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

Abstract

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:

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

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+ Show Author Affiliations

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

Publication Date:

Tue Apr 12 00:00:00 EDT 2016

Research Org.:

Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:

1339649

Grant/Contract Number:  

AC02-06CH11357

Resource 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

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