We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. Citation CORC Report TR-2005-07, Columbia University Article Download View Using mixed-integer programming … Read more
We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. A mixed integer mathematical formulation is presented. We propose … Read more
In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more
We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V,E) with nonnegative edge weight d(u,v), (u,v) in E, and two integers K and B, find a partition of the nodes of G into K subsets so that … Read more
Given r real functions F1 (x), . . . , Fr (x) and an integer p between 1 and r, the Low Order- Value Optimization problem (LOVO) consists of minimizing the sum of the functions that take the p smaller values. If (y1 , . . . , yr ) is a vector of data … Read more
In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on Semi-Definite Programming (SDP). We introduce several SDP relaxation models for MIMO systems, with … Read more
We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modelled by a geometric Brownian motion or a number of mean-reverting processes of interest. This methodology identifies derivative prices with infinite-dimensional linear programming problems involving the moments … Read more
We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities … Read more
This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules. … Read more
This paper is concerned with the optimization of continuum structures under dynamic loading using methods from topology design. The constraint functions are non-linear and implicit, their evaluation requires the resolution of a computation-intensive finite-element analysis performed by a black-box commercial structural mechanics software such as MSC/Nastran. We first present a brief overview of topology optimization … Read more