Pierre Hosteins

Local search metaheuristics for the critical node problem

We present two metaheuristics for the Critical Node Problem, that is, the maximal fragmentation of a graph through the deletion of k nodes. The two metaheuristics are based on the Iterated Local Search and Variable Neighborhood Search frameworks. Their main characteristic is to exploit two smart and computationally efficient neighborhoods which we show can be implemented far more efficiently than the classical neighborhood based on the exchange of any two nodes in the graph, and which we prove is equivalent to the classical neighborhood in the sense that it yields the same set of neighbors. Solutions to improve the overall running time without deteriorating the quality of the solution computed are also illustrated. The results of the proposed metaheuristics outperform those currently available in literature.

VNS solutions for the critical node problem

Abstract We present a VNS algorithm for the Critical Node Problem, i.e., the maximal fragmentation of a graph through the deletion of k nodes. Two computational efficient neighbourhoods are proposed proving also their equivalence to the straightforward exchange of two nodes. The results of the proposed VNS algorithms outperform those currently available in literature.

A general Evolutionary Framework for different classes of Critical Node Problems

We design a flexible Evolutionary Framework for solving several classes of the Critical Node Problem (CNP), i.e. the maximal fragmentation of a graph through node deletion, given a measure of connectivity. The algorithm uses greedy rules in order to lead the search towards good quality solutions during reproduction and mutation phases. Such rules, which are only partially reported in the literature, are generalised and adapted to the six different formulations of the CNP considered along the paper. The link between solutions of different CNP formulations is investigated, both quantitatively and qualitatively. Furthermore, we provide a comparison with best known results when those are available in literature that confirms the good overall quality of our solutions.

A Genetic Algorithm for a class of Critical Node Problems

Abstract In this paper, we deal with two different variants of the Critical Node Problem, designing a flexible genetic algorithm for tackling them both. The results are compared with the best known results available in the literature.

A preliminary analysis of the Distance Based Critical Node Problem

Abstract We discuss how to develop efficient heuristics for the distance based critical node problem, that is the problem of deleting a subset of nodes from a graph G in such a way that the distance between each pair of nodes is as large as possible.

Simple but effective heuristics for the 2-constraint bin packing problem

The 2-constraint bin packing problem consists in packing a given number of items, each one characterised by two different but not related dimensions, into the minimum number of bins in such a way to do not exceed the capacity of the bins in either dimension. The development of the heuristics for this problem is challenged by the need of a proper definition of the criterion for evaluating the feasibility of the two capacity constraints on the two different dimensions. In this paper, we propose a computational evaluation of several criteria, and two simple but effective algorithms—a greedy and neighbourhood search algorithms—for solving the 2-constraint bin packing problem. An extensive computational analysis supports our main claim.

A Branch-and-Bound Algorithm for the Prize-Collecting Single-Machine Scheduling Problem with Deadlines and Total Tardiness Minimization

We study a prize-collecting single-machine scheduling problem with hard deadlines, where the objective is to minimize the difference between the total tardiness and the total prize of the selected jobs. This problem is motivated by industrial applications, both as a stand-alone model and as a pricing subproblem in column-generation algorithms for parallel machine scheduling problems. A preprocessing rule is devised to identify jobs that cannot belong to any optimal schedule. The resulting reduced problem is solved to optimality by a branch-and-bound algorithm and two integer linear programming formulations. The algorithm and the formulations are experimentally compared on randomly generated benchmark instances.

Polynomial and pseudo-polynomial time algorithms for different classes of the Distance Critical Node Problem

Abstract We study the Distance Critical Node Problem, a generalisation of the Critical Node Problem where the distances between node pairs impact on the objective function. We establish complexity results for the problem according to specific distance functions and provide polynomial and pseudo-polynomial algorithms for special graph classes such as paths, trees and series–parallel graphs. We also provide additional insights about special cases of the Critical Node Problem variants already tackled in the literature.

The Prize-collecting Scheduling Problem with Deadlines

Abstract We study a prize-collecting single machine scheduling problem with hard deadlines, where the objective is to minimise the difference between the total tardiness and the total prize of selected jobs. This problem is motivated by industrial applications, both as a standalone model and as a pricing problem for column generation approaches to parallel machine scheduling problems. It is handled through the use of exact approaches, in the form of a Branch and Bound (B&B) algorithm and an Integer Linear Programming (ILP) formulation. The B&B and ILP formulation are compared in their efficiency on randomly generated benchmark instances.