The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. … Read more
This paper presents a bi-directional resource-bounded label setting algorithm for the traveling salesman problem with time windows, in which the objective is to minimize travel times. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant … Read more
This paper presents a bi-directional resource-bounded label setting algorithm for the traveling salesman problem with time windows, in which the objective is to minimize travel times. Label extensions and dominance start simultaneously in both forward and backward directions: the forward direction from the starting depot and the backward direction from the terminating depot. The resultant … Read more
The Sensor Network Localization Problem (SNLP), arising from many applied fields related with environmental monitoring, has attracted much research during the last years. Solving the SNLP deals with the reconstruction of a geometrical structure from incomplete pairwise distances between sensors. In this paper we present an heuristic multistage approach in which the solving strategy is … Read more
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we introduce a hierarchy … Read more
This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly \NP-hard in general. We provide pseudo-polynomial algorithms for three special cases … Read more
We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to onstruct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the … Read more
We propose an approach to linear optimization with recourse that does not involve a probabilistic description of the uncertainty, and allows the decision-maker to adjust the degree of robustness of the model while preserving its linear properties. We model random variables as uncertain parameters belonging to a polyhedral uncertainty set and minimize the sum of … Read more
Branching variable selection can greatly a ffect the eff ectiveness and efficiency of a branch-and- bound algorithm. Traditional approaches to branching variable selection rely on estimating the eff ect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from … Read more
The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the single-row facility layout problem (SRFLP), the one-dimensional version of facility layout that is also … Read more