambhampati 1998), and domain-specific knowledge (=-=Kautz & Selman 1998-=-b). Despite this generality, certain limitations in the framework still prevent it from being used for many practical, real-world domains. One problem is the difficulty in dealing with resources and t... |

77 |
The case for domain-specific frame axioms
- Haas
- 1987
(Show Context)
Citation Context ...ogical properties of STRIPS operators are encoded by the following kinds of axioms: (i) explanatory frame-axioms (if a state-change occurs, one action that could account for it must have taken place (=-=Haas 1987-=-; Schubert 1989; Kautz, McAllester, & Selman 1996)); (ii) an occurring action implies its effects and preconditions; (iii) exclusiveness of logically conflicting actions; and (iv) state invariant axio... |

53 |
A quantitative approach to logical inference", Decision Support Systems
- Hooker
- 1988
(Show Context)
Citation Context ...onstraints and optimization functions as linear inequalities. ILP generalizes SAT because any clause can be written as a linear inequality over 0/1 variables (e.g., (ps:q) becomes p + (1 \Gamma q)s1 (=-=Hooker 1988-=-)). ILP is a standard tool for Operations Research, but has been rarely exploited in AI applications. The first part of this paper will demonstrate how STRIPS-style planning problems extended with cos... |

50 | Temporal and resource reasoning in planning: the parcPLAN approach
- El-Kholy, Richards
- 1996
(Show Context)
Citation Context ...like local search or branch-and-bound. Other planners that extended nonlinear planning to include metric constraints in constraint programming type frameworks include O-PLAN (Tate 1996) and parcPLAN (=-=El-Kholy & Richards 1996-=-). The IxTeT planner (Laborie & Ghallab 1995) is a leastcommitment planner notable for using an efficient graphbased algorithm for detecting resource conflicts between parallel actions. Recent work by... |

48 | Solving linear Pseudo-Boolean constraint problems with local search - Walser - 1997 |

46 | On the use of integer programming models in AI planning - Vossen, Ball, et al. - 1999 |

45 | Conditional effects in graphplan - Anderson, Smith, et al. - 1998 |

35 | Representing Plans as a Set of Constraints – the <I-N-OVA> Model
- Tate
- 1996
(Show Context)
Citation Context ...chnique (as in ILP-PLAN) like local search or branch-and-bound. Other planners that extended nonlinear planning to include metric constraints in constraint programming type frameworks include O-PLAN (=-=Tate 1996-=-) and parcPLAN (El-Kholy & Richards 1996). The IxTeT planner (Laborie & Ghallab 1995) is a leastcommitment planner notable for using an efficient graphbased algorithm for detecting resource conflicts ... |

19 | Mixed integer programming models for planning problems - Bockmayr, Dimopoulos - 1998 |

15 | Encoding htn planning in propositional logic
- Mali, Kambhampati
- 1998
(Show Context)
Citation Context ...nance goals, causal planning (Kautz, McAllester, & Selman 1996), automatic generation of axioms from STRIPS operators (Ernst, Millstein, & Weld 1997; Kautz & Selman 1999), hierarchical task networks (=-=Mali & Kambhampati 1998-=-), and domain-specific knowledge (Kautz & Selman 1998b). Despite this generality, certain limitations in the framework still prevent it from being used for many practical, real-world domains. One prob... |

14 |
Mixed logical/linear programming. Discrete Applied Mathematics
- Hooker, Osorio
- 1997
(Show Context)
Citation Context ... domain. Finally, while the ILP solvers used in our work so far (CPLEX and WSAT(OIP)) require all constraints to take the form of linear inequalities, recent work on mixed logical/linear programmings(=-=Hooker & Osorio 1997-=-) may provide the underpinnings for systems that more efficiently handle ILPs that have a large logical component. 7 Conclusions We have described ILP-PLAN, a new framework for solving AI planning pro... |

11 |
Temporal planning with continous change
- Penberthy, Weld
- 1994
(Show Context)
Citation Context ...an to handle resource constraints. Unlike ILP-PLAN, however, that system handled resource usage strictly by annotations on STRIPS operators, and did not include objective functions. The ZENO planner (=-=Penberthy & Weld 1994-=-) included a rich language that could express complex resource constraints, although it too lacked explicit optimization functions. It also differed from ILP-PLAN in that the underlying planner was a ... |

10 | Domain-independent Local Search for Linear Integer Optimization
- Walser
- 1998
(Show Context)
Citation Context ...ver-Constrained Integer Programs. To include optimization objectives into local search, the integer local search framework uses a representation introduced as overconstrained integer programs (OIPs) (=-=Walser 1998-=-). OIP formulates optimization criteria by means of soft inequality constraints over bounded integer variables and can be reduced to ILP. An OIP consists of hard and soft inequality constraints, where... |

1 |
Unifying SAT-based and graphbased planning. Under review
- Kautz, Selman
- 1999
(Show Context)
Citation Context ... representations of change, conditional and maintenance goals, causal planning (Kautz, McAllester, & Selman 1996), automatic generation of axioms from STRIPS operators (Ernst, Millstein, & Weld 1997; =-=Kautz & Selman 1999-=-), hierarchical task networks (Mali & Kambhampati 1998), and domain-specific knowledge (Kautz & Selman 1998b). Despite this generality, certain limitations in the framework still prevent it from being... |