The famous Padberg–Rao separation algorithm for b-matching polyhedra can be implemented to run in O(|V |2|E| log(|V |2/|E|)) time in the uncapacitated case, and in O(|V ||E|2 log (|V |2/|E|)) time in the capacitated case. We give a new and simple algorithm for the capacitated case which can be implemented to run in O(|V |2|E| log(|V |2/|E|)) time.

Combinatorial optimization problems are by nature very difficult to solve, and the Capacitated Minimum Spanning Tree problem is one such problem. Much work has been done in the management sciences to develop heuristic solution procedures that suboptimally solve large instances of the Capacitated Minimum Spanning Tree problem in a reasonable amount of time. The Capacitated Minimum Spanning Tree ...

The cuckoo search algorithm is a novel metaheuristic based on the reproduction behavior of some cuckoo species in combination with the Lévy flight behavior of some birds and fruit flies. It has been applied to a wide range of optimization problems with good performance such as a TSP; nonetheless, it has yet to be applied to the vehicle routing problem, specifically the capacitated vehicle routi...

The covering of a graph with (possibly disjoint) connected subgraphs is fundamental problem in theory. In this paper, we study version to cover graph's vertices by subject lower and upper weight bounds, propose column generation approach dynamically generate feasible promising subgraphs. Our focus on the solution pricing which turns out be variant NP-hard Maximum Weight Connected Subgraph Probl...

We consider the node-capacitated routing problem in an undirected ring network along with its fractional relaxation, the node-capacitated multicommodity flow problem. For the feasibility problem, Farkas’ lemma provides a characterization for general undirected graphs asserting roughly that there exists such a flow if and only if the so-called distance inequality holds for every choice of distan...

In this talk we present a unified Variable Neighborhood Search (VNS) algorithm for the Capacitated Arc Routing Problem (CARP) and some of its variants the Capacitated Arc Routing Problem with Intermediate Facilities (CARPIF) and the Capacitated Arc Routing Problem with Intermediate Facilities and Length restrictions (CLARPIF). Routing problems represent one of the most prominent classes of mode...