Genetic Algorithms for Multiple-Choice Problems

by

Uwe Aickelin (Dipl Kfm, EMBSc)

School of Computer Science University of Nottingham NG8 1BB UK uxa@cs.nott.ac.uk

Thesis submitted to the University of Wales In candidature for the Degree of Doctor of Philosophy

European Business Management School University of Wales Swansea

September 1999 Declaration

This work has not previously been accepted in substance for any degree and is not concurrently being submitted in candidature for any degree.

Signed ………………………………. (Candidate) Date ……………………………….

Statement 1

This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged by endnotes giving explicit reference. A bibliography is appended.

Signed ………………………………. (Candidate) Date ……………………………….

Statement 2

I hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisations.

Signed ………………………………. (Candidate) Date ………………………………. Acknowledgements

Everybody has someone or something to thank for their success. Primarily I want to use this opportunity to thank my supervisor Dr Kathryn Dowsland for her guidance and support throughout my work. No doubt without the many of our discussions both this thesis and my research would not have been possible. Additionally, I am very grateful for the advice and support of Dr Bill Dowsland, the computer support staff and other people of the European Business Management School. Furthermore, special thanks go to Dr Jonathan Thompson for his early work on the nurse scheduling problem. I would also like to thank my family who in their own ways always supported me. Finally, thank you to Sonya for motivation, support and distraction at the appropriate times over the past years. Summary

This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems. It shows that such information can significantly enhance performance, but that the choice of information and the way it is included are important factors for success. Two multiple-choice problems are considered. The first is constructing a feasible nurse roster that considers as many requests as possible. In the second problem, shops are allocated to locations in a mall subject to constraints and maximising the overall income. Genetic algorithms are chosen for their well-known robustness and ability to solve large and complex discrete optimisation problems. However, a survey of the literature reveals room for further research into generic ways to include constraints into a genetic algorithm framework.
Hence, the main theme of this work is to balance feasibility and cost of solutions. In particular, co-operative co-evolution with hierarchical sub-populations, problem structure exploiting repair schemes and indirect genetic algorithms with self-adjusting decoder functions are identified as promising approaches. The research starts by applying standard genetic algorithms to the problems and explaining the failure of such approaches due to epistasis. To overcome this, problem-specific information is added in a variety of ways, some of which are designed to increase the number of feasible solutions found whilst others are intended to improve the quality of such solutions. As well as a theoretical discussion as to the underlying reasons for using each operator, extensive computational experiments are carried out on a variety of data. These show that the indirect approach relies less on problem structure and hence is easier to implement and superior in solution quality. The most successful variant of our algorithm has a more than 99% chance of finding a feasible solution which is either optimal or within a few percent of optimality.

Contents

1 INTRODUCTION………………………………………………………………………………………1 1.1 THE NATURE OF THE PROBLEM……………………………………………………………………1 1.2 THE SOLUTION METHOD AND RESULTS ………………………………………………………..2 1.3 THE STRUCTURE OF THE THESIS…………………………………………………………………..4 2 INTRODUCTION TO NURSE SCHEDULING…………………………………………..6 2.1 PROBLEM FORMULATION ……………………………………………………………………………6 2.2 INTRODUCTION TO NURSE SCHEDULING ……………………………………………………..14 2.3 CYCLIC NURSE SCHEDULING …………………………………………………………………….15 2.4 LINEAR, INTEGER, CONSTRAINT AND GOAL PROGRAMMING ………………………….16 2.5 HEURISTIC SCHEDULIN

…(Full text truncated)…