Optimization Problems with Multiple Characteristics

We are working on real-world, large-scale, hard optimization problems that have multiple, interesting problem characteristics. While they can be broadly grouped under the category of mixed-integer nonlinear programming problems, the following examples can exhibit any of the following problem components: discrete variables, continuous variables, linear functions, nonlinear functions, cone constraints, complementarity/equilibrium constraints.

Portfolio Optimization Problems

These are examples of mixed-integer second-order cone programming problems arising in portfolio optimization.

Multivehicle Path Coordination under Communication Constraints

These are nonconvex nonlinear reformulations of mixed-integer programming problems arising in the discretization of the multivehicle path coordination problem. The paths are represented by cubic splines, and the vehicles are required to be in communication with a given number of others at all times. The nonlinear models include second-order cone constraints to limit distance between vehicles in communication and complementarity constraints to ensure sufficient communication and arrival information.

4 vehicles: Model and Data
10 vehicles: Model and Data
20 vehicles: Model and Data
50 vehicles: Model and Data

We also considered a scenario with 10 vehicles and a moving jammer: Model and Data

Cell Manufacturing Problems with No Partial Leftover Lots

These are lot-sizing problems arising in manufacturing, where the lot-size left at the end of a manufacturing cycle cannot be a partial lot. This requires the lot-sizes to be a fraction (with integer denominator) or an integer multiple of the demand. As such, these problems have integer variables and complementarity constraints.

The development of this page and all posted materials was supported by NSF Grant CCF-0725692. Other materials are available here and here.