CRIKEY is a planner that separates out the scheduling from the classical parts of temporal planning. This can be seen as a relaxation of the temporal information during the classical planning phase. Relaxations in planning are used to guide the search. However, the quality of the relaxation greatly affects the performance of the planner, and in some cases can lead the search into a dead end. This can happen whilst separating out the planning and scheduling problems, leading to the production of an unschedulable plan. CRIKEY can detect these cases and change the relaxation accordingly

Fox, M.

Halsey, K.

Long, D.

English

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Multiple relaxations in temporal planning

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryHalsey, K. and Long, D. and Fox, M. (2004) Multiple relaxations in temporal planning. In: 16thEuropean Conference on Artificial Intelligence, 2004-08-23 - 2004-08-27, Valencia.Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/Multiple Relaxations in Temporal PlanningKeith Halsey and Derek Long and Maria Fox1Abstract. CRIKEY is a planner that separates out the schedulingfrom the classical parts of temporal planning. This can be seen as arelaxation of the temporal information during the classical planningphase. Relaxations in planning are used to guide the search. However,the quality of the relaxation greatly affects the performance of theplanner, and in some cases can lead the search into a dead end. Thiscan happen whilst separating out the planning and scheduling prob-lems, leading to the production of an unschedulable plan. CRIKEYcan detect these cases and change the relaxation accordingly.1 CRIKEYCRIKEY is a planner that uses relaxations to solve temporal plan-ning problems. By successively reducing the complexity of the prob-lem, the solutions to these relaxed problems are used to either guidethe search for the unrelaxed version, or as a skeleton solution, roundwhich a full solution can be built.CRIKEY performs forward heuristic search and can cope withmetric and temporal domains and is closely based on MetricFF [5].For this reason, it is the temporal aspects of the planner and the re-laxations of the temporal information, that is the focus of this paper.CRIKEY is a re-implementation, with improvements, of the systemdescribed in [3], and follows the architecture as detailed in Figure 1.The principle is to firstly extract the temporal information from atemporal planning problem. The resulting metric planning problemis solved with forward heuristic search, using a relaxed plan graph asa guide to finding a totally ordered plan. A partial order is extractedfrom this plan using a modified Veloso algorithm [6] to find order-ing constraints based on logical and metric reasoning. Then, alongwith the temporal information, a Simple Temporal Network is usedto produce a valid temporal plan of time stamped actions. Signific-antly, there is no feedback from the scheduling to the planning phase;These are separate, happening one after the other. Whilst this will notfind an optimal plan, that is to say one that exploits all concurrencypossible, it is complete and sound.This architecture separates the planning and scheduling problemsfound in temporal problems solving each half separately. In this as-spect it is similar to MIPS [1]. Actions, that can have a duration, mustboth be chosen for their logical and metric effects (planning) and thenarranged in time so as not to break any constraints (scheduling). Thishas the advantage of making each problem on its own easier to solveand has proved sucessful in the domains of the IPC’02 (InternationalPlanning Competition 2002) [2]. The problem with this architectureas it stands is where the planning and scheduling interact. Here, therelaxation fails and an unschedulable plan can be produced.1 University of Strathclyde, Glasgow, UKemail: keith.halsey@cis.strath.ac.ukSCHEDULING&%'$Total toPartial OrderLifter &%'$SimpleTemporalNetworkPLANNINGﬀMini-Scheduler &%'$ForwardSearch &%'$RelaxedPlanGraph&%'$DomainAnalysis???-ﬀ-ﬀ- ﬀ?ActionsSTNConsistencyTemporal DomainClassicalProblemTotallyOrdered PlanExtractedTemporalInformationCurrentStateHeuristicDistance &Helpful ActionsPartialOrderedPlanTemporal PlanFigure 1. Architecture Overview of CRIKEY2 UNSCHEDULABLE PLANSWhilst CRIKEY can perform competitively against other state of theart technology (see [3] for some results), the approach of separat-ing the planning and scheduling has a major flaw. In the domainsof IPC’02, all the solution plans could be sequentialised (the actionsperformed in a strictly ordered manner). That is to say that actionscould happen in parallel if they didn’t interfere, but that, however,was a choice of the planner, and not enforced by the domain. How-ever, it is possible to have domains where some actions must happenin parallel.Take for example the Match Domain (Figure 2) as described inPDDL2.1. In this domain, the goal is to mend fuses. To mend a fuse(which takes 5 time units) you must have a hand free (i.e. you canonly mend one fuse at once) and there must be light (provided bystriking a match that lasts 8 time units). It should be obvious that ina problem instance where there are two fuses to fix, two matches areneeded. If the problem is completely separated, CRIKEY will notrealise this and try only to use one match. Here an unschedulableplan is produced and the temporal planner fails. In this case the sub-problems of planning and scheduling are more tightly coupled andare interdependent. The planning part critically effects the schedulingproblem, and so in this case, the two cannot be separated.(:durative-action LIGHT_MATCH:parameters (?match - match):duration (= ?duration 8):condition (and (over all (light))(at start (unused ?match))):effect (and (at start (light))(at start (not (unused ?match)))(at end (not (light)))))(:durative-action MEND_FUSE:parameters (?fuse - fuse):duration (= ?duration 5):condition (at start (handfree))(and (over all (light))):effect (and(at start (not (handfree)))(at end (mended ?fuse))(at end (handfree)))))Figure 2. Two Actions in the Match DomainA more in-depth look at where planning and scheduling inter-act in temporal planning (with particular reference to PDDL2.1)can be found in [4]. A very brief summary follows. Interactionsbetween scheduling and planning occur where there are durativeactions (called content actions) that must be executed in the timethat another sequence of actions (called envelope actions) execute.In these cases, the minimum length of time for the content actionsmust be less (or fit into) the maximum total length of time for theenvelope actions. If this is not the case, then an un-schedulable planis produced.2.1 Mini-SchedulerWhere the two problems interact, (i.e. where there are envelope ac-tions), some of the logical and temporal reasoning must be done to-gether to make sure that the plan is schedulable (i.e. that there isenough time to execute the content actions within the time of the en-velope actions). This is achieved by attaching a mini-scheduler forthese cases onto the planner.When an envelope action is placed in the plan, a new mini-scheduler is associated with it. This mini-scheduler consists of aSimple Temporal Network, a set of content actions (initially empty)and a set of orderings between these actions. The mini-schedulersuse the same algorithms as the main scheduling part of CRIKEY.Any (content) actions which are now considered, must be checkedagainst this mini-scheduler to ensure that if they must go in the en-velope, that the STN is consistent (that is to say that there is enoughtime to execute the action). If not, then the action is not consideredapplicable, and that branch is removed from the search space. Whenthe envelope’s end effects are placed in the plan, the mini-scheduleris then discarded.In the case of the match actions, assuming it is part of a bigger do-main, CRIKEY will search forward ignoring temporal information.When it comes to put in the light match action (an envelope), it willinstantiate a new mini-scheduler. It will then test to see if a fix fuseaction need go in this mini-scheduler, and if so, if it is consistent.Indeed, it fits, so the action is applicable and choosen for the plan. Itwill then test the second fix fuse action. This is not consistent withmini-scheduler (there is not enough time left to fix it before the matchruns out), so cannot be put in the plan. (If the fuses could be fixed inparallel, then this second action would be consistent and so chosen).The mini-scheduler would be closed and the end effects of the lightmatch action applied. CRIKEY would then go on to either light asecond match (and so start a new mini-scheduler) or solve anotherpart of the problem. In this way a schedulable plan is produced.3 CONCLUSIONS AND FURTHER WORKCRIKEY shows that it is possible to separate out temporal and lo-gical reasoning, whilst combining them where necessary. CRIKEYperforms the reasoning necessary to do this. It also demonstrates thatit is possible to perform a series of relaxations in order to find a plan,and tighten these relaxations where necessary. It is hoped that thesethemes will be explored further in the near future. The scheduler isof particular interest since at the moment it only performs a greedysearch. It could perform some search to improve the quality of theplan, depending on the metric of the original problem. Also, it isthought that the metric reasoning and logical reasoning can also beseparated out in the scheduler, particually since currently CRIKEYcannot accurately schedule domains where the resource consump-tion or production levels are dependent on the state. Further researchis intended to tighten the relaxed plan graph heuristic such that whenthis fails (i.e. when a plateaux is found), rather then searching a wayout of the space, a better (but more costly) heuristic is used.CRIKEY participated in the 4th International Planning Competi-tion, so results from that are hoped to provide an understanding of itpotential. However, the domains used were limited in the complexityin which the planning and scheduling interacted. Further testing willbe done with other temporal planners, on domains where there is aclose coupling between the two parts of the problem.REFERENCES[1] S. Edlekamp and M. Helmert, ‘On the implementation of mips’, in Pro-ceedings from the 4th Artificial Intelligence Planning and Scheduling(AIPS), Workshop on Decision-Theoretic Planning, pp. 18–25. Breken-ridge, Colorado:AAAI-Press, (2000).[2] M. Fox and D. Long, ‘The third international planning competition:Temoral and metric planning’, in Proceedings from the 6th Interna-tional Conference on Artificial Intelligence Planning and Scheduling(AIPS’02), pp. 115–117, (2002).[3] K. Halsey, ‘Temporal planning with a non-temporal planner’, in Doc-toral Consortium at the 13th International Conference on AutomatedPlanning and Scheduling (ICAPS), pp. 48–52, (June 2003).[4] Keith Halsey, Derek Long, and Maria Fox, ‘Isolating where planningand scheduling interact’, in Proceedings from the 22nd UK Planningand Scheduling Special Interest Group (PlanSIG’03), pp. 104–114, (Dec2003).[5] Jo¨rg Hoffmann, ‘Extending FF to numerical state variables’, in Proceed-ings of the 15th European Conference on Artificial Intelligence (ECAI-02), pp. 571–575, Lyon, France, (July 2002).[6] Manuela M. Veloso, M. Alicia Pe´rez, and Jaime G. Carbonell, ‘Non-linear planning with parallel resource allocation’, in Proceedings of theDARPA Workshop on Innovative Approaches to Planning, Scheduling,and Control, pp. 207–212. Morgan Kaufmann, (nov 1990).

Extending FF to numerical state variables’,

Isolating where planning and scheduling interact’,

Nonlinear planning with parallel resource allocation’,

On the implementation of mips’,

Temporal planning with a non-temporal planner’,

The third international planning competition: Temoral and metric planning’,

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Multiple relaxations in temporal planning

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