# <u>Correction</u> to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths"

@article{Hart1972uCorrectionuT, title={<u>Correction</u> to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths"}, author={Peter E. Hart and Nils J. Nilsson and Bertram Raphael}, journal={SIGART Newsl.}, year={1972}, volume={37}, pages={28-29} }

Our paper on the use of heuristic information in graph searching defined a path-finding algorithm, A*, and proved that it had two important properties. In the notation of the paper, we proved that if the heuristic function ñ (n) is a lower bound on the true minimal cost from node n to a goal node, then A* is <u>admissible;</u> i.e., it would find a minimal cost path if any path to a goal node existed. Further, we proved that if the heuristic function also satisfied something called the <u…

## 165 Citations

### Completeness and Admissibility for General Heuristic Search Algorithms—A Theoretical Study: Basic Concepts and Proofs

- Computer ScienceJ. Heuristics
- 1999

General theorems about the completeness and the sub-admissibility that widely extend the previous results are proved and provide a theoretical support for using diverse kinds of Heuristic Search algorithms in enlarged contexts, specially when the state graphs and the evaluation functions are less constrained than ordinarily.

### A heuristic search approach for solving a minimum path problem requiring arc cost determination

- BusinessIEEE Trans. Syst. Man Cybern. Part A
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Two generalizations of A*, BA* and DA, which consider the problem of finding a minimum cost path from the start node to a finite goal node set in a directed OR-graph, are presented and analyzed.

### A Metric Space Approach to the Specification of the Heuristic Function for the A* Algorithm

- Computer ScienceIEEE Trans. Syst. Man Cybern. Syst.
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It is shown how to specify an admissible and monotone heuristic function for a wide class of problem domains and applications to an optimal parts distribution problem in flexible manufacturing systems and artificial intelligence planning problems are provided.

### Reconsideration of a theorem on admissible ordered search algorithms

- MathematicsACM '76
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An improved proof is presented for a theorem on search algorithms which find minimal cost paths in a graph. The theorem essentially states that when searching for a minimal cost path in a graph, a…

### A heuristic search algorithm for path determination with learning

- Computer ScienceIEEE Trans. Syst. Man Cybern. Part A
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An algorithm for finding a least-cost-path from start node to goal node set in a directed graph, adaptive A*(AA*), which can be used to automate knowledge acquisition, so that A* exhibits a form of machine learning.

### A best-first search algorithm guided by a set-valued heuristic

- Computer ScienceIEEE Trans. Syst. Man Cybern.
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Presents an algorithm, called A/sup G/, for finding the least-cost path from start node to goal node set in an OR-graph, where arc costs are scalar-valued and the cost of each path is the sum of the…

### Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties

- Computer ScienceAlgorithms
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This paper focuses on a variant of this problem in which additional penalties are incurred at the vertices, and proposes two variants of Dijkstra’s algorithm that operate on the original, unexpanded graph.

### Multiobjective A*

- Computer ScienceJACM
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A multiobjective generalization of the heuristic search algorithm A* is presented and it is shown that &fOA * is complete and, when used with a suitably defined set of admissible heuristic functions, admissible.

### A methodology for solving facility layout problem considering barriers: genetic algorithm coupled with A* search

- BusinessJ. Intell. Manuf.
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This work proposes a new methodology and mathematical formulation to address the facility layout problem to minimise the total material handling cost subjected to production-derived constraints and combines a genetic algorithm and a homogenous methodology to improve the quality of the facility layouts.

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