Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover … Read more
The problem of routing and wavelength assignment (RWA) in wavelength division multiplexing (WDM) optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned different wavelengths. This problem was shown to be NP-hard when the objective is to … Read more
Path-relinking is major enhancement to heuristic search methods for solving combinatorial optimization problems, leading to significant improvements in both solution quality and running times. We review its fundamentals and implementation strategies, as well as advanced hybridizations with more elaborate metaheuristic schemes such as genetic algorithms and scatter search. Numerical examples are discussed and algorithms compared … Read more
In this paper we focus on connected directed/undirected circulant graphs Cn(a,b). We investigate some topological characteristics, and define a simple combinatorial model, which is new for the topic. Building on such a model, we derive a necessary and sufficient condition to test whether two circulant graphs Cn(a, b) and Cn(a’,b’) are isomorphic or not. The … Read more
This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell’Amico, Righini … Read more
We consider a complex planning problem in integrated steel production. A sequence of coils of sheet metal needs to be color coated in consecutive stages. Di erent coil geometries and changes of coatings may necessitate time-consuming setup work. In most coating stages one can choose between two parallel color tanks in order to reduce setup times. … Read more
We consider two approaches for solving the classical minimum vertex coloring problem�that is, the problem of coloring the vertices of a graph so that adjacent vertices have different colors and minimizing the number of used colors, namely, constraint programming and column generation. Constraint programming is able to solve very efficiently many of the benchmarks but … Read more
Run time distributions or time-to-target plots are very useful tools to characterize the running times of stochastic algorithms for combinatorial optimization. We further explore run time distributions and describe a new tool to compare two algorithms based on stochastic local search. For the case where the running times of both algorithms fit exponential distributions, we … Read more
Given a graph with nonnegative edge weights and a set of pairs of nodes Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia, … Read more
In the paper we consider degree, spectral, and semidefinite bounds on the stability and chromatic numbers of a graph: so-called weak sandwich theorems. We examine the additivity properties of the bounds (the sum of two graphs is their disjoint union), and as an application we tighten the bounds in the weak sandwich theorems, if the … Read more