Fitness scaling

Just as there is no prescription in the algorithm that defines the fitness function itself, we are free to choose a method for scaling that seems to be 

The Number of Copies of a Set of Strings Made by Running Different Selection Strategies 

String Fitness Scaled Fitness Binary Tournament 3-String Tournament Roulette Wheel Stochastic Remainder 

Note Since each of the selection methods contains a stochastic element, different results would be obtained if the selection were run a second time. 

Fitness scaling. The original range of fitnesses from 1.21 to 1.27 is stretched to cover a wider range. 

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Fitness scaling stretches out the fitness of the set of strings so that they span a wider range (Figure 5.18). Because the fitnesses now show a greater spread, it is easier for the selection operator to notice and select the better strings. 

Fig. 4.34 SANS peak position, q, rescaled by 0(U2S as a function of polymer volume fraction in mixtures of normal and deuterated toluene and toluene at room temperature (Mayes et al. 1994) (a) dPS-PMMA diblock (AL, = 301 kg mol1, /mMA = 0.43) (b) PMMA-c/PS-PMMA triblock (AL — 93 kg mor /pMMA - 0.5). The solid lines indicate the best fit scaling relation q

There are more than 50 species of sea snakes that thrive in marine environments. Sea snakes possess adaptations such as nasal valves and close-fitting scales around the mouth that keep water out during diving. Flattened tails that look like small paddles... 

Horsetails, the top of the plant carries a little cone, covered with close-fitting scales. The underside of each scale is... 

The dependence on the binning of the input distribution is checked by repeating the fit for different numbers of bins. The fit is found to be stable and the small deviations of the fitted scaling factors are within the statistical errors of the fit. 

Fig. 4.15 deviation ofthe fitted scale factor for 6-events from the true value a jin repeated... 

Fig. A.2 Deviation of the fitted scale factor a in fc-events from the true value a when using the apiuoximate fitting method. The results are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb . All bins in muon transverse momentum are shown...

One is rank-based fitness function the other is to set a fitness function through appropriate adjustments (called fitness scaling) of the actual target value. For the second method, in initial phase there are often chromosomes with a hypemormal fitness which constitute a larger proportion of the population if we reproduce them in proportion. Because of their outstanding competitiveness which may lead to their control of the selection process, they may further influence the global optimization... 

Fig. 14. Scaling of characteristic distances between anionic K-TEMPO spin probes in ionomers based on diblock copolymers, (a) Direct neighbor distance between clusters in zwitterionic diblock copolymers Q-PS-PI-S (o), cluster radii of all samples ( ). Solid lines are best-fit scaling laws (see text), (b) Direct neighbor distance in monoionic diblock copolymers PS-PI-S (o) and in monoionic homopol3rmers PI-S ( ). The solid line is the best fit for a scaling law with exponent 1/3, and the dashed line is the best fit for a scaling law with exponent 1/2.

Fig. 15. Pulsed ELDOR (DEER) distance measurements on the ionic spin-probe TEMPO-4-carboxylate attached to ionic clusters in ionically modified diblock copolymers, (a) Schematic structure of a monoionic polystyiene-polyisoprene diblock copolymer modified by sulfonate end groups on the polyisoprene bloek (sample series S). (b) Schematic structure of an a,0)-zwitterionic polystyrene- ly-isoprene diblock copolymer modified by a quaternary ammonium end group on the polystyrene block and a sulfonate end group on the polyisoprene block (sample series Z). (c) Schematic structures of the polymer chains. Tlie solid line corresponds to the harder block polystyrene, the dotted line to the softer block polyisoprene. (d) Dependence of ionic cluster size (ri) and intercluster distance (r2> on molecular weight. Squares correspond to sample series Z, circles to sample series S, and diamonds to monionic homopolymers (polystyrene modified with quaternary ammonium end groups). The dotted and dashed lines are fits of a constant function. The solid line is the best-fit scaling law r2 = 2.09...

Typical behavior is shown in Fig. 3.12(a), where the storage modulus in the plateau and terminal regions for a commercial polystyrene melt is plotted against frequency at several temperatures [17]. A reference temperature is selected, in this case To = 160 °C, and best-fit scale factors for data obtained at other temperatures are determined empirically to form Fig. 3.12(b). The timescale can shift very rapidly, as indicated by the plot of ar versus T in Fig. 3.13 [17]. The Williams-Landel-Ferry (WLF) equation, introduced in Chapter 2 and shown for this particular sample and choice of reference temperature in Fig. 3.13, describes rather well the temperature dependence of aj for most polymer melts and concentrated solutions. 

Rank Member Raw Fitness Scaled Fitness Probability of Selection... 

The best-fit scale factor ki of each horizontal ground motion component was determined as the value minimizing the function logC i Acomponent/S Atarget) over the period range of interest, in a least mean square sense. In other words, the aim was to find via an interactive procedure the k value that minimizes the sum ... 

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