We investigate the algorithmic and implementation issues related to the eeective and eecient use of lifted cover inequalities and lifted GUB cover inequalities in a branch-and-cut algorithm for 0-1 integer programming. We have tried various strategies on several test problems and we identify the best ones for use in practice. Branch-and-cut, with lifted cover inequalities as cuts, has been used...

We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute signi cantly to the expressive power, ease of use, and e ciency of constraint programs.

Solving the multi-hour survivable network design problem entails finding the most cost efficient network design given two or more demand matrices that represent network traffic for different (busy-)hours. In addition to capacity installations, feasible routings that satisfy the traffic requirements for all of the demand matrices need to be determined. The problem is formulated as a mixed-intege...

In this paper we analyze a continuous version of the maximal covering location problem, in which facilities are required to be linked by means given graph structure (provided that two allowed if distance is not exceed). We propose mathematical programming framework for problem and different resolution strategies. First, provide Mixed Integer Non Linear Programming formulation derive some geomet...

We consider a realistic modelling of interferences for frequency allocation in hertzian telecommunication networks. In contrast with traditional interference models based only on binary interference constraints, this new approach considers the case of a receiver disrupted simultaneously by several senders yielding cumulative disruptions that are modelled through a unique non-binary constraint. ...

The bounded diameter minimum spanning tree problem is an NP-hard combinatorial optimization problem arising for example in network design when quality of service is of concern. We solve a strong integer linear programming formulation based on so-called jump cuts by a novel Branch&Cut algorithm, using various heuristics including tabu search to solve the separation problem.

Discrete and continuous nonconvex programming problems arise in a host of practical applications in the context of production planning and control, location-allocation, distribution, economics and game theory, quantum chemistry, and process and engineering design situations. Several recent advances have been made in the development of branch-and-cut type algorithms for mixed-integer linear and ...

We study the polyhedral structure of variants of the discrete lot–sizing problem viewed as special cases of convex integer programs. Our approach in studying convex integer programs is to develop results for simple mixed integer sets that can be used to model integer convex objective functions. These results allow us to define integral linear programming formulations for the discrete lot–sizing...

Given a directed graph G = (V,A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If negative costs are allowed, the problem is NP-hard. In this paper, several integer programming formulations for the ESPP are compared. We present analytical results based on a...

This article presents a branch-and-cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose vertex set is partitioned into clusters, the GMSTP consists of determining a minimum cost tree including exactly one vertex per cluster. Applications of the GMSTP are encountered in telecommunications. An integer linear programming formulation is presented ...