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Title: A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model that coarsens with respect to variables and a coarse model that coarsens with respect to both variables and constraints. We coarsen binary variables by selecting a small number of prespecified on/off profiles. We aggregate constraints by partitioning them into groups and taking convex combination over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence provides an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. Here, the coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILPmore » solvers.« less
Authors:
 [1] ;  [1] ;  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
Publication Date:
Grant/Contract Number:
AC02-06CH11357
Type:
Accepted Manuscript
Journal Name:
Computational Optimization and applications
Additional Journal Information:
Journal Volume: 65; Journal Issue: 1; Journal ID: ISSN 0926-6003
Publisher:
Springer
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; coarsened models; distributed generation; large-scale problems; two-level approach; multi-period planning; resource and cost allocation; two-stage mixed-integer programs
OSTI Identifier:
1339649

Lin, Fu, Leyffer, Sven, and Munson, Todd. A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings. United States: N. p., Web. doi:10.1007/s10589-016-9842-0.
Lin, Fu, Leyffer, Sven, & Munson, Todd. A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings. United States. doi:10.1007/s10589-016-9842-0.
Lin, Fu, Leyffer, Sven, and Munson, Todd. 2016. "A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings". United States. doi:10.1007/s10589-016-9842-0. https://www.osti.gov/servlets/purl/1339649.
@article{osti_1339649,
title = {A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings},
author = {Lin, Fu and Leyffer, Sven and Munson, Todd},
abstractNote = {We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model that coarsens with respect to variables and a coarse model that coarsens with respect to both variables and constraints. We coarsen binary variables by selecting a small number of prespecified on/off profiles. We aggregate constraints by partitioning them into groups and taking convex combination over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence provides an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. Here, the coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILP solvers.},
doi = {10.1007/s10589-016-9842-0},
journal = {Computational Optimization and applications},
number = 1,
volume = 65,
place = {United States},
year = {2016},
month = {4}
}