📄 chapter6.ps
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4 10 Q(or) 186.79 622.13 T(not) 162.95 599.4 T(d1) 165.6 578.84 T(d2) 206.65 598.86 T(or) 185.03 673.11 T185.02 671.03 164.82 651.12 2 L0.5 H2 ZN192.19 671.14 209.74 654.25 2 LN(not) 154.12 644.85 T(and) 206.21 646.05 T209.74 644.51 193.85 629.9 2 LN217.68 644.51 233.57 629.9 2 LN158.54 642.89 149.82 626.77 2 LN(d1) 141.77 619.42 T(not) 230.63 622.13 T239.46 620.49 250.45 604.59 2 LN(d0) 246.82 596.15 T193.85 620.16 209.74 605.55 2 LN185.9 620.16 170.01 605.55 2 LN170.01 598.64 170.01 586.07 2 LN328.66 639.82 348.77 633.74 328.5 628.24 328.58 634.03 4 YV276.49 634.77 328.58 634.03 2 L3 HN194.73 653.17 155 611.92 155 575.24 266.23 575.24 266.23 634.84 234.45 653.17 6 Y1 H0 Z2 XN0 X(or) 413.26 676.71 T409.28 674.09 393.39 659.48 2 L0.5 H2 ZN425.17 674.09 441.06 659.48 2 LN(not) 384.56 651.43 T389.86 650.28 389.86 635.67 2 LN(d1) 385.01 627.35 T5 F(newfunc) 426.93 651.66 T(new) 351.71 598.78 T(func) 371.15 598.78 T6 14 Q(\256) 395.03 598.78 T4 10 Q(\050and \050or \050not d1\051 d2\051) 412.34 598.78 T7 F(compression) 274.12 639.96 T(operator) 280.5 622.43 T4 F(\050not d0\051\051) 427.16 586.43 T108 90 540 702 C0 0 612 792 CFMENDPAGE%%EndPage: "107" 5%%Page: "108" 5612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(108) 522.01 712 T108 90 540 702 R7 XV0 X1.02 (Exactly how the randomly selected subtree is pruned to create a module\325) 126 475.19 P1.02 (s de\336nition) 485.33 475.19 P0.98 (depends on the compression method in use. The) 108 457.19 P2 F0.98 (depth compr) 349.33 457.19 P0.98 (ession) 410.15 457.19 P0 F0.98 ( method extracts the) 440.14 457.19 P0.56 (subtree from its root node and clips of) 108 439.19 P0.56 (f any branch exceeding a randomly selected maxi-) 294.6 439.19 P0.19 (mum depth. The maximum depth for each new module is generated by a uniform random) 108 421.19 P-0.11 (variable over a user de\336ned range. Figure 24 shows the result of a compression when each) 108 403.19 P0.52 (branch of the subtree is within the selected maximum depth. Here, compression removes) 108 385.19 P0.31 (the entire subtree from the genotype, assigns it a unique module name) 108 367.19 P1 F0.31 (,) 447.18 367.19 P0 F0.31 (and de\336nes it as a) 453.49 367.19 P0.86 (new LISP function with no parameters. A call to the newly de\336ned module replaces the) 108 349.19 P1.28 (original subtree as shown in Figure 24. When GLiB evaluates the genotype\325) 108 331.19 P1.28 (s \336tness, it) 486.46 331.19 P2.03 (retrieves the compressed module\325) 108 313.19 P2.03 (s de\336nition instead of directly executing the original) 274.96 313.19 P(subtree.) 108 295.19 T0.67 (When one or more subtree branches exceed the maximum depth, the de\336ned module) 126 265.19 P0.37 (has a very dif) 108 247.19 P0.37 (ferent de\336nition. Rather than extracting the entire subtree, only the portions) 173.85 247.19 P0.55 (within the selected depth appear in the new module\325) 108 229.19 P0.55 (s de\336nition. The branches exceeding) 362.25 229.19 P1.36 (the depth are replaced with unique variable names. GLiB then de\336nes the new module) 108 211.19 P-0.29 (with the variables de\336ned as parameters to the module. When GLiB replaces the subtree in) 108 193.19 P1.22 (the genotype with the call to the module, the sections of the original subtree below the) 108 175.19 P0.88 (selected depth become the parameter bindings. Figure 25 shows this instance of module) 108 157.19 P(creation.) 108 139.19 T108 90 540 702 C124.88 483.19 523.12 702 C140.62 501.19 500.62 528.19 R7 X0 KV3 12 Q0 X3.88 (Figure 25:) 140.62 520.19 P2 F3.88 (Depth compr) 204.37 520.19 P3.88 (ession applied to a subtr) 270.76 520.19 P3.88 (ee lar) 403.8 520.19 P3.88 (ger than the) 434.89 520.19 P(maximum depth. The module\325) 140.62 508.19 T(s de\336nition has parameters as a r) 281.64 508.19 T(esult.) 441.78 508.19 T4 10 Q(or) 212.82 670.64 T(d0) 212.82 585.66 T(d0) 181.55 556.03 T218.03 669.2 197.18 652.21 2 L0.5 H0 ZN218.03 669.2 238.88 652.21 2 LN(not) 186.76 639.84 T218.03 612.55 218.03 595.55 2 LN(or) 235.41 641 T238.88 640.88 218.03 623.88 2 LN238.88 640.88 259.73 623.88 2 LN(d2) 254.52 608.32 T282.49 681.46 285.79 693 289.1 681.46 285.79 681.46 4 YV289.1 619.56 285.79 608.02 282.49 619.56 285.79 619.56 4 YV285.79 681.46 285.79 619.56 2 L1 HN(maxdepth) 0 -270 293.16 623.72 TF(not) 212.82 612.68 T191.97 640.88 171.12 623.88 2 LN(and) 160.7 612.68 T165.91 612.55 145.06 595.55 2 L0.5 HN165.91 612.55 186.76 595.55 2 LN(d1) 139.85 585.66 T150.27 611.24 150.27 605.58 285.79 605.58 218.03 690.55 4 Y1 HN5 F(newfunc) 391.85 582.67 T4 F( \050) 432.38 582.67 T7 F(p1 p2 p3) 438.49 582.67 T4 F(\051) 477.39 582.67 T6 14 Q(\256) 483.22 582.67 T4 10 Q(\050or \050not \050and) 413.44 570.97 T7 F( p1 p2) 468.43 570.97 T4 F(\051\051) 496.22 570.97 T(\050or \050not) 428.74 559.27 T7 F(p3) 463.73 559.27 T4 F(\051 d2\051\051\051) 474.85 559.27 T(not) 181.54 584.35 T186.76 582.92 186.76 565.92 2 L0.5 HN371.15 628.34 391.34 622.56 371.15 616.77 371.15 622.56 4 YV318.23 622.56 371.15 622.56 2 L3 H2 ZN7 F(compression) 318.49 610.05 T(depth) 330.65 632.06 T5 F(newfunc) 451.3 675.82 T456.07 675 431.74 648.82 2 L0.5 HN4 F(d1) 423.63 639.82 T464.17 675 464.17 648.82 2 LN(not) 456.07 639.82 T(d0) 456.07 612.82 T(d0) 488.5 639.82 T472.28 675 496.61 648.82 2 LN464.17 639 464.17 621 2 LN108 90 540 702 C0 0 612 792 CFMENDPAGE%%EndPage: "108" 6%%Page: "109" 6612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(109) 522.01 712 T108 90 540 702 R7 XV0 X0.61 (Depth compression is but one method for extracting a module from an individual for) 126 442 P1.01 (compression. An example of another modularization method is) 108 424 P2 F1.01 (leaf compr) 421.51 424 P1.01 (ession) 473.7 424 P0 F1.01 (, which) 503.68 424 P-0.12 (again selects a random node as the root of the subtree. However) 108 406 P-0.12 (, in leaf compression, each) 412.59 406 P0.22 (unique leaf is replaced with a unique parameter name, as shown in Figure 26. The advan-) 108 388 P1.54 (tage of leaf compression over depth compression is the reuse of parameters within the) 108 370 P2.27 (de\336ned module. Depth compression always produces a module in which a parameter) 108 352 P-0.07 (appears only once. On the other hand, depth compression has the ability to construct mod-) 108 334 P0.89 (ules from partial subtrees while leaf compression always compresses the full subtree. In) 108 316 P0.89 (the experiments that follow) 108 298 P0.89 (, each instance of compression randomly selects between the) 241.46 298 P(depth compression and leaf compression methods with equal probability) 108 280 T(.) 454.99 280 T0.44 (Like the components of Hora\325) 126 250 P0.44 (s watches, the modules formed by compression are sta-) 271.66 250 P0.83 (ble and protected from dissessembly by other operators. Because the modules are repre-) 108 232 P-0.19 (sented by single symbols, no crossover operation can af) 108 214 P-0.19 (fect its de\336nition. The modules are) 373.73 214 P1.51 (structurally preserved until an expansion operation replaces the symbol in the program) 108 196 P0.59 (with its de\336nition. Schaf) 108 178 P0.59 (fer and Morishima \0501987\051 discribe a dif) 227.49 178 P0.59 (ferent method for evolv-) 420.66 178 P1.29 (ing appropriate crossover points in a \336xed-length representation but with very dif) 108 160 P1.29 (ferent) 512.03 160 P(properties.) 108 142 T107.5 450 540.5 702 C127.79 474.19 509.68 516.25 R7 X0 KV3 12 Q0 X1.73 (Figure 26:) 127.79 508.25 P2 F1.73 (Leaf compr) 187.23 508.25 P1.73 (ession applied to a selected subtr) 243.49 508.25 P1.73 (ee.ote that identical) 411.28 508.25 P1.83 (leaves ar) 127.79 496.25 P1.83 (e r) 172.81 496.25 P1.83 (epr) 187.19 496.25 P1.83 (esented by the same parameter name in the de\336ned function.) 202.73 496.25 P(Expansion is the r) 127.79 484.25 T(everse of this pr) 214.3 484.25 T(ocess.) 290.81 484.25 T4 F(or) 192.99 672.19 T(d0) 193 579.86 T(d0) 158.53 547.66 T198.74 670.39 175.76 651.92 2 L0.5 H0 ZN198.74 670.39 221.72 651.92 2 LN(not) 164.27 638.73 T198.74 608.83 198.74 590.37 2 LN(or) 217.9 639.99 T221.72 639.61 198.74 621.14 2 LN221.72 639.61 244.7 621.14 2 LN(d2) 238.96 604.48 T(not) 192.99 609.22 T165.48 635.49 145.48 617.82 2 LN(and) 135.54 609.22 T141.29 608.83 118.3 590.37 2 LN141.29 608.83 164.27 590.37 2 LN(d1) 112.56 579.86 T5 F(newfunc) 377.87 568.15 T4 F( \050) 426.51 568.15 T7 F(p1 p2 p3) 433.84 568.15 T4 F(\051) 480.52 568.15 T6 F(\256) 487.51 568.15 T4 F(\050or \050not \050and) 401.67 555.41 T7 F( p1 \050) 467.66 555.41 T4 F(not) 491.66 555.41 T7 F( p2) 508.33 555.41 T4 F(\051\051\051) 525 555.41 T(\050or \050not) 418.54 542.7 T7 F(p) 460.53 542.7 T4 F(2\051) 467.2 542.7 T7 F(p3) 481.19 542.7 T4 F(\051\051) 494.53 542.7 T(not) 158.52 578.44 T164.27 576.64 164.27 558.17 2 LN352.38 623.4 363.91 620.09 352.38 616.79 352.38 620.09 4 YV283.32 620.09 352.38 620.09 2 L1 H2 ZN7 F(compression) 283.62 606.75 T(leaf) 306.82 626.69 T5 F(newfunc) 426.58 655.31 T439.34 650.53 412.53 622.09 2 L0.5 HN4 F(d1) 403.59 612.55 T448.28 650.53 448.28 622.09 2 LN(d0) 439.01 606.75 T(d2) 475.09 612.55 T457.22 650.53 484.04 622.09 2 LN195.26 691.66 115.9 613.43 155.58 564.53 175.42 564.53 185.34 593.87 215.1 603.65 254.79 642.76 7 YN0 0 612 792 CFMENDPAGE%%EndPage: "109" 7%%Page: "110" 7612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(1) 522.45 712 T(10) 528.01 712 T108 90 540 702 R7 XV1 F0 X(6.2.2 Expansion of Compr) 108 694 T(essed Modules) 244.39 694 T0 F0.54 (One drawback to the compression operator is that each compression removes genetic) 126 668 P0.07 (material from the population and thus reduces the variability of the population. After only) 108 650 P0.38 (a few generations of moderately applying the compression operator) 108 632 P0.38 (, the available genetic) 434.29 632 P0.93 (material in the population is insuf) 108 614 P0.93 (\336cient to signi\336cantly improve the performance of the) 274.01 614 P-0.15 (population. The loss of genetic diversity in a population leading to premature conver) 108 596 P-0.15 (gence) 512.03 596 P0.07 (to a suboptimal solution is a well known problem in genetic algorithms research \050De Jong) 108 578 P0.74 (1975; Goldber) 108 560 P0.74 (g 1989a; Davis 1991\051.) 178.15 560 P0.74 (T) 289.47 560 P0.74 (ypical solutions include altering the scaling of the) 295.95 560 P0.05 (\336tness values or altering the frequency of crossovers and mutations.) 108 542 P0.05 (Neither of these solu-) 436.26 542 P(tions are appropriate for GLiB.) 108 524 T
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