📄 chapter3.ps
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18 .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: "41" 1%%BeginPaperSize: Letter%%EndPaperSize612 792 0 FMBEGINPAGE108 72 540 81 R7 X0 KV0 12 Q0 X(41) 312.01 73 T108 90 540 648 R7 XV0 X(CHAPTER III) 289.19 640 T(THE EVOLUTIONAR) 124.15 604 T(Y WEAK METHOD AND EMERGENT INTELLIGENCE) 235.74 604 T1 F(3.0 The Evolutionary W) 108 562 T(eak Method and Emergent Intelligence) 233.62 562 T0 F0.89 (The commonalities of evolutionary algorithms combined with their lack of task-spe-) 126 536 P0.97 (ci\336c knowledge indicates their status as a weak method which this dissertation calls the) 108 518 P2 F0.17 (evolutionary weak method) 108 500 P0 F0.17 (. The major dif) 234.92 500 P0.17 (ference between standard weak methods and the) 307.17 500 P-0.09 (evolutionary weak is the adaptive behavior of evolutionary algorithms. Over time, an evo-) 108 482 P1.33 (lutionary weak method garners information about the search environment and uses this) 108 464 P1.6 (information to constrain future search. Thus evolutionary weak methods begin without) 108 446 P1.66 (any informedness and become increasingly informed during the search. This is unique) 108 428 P(among the collection of weak methods discussed in the previous chapters.) 108 410 T0.54 (In this chapter) 126 380 P0.54 (, I show that the evolutionary weak method\325) 195.21 380 P0.54 (s technique of reproducing) 410.16 380 P2.56 (with probabilistic variations de\336nes a weak, i.e. task-independent, approach to credit) 108 362 P0.02 (assignment that has an empirical nature. This form of credit assignment allows the natural) 108 344 P-0.24 (constraints of the task environment to emer) 108 326 P-0.24 (ge as structures in the population without intro-) 314.18 326 P0.99 (ducing explicit knowledge into the evolutionary weak method. Based on this method of) 108 308 P1.6 (credit assignment,) 108 290 P2 F1.6 (emer) 201.48 290 P1.6 (gent intelligence) 225.01 290 P0 F1.6 (, a new computational approach to intelligence) 306.22 290 P0.23 (and problem solving, is de\336ned. The goal of emer) 108 272 P0.23 (gent intelligence is to reduce or remove) 348.78 272 P-0.22 (AI\325) 108 254 P-0.22 (s reliance on explicit knowledge in a problem solver by favoring instead the) 123.99 254 P2 F-0.22 (emer) 488.5 254 P-0.22 (gence) 512.03 254 P0 F(of problem speci\336c constraints through direct interaction with the task environment.) 108 236 T1 F(3.1 Empirical Cr) 108 200 T(edit Assignment) 197.06 200 T0 F-0.18 (Evolutionary weak methods are distinct from standard weak methods because they use) 126 176 P0.9 (past search points to increase their level of informedness during the search. The mecha-) 108 158 P0.36 (nism that gathers this information during the search, which I call) 108 140 P2 F0.36 (empirical cr) 425.12 140 P0.36 (edit assign-) 484 140 P0.44 (ment) 108 122 P0 F0.44 (, works at a coarse grained, task-independent level. It relies on the empirical aspects) 131.32 122 P-0.21 (of evolutionary weak methods and the \336nite resource of the population for its implementa-) 108 104 PFMENDPAGE%%EndPage: "41" 2%%Page: "42" 2612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(42) 528.01 712 T108 90 540 702 R7 XV0 X0.46 (tion. Because it is task-independent, empirical credit assignment is a weak form of credit) 108 694 P1.66 (assignment. The features of empirical credit assignment that distinguish it from strong) 108 676 P-0 (forms of credit assignment are its representation speci\336c operators, its ability to propagate) 108 658 P(abstract features and the inherent strength of the empirical process at its core.) 108 640 T1 F(3.1.1 Repr) 108 604 T(esentation Speci\336c Operators) 163.74 604 T0 F0.93 (As discussed in the last chapter) 126 578 P0.93 (, standard weak methods are augmented by task-spe-) 280.38 578 P0.78 (ci\336c knowledge in order to direct their problem solving ability) 108 560 P0.78 (. T) 413.71 560 P0.78 (ask-speci\336c knowledge) 426.97 560 P0.87 (typically requires an understanding of the task environment to justify its presence in the) 108 542 P0.36 (problem solving algorithm. In other words, task-speci\336c knowledge encodes some aspect) 108 524 P0.48 (of the task environment that is generally invalid outside the task environment. This often) 108 506 P0.8 (includes the de\336nition of task-speci\336c operators that transform a given solution into one) 108 488 P(better able to solve the problem.) 108 470 T0.15 (In an evolutionary weak method, the reproduction operators are de\336ned to manipulate) 126 440 P3.36 (a speci\336c representation independent of its interpretation by a \336tness function. For) 108 422 P3.06 (instance, genetic algorithms de\336ne crossover and point mutation speci\336cally for the) 108 404 P0.44 (manipulation of bit strings. The operators in evolution strategies are similarly de\336ned for) 108 386 P-0.28 (the real valued features that are typical in those weak methods. Evolutionary programming) 108 368 P0.37 (also uses representation speci\336c operators to manipulate whatever representation is being) 108 350 P0.39 (used. The distinctions between these methods lie in the amount of representation-speci\336c) 108 332 P0.33 (knowledge they place into their respective reproduction operators. GAs are in a sense the) 108 314 P-0.25 (weakest in representation-speci\336c knowledge since the \336xed-length bit string is often rein-) 108 296 P1.23 (terpreted as a new structure before being evaluated.) 108 278 P0 10 Q1.02 (1) 363.71 282.8 P0 12 Q1.23 ( Manipulations of the bit string by) 368.71 278 P0.12 (crossover and point mutation can violate the representational constraints of the interpreta-) 108 260 P0.79 (tion. In genetic and evolutionary programming, more knowledge of the representation is) 108 242 P-0.04 (provided to the operators to discourage unwarented manipulation. Genetic programming\325) 108 224 P-0.04 (s) 535.33 224 P-0.28 (crossover parses the program and manipulates the representation at the subtree level. Like-) 108 206 P-0.15 (wise, evolutionary programs also mainpulate at a high representational level. For instance,) 108 188 P3.52 (Angeline, Saunders and Pollack \0501994\051 provide separate reproduction heuristics for) 108 170 P1.5 (manipulating the structural and parametric features of recurrent neural networks. Thus,) 108 152 P0.05 (GAs are representationally weaker than GP and EP and, as with standard weak and strong) 108 134 P108 104 540 124.09 C108 111.99 239.98 111.99 2 L0.25 H2 Z0 X0 KN0 0 612 792 C0 10 Q0 X0 K(1. See Chapter 4 of this dissertation for an example and discussion of this point.) 108 97.33 TFMENDPAGE%%EndPage: "42" 3%%Page: "43" 3612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(43) 528.01 712 T108 90 540 702 R7 XV0 X2.02 (methods, perform less ef) 108 694 P2.02 (\336cient searches and require longer search times for the same) 232.42 694 P-0.28 (tasks. Such a perspective suggests that Holland\325) 108 676 P-0.28 (s \0501975\051 conclusion that binary representa-) 335.87 676 P-0.09 (tions should be preferred in genetic algorithms since they allow maximal implicit parallel-) 108 658 P2.09 (ism is erroneous and that genetic algorithms using multi-valued string representations) 108 640 P(should perform quicker but at the expense of generality \050cf. Antonisse 1989\051.) 108 622 T2.03 (Some GA researchers have investigated the augmentation of a genetic algorithm\325) 126 592 P2.03 (s) 535.33 592 P-0.04 (operators by task-speci\336c knowledge \050Grefensttete 1987; Michalewicz 1993\051. Given GA) 108 574 P-0.04 (\325) 532 574 P-0.04 (s) 535.33 574 P1 (status as an evolutionary weak method, the associated increases in performance demon-) 108 556 P0.74 (strated in these studies is not surprising. Designing operators with a priori knowledge of) 108 538 P1.21 (the task is the basic philosophy of weak method and the subsequent increase in perfor-) 108 520 P1.68 (mance should be expected. However) 108 502 P1.68 (, while a short term bene\336t often results from the) 290.41 502 P-0.07 (injection of knowledge into an evolutionary algorithm\325) 108 484 P-0.07 (s operators, this practice eventually) 370.74 484 P0.91 (leads to the same dif) 108 466 P0.91 (\336culties experienced by standard AI strong methods. From the per-) 210.03 466 P0.86 (spective of this dissertation, the addition of representation-speci\336c knowledge should be) 108 448 P(similarly bene\336cial without overly narrowing the generality of the technique.) 108 430 T1 F(3.1.2 Abstract Featur) 108 394 T(e Pr) 220.03 394 T(opagation) 240.79 394 T0 F0.56 (Empirical credit assignment assigns credit at a coarse level to the abstract features of) 126 368 P1.3 (population members. These points were \336rst made about genetic algorithms in Holland) 108 350 P0.34 (\0501975\051. However) 108 332 P0.34 (, the form of the theory in Holland \0501975\051 is too speci\336c to the bit string) 189.79 332 P-0.18 (representations he assumed. In this subsection I generalize Holland\325) 108 314 P-0.18 (s schema so it is appli-) 431.97 314 P(cable to all evolutionary weak methods. First a review of schema is presented.) 108 296 T1 F(3.1.2.1 Schema Theory) 108 260 T0 F1.56 (Holland \0501975\051 hypothesizes that genetic algorithms preserve and recombine at the) 126 234 P1 (representational level of schema. A) 108 216 P2 F1 (schema) 285.52 216 P0 F1 ( designates a set of bit string patterns across) 321.49 216 P1.79 (the assumed \336xed-width binary string representation of the population. Designation of) 108 198 P0.25 (schemata take the form \0501, 0, #\051) 108 180 P2 8 Q0.17 (n) 262.04 184 P0 12 Q0.25 ( where) 266.04 180 P2 F0.25 (n) 301.83 180 P0 F0.25 ( is the length of the binary string representation.) 307.83 180 P0.24 (A \3221\323 or a \3220\323 at position) 108 162 P2 F0.24 (i) 235.28 162 P0 F0.24 ( in a schema signi\336es that each string in the set represented by) 238.61 162 P0.55 (the schema contains that value at that position. A \322#\323 at position) 108 144 P2 F0.55 (i) 426.08 144 P0 F0.55 ( designates strings that) 429.41 144 P0.41 (contain either a \3221\323 or a \3220\323 at position) 108 126 P2 F0.41 (i) 302.51 126 P0 F0.41 ( are in the set. Notice that the possible schemata) 305.84 126 P1.23 (for a given length) 108 108 P2 F1.23 (n) 200.86 108 P0 F1.23 ( do not cover all possible subsets of binary strings of length) 206.86 108 P2 F1.23 (n) 510.12 108 P0 F1.23 (. For) 516.11 108 PFMENDPAGE%%EndPage: "43" 4%%Page: "44" 4612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(44) 528.01 712 T108 90 540 700.88 R7 XV0 X0.32 (instance, there is no schema of length four that represents the set {0101, 1010}. The con-) 108 692.88 P0.17 (cept of a schema encodes an assumption of sets of features. This is natural given the typi-) 108 674.88 P(cal binary feature vector interpretation usually used in genetic algorithms.) 108 656.88 T0.61 (Holland \0501975\051 ar) 126 626.88 P0.61 (gues that a genetic algorithm assigns credit not to the strings in the) 212.93 626.88 P1.69 (population but to schemata of the population, i.e. to sets of features. He observes that) 108 608.88 P1.18 (assuming schema are assigned credit, feedback to a single population member provides) 108 590.88 P(information about the various schemata it is a member in:) 108 572.88 T-0.32 (Given) 162 542.88 P2 F-0.32 (l) 193.99 542.88 P0 F-0.32 ( [features], a single structure) 197.32 542.88 P2 F-0.32 (A) 335.58 542.88 P0 F-0.32 ( ... is an instance of 2) 342.9 542.88 P2 10 Q-0.27 (l) 442.55 547.67 P0 12 Q-0.32 ( distinct) 445.33 542.88 P(schemata, as can be easily af) 162 524.88 T(\336rmed by noting that) 299.66 524.88 T2 F(A) 403.61 524.88 T0 F( is an instance) 410.93 524.88 T-0.22 (of any schema) 162 506.88 P3 F-0.22 (x) 233.62 506.88 P0 F-0.22 ( de\336ned by substituting [#\325) 239.54 506.88 P-0.22 (s] for one or more of the) 367.28 506.88 P2 F(l) 162 488.88 T0 F( attribute values in [the structure\325) 165.33 488.88 T(s] representation. \050p. 69\051) 324.22 488.88 T0.36 (In ef) 108 458.88 P0.36 (fect, Holland \0501975\051 ar) 130.45 458.88 P0.36 (gues that while only a single population member is rated by a) 241.23 458.88 P1.42 (\336tness function, information is garnered about all 2) 108 440.88 P2 10 Q1.18 (l) 363.75 445.67 P0 12 Q1.42 ( schemata of which that string is a) 366.53 440.88 P1.68 (member) 108 422.88 P1.68 (. Holland \0501975\051 calls this property) 146.64 422.88 P2 F1.68 (intrinsic parallelism) 328.28 422.88 P0 F1.68 ( and ar) 427.58 422.88 P1.68 (gues that credit) 463.36 422.88 P-0.12 (assignment \050which he called \322apportionment of credit\323\051 was performed on schema present) 108 404.88 P(in the population.) 108 386.88 T2.07 (Holland\325) 126 356.88 P2.07 (s \0501975\051) 167.98 356.88 P2 F2.07 (schema theor) 214.76 356.88 P2.07 (em) 280.67 356.88 P0 F2.07 ( provides the following lower bound for schema) 294.66 356.88 P(growth in a standard genetic algorithm:) 108 338.88 T0 10 Q(\050EQ 2\051) 512.53 297.86 T0 12 Q0.62 (where) 108 251.86 P2 F0.62 (m\050H, t\051) 140.92 251.86 P0 F0.62 ( is the number of population members with schema) 176.18 251.86 P2 F0.62 (H) 430.65 251.86 P0 F0.62 ( at time) 439.31 251.86 P2 F0.62 (t) 480.16 251.86 P0 F0.62 (,) 483.49 251.86 P2 F0.62 (f\050H\051) 490.12 251.86 P0 F0.62 ( is the) 510.1 251.86 P0.77 (average \336tness of the population members with schema) 108 233.86 P2 F0.77 ( H) 379.57 233.86 P0 F0.77 (,) 392.01 233.86 P402.11 243.21 398.78 243.21 2 LV0.58 H0 ZN2 F0.77 (f) 398.78 233.86 P0 F0.77 ( is the average \336tness of the) 402.11 233.86 P0.6 (population and) 108 215.86 P3 F0.6 (e) 183.82 215.86 P2 F0.6 (\050H,t\051) 189.08 215.86 P0 F0.6 ( is the probability that schema) 212.06 215.86 P2 F0.6 (H) 362.88 215.86 P0 F0.6 ( is disrupted by an operator) 371.54 215.86 P0.6 (. Equa-) 504.77 215.86 P(tion 2 can be rewritten in the following form:) 108 197.86 T0 10 Q(\050EQ 3\051) 512.53 156.84 T213.71 283.86 406.82 316.88 C2 12 Q0 X0 K(m) 214.71 297.86 T(H) 227.36 297.86 T(t) 242.02 297.86 T0 F(1) 257.93 297.86 T3 F(+) 248.35 297.86 T(,) 236.02 297.86 T(\050) 223.37 297.86 T(\051) 263.93 297.86 T2 F(m) 280.51 297.86 T(H) 293.16 297.86 T(t) 307.82 297.86 T3 F(,) 301.82 297.86 T(\050) 289.17 297.86 T(\051) 311.15 297.86 T2 F(f) 320.61 306.45 T(H) 327.93 306.45 T3 F(\050) 323.94 306.45 T(\051) 336.59 306.45 T2 F(f) 328.93 288.25 T0 F(1) 349.39 297.86 T3 F(e) 367.97 297.86 T2 F(H) 377.23 297.86 T(t) 391.89 297.86 T3 F(,) 385.89 297.86 T(\050) 373.24 297.86 T(\051) 395.22 297.86 T(-) 358.39 297.86 T([) 344.29 297.86 T(]) 399.83 297.86 T(\263) 270.93 297.86 T329.93 298.45 332.26 298.45 2 L0.33 H0 ZN320.61 300.45 340.34 300.45 2 LN0 0 612 792 C202.06 119.94 418.46 175.86 C2 12 Q0 X0 K(m) 206.41 156.84 T(H) 219.07 156.84 T(t) 233.72 156.84 T0 F(1) 249.64 156.84 T3 F(+) 240.06 156.84 T(,) 227.73 156.84 T(\050) 215.07 156.84 T(\051) 255.64 156.84 T2 F(m) 272.22 156.84 T(H) 284.87 156.84 T(t) 299.53 156.84 T3 F(,) 293.53 156.84 T(\050) 280.88 156.84 T(\051) 302.86 156.84 T2 F(f) 319.86 165.43 T(H) 327.18 165.43 T3 F(\050) 323.19 165.43 T(\051) 335.84 165.43 T2 F(f) 333.47 145.11 T(i) 340.8 145.11 T3 F(\050) 336.81 145.11 T(\051) 344.14 145.11 T2 9 Q(i) 311.56 132.81 T(P) 324.97 132.81 T2 6 Q(t) 330.81 130.36 T3 9 Q(\316) 316.31 132.81 T3 18 Q(\345) 315.6 141.91 T0 12 Q(1) 357.69 156.84 T3 F
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