Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

Deng, Yan; Jia, Huiwen; Ahmed, Shabbir; Lee, Jon; Shen, Siqian

doi:10.1287/ijoc.2020.0970

Title: Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

Journal Article · Tue Oct 13 00:00:00 EDT 2020 · INFORMS Journal on Computing

DOI:https://doi.org/10.1287/ijoc.2020.0970· OSTI ID:1735791

Deng, Yan ^[1];

^[1]; Ahmed, Shabbir ^[2];

^[1];

^[1]

Univ. of Michigan, Ann Arbor, MI (United States)
Georgia Inst. of Technology, Atlanta, GA (United States)

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.

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Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); ONR

Grant/Contract Number:: SC0018018; CMMI-1633196; N00014-14-0315; N00014-17-1-2296; CMMI-1433066

OSTI ID:: 1735791

Journal Information:: INFORMS Journal on Computing, Vol. 33, Issue 2; Related Information: http://www-personal.umich.edu/~siqian/docs/scen_decom_data_source_code.zip; ISSN 1091-9856

Publisher:: INFORMSCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Chance-constrained programming
quantile bounds
scenario grouping
mixed-integer programming
branch-and-cut
scenario decomposition

Title: Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

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