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Planning

Planning. Chapter 11- Part2 Author: Vali Derhami. Planning with state-space search. 1- Forward state-space search (progression planning) 2- Backward state-space search. Forward state-space search (progression planning). Start form initial state.

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Planning

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  1. Planning Chapter 11- Part2 Author: Vali Derhami

  2. Planning with state-space search 1- Forward state-space search (progression planning) 2- Backward state-space search

  3. Forward state-space search (progression planning) • Start form initial state. • Successor states are generated with applying Applicable actions (The step cost of each action is typically 1). • Goal test. • The approach quickly bogs down without a good heuristic.

  4. Backward state-space search (Regressive planners) • Start from goal state • Relevant and Consistent actions: • An action is relevant to a conjunctive goal if it achieves one of the conjuncts of the goal. • In addition to insisting that actions achieve some desired literal, we must insist that the actions not undo any desired literals. An action that satisfies this restriction is called consistent. • predecessor state is generated as follows: • Any positive effects of A that appear in G are deleted. • Each precondition literal of A is added to G, unless it already appears. • Test for Termination: a Generated predecessor is satisfied by the initial state of the planning problem.

  5. Air cargo example • Goal: At(C1,B)  At(C2, B) ...  At(C20, B) • relevant action Unload (C1,p, B). • Action(Unload(c, p, a), • PRECOND: In(c, p)  At(p, a)  Cargo(c)  Plane(p)  Airport(a) • EFFECT: At(c, a) In(c, p)) • Therefore, any predecessor state must include these preconditions: In(C1,p)  At(p, B)  Cargo(c1)  Plane(p)  Airport(B) • The subgoal At(C1,B) should not be true in the predecessor state. Thus, the predecessor description the predecessor description is In(C1,p)  At(p, B)  Cargo(c1)  Plane(p)  Airport(B)  At(C2, B)  ...  At(C20, B) . • One Irreleavnt action: • fly an empty plane from JFK to SFO; this action reaches a goal state from a predecessor state in which the plane is at JFK and all the goal conjuncts are satisfied.

  6. Heuristics for state-space search • Derive a relaxed problem (مساله تعدیل شده) • A approach is to pretendthat a pure divide-and-conquer algorithm will work. This is called the subgoal independence assumption: the cost of solving a conjunction of subgoals is approximated by the sum of the costs of solving each subgoal independently. • وانمود کنیم که یک الگوریتم تقسیم و حل در اینجا کار خواهد کرد. این روش فرص استقلال اهداف فرعی نامیده می شود. بیان میکند که هزینه حل ترکیب عطفی اهداف فرعی، تقریبا برابر با مجموع هزینه های حل هر یک از آن اهداف فرعی بصورت مستقل خواهد بود. • The subgoal independence assumption can be optimistic or pessimistic. It is optimistic when there are negative interactions between the subplans for each subgoal • The simplest idea is to relax the problem by removing all preconditions from the actions.

  7. Partial-Order Planning • Forward and backward state-space search are particular forms of totally ordered plan search. هر دوی روشهای جستجوی پیش رو پس رو فضای حالت، شکلهای خاصی از یک جستجوی برنامه ریزی کاملا مرتب محسوب می شوند. • عدم بهره بندی از مزایای تجزيه در برنامه ريزی کاملا مرتب

  8. Putting of pair shoes

  9. قسمت های برنامه ریزی • هر برنامه ریزی شامل 4 قسمت اساسی • دو بخش اول معرف مراحل برنامه ریزی • دو بخش آخر بازگو کننده چگونگی توسعه 1- مجموعه ای از اقدامات: مراحل اجرایی برنامه ریزی. برنامه ریزی تهی شامل دو اقدام start و Finish • Start هیچ پیش شرطی ندارد ولی در قسمت اثر شامل همه لیترالهای حالت اولیه مساله • Finish بدون اثر و لیترالهای هدف در قسمت پیش شرط آن

  10. قسمت های برنامه ریزی (ادامه) 2- مجموعه ای از محدودیتهای ترتیب. • A before B" and means that action A must be executed sometime beforeaction B • No cycle:

  11. قسمت های برنامه ریزی (ادامه) 3- رابطهای سببی: عمل A به P می رسد بخاطر B. Pاثر A و پیش شرط B است. P باید در فاصله زمانی پس از اقدام A تا اقدام B درست باقی بماند. نباید برنامه با افزودن اقدام جدیدی مانند Cکه اثر P دارد انرا نقض کند.

  12. قسمت های برنامه ریزی (ادامه) 4- پیش شرطهای باز: یک پیش شرط باز است در صورتی که بوسیله برخی از اقدامات موجود در برنامه ریزی بدست نیاید. • هدف کوچک نمودن آنها تا رسیدن به مجموعه تهی است. -برنامه سازگار: یک برنامه ریزی که دارای هیچ حلقه ای در ترتیب محدودیتها یا تناقضی در رابطه های سببی نباشد.

  13. Example: Flat Tire Problem (search) Pick an open precondition At(Spare,Axle) Only PutOn(Spare,Axle) achieves that

  14. Example: Flat Tire Problem (Cont.)

  15. Example: Flat Tire Problem (Cont.)

  16. Example: Flat Tire Problem (Cont.) • The only remaining open precondition at this point is the At(Spare, Trunk) precondition of the action Remove(Spare, Trunk). The only action that can achieve it is the existing Start action, but the causal link from Start to Remove(Spare, Trunk) is in conflict with the At(Spare, Trunk) effect of LeaveOvernight. • We are forced to back up, remove the LeaveOvernight action and the last two causal links,

  17. Example: Flat Tire Problem (Cont.)

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