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Chapter 3. Immune Systems for Scheduling 89of jobs on one of the 5 machines. Therefore, 5 antigen universes, one for each machine,are generated, and each universe contains 10 antigens, one derived from eachtest-scenario. The universes are treated independently, and thus an independent set ofantibodies discovered for each machine.3.13 Experimental ResultsExperiments were performed to identify good settings for three main parameters; theantibody sample size σ, the antigen sample size τ, and the length of the antibody l.These initial experiments also attempted to answer several questions in order to assesswhether the evolved antibodies would be useful pattern recognisers in the context of ascheduling system, for example:How many antigens are matched by at least one antibody ?¢¢ How many unique antibodies are found ?¢ What is the average number of antigens matched by an antibody ?¢ How many actual jobs are represented in the set of antibody patterns ?All reported experiments were performed using a population of size 100, with thelength of each antibody in the population equal to 5 jobs, i.e 1/3 the length of the antigenstring. The length of each antigen was 15, as each machine required 15 operationsto be scheduled. Every experiment was run for 250 generations and was repeated 10times. The mutation rate in each case was 1/l = 0.2. Details of the settings for σand τ are described under the relevant headings. As a separate set of antibodies areevolved for each machine, results are reported for only one of the machines, machine1, however, the reported trends were applicable to all machines.In the following section, many of the experiments are analysed with reference to aquantity described as the match-threshold. The match-function M described in section3.11.3 quantifies the extent of the match between an antibody and an antigen. However,a qualitative statement regarding whether or not a match has occurred can be made —a match is only said to occur if the match-score M is greater than or equal to some
Chapter 3. Immune Systems for Scheduling 90threshold value M T . (A similar phenomenon is observed in natural systems in whichan antibody does not bind to an antigen until the strength of the bond between the two— the antibody affinity — reaches a certain value). In this case, the match-thresholdis more specifically defined as the number of non wild-card places in which an antigenand antibody match.3.13.1 How many antigens are matched by at least one antibody ?The aim of these experiments is to investigate the amount of overlap occurring in theantibody population, and also to determine whether or not all antigens are at leastpartially recognised. Table 3.4 shows the average number of antigens (from a universecontaining 10 antigens) that were not matched by any antibody, for match-thresholdsM T ranging from 2 to 5. Experiments are performed over a range of values for σ andτ, the size of the antibody and antigen samples respectively.For certain combinations of values of m¤ σ¤ τ¥ , it can be seen that no antibodiesmatch some of the antigens. This is particularly noticeable as the size of τ increases.£This is explained with reference to the fitness function used; for high values of τ,antibodies that successfully match more than one antigen are rewarded most highly.However, in many antigen-universes, it may be impossible to detect common patternsbetween certain subsets of antigen, and hence the completely generalist antibody maynot exist. Examining the actual antigen universe for machine 1 indicates that for somesubsets of antigen, common schemas do exist. Similarly, low values of σ also encouragegeneralist antibodies to evolve, so we may expect poor performance if the value ofσ is too low for certain antigen universes.3.13.2 How many unique antibodies are evolved ?Recalling that the aim of SCHED2 IS is to acquire a collection of antibodies, eachof which represents some commonly occurring pattern in the antigen-universe, thenthe more unique patterns we are able to detect, the more useful the antibodies will beas building blocks for constructing new schedules. Therefore, the final population ofantibodies is examined to determine the exact number of unique antibodies that match
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AbstractThe biological immune syste
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DeclarationI declare that this thes
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Table of Contents1 Introduction 11.
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List of Figures2.1 ’Lock and Key
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Chapter 1IntroductionThe study of b
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Chapter 1. Introduction 3scientists
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Chapter 7Conclusion7.1 OverviewThis
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Chapter 7. Conclusion 183features m
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Chapter 7. Conclusion 185In additio
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Chapter 7. Conclusion 187ter, sched
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Chapter 7. Conclusion 189Clustering
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Chapter 7. Conclusion 191nature in
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Appendix ACoincidences in permutati
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Appendix BExperimental results obta
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Appendix B. Experimental results ob
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Bibliography 203[Cooke and Hunt, 19
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Bibliography 205[Farmer et al., 198
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Bibliography 207[Hart et al., 1998]
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Bibliography 209[Kohonen, 1982b] Ko
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Bibliography 211[Potter and De Jong
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Bibliography 213[Timmis et al., 199
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