Pisinger et al. introduced the concept of `aggressive reduction’ for large-scale combinatorial optimisation problems. The idea is to spend much time and effort in reducing the size of the instance, in the hope that the reduced instance will then be small enough to be solved by an exact algorithm. We present an aggressive reduction scheme … Read more
A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available. When non-convexities are present, however, things become much more difficult, since then even the continuous relaxation is … Read more
We develop an exact algorithm for integer programs that uses restrictions of the problem to produce high-quality solutions quickly. Column generation is used both for generating these problem restrictions and for producing bounds on the value of the optimal solution. The performance of the algorithm is greatly enhanced by using structure, such as arises in … Read more
We are interested in methods to solve mixed-integer nonlinear optimal control problems (MIOCPs) constrained by ordinary di erential equations and combinatorial constraints on some of the control functions. To solve these problems we use a rst discretize, then opti- mize approach to get a specially structured mixed-integer nonlinear program (MINLP). We decompose this MINLP into an … Read more
We present integer programming models of the service network design problem faced by less-than-truckload (LTL) freight transportation carriers, and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers, and … Read more
This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. … Read more
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
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
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