A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings
Abstract
We study a twostage mixedinteger linear program (MILP) with more than 1 million binary variables in the second stage. We develop a twolevel approach by constructing a semicoarse 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 semicoarse 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 semicoarse 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 twolevel approach scales to large problems that are beyond the capacity of stateoftheart commercial MILPmore »
 Authors:

 Argonne National Lab. (ANL), Lemont, IL (United States)
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1339649
 Grant/Contract Number:
 AC0206CH11357
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computational Optimization and applications
 Additional Journal Information:
 Journal Volume: 65; Journal Issue: 1; Journal ID: ISSN 09266003
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; coarsened models; distributed generation; largescale problems; twolevel approach; multiperiod planning; resource and cost allocation; twostage mixedinteger programs
Citation Formats
Lin, Fu, Leyffer, Sven, and Munson, Todd. A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings. United States: N. p., 2016.
Web. doi:10.1007/s1058901698420.
Lin, Fu, Leyffer, Sven, & Munson, Todd. A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings. United States. doi:10.1007/s1058901698420.
Lin, Fu, Leyffer, Sven, and Munson, Todd. Tue .
"A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings". United States. doi:10.1007/s1058901698420. https://www.osti.gov/servlets/purl/1339649.
@article{osti_1339649,
title = {A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings},
author = {Lin, Fu and Leyffer, Sven and Munson, Todd},
abstractNote = {We study a twostage mixedinteger linear program (MILP) with more than 1 million binary variables in the second stage. We develop a twolevel approach by constructing a semicoarse 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 semicoarse 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 semicoarse 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 twolevel approach scales to large problems that are beyond the capacity of stateoftheart commercial MILP solvers.},
doi = {10.1007/s1058901698420},
journal = {Computational Optimization and applications},
number = 1,
volume = 65,
place = {United States},
year = {2016},
month = {4}
}
Web of Science