{"type":"ScholarlyArticle","title":"Improved Bin Completion for Optimal Bin Packing and Number Partitioning","authors":[{"name":"Ethan L. Schreiber","slug":"ethan-l-schreiber","given":"Ethan L.","family":"Schreiber","affiliation":""},{"name":"Richard E. Korf","slug":"richard-e-korf","given":"Richard E.","family":"Korf","affiliation":""}],"abstract":"The bin-packing problem is to partition a multiset of n numbers into as few bins of capacity C as possible, such that the sum of the numbers in each bin does not exceed C. We compare two existing algorithms for solving this problem: bin completion (BC) and branch-and-cut-and-price (BCP). We show experimentally that the problem difficulty and dominant algorithm are a function of n, the precision of the input elements and the number of bins in an optimal solution. We describe three improvements to BC which result in a speedup of up to five orders of magnitude as compared to the original BC algorithm. While the current belief is that BCP is the dominant bin-packing algorithm, we show that improved BC is up to five orders of magnitude faster than a state-of-the-art BCP algorithm on problems with relatively few bins. We then explore a closely related problem, the number-partitioning problem, and show that an algorithm based on improved bin packing is up to three orders of magnitude faster than a BCP solver called DIMM which claims to be state of the art. Finally, we show how to use number partitioning to generate difficult bin-packing instances.","doi":null,"url":"https://ijcai.org/proceedings/2013/103","pdf":"https://ijcai.org/proceedings/2013/0103.pdf","markdown":"https://ijcai.org/proceedings/2013/103.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/103","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":103,"pages":{"first":651,"last":657},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}