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 »

- 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}

}