Facility location-network design problems seek to simultaneously determine the locations of fa- cilities and the design of the network connecting the facilities so as to best serve a set of clients accessing the facilities via the network. Here we study a dynamic (multi-period) version of the problem, subject to a budget constraint limiting the investment … Read more
We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In our previous article, we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to … Read more
Mathematical programming problems involving nonconvexities are usually solved to optimality using a (spatial) Branch-and-Bound algorithm. Algorithmic efficiency depends on many factors, among which the widths of the bounding box for the problem variables at each Branch-and-Bound node naturally plays a critical role. The practically fastest box-tightening algorithm is known as FBBT (Feasibility-Based Bounds Tightening): an … Read more
The feasibility pump is a recent, highly successful heuristic for general mixed integer linear programming problems. We show that the feasibility pump heuristic can be interpreted as a discrete version of the proximal point algorithm. In doing so, we extend and generalize some of the fundamental results in this area to provide new supporting theory. … Read more
The Feasibility Pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a rounding procedure and a projection procedure, which together provide a sequence of points alternating between LP feasible but fractional solutions, and integer but LP relaxed infeasible solutions. The process attempts to … Read more
This paper introduces novel formulations for optimally responding to epidemics and cyber attacks in networks. In our models, at a given time period, network nodes (e.g., users or computing resources) are associated with probabilities of being infected, and each network edge is associated with some probability of propagating the infection. A decision maker would like … Read more
In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing on the order of n choose d many variables for the level-d closure. When large amounts of symmetry are present in the problem … Read more
The quadratic traveling salesman problem asks for a tour of minimal costs where the costs are associated with each two arcs that are traversed in succession. This structure arises, e. g., if the succession of two arcs represents the costs of loading processes in transport networks or a switch between different technologies in communication networks. … Read more
The increasing diffusion of Automatic Meter Reading (AMR) has raised many concerns about the protection of personal data related to energy, water or gas consumption, from which details about the habits of the users can be inferred. On the other hand, aggregated measurements about consumption are crucial for several goals, including resource provisioning, forecasting, and … Read more
Column generation for solving linear programs with a huge number of variables alternates between solving a master problem and a pricing subproblem to add variables to the master problem as needed. The method is known to suffer from degeneracy of the master problem, exposing what is called the tailing-off effect. Inspired by recent advances in … Read more