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Efficient algorithms with performance guarantees for the stochastic multiple-choice knapsack problem

Efficient algorithms with performance guarantees for the stochastic multiple-choice knapsack problem
Efficient algorithms with performance guarantees for the stochastic multiple-choice knapsack problem
We study the stochastic multiple-choice knapsack problem, where a set of K items, 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 of 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(sqrt{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(sqrt{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.
403-409
ACM
Tran-Thanh, Long
e0666669-d34b-460e-950d-e8b139fab16c
Xia, Yingce
e57e1a80-edf9-4292-a906-7fec49150e07
Qin, Tao
e1e8d0c9-d21a-4907-a401-64ed11c288a5
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Tran-Thanh, Long
e0666669-d34b-460e-950d-e8b139fab16c
Xia, Yingce
e57e1a80-edf9-4292-a906-7fec49150e07
Qin, Tao
e1e8d0c9-d21a-4907-a401-64ed11c288a5
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Tran-Thanh, Long, Xia, Yingce, Qin, Tao and Jennings, Nicholas R. (2015) Efficient algorithms with performance guarantees for the stochastic multiple-choice knapsack problem. In IJCAI'15 Proceedings of the 24th International Conference on Artificial Intelligence. ACM. pp. 403-409 .

Record type: Conference or Workshop Item (Paper)

Abstract

We study the stochastic multiple-choice knapsack problem, where a set of K items, 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 of 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(sqrt{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(sqrt{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.

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More information

Accepted/In Press date: 16 April 2015
e-pub ahead of print date: 2 May 2015
Published date: July 2015
Venue - Dates: 24th International Joint Conference on Artificial Intelligence (IJCAI-15), Buenos Aires, Brazil, 2015-07-25 - 2015-07-31

Identifiers

Local EPrints ID: 376978
URI: http://eprints.soton.ac.uk/id/eprint/376978
PURE UUID: 652dcff2-a717-4b3d-ba0a-a6a0260eb97b
ORCID for Long Tran-Thanh: ORCID iD orcid.org/0000-0003-1617-8316

Catalogue record

Date deposited: 11 May 2015 23:11
Last modified: 04 Dec 2019 01:33

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Contributors

Author: Long Tran-Thanh ORCID iD
Author: Yingce Xia
Author: Tao Qin
Author: Nicholas R. Jennings

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