Optimisation evolutionary operations

W. Spendley, G. R. Hext and F. R. Himsworth, Sequential application of simplex designs in optimisation and evolutionary operation. Technometrics, 4(4), 1962, 441-461. 

There are limits to the applicability of virtually every optimisation method. A GA may only be applied to a problem if it is possible to express the solution as a sequence of values. This sequence is referred to as a chromosome or a string, and each parameter within the chromosome is a gene. The entire set of genes constitutes the genotype, and the solution to which this genotype corresponds is known as the phenotype (Fig. 8). The GA works to refine strings with the help of the evolutionary operators outlined previously. 

The application of a factorial design associated with evolutionary operation allowed a suitable and efficient optimisation of the FI-CVG-ICP-OES method for mercury determination. Inially a fractional two-level 2 factorial design with 16 experiments and a triplicate of the central point was carried out. In view of the results, a second two-level 2 full factorial design was carried out. 

Competition unavoidably requires a population size greater than 1 - a single individual cannot compete with itself. Since EAs show evolutionary behaviour, it is reasonable to anticipate that they too will normally need to work upon a group of individuals. This requires that these algorithms must operate on many potential solutions simultaneously, so that selection pressure can be applied to cull the poorer solutions and drive the search towards those of higher quality. This manipulation of a group, or population of solutions, is a fundamental difference with most other optimisation methods, which typically create and then refine a single solution. 

Based on genetic and evolutionary principles, GAs work by repeatedly modifying a population of artificial structures (chromosomes) through the application of selection, crossover, and mutation operators. The evaluation of optimisation happens with the adaptation function (fitness), which is represented by the objective problem function in study (involving the mathematical model of the analysed system), that determines the process performance. 

Fig. 19 Evolutionary optimisation at the atomic level. A combination of rule-based and genetic algorithm strategies is used to coerce an STM tip to produce one of two distinct image types, with no human operator involvement, (a) and (b) are the experimental images (c) and (d) the target structures (e) and (f) show profiles along the lines shown in (a) and (b). From Ref. 82.

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