Most of the previous studies in heuristic search have assumed that the heuristic estimate of a node remains constant during the execution of algorithms In a recent study, L. Mero suggested a method for run-time modification of heuristic estimate of nodes. This method of modifiable heuristics can in general reduce the total number of node expansions. It is shown in this paper, with counter examples, that Mero’s algorithm (B′) is not as good as claimed.

Network search algorithms with modifiable heuristics

In this thesis we investigate path finding problems, that is, planning routes from a start node to some goal nodes in a graph. Such problems arise in many fields of technology, for example, production planning, energy-aware message routing in large networks, resource allocation, and vehicle navigation systems. We concentrate mostly on planning a minimum cost path using the A algorithm. We begin by proving new theorems comparing the performance of A to other (generalized) path finding algorithms. In some cases, A is an optimal method in a large class of algorithms. This means, roughly speaking, that A explores a smaller region of the search space than the other algorithms in the given class. We develop a new method of improving a given (static) heuristic for A dynamically, during search. A heuristic controls the search of A so that unnecessary branches of the tree of nodes that A visits are pruned. The new method also finds an optimal path to any node it visits for the first time so that every node will be visited only once. The latter is an important property considering the efficiency of the search. We examine the use of A as a higher level method to allocate resources among several path finding algorithms. In some cases, the A is an optimal resource allocation method, which means that the number of the nodes the path finding algorithms together visit is minimized. As applications of A, we have developed new hierarchical algorithms for robot point-to-point path planning tasks, and new algorithms for power-aware routing of messages in large communication networks. The new algorithms are more robust than some older ones to which we compare. Moreover, one of the message routing algorithms produces higher average lifetimes of the network than those of the widely quoted max-min zPmin algorithm.

Extensions and applications of the A* algorithm

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Solutions and Heuristics for Troubleshooting with Dependent Actions and Conditional Costs

In a recent study, L. Mero suggested a method for run-time modification of heuristic estimate of nodes. An algorithm, called B′, was presented. Performance of B′ was analysed under modifiable and admissible heuristics. It was claimed that B′ was an improved version of a polynomial time bound algorithm, namely B, originally due to Martelli. While in turn B was based on the Algorithm A introduced by Hart, Nilsson et al.Surprisingly, it is observed that B′ can make exponential number of node expansions in the worst case. In particular B′ can make more node expansions than B and also than A! If heuristic is not admissible B′ can output worse solution that B (or A). Under the same framework of modifiable heuristics a new algorithm, called D, is proposed. It is shown that D makes polynomial number of node expansions in the worst case and always finds a solution which is at least as good as that found by B′ and B. Algorithm D is compared with Algorithm C presented by Bagchi and Mahanti. Algorithm C, in general, showed better performance than other algorithms. Here it is shown that C and D output same solution but D makes less number of node expansions than C. The admissibility condition is relaxed and results are proved under a general assumption that heuristic estimate is only non-negative.

A. Mahanti

Papers

Heuristic search in networks with modifiable estimate