Name
Title | ||
|---|---|---|
A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem |
Abstract | ||
|---|---|---|
AbstractWe examine bilevel mixed-integer programs whose constraints and objective functions depend on both upper-and lower-level variables. The class of problems we consider allows for nonlinear terms to appear in both the constraints and the objective functions, requires all upper-level variables to be integer, and allows a subset of the lower-level variables to be integer. This class of bilevel problems is difficult to solve because the upper-level feasible region is defined in part by optimality conditions governing the lower-level variables, which are difficult to characterize because of the nonconvexity of the follower problem. We propose an exact finite algorithm for these problems based on an optimal-value-function reformulation. We demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior. Computational experiments demonstrate that our approach outperforms a state-of-the-art algorithm for solving bilevel mixed-integer linear programs. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1287/opre.2017.1589 | Periodicals |
Keywords | Field | DocType |
bilevel optimization,integer programming,nonlinear programming,scheduling | Integer,Mathematical optimization,Nonlinear system,Bilevel optimization,Scheduling (computing),Nonlinear programming,Bellman equation,Feasible region,Integer programming,Mathematics | Journal |
Volume | Issue | ISSN |
65 | 3 | 0030-364X |
Citations | PageRank | References |
7 | 0.45 | 21 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Leonardo Lozano | 1 | 59 | 4.52 |
| J. Cole Smith | 2 | 610 | 43.34 |