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

Chapter 3. Immune Systems for Scheduling 81V1 V2 V3V1V1 V2V2J1a) combinatorial gene rearrangement b) Somatic recombination c) Nucleotide additionFigure 3.12: The figure shows three mechanisms by which the biological immune systemgenerates diversity by combining variable gene regions.(a) Combinatorial gene rearrangement: a large number of genes in the germline canrandomly recombine to form a new protein(b) Somatic recombination: imperfect recombination of genes sometimes results in newproteins that are shorter than the original recombining segments(c) Nucleotide addition: extra nucleotides encoding for additional amino acids are sometimesinserted between two joining segmentsassume that the germ-line contains n DNA chunks or antibodies representing a partialsequence of jobs, each of length l, and that a minimum of s chunks are required tonconstruct a schedule. At least >= s? C possible combinations of these antibodies canbe produced. Now, for a scenario in which j jobs need to be scheduled on a single machine,then examining all possible sequences of these jobs would result in j! possibleschedules. However, we postulate that C v , the number of valid schedules in C is @ j!for two reasons:n1. Many of the = s? theoretical schedules will contain multiple instances of jobs ormissing jobs, and hence the schedules are illegal and can be discarded.2. The n partial schedules encapsulate prior knowledge, and hence are guaranteedto be suitable subsequences, i.e to be the most promising of the l! possible subsequences.Therefore, if a suitable method can be found of combining the antibodies evolvedusing SCHED2 IS, then the complete system should represent an efficient method of