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/ALDsave FMLOCAL /ALDmatrix matrix def ALDmatrix currentmatrix pop/StartALD { /ALDsave save def savematrix ALDmatrix setmatrix } bind def/InALD { restorematrix } bind def/DoneALD { ALDsave restore } bind def%%EndProlog%%BeginSetup(3.0) FMVERSION1 1 595.3 841.9 0 1 21 FMDOCUMENT0 0 /Times-Italic FMFONTDEFINE1 0 /Times-Bold FMFONTDEFINE2 0 /Times-Roman FMFONTDEFINE3 0 /Courier FMFONTDEFINE4 1 /Symbol FMFONTDEFINE5 0 /Times-BoldItalic FMFONTDEFINE6 0 /Courier-BoldOblique FMFONTDEFINE32 FMFILLS0 0 FMFILL1 .1 FMFILL2 .3 FMFILL3 .5 FMFILL4 .7 FMFILL5 .9 FMFILL6 .97 FMFILL7 1 FMFILL8 <0f1e3c78f0e1c387> FMFILL9 <0f87c3e1f0783c1e> FMFILL10 <cccccccccccccccc> FMFILL11 <ffff0000ffff0000> FMFILL12 <8142241818244281> FMFILL13 <03060c183060c081> FMFILL14 <8040201008040201> FMFILL16 1 FMFILL17 .9 FMFILL18 .7 FMFILL19 .5 FMFILL20 .3 FMFILL21 .1 FMFILL22 0.03 FMFILL23 0 FMFILL24 <f0e1c3870f1e3c78> FMFILL25 <f0783c1e0f87c3e1> FMFILL26 <3333333333333333> FMFILL27 <0000ffff0000ffff> FMFILL28 <7ebddbe7e7dbbd7e> FMFILL29 <fcf9f3e7cf9f3f7e> FMFILL30 <7fbfdfeff7fbfdfe> FMFILL%%EndSetup%%Page: "1" 1%%BeginPaperSize: A4%%EndPaperSize595.3 841.9 0 FMBEGINPAGE0 10 Q0 X0 K(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T(1-1) 518.33 61.29 T1 28 Q(1 T) 63.65 726.29 T(utorial) 100.75 726.29 T2 12 Q4.82 (M) 135.65 692.95 P2 10 Q4.02 (A) 146.31 692.95 P4.02 (TLAB) 152.42 692.95 P2 12 Q4.82 ( has a wide variety of functions useful to the genetic algorithm) 178.51 692.95 P1.63 (practitioner and those wishing to experiment with the genetic algorithm for the) 135.65 678.95 P-0.03 (\336rst time. Given the versatility of M) 135.65 664.95 P2 10 Q-0.02 (A) 309.05 664.95 P-0.02 (TLAB) 315.16 664.95 P2 12 Q-0.03 (\325) 341.26 664.95 P-0.03 (s high-level language, problems can be) 344.59 664.95 P0.58 (coded in m-\336les in a fraction of the time that it would take to create C or Fortran) 135.65 650.95 P3.7 (programs for the same purpose. Couple this with M) 135.65 636.95 P2 10 Q3.09 (A) 412.78 636.95 P3.09 (TLAB) 418.88 636.95 P2 12 Q3.7 (\325) 444.98 636.95 P3.7 (s advanced data) 448.31 636.95 P0.17 (analysis, visualisation tools and special purpose application domain toolboxes and) 135.65 622.95 P2.91 (the user is presented with a uniform environment with which to explore the) 135.65 608.95 P(potential of genetic algorithms.) 135.65 594.95 T1.02 (The Genetic Algorithm T) 135.65 568.95 P1.02 (oolbox uses M) 260.1 568.95 P2 10 Q0.85 (A) 332.76 568.95 P0.85 (TLAB) 338.87 568.95 P2 12 Q1.02 ( matrix functions to build a set of) 364.97 568.95 P0.87 (versatile tools for implementing a wide range of genetic algorithm methods. The) 135.65 554.95 P1.04 (Genetic Algorithm T) 135.65 540.95 P1.04 (oolbox is a collection of routines, written mostly in m-\336les,) 237.48 540.95 P(which implement the most important functions in genetic algorithms.) 135.65 526.95 TFMENDPAGE%%EndPage: "1" 2%%Page: "2" 2595.3 841.9 0 FMBEGINPAGE0 10 Q0 X0 K(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T(1-2) 518.33 61.29 T63.65 716.95 531.65 726.95 C63.65 725.95 531.65 725.95 2 L1 H2 Z0 X0 KN-8.35 24.95 603.65 816.95 C1 18 Q0 X0 K(Installation) 63.65 732.95 T2 12 Q2.37 (Instructions for installing the Genetic Algorithm T) 135.65 694.95 P2.37 (oolbox can be found in the) 391.55 694.95 P0.36 (M) 135.65 680.95 P2 10 Q0.3 (A) 146.31 680.95 P0.3 (TLAB) 152.42 680.95 P2 12 Q0.36 ( installation instructions. It is recommended that the \336les for this toolbox) 178.51 680.95 P(are stored in a directory named genetic of) 135.65 666.95 T(f the main matlab/toolbox directory) 334.93 666.95 T(.) 504.71 666.95 T3.33 (A number of demonstrations are available. A single-population binary-coded) 135.65 640.95 P-0.13 (genetic algorithm to solve a numerical optimization problem is implemented in the) 135.65 626.95 P-0.25 (m-\336le) 135.65 612.95 P3 F-0.61 (sga.m) 167.04 612.95 P2 F-0.25 (. The demonstration m-\336le) 203.02 612.95 P3 F-0.61 (mpga.m) 332.93 612.95 P2 F-0.25 ( implements a real-valued multi-) 376.1 612.95 P1.29 (population genetic algorithm to solve a dynamic control problem. Both of these) 135.65 598.95 P(demonstration m-\336les are discussed in detail in the) 135.65 584.95 T0 F(Examples) 382.16 584.95 T2 F( Section.) 428.79 584.95 T1.06 (Additionally) 135.65 558.95 P1.06 (, a set of test functions, drawn from the genetic algorithm literature,) 195.51 558.95 P2.55 (are supplied in a separate directory) 135.65 544.95 P2.55 (,) 315.12 544.95 P3 F6.11 (test_fns) 323.66 544.95 P2 F2.55 (, from the Genetic Algorithm) 381.23 544.95 P0.05 (T) 135.65 530.95 P0.05 (oolbox functions. A brief description of these test functions is given at the end of) 142.14 530.95 P0.93 (the) 135.65 516.95 P0 F0.93 (Examples) 154.23 516.95 P2 F0.93 ( Section. A further document describes the implementation and use) 200.86 516.95 P(of these functions.) 135.65 502.95 TFMENDPAGE%%EndPage: "2" 3%%Page: "3" 3595.3 841.9 0 FMBEGINPAGE0 10 Q0 X0 K(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T(1-3) 518.33 61.29 T63.65 716.95 531.65 726.95 C63.65 725.95 531.65 725.95 2 L1 H2 Z0 X0 KN-8.35 24.95 603.65 816.95 C1 18 Q0 X0 K(An Overview of Genetic Algorithms) 63.65 732.95 T2 12 Q-0.06 (In this Section we give a tutorial introduction to the basic Genetic Algorithm \050GA\051) 135.65 694.95 P(and outline the procedures for solving problems using the GA.) 135.65 680.95 T1 16 Q(What ar) 135.65 652.29 T(e Genetic Algorithms?) 192.66 652.29 T2 12 Q0.56 (The GA is a stochastic global search method that mimics the metaphor of natural) 135.65 624.95 P0.66 (biological evolution. GAs operate on a population of potential solutions applying) 135.65 610.95 P2.41 (the principle of survival of the \336ttest to produce \050hopefully\051 better and better) 135.65 596.95 P0.86 (approximations to a solution. At each generation, a new set of approximations is) 135.65 582.95 P0.15 (created by the process of selecting individuals according to their level of \336tness in) 135.65 568.95 P1.29 (the problem domain and breeding them together using operators borrowed from) 135.65 554.95 P0.63 (natural genetics. This process leads to the evolution of populations of individuals) 135.65 540.95 P2.41 (that are better suited to their environment than the individuals that they were) 135.65 526.95 P(created from, just as in natural adaptation.) 135.65 512.95 T3.17 (Individuals, or current approximations, are encoded as strings,) 135.65 486.95 P0 F3.17 (chr) 463.14 486.95 P3.17 (omosomes) 478.68 486.95 P2 F3.17 (,) 528.65 486.95 P0.8 (composed over some alphabet\050s\051, so that the) 135.65 472.95 P0 F0.8 (genotypes) 357.07 472.95 P2 F0.8 ( \050chromosome values\051 are) 405.03 472.95 P3.66 (uniquely mapped onto the decision variable \050) 135.65 458.95 P0 F3.66 (phenotypic) 374.11 458.95 P2 F3.66 (\051 domain. The most) 426.73 458.95 P0.03 (commonly used representation in GAs is the binary alphabet {0, 1} although other) 135.65 444.95 P1.05 (representations can be used, e.g. ternary) 135.65 430.95 P1.05 (, integer) 331.97 430.95 P1.05 (, real-valued etc. For example, a) 371.85 430.95 P2.13 (problem with two variables,) 135.65 416.95 P0 F2.13 (x) 281.76 416.95 P0 10 Q1.78 (1) 287.08 413.95 P2 12 Q2.13 ( and) 292.08 416.95 P0 F2.13 (x) 319.66 416.95 P0 10 Q1.78 (2) 324.98 413.95 P2 12 Q2.13 (, may be mapped onto the chromosome) 329.98 416.95 P(structure in the following way:) 135.65 402.95 T-0.3 (where) 135.65 299.98 P0 F-0.3 (x) 167.65 299.98 P0 10 Q-0.25 (1) 172.98 296.98 P2 12 Q-0.3 ( is encoded with 10 bits and) 177.97 299.98 P0 F-0.3 (x) 312.82 299.98 P0 10 Q-0.25 (2) 318.14 296.98 P2 12 Q-0.3 ( with 15 bits, possibly re\337ecting the level of) 323.14 299.98 P-0.2 (accuracy or range of the individual decision variables. Examining the chromosome) 135.65 285.98 P0.43 (string in isolation yields no information about the problem we are trying to solve.) 135.65 271.98 P0.11 (It is only with the decoding of the chromosome into its phenotypic values that any) 135.65 257.98 P1.35 (meaning can be applied to the representation. However) 135.65 243.98 P1.35 (, as described below) 409.1 243.98 P1.35 (, the) 509.64 243.98 P0.55 (search process will operate on this encoding of the decision variables, rather than) 135.65 229.98 P0.8 (the decision variables themselves, except, of course, where real-valued genes are) 135.65 215.98 P(used.) 135.65 201.98 T-0.19 (Having decoded the chromosome representation into the decision variable domain,) 135.65 175.98 P1.94 (it is possible to assess the performance, or) 135.65 161.98 P0 F1.94 (\336tness) 356.04 161.98 P2 F1.94 (, of individual members of a) 386.03 161.98 P3.53 (population. This is done through an objective function that characterises an) 135.65 147.98 P0.6 (individual\325) 135.65 133.98 P0.6 (s performance in the problem domain. In the natural world, this would) 187.63 133.98 P0.08 (be an individual\325) 135.65 119.98 P0.08 (s ability to survive in its present environment. Thus, the objective) 216.42 119.98 P63.65 96.95 531.65 744.95 C135.65 321.98 531.65 398.95 C146.65 328.95 520.65 391.95 C146.65 328.95 520.65 391.95 R7 X0 KV3 12 Q0 X(1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1) 157.35 369.97 T170.49 343.64 158.95 346.95 170.49 350.26 170.49 346.95 4 YV282.42 350.26 293.95 346.95 282.42 343.64 282.42 346.95 4 YV170.49 346.95 282.42 346.95 2 L0.5 H0 ZN297.08 382.95 297.08 337.95 2 L2 Z11 XN311.49 343.64 299.95 346.95 311.49 350.26 311.49 346.95 4 Y0 XV495.42 350.26 506.95 346.95 495.42 343.64 495.42 346.95 4 YV311.49 346.95 495.42 346.95 2 L0 ZN0 F(x) 221.29 353.75 T0 10 Q(1) 226.62 350.75 T0 12 Q(x) 398.29 353.75 T0 10 Q(2) 403.61 350.75 T135.65 321.98 531.65 398.95 C63.65 96.95 531.65 744.95 C-8.35 24.95 603.65 816.95 CFMENDPAGE%%EndPage: "3" 4%%Page: "4" 4595.3 841.9 0 FMBEGINPAGE0 10 Q0 X0 K(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T(1-4) 518.33 61.29 T2 12 Q2.35 (function establishes the basis for selection of pairs of individuals that will be) 135.65 736.95 P(mated together during reproduction.) 135.65 722.95 T0.45 (During the reproduction phase, each individual is assigned a \336tness value derived) 135.65 696.95 P0.94 (from its raw performance measure given by the objective function. This value is) 135.65 682.95 P1.18 (used in the selection to bias towards more \336t individuals. Highly \336t individuals,) 135.65 668.95 P2.11 (relative to the whole population, have a high probability of being selected for) 135.65 654.95 P2.56 (mating whereas less \336t individuals have a correspondingly low probability of) 135.65 640.95 P(being selected.) 135.65 626.95 T0.54 (Once the individuals have been assigned a \336tness value, they can be chosen from) 135.65 600.95 P5.22 (the population, with a probability according to their relative \336tness, and) 135.65 586.95 P2.85 (recombined to produce the next generation. Genetic operators manipulate the) 135.65 572.95 P0.61 (characters \050genes\051 of the chromosomes directly) 135.65 558.95 P0.61 (, using the assumption that certain) 364.71 558.95 P0.18 (individual\325) 135.65 544.95 P0.18 (s gene codes, on average, produce \336tter individuals. The recombination) 187.63 544.95 P0.68 (operator is used to exchange genetic information between pairs, or lar) 135.65 530.95 P0.68 (ger groups,) 477.01 530.95 P4.62 (of individuals. The simplest recombination operator is that of single-point) 135.65 516.95 P(crossover) 135.65 502.95 T(.) 180.95 502.95 T(Consider the two parent binary strings:) 135.65 476.95 T3 F(P) 171.65 450.95 T3 10 Q(1) 178.84 447.95 T3 12 Q( = 1 0 0 1 0 1 1 0) 184.84 450.95 T2 F(, and) 314.37 450.95 T3 F(P) 171.65 424.95 T3 10 Q(2) 178.84 421.95 T3 12 Q( = 1 0 1 1 1 0 0 0) 184.84 424.95 T2 F(.) 314.37 424.95 T0.59 (If an integer position,) 135.65 398.95 P0 F0.59 (i) 244.27 398.95 P2 F0.59 (, is selected uniformly at random between 1 and the string) 247.6 398.95 P0.97 (length,) 135.65 384.95 P0 F0.97 (l) 172.6 384.95 P2 F0.97 (, minus one [1,) 175.93 384.95 P0 F0.97 (l) 254.42 384.95 P2 F0.97 (-1], and the genetic information exchanged between the) 257.76 384.95 P0.15 (individuals about this point, then two new of) 135.65 370.95 P0.15 (fspring strings are produced. The two) 351.03 370.95 P(of) 135.65 356.95 T(fspring below are produced when the crossover point) 145.42 356.95 T0 F(i = 5) 403.22 356.95 T2 F( is selected,) 426.64 356.95 T3 F(O) 171.65 330.95 T3 10 Q(1) 178.84 327.95 T3 12 Q( = 1 0 0 1 0 0 0 0) 184.84 330.95 T2 F(, and) 314.37 330.95 T3 F(O) 171.65 304.95 T3 10 Q(2) 178.84 301.95 T3 12 Q( = 1 0 1 1 1 1 1 0) 184.84 304.95 T2 F(.) 314.37 304.95 T3.99 (This crossover operation is not necessarily performed on all strings in the) 135.65 278.95 P0.87 (population. Instead, it is applied with a probability) 135.65 264.95 P0 F0.87 (Px) 387.77 264.95 P2 F0.87 ( when the pairs are chosen) 400.42 264.95 P-0.2 (for breeding. A further genetic operator) 135.65 250.95 P-0.2 (, called mutation, is then applied to the new) 324.02 250.95 P1.8 (chromosomes, again with a set probability) 135.65 236.95 P1.8 (,) 347.08 236.95 P0 F1.8 (Pm) 354.88 236.95 P2 F1.8 (. Mutation causes the individual) 370.87 236.95 P1.06 (genetic representation to be changed according to some probabilistic rule. In the) 135.65 222.95 P0.41 (binary) 135.65 208.95 P0.41 (string) 172.7 208.95 P0.41 ( representation,) 206.01 208.95 P0.41 ( mutation will cause a single bit to change its state,) 283.36 208.95 P0.74 (0) 135.65 194.95 P4 F0.74 (\336) 145.38 194.95 P2 F0.74 (1 or 1) 160.96 194.95 P4 F0.74 (\336) 194.15 194.95 P2 F0.74 ( 0. So, for example, mutating the fourth bit of) 205.99 194.95 P3 F1.77 (O) 434.89 194.95 P3 10 Q1.48 (1) 442.09 191.95 P2 12 Q0.74 ( leads to the new) 448.09 194.95 P(string,) 135.65 180.95 T3 F(O) 171.65 154.95 T3 10 Q(1m) 178.84 151.95 T3 12 Q( = 1 0 0 0 0 0 0 0) 190.84 154.95 T2 F(.) 320.37 154.95 T0.19 (Mutation is generally considered to be a background operator that ensures that the) 135.65 128.95 P0.61 (probability of searching a particular subspace of the problem space is never zero.) 135.65 114.95 PFMENDPAGE%%EndPage: "4" 5%%Page: "5" 5595.3 841.9 0 FMBEGINPAGE0 10 Q0 X0 K(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T(1-5) 518.33 61.29 T2 12 Q1.57 (This has the ef) 135.65 736.95 P
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