{"type":"ScholarlyArticle","title":"From Approximate to Optimal Solutions: Constructing Pruning and Propagation Rules","authors":[{"name":"Ian P. Gent","slug":"ian-p-gent","given":"Ian P.","family":"Gent","affiliation":""},{"name":"Toby Walsh","slug":"toby-walsh","given":"Toby","family":"Walsh","affiliation":""}],"abstract":"At the heart of many optimization procedur es are powerful pruning and propagation rul es. This paper presents a case study in the construction of such rules. We develop a new algorithm, Complete Decreasing Best Fit, that finds the optimal packing of objects into bins. The algorithm use a branching rule based on the well known Decreasing Best Fit approximation algorithm. In addition, it includes a powerful pruning rule derived from a bound on the solution to the remaining subproblem. Th e bound is constructed by using modular arithmetic to decompose the numerical constraints. We show that the pruning rule adds essentially a constant factor overhead to runtime, whilst reducing search significantly. On the hardest problems , runtime can be redu ce d by an order of magnitude . Finally we demonstrate how propagation rules can be built by adding lookahead to pruning rules. This general approach - optimization procedures built from branching rules based on good approximation algorithms, and pruning and propagation rul es derived from bounds on the remaining subproblem - may be effective on other NP-complete problems.","doi":null,"url":"https://ijcai.org/proceedings/1997/201","pdf":"https://ijcai.org/proceedings/1997/0201.pdf","markdown":"https://ijcai.org/proceedings/1997/201.md","bibtex":"https://ijcai.org/proceedings/1997/bibtex/201","volume":{"slug":"1997","title":"Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1997","url":"https://ijcai.org/proceedings/1997/","year":1997,"location":"Nagoya, Japan","dates":"","editors":"Martha E. Pollack","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Search","track":"Search","number":201,"pages":{"first":1396,"last":1400},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}