Bezalel Gavish

Topological design of centralized computer networks—formulations and algorithms

In recent years we have evidenced an extensive effort in the development of computer communication networks. One of the important aspects of the network design process is the solution of the topological design questions involved in establishing a communication network. In this article, formulations are presented for a variety of centralized network design problems such as the minimal spanning tree problem, capacitated and degree constrained minimal spanning tree problems, The Telpak problem, and, heterogeneous network design problems. The applicability of these formulations to algorithmic development is demonstrated by developing an efficient algorithm for solving the degree constrained minimal spanning tree problem. Computational results are reported for 630 test problems. A Benders decomposition procedure is developed and tested for the capacitated minimal spanning tree problem with less favorable results.

Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality

The multiconstraint 0–1 knapsack problem is encountered when one has to decide how to use a knapsack with multiple resource constraints. Even though the single constraint version of this problem has received a lot of attention, the multiconstraint knapsack problem has been seldom addressed.This paper deals with developing an effective solution procedure for the multiconstraint knapsack problem. Various relaxation of the problem are suggested and theoretical relations between these relaxations are pointed out. Detailed computational experiments are carried out to compare bounds produced by these relaxations. New algorithms for obtaining surrogate bounds are developed and tested. Rules for reducing problem size are suggested and shown to be effective through computational tests. Different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with two previously developed optimal algorithms. Solution times with the new procedure are found to be considerably lower. This procedure can also be used as a heuristic for large problems by early termination of the search tree. This scheme was tested and found to be very effective.

A system for routing and capacity assignment in computer communication networks

The combined problem of selecting a primary route for each communicating pair and a capacity value for each link in computer communication networks is considered. The network topology and traffic characteristics are given: a set of candidate routes and of candidate capacities for each link are also available. The goal is to obtain the least costly feasible design where the costs include both capacity and queuing components. Lagrangean relaxation and subgradient optimization techniques were used to obtain verifiable solutions to the problem. The method was tested on several topologies, and in all cases good feasible solutions, as well as tight lower bounds, were obtained. The model can be generalized to deal with different classes of customers, characterized by different priorities, message lengths, and/or delay requirements. >

Optimal Lot-Sizing Algorithms for Complex Product Structures

Lot sizing of products that have complex bills of materials plays an important role in the efficient operations of modern manufacturing and assembly processes. In this paper we develop algorithms for optimal lot sizing of products with a complex product structure. We convert the classical formulation of the general structure problem into a simple but expanded assembly structure with additional constraints, and solve the transformed problem by a branch-and-bound based procedure. The algorithm uses a Lagrangean relaxation and subgradient optimization procedure to generate tight lower bounds on the optimal solutions. In computational experiments, a code based on this method was able to solve single end product problems with up to 40 stages in the product structure. The model is extended to handle problems with multi-end items in the product structure, but with less favorable computational results.

Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem

The Capacltated Minmaal Directed Tree Problem is fundamental m many network design problems. A new linear integer programming formulauon of the problem which leads to a Dantzlg-Wolfe decomposmon and to a new Lagrangean relaxation procedure for the Capacaated Mmunal Directed Tree Problem as presented This relaxation is used for deriving tight lower bounds on the optunal solution and m heunsucs for obtaining approxtmate solutions The effectiveness of the procedure is demonstrated in computational tests Categories and SubJect Descriptors: C.2.1 [Computer-Communication Networks]: Network Architecture and Design--network topology; D 4.8 [Operating Systems]: Performance--modehng and predwtion; G 2.1 [Discrete Mathematics]: Combinatoncs--combmatorml algorithms; G.2.2 [Di~tete Mathematics]. Graph Theory--trees General Terms. Algonthrns, Management, Theory Ad&tional

Topological design of telecommunication networks-local access design methods

Computer communication networks and telecommunication systems are growing at an explosive rate. Some of the major factors influencing this phenomenal growth rate have been technology driven, deregulation of the telecommunication industry and the breakup of AT&T, product and service introductions and competition, new application areas, price reductions and improved services. Corporations have discovered how to use telecommunication-based systems and computer networks as a strategic competitive weapon. Modern computer networks consist of backbone networks which serve as major highways to transfer large volumes of communication traffic, and local access networks which feed traffic between the backbone network and end user nodes. The design of the local access network is a complex process which builds on many difficult combinatorial optimization problems. This paper surveys many of the problems, presents the state of the art in solving them, and demonstrates a variety of solution procedures. The paper concludes with a list of open problems and areas open for further investigation.

An Algorithm for Optimal Route Selection in SNA Networks

The problem of selecting a single route for each class of service and each pair of communicating nodes in an SNA network is considered. The nodes, links, sets of candidate routes, and traffic characteristics are given. The goal is to select a set of routes which minimizes the expected network end-to-end queueing and transmission delay. Queueing is modeled as a network of M/M/1 queues which leads to a nonlinear combinatorial optimization problem. Using Lagrangean relaxation and subgradient optimization techniques, we obtain a tight lower bound on the minimal expected delay as well as sets of feasible solutions for the problem. An experimental interactive system has been used to evaluate the procedure; very favorable results have been obtained on a variety of networks.

Parallel Savings Based Heuristics for the Delivery Problem

The delivery problem consists of finding a set of routes for a fleet of capacitated vehicles to satisfy the cargo delivery requirements of customers. The vehicles are located in a central depot, and have to fulfill the delivery requirements in a sequence that minimizes total delivery costs. Each vehicle tour starts and terminates at the central depot, and each node is supplied by exactly one vehicle. All vehicles have the same cargo carrying capacity. The paper presents parallel savings algorithms PSAs for generating feasible solutions to this problem. The new algorithms combine the savings approach, with matching based procedures. In computational tests the heuristic produces better solutions than the best known solutions for six problems out of a standard set of 14 difficult test problems. Augmented Lagrangian based lower bounding procedures are developed, and used to evaluate the quality of the solutions generated by PSAs. The lower bounds generated by the augmented Lagrangian are the tightest bounds known for delivery problems. The performance of the PSAs is also compared to tour partitioning based heuristics which have better worst case error bounds. The average quality of solutions generated by PSAs is shown to be significantly superior on large sets of test problems.

Dynamic file migration in distributed computer systems

The importance of file migration is increasing because of its potential to improve the performance of distributed office, manufacturing and hospital information systems. To encourage research in the file migration problem, the authors summarize accomplishments of researchers of the problem, provide a detailed comparison of file migration and dynamic file allocation problems, and identify important areas of research to support the development of effective file migration policies.

Topological design of computer communication networks -- The overall design problem

Abstract Mathematical formulations of the topological design problem of computer communication networks are developed. The topological design of computer networks involves decisions on where to place network control processors (NCPs), selecting the set of backbone links to connect NCPs, linking end user nodes to the NCPs, and deciding on the set of routes which support communications between communicating end user node pairs. The overall design problem is formulated as a nonlinear combinatorial optimization problem, a Lagrangean relaxation of the problem is presented and effective solution procedures of the Lagrangean problem are developed. The Lagrangean solutions provide lower bounds on the optimal solutions to the complete problem. The Lagrangean-based solutions are further improved using subgradient optimization procedures. Three heuristics are developed for generating feasible solutions to the problem. The heuristic solutions are demonstrated on problems involving 200 end user nodes and up to 30 NCP locations.