{"type":"ScholarlyArticle","title":"Efficient Algorithms with Performance Guarantees for the Stochastic Multiple-Choice Knapsack Problem","authors":[{"name":"Long Tran-Thanh","slug":"long-tran-thanh","given":"Long","family":"Tran-Thanh","affiliation":""},{"name":"Yingce Xia","slug":"yingce-xia","given":"Yingce","family":"Xia","affiliation":""},{"name":"Tao Qin","slug":"tao-qin","given":"Tao","family":"Qin","affiliation":""},{"name":"Nicholas R. Jennings","slug":"nicholas-r-jennings","given":"Nicholas R.","family":"Jennings","affiliation":""}],"abstract":"We study the stochastic multiple-choice knapsack problem, where a set of Kitems, whose value and weight are random variables, arrive to the system at each time step, and a decision maker has to choose at most one item to put into the knapsack without exceeding its capacity. The goal is the decision-maker is to maximise the total expected value of chosen items with respect to the knapsack capacity and a finite time horizon.We provide the first comprehensive theoretical analysis of the problem. In particular, we propose OPT-S-MCKP, the first algorithm that achieves optimality when the value-weight distributions are known. This algorithm also enjoys O(√{T}) performance loss, where T is the finite time horizon, in the unknown value-weight distributions scenario.We also further develop two novel approximation methods, FR-S-MCKP and G-S-MCKP, and we prove that FR-S-MCKP achieves O(√{T}) performance loss in both known and unknown value-weight distributions cases, while enjoying polynomial computational complexity per time step. On the other hand, G-S-MCKP does not have theoretical guarantees, but it still provides good performance in practice with linear running time.","doi":null,"url":"https://ijcai.org/proceedings/2015/63","pdf":"https://ijcai.org/proceedings/2015/0063.pdf","markdown":"https://ijcai.org/proceedings/2015/63.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/63","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Constraints, Satisfiability, and Search","track":"Main Track","number":63,"pages":{"first":403,"last":409},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}