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

Chapter 3. Immune Systems for Scheduling 603.6.1 Experimental DataAntigen universes, (AUs), were generated based on a set of benchmark schedulingproblems given by Morton&Pentico in [Morton and Pentico, 1993]. These problemshave been commonly used in a large number of scheduling studies. Results are reportedhere for the problem known as jb11.ss, which was selected as being typical ofa medium-sized problem from this set. This problem contains 15 jobs, to be processedon 5 machines, and is known to have an optimal solution where no job arrives late.Each AU generated contained 10 antigens — an antigen was generated by mutatingthe original arrival date for each job with probability p u to another random date, inthe range (0,300), subject to the condition that the new arrival date was at least ptdays before the due-date of the job, where pt was the minimum processing time requiredto complete the job. (Note that this method does not guarantee that the resultingconditions can lead to an optimum schedule where no job is tardy.)3.6.2 Common parametersIn all experiments, a population of 100 random individuals was generated, with eachindividual characterised by l 5¤ c 5¥ and therefore s 15 (as the total length of anantibody produced from an individual must equal the number of operations, 75). Thus,£a total of c l 3125 antibodies can be formulated from a single immune system. Thesevalues were chosen after considerable experimentation with combinations of c and l.The value of c can be increased independently of l and s, however, clearly there is atrade-off between the amount of diversity that can be achieved within the system, andthe amount of time required to evolve the system, given that selection pressure actsonly on the phenotype. A similar trade-off exists in balancing l and s — the length s ofthe segment represents a common sequence of instructions for building a schedule. Thelikelihood of finding common sequences decreases as s increases, but the size of thesearch space increases exponentially as s decreases (and therefore l increases). Thevalues c¤ l¤ of s reported here appeared to be a satisfactory compromise that allowedevolution to take place over a tractable amount of time, yet still produce satisfactoryresults.