{"type":"ScholarlyArticle","title":"Multi-Dimensional Heuristic Searching","authors":[{"name":"Peter C. Nelson","slug":"peter-c-nelson","given":"Peter C.","family":"Nelson","affiliation":"Dept. of Electrical Engineering and Computer Science University of Illinois at Chicago Chicago , Illinois 60680"},{"name":"Lawrence J. Henschen","slug":"lawrence-j-henschen","given":"Lawrence J.","family":"Henschen","affiliation":""}],"abstract":"A heuristic improvement technique referred to as multi-dimensional heuristics is presented. Instead of only applying the heuristic between two states xl and x2, when a distance estimate of X 1 X 2 is needed, this technique uses a reference state R and applies the heuristic function to (X1 ,R) and (X2,R) and compares the resulting values. If two states are close to each other, then they should also be approximately equidistant to a third reference state. It is possible to use many such reference states to improve some heuristics. The reference states are used to map the search into an N-dimensional search space. The process of choosing reference states can be automated and is in fact a learning procedure. Test results using the 15-puzzle are presented in support of the effectiveness of multi-dimensional heuristics. This method has been shown to improve both a weak 15-puzzle heuristic, the tile reversal heuristic, as well as the stronger Manhattan distance heuristic.","doi":null,"url":"https://ijcai.org/proceedings/1989/50","pdf":"https://ijcai.org/proceedings/1989/0050.pdf","markdown":"https://ijcai.org/proceedings/1989/50.md","bibtex":"https://ijcai.org/proceedings/1989/bibtex/50","volume":{"slug":"1989","title":"Proceedings of the Eleventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1989","url":"https://ijcai.org/proceedings/1989/","year":1989,"location":"Detroit, Michigan, USA","dates":"August 20-25 1989","editors":"N. S. Sridharan","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Search","track":"Search","number":50,"pages":{"first":316,"last":320},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[De Champeaux and Sint, 1977] D. De Champeaux and L. Sint. An Improved Bidirectional Heuristic Search Algorithm. Journal ofthe ACM, 24:177-191, 1977.","title":"An Improved Bidirectional Heuristic Search Algorithm","authors":"D De Champeaux, L Sint","year":"1977","venue":"Journal ofthe ACM","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Hart et al., 1968] P. Hart, R. Duda, and B. Raphael. A Formal Basis for the Heuristic Determination of Min- imum Cost Paths. IEEE Trans. on SSG, 4 1968.","title":"A Formal Basis for the Heuristic Determination of Minimum Cost Paths","authors":"P Hart, R Duda, B Raphael","year":"1968","venue":"IEEE Trans. on SSG","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Korf, 1985] Richard E. Korf. Depth-First Iterative- Deepening: An Optimal Admissible Tree Search. Ar- tificial Intelligence, 27:97-109 , July 1985 .","title":"Depth-First Iterative-Deepening: An Optimal Admissible Tree Search","authors":"Richard E Korf","year":"1985","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Nelson, 1988] Peter C. Nelson. Parallel Bidirectional Search using Multi-Dimensional Heuristics. Ph.D. Dissertation, Dept. of Electrical Engineering and Computer Science, Northwestern University, June 1988.","title":"Parallel Bidirectional Search using Multi-Dimensional Heuristics","authors":"C Peter, Nelson","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Rich, 1983] Elaine Rich. Artificial Intelligence .","title":"Artificial Intelligence","authors":"Elaine Rich","year":null,"venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}