This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0-1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial problems. This approach is numerically tested on knapsack and multi-dimensional knapsack problems. The results obtained outperform many methods based on earlier literature.
Keywords: integer linear programming, chance constraints, robust optimization, heuristic
@article{RO_2009__43_2_157_0,
author = {Klopfenstein, Olivier},
title = {Tractable algorithms for chance-constrained combinatorial problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {157--187},
year = {2009},
publisher = {EDP Sciences},
volume = {43},
number = {2},
doi = {10.1051/ro/2009010},
mrnumber = {2527861},
zbl = {1173.90478},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2009010/}
}
TY - JOUR AU - Klopfenstein, Olivier TI - Tractable algorithms for chance-constrained combinatorial problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2009 SP - 157 EP - 187 VL - 43 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2009010/ DO - 10.1051/ro/2009010 LA - en ID - RO_2009__43_2_157_0 ER -
%0 Journal Article %A Klopfenstein, Olivier %T Tractable algorithms for chance-constrained combinatorial problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 157-187 %V 43 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2009010/ %R 10.1051/ro/2009010 %G en %F RO_2009__43_2_157_0
Klopfenstein, Olivier. Tractable algorithms for chance-constrained combinatorial problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 2, pp. 157-187. doi: 10.1051/ro/2009010
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