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

Journal Article · Tue Apr 12 00:00:00 EDT 2016 · Computational Optimization and Applications

DOI:https://doi.org/10.1007/s10589-016-9842-0· OSTI ID:1339649

Lin, Fu ^[1]; Leyffer, Sven ^[1]; Munson, Todd ^[1]

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1. Argonne National Lab. (ANL), Lemont, IL (United States)

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.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1339649
• Journal Information: Computational Optimization and Applications, Vol. 65, Issue 1; ISSN 0926-6003
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

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