Alan Soper

A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning

The graph-partitioning problem is to divide a graph into several pieces so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges is minimised. Important applications of the problem arise, for example, in parallel processing where data sets need to be distributed across the memory of a parallel machine. Very effective heuristic algorithms have been developed for this problem which run in real-time, but it is not known how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. A distinctive feature is the use of a multilevel heuristic algorithm to provide an effective crossover. The technique is tested on several example graphs and it is demonstrated that our method can achieve extremely high quality partitions significantly better than those found by the state-of-the-art graph-partitioning packages.

Intelligent design assistant (IDA): a case base reasoning system for material and design

This paper describes the approach to the modelling of experiential knowledge in an industrial application of Case-Based Reasoning (CBR). The CBR involves retrieval techniques in conjunction with a relational database. The database is especially designed as a repository of experiential knowledge, and includes qualitative search indices. The system is intended to help design engineers and material engineers in the submarine cable industry. It consists of three parts: a materials database; a database of experiential knowledge; and a CBR system used to retrieve similar past designs based upon component and material qualitative descriptions. The system is currently undergoing user testing at the Alcatel Submarine Networks site in Greenwich.

Use of Genetic Algorithms for Optimal Topology Determination in Back Propagation Neural Networks

A genetic algorithm is applied to evolve neural network topologies suitable for given problem domains. Certain concepts, from the fields of statistics and genetics, are considered with a view to possible future improvements to the genetic algorithm.

The application of Multilevel Refinement to the Vehicle Routing Problem

We discuss the application of the multilevel (ML) refinement technique to the vehicle routing problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL heuristic, termed the combined node-exchange composite heuristic (CNCH), is developed first to solve instances of the VRP. A ML version (the ML-CNCH) is then created, using the construction and improvement heuristics of the CNCH at each level. Experimentation is used to find a suitable combination, which extends the global view of these heuristics. Results comparing both SL and ML are presented

AN IMPROVED APPROXIMATION ALGORITHM FOR THE TWO-MACHINE FLOW SHOP SCHEDULING PROBLEM WITH AN INTERSTAGE TRANSPORTER

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.

A Multilevel Force-directed Graph Drawing Algorithm Using Multilevel Global Force Approximation

In this paper we discuss an efficiency saving for multilevel force directed placement algorithms. Typically such algorithms use a Barnes Hut octree (or sometimes a grid) in order to approximate global repulsive forces. Here we instead exploit the graph coarsening structure, already in place to facilitate the multilevel scheme, in order to provide a hierarchical approximation to the global forces. Not only is this more efficient, but also it takes better account of the graph structure than an octree or a grid.

Single parameter analysis of power of preemption on two and three uniform machines

We consider scheduling problems on two and three uniform parallel machines. In the case of three machines we focus on the instances in which two machines have the same speed. For these models, we analyze the power of preemption defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. We derive tight upper bounds on the power of preemption expressed as piecewise functions of a single parameter, which is the speed of the fastest machine.

Power of Preemption for Minimizing Total Completion Time on Uniform Parallel Machines

For scheduling problems on parallel machines, the power of preemption is defined as the supremum ratio of the cost of an optimal nonpreemptive schedule over the cost of an optimal preemptive schedule (for the same input), where the cost is defined by a fixed common cost function. We present a tight analysis of the power of preemption for the problem of minimizing the total completion time on

Power of Preemption on Uniform Parallel Machines

m\geq 2

A cyclical search for the two machine flow shop and open shop to minimise finishing time

uniformly related machines, showing that its value for m=2 is equal to 1.2, and its overall value is approximately 1.39795.