Immunology as a Metaphor for Computational ... - Napier University

Chapter 3. Immune Systems for Scheduling 92707060Antigen Exposure Rate = 260Antigen Exposure Rate = 8Number of antibodies5040302010Number of antibodies504030201001 2 3 4 5 6 7 8 9 10Number of antigens matched01 2 3 4 5 6 7 8 9 10Number of antigens matchedFigure 3.18: Match Threshold 2 : Number of antibodies matching B1 antigen forantibody sample size = 30. The graphs compare the overlap when τ C 2 and τ C 83.13.3 Measuring OverlapThe two previous sections have shown that it is possible to evolve a set of unique antibodies,and also that those antibodies tend to match at least one antigen. In order tomeasure how much overlap is occurring between those antibodies however, the numberof antigens matched by each antibody in the population is recorded. Figure 3.18shows the number of antibodies that match n antigens, where n takes values between1 and 10. The diagram contrasts the results obtained for a match-threshold of 2 andfixed antibody sample size C σ 30 for various values of τ. Clearly, more antigens arematched at high values of τ, as expected.It is interesting to observe how the number of antibodies matching more than 1antigen increases as the GA runs. The graphs in figure 3.19 illustrate the point. Experimentsare performed in which the match-threshold m is varied from 2 to 5, forpopulations of antibodies in which the antibody length is varied from m to 5 also.When the match-threshold is equal to the antibody length, there is a rapid increase inthe number of matching antibodies in the C m 2 case after which the number remainsrelatively constant. For C m 3, the number rises steadily. For values of D m l, in eachcase, there is an immediate increase at the the start of each run to a level which is maintainedthroughout the remainder of the experiment. The initial rise is more pronouncedwhen m is significantly less than l.