We provide two algorithms for computing the volume of the convex polytope $\Omega:=\{x\in \R^n_+ \,|\,Ax\leq b\}$, for $A\in\R^{m\times n}, b\in\R^n$. The computational complexity of both algorithms is essentially described by $n^m$, which makes them especially attractive for large $n$ and relatively small $m$, when the other methods with $O(m^n)$ complexity fail. The methodology which differs … Read more
This paper illustrates results obtained by a new metaheuristic approach, Greedy Randomized Adaptive Path Relinking, applied to solve static power transmission network design problems. This new approach consists of a generalization of GRASP concepts to explore different trajectories between two CitationAT&T Labs Research Report, December 2001 Submitted to PSCC’02.ArticleDownload View PDF
The Dedicated Aircraft Recovery Problem (DARP) involves decisions concerning aircraft to flight assignments in situations where unforeseen events have disrupted the existing flight schedule, e.g. bad weather causing flight delays. The dedicated aircraft recovery problem aims to recover these flight schedules through a series of reassignments of aircraft to flights, delaying of flights and cancellations … Read more
We present a heuristic method for general 0-1 mixed integer programming, intended for eventual incorporation into parallel branch-and-bound methods for solving such problems exactly. The core of the heuristic is a rounding method based on simplex pivots, employing only gradient information, for a strictly concave, differentiable merit function measuring integer feasibility. When local minima of … Read more
In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job … Read more
The $p$-Center problem consists in locating $p$ facilities among a set of $M$ possible locations and assigning $N$ clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. We present a new integer linear programming formulation for this Min-Max problem with a polynomial number … Read more
We describe extensions to algebraic modeling languages and their solver interfaces that will be needed to take advantage of constraint programming solvers, particularly in the area of combinatorial optimization. CitationTechnical Report, Department of Industrial Engineering and Management Sciences, Northwestern University (2001); based on a shorter version that appeared in the Proceedings of the Third International … Read more
We compare several semidefinite relaxations for the cut polytope obtained by applying the lift and project methods of Lov\’asz and Schrijver and of Lasserre. We show that the tightest relaxation is obtained when aplying the Lasserre construction to the node formulation of the max-cut problem. This relaxation $Q_t(G)$ can be defined as the projection on … Read more
With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most … Read more
A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous … Read more