Jean-Marie Bourjolly

Topological design of computer communication networks using simulated annealing

Abstract This paper presents an application of the simulated annealing heuristic to the problem of designing computer communication networks. This problem essentially consists in finding the least-cost network topologies that satisfies a given set of performance and reliability constraints. The results of the computational experiments show that simulated annealing is a suitable approach for solving this very difficult combinatorial optimization problem, in the sense that it provides feasible and low-cost solutions within reasonable CPU times.

An exact algorithm for the maximum k-club problem in an undirected graph

Abstract In this paper, we prove that the maximum k -club problem (M k CP) defined on an undirected graph is NP-hard. We also give an integer programming formulation for this problem as well as an exact branch-and-bound algorithm and computational results on instances involving up to 200 vertices. Instances defined on very dense graphs can be solved to optimality within insignificant computing times. When k =2, the most difficult cases appear to be those where the graph density is around 0.15.

Branch-and-bound algorithms for the multi-product assembly line balancing problem

Abstract This paper considers a flexible manufacturing system for several products, each requiring a number of sequential nonpreemptive tasks, some of which may be common to many products. Work stations are capable of handling any task. The objective is to minimize the number of work stations necessary to manufacture all products so that tasks are performed in the proper order and so that all tasks assigned to any given station can be executed within a prescribed time frame. A new branch-and-bound approach for this problem is presented. It contains two main improvements over previously published tree search algorithms: an improved lower-bounding procedure and a more powerful partitioning scheme. The algorithm can be used either as a heuristic (in its truncated version) or as an exact method (in its full version). Tests performed on randomly generated problems confirm the effectiveness of the proposed improvements.

König-Egerváry graphs, 2-bicritical graphs and fractional matchings☆

A fractional node cover of a graph is an assignment of the values 0, 12, 1 to the nodes, so that for each edge, the sum of the values assigned to its two ends is at least one. Such a cover is minimum if the sum of the assigned values is minimized. A Konig-Egervary graph is a graph for which there exists a minimum fractional cover in which all nodes receive the value 0 or 1. A 2-bicritical graph is one for which the unique minimum fractional cover is obtained by assigning 12 to all the nodes. We describe a polynomial method for decomposing a graph into 2-bicritical components and Konig-Egervary components. This decomposition yields a minimum fractional node cover in which the number of nodes receiving the value 12 is minimized. We also show how excluded minor characterizations by Deming, Sterboul and Lovasz of Konig-Egervary graphs can be used to obtain a structural characterization of 2-bicritical graphs.

Heuristics for finding k-clubs in an undirected graph

Abstract In a graph G, a k-club is a vertex set inducing a subgraph of diameter k. These structures play an important role in several applications arising in social and behavioral sciences. We derive some properties of k-clubs and we propose three heuristics for determining a largest k-club in a graph. Comparative computational results confirm the speed and efficiency of these heuristics. Scope and purpose Social and behavioral scientists frequently use network analysis to study linkages between groups, individuals or abstract entities. Applications are encountered in psychology, marketing, organization theory, anthropology, economics, sociology, etc. A common problem is to identify dense structures in a graph. This article is about the determination of one such type of structure called k-club. Three efficient heuristics for the determination of k-clubs are developed and compared.

Decoupage Electoral Automatise: Application A L’Lle De Montreal

AbstractIn a majority vote election, the topography of electoral districts plays a significant part in the translation of votes into seats. “Gerrymandering” is the process of defining electoral boundaries so as to favour one party over the others. To combat this dubious practice, political parties have agreed in some countries to delegate the task of drawing up the electoral map to a “neutral” multi-party commission. Since the sixties, some of these commissions have begun to involve operations research specialists in their work. This article reviews the main algorithmic methods for electoral mapping. A heuristic solution technique to the problem is presented together with results obtained on the island of Montreal.

BOOLEAN-COMBINATORIAL BOUNDING OF MAXIMUM 2-SATISFIABILITY

ABSTRACT We consider the weighted maximum 2-satisfiability problem in its equivalent form of finding the minimum z* of a quadratic posiform. We describe a polynomial-time algorithm for computing a lower bound on z*. The algorithm consists of a finite sequence of elementary boolean operations of two types: fusions ( ) and exchanges ( ). Our main result is that the bound obtained by this method is equivalent to the roof duality bound, which is known to be computable by linear programming. Furthermore, one can check in polynomial time whether such bound coincides with z*. If not, one can obtain strictly sharper lower bounds making use of two further elementary boolean operations, namely condensations and consensus.

Optimizing Frequency Hopping in GSM Cellular Phone Networks

The mobile telephony market has been undergoing a dramatic increase in the volume of demand as well as in the quality requirements. The limiting resource in this highly competitive market is the available frequency spectrum. In GSM networks, frequency reuse has been the basic tool for optimizing the spectrum management. This method is sometimes insufficient, however, for the most congested networks. Frequency Hopping (FH) is a method that allows one to expand the available capacity of mobile networks or to improve the quality of service through interference averaging and frequency diversity. Current implementations of FH are based on Random or Cyclic Hopping patterns. In this paper, we propose to optimize FH. We describe a simple heuristic algorithm for allocating frequencies to cells and scheduling the frequency hopping for each mobile. The performance of the proposed approach in a synchronized network is compared to Random and Cyclic FH and to the optimized static frequency reuse implementations. We show that hopping algorithms that use some form of controlled optimization beyond random and cyclic hopping could significantly improve the quality of service and achieve interference averaging, should the telecommunications equipment manufacturers decide to implement such a feature or to allow the operators to control frequency hopping by using their own algorithms.

Using Simulated Annealing To Minimize The Cost Of Centralized Telecommunications Networks

The network design problems studied in this paper are typically known in the Telecommunications literature as the Concentrator Location, Terminal Assignment and Terminal Layout Problems. These are versions of well-known Operations Research models such as Capacitated Location, Capacitated Assignment, Capacitated Minimum Spanning Tree, and Vehicle Routing. We describe two Simulated Annealing algorithms for solving them and analyze the results obtained through computational testing.

An extension of the Ko¨nig-Egerva´ry property to node-weighted bidirected graphs

Given a bidirected graphG and a vectorb of positive integral node-weights, an integer linear program IP is defined on (G, b). IP generalizes the node packing problem on a node-weighted (undirected) graph in the sense that it reduces to the latter whenG is undirected. A polynomial time algorithm is given that recognizes whether CP (the linear program obtained by relaxing the integrality constraints of IP) has an integral optimal solution. Also an efficient method for solving the linear programming dual of CP is described.