We study the minimum spanning tree problem, the maximum matching problem and the shortest path problem subject to binary disjunctive constraints: A negative disjunctive constraint states that a certain pair of edges cannot be contained simultaneously in a feasible solution. It is convenient to represent these negative disjunctive constraints in terms of a so-called conflict … Read more
We propose a unifying framework for polyhedral approximation in convex optimization. It subsumes classical methods, such as cutting plane and simplicial decomposition, but also includes new methods, and new versions/extensions of old methods, such as a simplicial decomposition method for nondifferentiable optimization, and a new piecewise linear approximation method for convex single commodity network flow … Read more
We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base … 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
In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal-dual infeasible and inexact interior point method for multi-objective linear network flow problems. A comparison with standard interior point methods is provided and experimental results on bi-objective … Read more
We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and the performance of each routing is assessed on … Read more
For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges … Read more
Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-levels hierarchical approach for point-to-point shortest paths computations to the time-dependent case. This method, also known as core routing in the literature for static graphs, … Read more
The computation of point-to-point shortest paths on time-dependent road networks has a large practical interest, but very few works propose efficient algorithms for this problem. We propose a novel approach which tackles one of the main complications of route planning in time-dependent graphs, which is the difficulty of using bidirectional search: since the exact arrival … Read more