As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators’ toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that … Read more
The vertex cover polytopes of graphs do not admit polynomial-size extended formulations. This motivates the search for polyhedral analogues to approximation algorithms and fixed-parameter tractable (FPT) algorithms. While the polyhedral approximability of vertex cover has been studied, we know of no extended formulations parameterized by the size of the vertex cover. To this end, we … Read more
We consider the problem of identifying the solution(s) to an optimization problem whose domain is a subset of the integer lattice, and whose objective and constraint functions can only be observed using a stochastic simulation. Such problems seem particularly prevalent (see www.simopt.org) within service systems having capacity or service-level constraints. We present cgR-SPLINE — a … Read more
In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovasz-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a … Read more
Scheduling elective surgeries is a complicated task due to the coupled effect of multiple sources of uncertainty and the impact of the proposed schedule on the downstream units. In this paper, we propose an adaptive robust optimization model to address the existing uncertainty in surgery duration and length-of-stay in the surgical intensive care unit. The … Read more
We study the polyhedron of the unit commitment problem, and consider a relaxation involving the ramping constraints. We study the three-period ramp-up polytope, and describe the convex-hull using a new class of inequalities. Citation [1] J. Ostrowski, M. F. Anjos, and A. Vannelli, \Tight mixed integer linear programming formulations for the unit commitment problem,” Power … Read more
We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more
In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more
We discuss an application of the well-known Multiplicative Weights Update (MWU) algorithm to non-convex and mixed-integer nonlinear programming. We present applications to: (a) the distance geometry problem, which arises in the positioning of mobile sensors and in protein conformation; (b) a hydro unit commitment problem arising in the energy industry, and (c) a class of … Read more
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e., number of iterations needed, can theoretically be improved by scaling methods. We extend these results by an … Read more