J. Pearl. A ffl --- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... map which represents a complex terrain of variable altitude, where the cost of a route is an indication of its quality [1] In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms such as A [4] or variants such as A ffl [9] to be applied. However, while such planners are complete and optimal (or optimal to some bound ffl) it can be difficult to formulate the route planning task in terms of minimising a single criterion. One way of incorporating multiple criteria (such as time, energy or visibility) into the ....

....step, so that even a solution with overestimated cost will eventually become cheaper than any other path expanded so far. If, in addition, the slack ordering is used and the true cost is never overestimated, the first solution found will be the cheapest. The formal argument is the same as for A [9]. 2 6 Comparison of ABC and A In the worst case, A requires exponential space (and hence exponential time) to find a solution. ABC is a strict generalisation of A : with a single admissible optimisation constraint its behaviour is identical to A , and in this case its worst case ....

J. Pearl. A ffl --- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

....of a route is an indication of its quality. In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms to be applied. A number of route planners in the literature are based on the A algorithm [5] or variants such as A ffl [11]. For example, A has been used in a number of Computer Generated Forces systems as the basis of their planning component, to plan road routes [2] avoid moving obstacles [6] avoid static obstacles [7] and to plan concealed routes [10] However, while such planners are complete and optimal (or ....

J. Pearl. A ffl -- An algorithm using search effort estimates, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 4, No. 4, pp. 392--399, 1982.

.... map which represents a complex terrain of variable altitude, where the cost of a route is an indication of its quality [1] In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms such as A [4] or variants such as A ffl [10] to be applied. However, while such planners are complete and optimal (or optimal to some bound ffl) it can be difficult to formulate the route planning task in terms of minimising a single criterion. One way of incorporating multiple criteria (such as time, energy, visibility) into the planning ....

....step, so that even a solution with overestimated cost will eventually become cheaper than any other path expanded so far. If, in addition, the slack ordering is used and the true cost is never overestimated, the first solution found will be the cheapest. The formal argument is the same as for A [10]. 2 6 Comparison of ABC and A In the worst case, A requires exponential space (and hence exponential time) to find a solution. ABC is a strict generalisation of A : with a single admissible optimisation constraint its behaviour is identical to A , and in this case its worst case ....

J. Pearl. A ffl --- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

....the algorithms we have compared it with A . Unfortunately, the huge amount of memory and computation required by classical A to solve this kind of problems has prevented us from being able to perform the comparison. However, we have been able to use a variant of A known as A ffl (see [10]) which is guaranteed to find solutions that can be worse than optimal by at most ffl. A plan produced by A ffl with ffl = 0:1 is shown in Figure 5(b) Although no definitive results are available, our experiments seem to suggest that GA outperforms A ffl . Also, we have observed that ....

J. Pearl. a ffl -- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

.... planning component, for example for planning road routes [1] avoiding moving obstacles [4] avoiding static obstacles [5] and for planning concealed routes [6] The memory requirements of A mean that it is impractical in its pure form, and for our tests we used the variant known as A ffl [8] which is guaranteed to find solutions that can be worse than optimal by at most ffl. For comparison, Figure 3 shows the plan produced by A ffl with ffl = 0:1 on the same test problem as Figure 2. Figure 3: An example route produced by the A ffl planner. Both planners used the same cost ....

J. Pearl. A ffl -- An algorithm using search effort estimates, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 4, No. 4, pp. 392--399, 1892.

.... represents a complex terrain of variable altitude, where the cost of a route is an indication of its quality [1] In this approach, planning is seen as a search problem in the space of partial plans, allowing many of the classic search algorithms such as A [5] or variants such as A ffl [11] to be applied. However, while such planners are complete and optimal (or optimal to some bound ffl) it can be difficult to formulate the planning task in terms of minimising a single criterion (cost function) One approach to incorporating multiple criteria into the planning process is to define ....

J. Pearl. A ffl -- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

....of a route is an indication of its quality. In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms to be applied. A number of route planners in the literature are based on the A algorithm [3] or variants such as A ffl [7]. For example, A has been used in a number of CGF systems as the basis of their planning component, to plan road routes [1] avoid moving obstacles [4] avoid static obstacles [5] and to plan concealed routes [6] However, while such planners are complete and optimal (or optimal to some bound ....

J. Pearl. A ffl -- An algorithm using search effort estimates, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 4, No. 4, pp. 392--399, 1982.

.... map which represents a complex terrain of variable altitude, where the cost of a route is an indication of its quality [1] In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms such as A [3] or variants such as A ffl [7] to be applied. A key assumption of all problem solving approaches based on utility theory, including heuristic search, is that we can assign a utility or cost to each state. This in turn requires that all criteria of interest can be reduced to a common ratio scale. For example, in a game of chess ....

....that costs are finite and non negative, so that even a solution with overestimated cost will eventually become cheaper than any other path expanded so far. If, in addition, the heuristics are admissible, the first solution found will be the cheapest. The formal argument is the same as for A [7]. 2 In the general case, for arbitrary constraints and an infinite search space, ABC is not complete. However, in many cases imposing restrictions on the types of constraints and the ordering of equivalence classes makes the algorithm complete. We give two examples below. Theorem 3 ABC is ....

J. Pearl. A ffl -- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

.... planning component, for example for planning road routes [1] avoiding moving obstacles [4] avoiding static obstacles [5] and for planning concealed routes [6] The memory requirements of A mean that it is impractical in its pure form, and for our tests we used the variant known as A ffl [8] which is guaranteed to find solutions that can be worse than optimal by at most ffl. For comparison, Figure 3 shows the plan produced by A ffl with ffl = 0:1 on the same test problem as Figure 2. 1 We are grateful to Richard Penney and Jeremy Baxter at DRA Malvern for providing the terrain ....

J. Pearl. A ffl -- An algorithm using search effort estimates, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 4, No. 4, pp. 392--399, 1892.

....sense that no other optimal algorithm is guaranteed to expand fewer nodes than A . For large real life problems, the memory requirements of A mean that it is impractical in its pure form, and in most cases it is necessary to use one of the ffl admissible variants of A such as A ffl [8], which are guaranteed to find solutions that can be worse than optimal by at most ffl. GA is a generalisation of A inspired by our previous work [11; 12] in which the operators are not constrained to be unary (i.e. an operator can take more than one node as input) and selection of the ....

J. Pearl. A ffl -- An algorithm using search effort estimates, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 4, No. 4, pp. 392--399, 1892.

.... map which represents a complex terrain of variable altitude, where the cost of a route is an indication of its quality [1] In this approach, planning is seen as a search problem in space of partial plans, allowing many of the classic search algorithms such as A [4] or variants such as A ffl [8] to be applied. However, while such planners are complete and optimal (or optimal to some bound ffl) it can be difficult to formulate the route planning task in terms of minimising a single criterion. One way of incorporating multiple criteria (such as time, energy, visibility) into the planning ....

....step, so that even a solution with overestimated cost will eventually become cheaper than any other path expanded so far. If, in addition, the slack ordering is used and the true cost is never overestimated, the first solution found will be the cheapest. The formal argument is the same as for A [8]. 2 6 Comparison of ABC and A In the worst case, A requires exponential space (and hence exponential time) to find a solution. ABC is a strict generalisation of A : with a single admissible optimisation constraint its behaviour is identical to A , and in this case its worst case ....

J. Pearl. A ffl --- an algorithm using search effort estimates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(4):392--399, 1982.

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