The widely used Support Vector Machine (SVM) method has shown to yield good results in Supervised Classification problems. Other methods such as Classification Trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in Data Mining. In this work, we propose an SVM-based method that automatically detects … Read more
Consider solving a linear program in standard form, where the constraint matrix $A$ is $m \times n$, with $n \gg m \gg 1$. Such problems arise, for example, as the result of finely discretizing a semi-infinite program. The cost per iteration of typical primal-dual interior-point methods on such problems is $O(m^2n)$. We propose to reduce … Read more
Working with an integer bilinear programming formulation of a one-dimensional cutting-stock problem, we develop an ILP-based local-search heuristic. The ILPs holistically integrate the master and subproblem of the usual price driven pattern-generation paradigm, resulting in a unified model that generates new patterns in situ. We work harder to generate new columns, but we are guaranteed … Read more
In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of … Read more
Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit representation, with an … Read more
In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formulation by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation … Read more
The Generalized Assignment Problem (GAP) is a classic scheduling problem with many applications. We propose a branch-and-cut-and-price for that problem featuring a stabilization mechanism to accelerate column generation convergence. We also propose ellipsoidal cuts, a new way of transforming the exact algorithm into a powerful heuristic, in the same spirit of the cuts recently proposed … Read more
We discuss interior point methods for large-scale linear programming, with an emphasis on methods that are useful for problems arising in telecommunications. We give the basic framework of a primal-dual interior point method, and consider the numerical issues involved in calculating the search direction in each iteration, including the use of factorization methods and/or preconditioned … Read more
We present the optimization component of a decision support system developed for a sedan service provider. The system assists supervisors and dispatchers in scheduling driver shifts and routing the fleet throughout the day to satisfy customer demands within tight time windows. We periodically take a snapshot of the dynamic data and formulate an integer program, … Read more
We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the … Read more