On handling indicator constraints in mixed integer programming

On handling indicator constraints in mixed integer programming

Mixed integer programming (MIP) is commonly used to model indicator constraints, i.e., constraints that either hold or are relaxed depending on the value of a binary variable. Unfortunately, those models tend to lead to weak continuous relaxations and turn out to be unsolvable in practice; this is what happens, for e.g., in the case of Classification problems with Ramp Loss functions that repre...

Workshop on Mixed Integer Programming

Mixed integer programming with a class of nonlinear convex constraints

We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second-order and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be g...

Mixed integer linear programming formulations for probabilistic constraints

We introduce two new formulations for probabilistic constraints based on extended disjunctive formulations. Their strength results from considering multiple rows of the probabilistic constraints together. The properties of the first can be used to construct hierarchies of relaxations for probabilistic constraints, while the second provides computational advantages over other formulations.

Comparing Mixed-Integer and Constraint Programming for the No-Wait Flow Shop Problem with Due Date Constraints

The impetus for this research was examining a flow shop problem in which tasks were expected to be successively carried out with no time interval (i.e., no wait time) between them. For this reason, they should be completed by specific dates or deadlines. In this regard, the efficiency of the models was evaluated based on makespan. To solve the NP-Hard problem, we developed two mathematical mode...