We investigate a new class of congestion games, called Totally Unimodular Congestion Games, in which the strategies of each player are expressed as binary vectors lying in a polyhedron defined using a totally unimodular constraint matrix and an integer right-hand side. We study both the symmetric and the asymmetric variants of the game. In the … Read more
The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of the enumeration tree. State-of-the-art procedures base the selection of variables on their “LP gains”, which is the dual bound … Read more
Given a set of departments, a number of rows and pairwise connectivities between these departments, the multi-row facility layout problem (MRFLP) looks for a non-overlapping arrangement of these departments in the rows such that the weighted sum of the center-to-center distances is minimized. As even small instances of the (MRFLP) are rather challenging, several special … Read more
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a “dual form” mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. This follows the general scheme of He and Lee, who did the case of Gomory … Read more
In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the … Read more
We study general two-stage stochastic programs and present conditions under which the second stage programs can be convexified. This allows us to relax the restrictions, such as integrality, binary, semi-continuity, and many others, on the second stage variables in certain situations. Next, we introduce two-stage stochastic disjunctive programs (TSS-DPs) and extend Balas’s linear programming equivalent … Read more
Optimal control problems (OCP) containing both integrality and partial differential equation (PDE) constraints are very challenging in practice. The most wide-spread solution approach is to first discretize the problem, it results in huge and typically nonconvex mixed-integer optimization problems that can be solved to proven optimality only in very small dimensions. In this paper, we … Read more
Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR based Branch and Bound (DSATUR) is an effective exact algorithm for the … Read more
This paper considers the risk-constrained stochastic traveling salesman problem with random arc costs. In the context of stochastic arc costs, the deterministic traveling salesman problem’s optimal solutions would be ineffective because the selected route might be exposed to a greater risk where the actual cost can exceed the resource limit in extreme scenarios. We present … Read more
In this paper, we prove that the sequential pairing cut-generating procedure of Guan et al. (2007) generalizes a special case of the mingled continuous multi-mixing cut-generating procedure. Citation Technical Report – MB2, Northwestern University, 10/2015