The “sequential ordering problem” (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a “multi-commodity flow” (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables … Read more
We consider distributed optimization where $N$ nodes in a connected network minimize the sum of their local costs subject to a common constraint set. We propose a distributed projected gradient method where each node, at each iteration $k$, performs an update (is active) with probability $p_k$, and stays idle (is inactive) with probability $1-p_k$. Whenever … Read more
For an infeasible network flow system with supplies and demands, we consider the problem of finding a minimum irreducible infeasible subsystem cover, i.e., a smallest set of constraints that must be dropped to obtain a feasible system. The special cases of covers which only contain flow balance constraints (node cover) or only flow bounds (arc … Read more
We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more
In many network applications, one searches for a connected subset of vertices that exhibits other desirable properties. To this end, this paper studies the connected subgraph polytope of a graph, which is the convex hull of subsets of vertices that induce a connected subgraph. Much of our work is devoted to the study of two … Read more
We consider the Critical Node Problem: given an undirected graph and an integer number K, at most K nodes have to be deleted from the graph in order to minimize a connectivity measure in the residual graph. We combine the basic steps used in common greedy algorithms with some flavour of local search, in order … Read more
We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of … Read more
We introduce, discuss, and solve a hard practical optimization problem which we call the ship traffic control problem (STCP). Since we plan bi-directional traffic, STCP relates to, and in fact generalizes train timetabling on single-track networks. The objective of finding quickest routes motivates the integration of recent algorithmic ideas from dynamic collision-free routing of automated … Read more
Hub location problems are strategic network planning problems. They formalise the challenge of mutually exchanging shipments between a large set of depots. The aim is to choose a set of hubs (out of a given set of possible hubs) and connect every depot to a hub so that the total transport costs for exchanging shipments … Read more
To facilitate fast solution of deterministic dynamic programming problems, we present a parameter-free variation of the Sampled Fictitious Play (SFP) algorithm. Its random tie-braking procedure imparts a natural randomness to the algorithm which prevents it from “getting stuck” at a local optimal solution and allows the discovery of an optimal path in a finite number … Read more