Geoff P. McKeown

Solving a Time-Space Network Formulation for the Convoy Movement Problem

We give a formal specification for a strategic network routing problem known as the convoy movement problem (CMP) and establish that the corresponding feasibility problem is NP-complete. We then introduce an integer programming (IP) model based on the concept of a time-space network and apply a Lagrangian relaxation to this model. We discuss how the dual function may be evaluated using a modified version of Dijkstras algorithm suitable to very large, implicitly defined graphs and show how heuristic solutions to the primal problem may be obtained. We present results for a number of instances of the CMP, most of which are based on real-world problems. The number of convoys in these instances varies between 15--25, and their movement time requires up to several thousand time units in networks ranging in size from a few dozen to several thousand vertices and edges. The most difficult instance tested involves 17 long convoys each taking four times the average link travel time to pass through a point in the network. This instance is solved within 3.3% of optimality in less than 3.5 hours of computing time on a Dell Precision 420 dual processor computer. Every other test instance is solved within 2% of the optimal value in less than 20 minutes of computing time.

Efficiency considerations in the implementation of parallel branch-and-bound

We discuss the abstraction of the branch-and-bound paradigm and the implementation on a transputer network of kernel software supporting this paradigm. We propose a new measure, which we call thepseudo efficiency of an implementation, and use this measure to decide which kernel is appropriate under certain conditions. We then discuss someefficiency anomalies and show that these can occur for genuine problems.

Branch-and-bound as a higher-order function

The branch-and-bound paradigm is presented as a higher-order function and illustrated by instantiations, providing two well-known branch-and-bound algorithms for the Steiner tree problem in graphs and one for the travelling salesman problem. We discuss the advantages of such a specification and various issues arising from sequential and parallel implementations of branch-and-bound kernels.

Scheduling a manufacturing plant using simulated annealing and simulation

A technique for scheduling a class of manufacturing plants is described. The technique uses a simulated annealing module to create partial schedules, which are then completed and evaluated by a simulation module. The simulation module is equipped with a number of rules which it uses to complete schedules. A mathematical specification is given defining the type of scheduling problem with which we have been concerned. The derivation of a mixed integer linear programming model from this specification is discussed. The complexity of such a model for practical instances justifies the use of heuristic approaches. Results from using our approach on a case study derived from a real-world problem are presented.

Application of GRASP to the Multiconstraint Knapsack Problem

A number of approaches based on GRASP are presented for the Multiconstraint Knapsack Problem. GRASP combines greedy construction of feasible solutions with local search. Results from applying our algorithms to standard test problems are presented and compared with results obtained by Chu and Beasley.

Distribution, Cooperation, and Hybridization for Combinatorial Optimization

In the literature there is a growing evidence that demonstrates the effectiveness of object-oriented frameworks in assisting software development. Furthermore, object-oriented frameworks may not only improve the development process of software, but can also improve the quality and maintainability of software. This chapter looks at the Templar framework from the University of East Anglia, UK, with a specific interest in distribution, hybridization, and cooperation.

Construction of factory schedules using reverse simulation

A real-world, multi-stage, industrial scheduling problem is presented. An algorithm is described that converts a sequence of jobs into a complete schedule. Backward simulation is used to determine minimum storage requirements when scheduling each job, and to calculate the minimum amount of delay required. Combining this algorithm with a metaheuristic, such as simulated annealing, results in an effective algorithm for schedule optimization.

The probe metaheuristic and its application to the multiconstraint knapsack problem

A new metaheuristic technique called PROBE is presented. The application of PROBE to the multiconstraint knapsack problem is described. Experimental results obtained using the resulting algorithm are compared with the results obtained by Chu and Beasley using a Genetic Algorithm.

The general problem solving algorithm and its implementation

By generalising problem solving techniques such as divide-and-conquer, dynamic programming, tree and graph searching, integer programming and branch-and-bound, a general problem solving algorithm is deduced. Various examples of the use of this algorithm are given and its implementation on both sequential and parallel machines, such as the cosmic cube, is discussed.

Communication problems on MIMD parallel computers

Abstract Various proposals for networks of large numbers of processors are reviewed. Bottleneck problems arise in these networks with the flow of data between processors. Communication problems which can arise in practical situations are discussed and techniques for reducing bottlenecks are developed. Some simulation results are given for the binary n-cube.