📄 chapter6.ps
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translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def ws 0 w getinterval is copy pop /cf currentfile def w h 8 [w 0 0 h neg 0 h] {ip} {gip} {bip} true 3 colorimage bitmapsave restore grestore } bind def/BITMAPTRUECOLOR { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def /gis w string def /bis w string def /cf currentfile def w h 8 [w 0 0 h neg 0 h] { cf is readhexstring pop } { cf gis readhexstring pop } { cf bis readhexstring pop } true 3 colorimage bitmapsave restore grestore } bind def/BITMAPTRUEGRAYc { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def ws 0 w getinterval is copy pop /cf currentfile def w h 8 [w 0 0 h neg 0 h] {ip gip bip w gray} image bitmapsave restore grestore } bind def/ww FMLOCAL/r FMLOCAL/g FMLOCAL/b FMLOCAL/i FMLOCAL/gray { /ww exch def /b exch def /g exch def /r exch def 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul b i get .114 mul add add r i 3 -1 roll floor cvi put } for r } bind def/BITMAPTRUEGRAY { gsave translate rotate scale /h exch def /w exch def /bitmapsave save def /is w string def /gis w string def /bis w string def /cf currentfile def w h 8 [w 0 0 h neg 0 h] { cf is readhexstring pop cf gis readhexstring pop cf bis readhexstring pop w gray} image bitmapsave restore grestore } bind def/BITMAPGRAY { 8 {fakecolorsetup} COMMONBITMAP } bind def/BITMAPGRAYc { 8 {fakecolorsetup} COMMONBITMAPc } bind def/ENDBITMAP { } bind defend /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 1 612 792 0 1 17 FMDOCUMENT0 0 /Times-Roman FMFONTDEFINE1 0 /Times-Bold FMFONTDEFINE2 0 /Times-Italic FMFONTDEFINE3 0 /Times-BoldItalic FMFONTDEFINE4 0 /Helvetica FMFONTDEFINE5 0 /Helvetica-Bold FMFONTDEFINE6 1 /Symbol FMFONTDEFINE7 0 /Helvetica-Oblique FMFONTDEFINE8 0 /Courier FMFONTDEFINE9 0 /Helvetica-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: "104" 1%%BeginPaperSize: Letter%%EndPaperSize612 792 0 FMBEGINPAGE108 72 540 81 R7 X0 KV0 12 Q0 X(104) 306.01 73 T108 90 540 648 R7 XV0 X(CHAPTER VI) 288.85 640 T(THE EMERGENCE OF PROBLEM DECOMPOSITIONS AND HIGH-LEVEL) 129.46 604 T(REPRESENT) 269.51 586 T(A) 335.86 586 T(TIONS) 343.18 586 T1 F(6.0 The Emergence of Pr) 108 544 T(oblem Decompositions and High-Level Repr) 237.68 544 T(esentations) 464.01 544 T0 F0.68 (In this chapter) 126 518 P0.68 (, modular programs are induced using genetic program with additional) 195.49 518 P0.62 (mutation operators designed to allow decompositions to emer) 108 500 P0.62 (ge naturally from the prob-) 407.61 500 P0.08 (lem solving process. Each created module serves as an abstract addition to the representa-) 108 482 P1.06 (tional language that re\337ects some constraints of the task environment. The evolutionary) 108 464 P0.55 (weak method described in this chapter acquires appropriate modules and abstractions for) 108 446 P-0 (the task in spite of an absence of explicit knowledge describing how to create modules for) 108 428 P(the tasks.) 108 410 T1 F(6.1 Pr) 108 374 T(oblem Decomposition) 141.43 374 T0 F0.56 (Often, a dif) 126 350 P0.56 (\336cult problem can be decomposed into several more simple subproblems,) 181.86 350 P1.18 (each of which may be more easily solved than the complete problem. In programming,) 108 332 P0.83 (humans build programs by identifying functions that solve reoccurring subproblems and) 108 314 P(thereby reduce the overall size of the code.) 108 296 T1.1 (Simon \0501969\051 ar) 126 266 P1.1 (gues that problem decomposition is an important aspect of problem) 206.61 266 P-0.1 (solving. Simon\325) 108 248 P-0.1 (s \0501969\051 parable of the two watchmakers T) 183.88 248 P-0.1 (empus and Hora relates another) 388.52 248 P0.97 (advantage for problem decomposition. In this parable, the two watchmakers build prod-) 108 230 P0.48 (ucts of similar complexity \0501000 parts\051 using dif) 108 212 P0.48 (fering design philosophies. T) 343.36 212 P0.48 (empus con-) 483.89 212 P1.64 (structs the entire watch directly from the primitive components. Consequently) 108 194 P1.64 (, if he is) 496.43 194 P0.45 (interrupted before completing a watch, say by a customer calling on the phone, the inter-) 108 176 P-0.11 (mediate state is lost and T) 108 158 P-0.11 (empus must rebuild the entire watch from the individual compo-) 231.53 158 P0.05 (nents. Hora\325) 108 140 P0.05 (s method of construction, on the other hand, uses stable intermediate modules) 166.68 140 P0.92 (which are individually created, assembled into lar) 108 122 P0.92 (ger and lar) 352.11 122 P0.92 (ger modules and eventually) 405.01 122 P0.45 (into the completed product. When Hora is interrupted, only the work for the module cur-) 108 104 PFMENDPAGE%%EndPage: "104" 2%%Page: "105" 2612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(105) 522.01 712 T108 90 540 702 R7 XV0 X0.55 (rently being constructed is lost. Simon\325) 108 694 P0.55 (s moral for computational problem solving is that) 298.64 694 P0.3 (the identi\336cation and solidi\336cation of subproblems carries with it bene\336ts of stability and) 108 676 P(speed.) 108 658 T0.83 (Fodor \0501983\051 elevates modularity to a property of the mind. Fodor hypothesizes that) 126 628 P0.46 (the mind itself is modular) 108 610 P0.46 (, that the mind can be compartmentalized such that the individ-) 232.62 610 P0.55 (ual compartments do very little intercommunication. Fodor ar) 108 592 P0.55 (gues that this compartmen-) 408.1 592 P(talization need not correspond with the apparent modularity of the brain.) 108 574 T-0.02 (Means-ends analysis \050Rich 1982; W) 126 544 P-0.02 (inston 1983\051, a standard AI weak method, embod-) 299.32 544 P-0.06 (ies a problem decomposition approach to solving problems. In means-ends analysis, prob-) 108 526 P0.5 (lem speci\336c knowledge is used to determine both how to decompose a problem and how) 108 508 P2.16 (to solve each identi\336ed sub-problem, possibly by further decomposition. The General) 108 490 P0.5 (Problem Solver \050GPS\051 \050Newell and Simon 1963\051 uses this weak method as its core com-) 108 472 P0.16 (putational mechanism. As in all weak methods, GPS uses task-speci\336c knowledge, in this) 108 454 P(case to determine the decomposition of problems and their eventual solutions.) 108 436 T0.49 (SOAR \050Newell 1990; Laird, Rosenbloom and Newell 1986a; Laird, Rosenbloom and) 126 406 P0.57 (Newell 1986b\051 is in a sense the ultimate version of GPS. It uses task-speci\336c knowledge) 108 388 P-0.11 (together with a technique called) 108 370 P2 F-0.11 (chunking) 263.65 370 P0 F-0.11 ( to determine decompositions of the task. When-) 307.62 370 P1.88 (ever no production rule is available in SOAR to ful\336ll any of the current outstanding) 108 352 P1.09 (goals, a default production rule creates appropriate subgoals. Whenever SOAR solves a) 108 334 P0.08 (subgoal, the conditions that lead to the subgoal\325) 108 316 P0.08 (s creation are \322chunked\323 together with the) 337.06 316 P0.01 (resulting state changes into a new production rule. When a similar set of conditions occur) 108 298 P0.01 (,) 537 298 P0.59 (SOAR uses the new \322chunk\323 rather than recreating the subgoal. Given a particular prob-) 108 280 P0.36 (lem space, SOAR always creates the same decompositions because of its static, task-spe-) 108 262 P(ci\336c knowledge for when to create subgoals and hence new chunks.) 108 244 T1.24 (Connectionist researchers are also investigating the bene\336ts of modularity) 126 214 P1.24 (. W) 490.19 214 P1.24 (ork by) 507.79 214 P0.25 (Jacobs, Jordan and Barto \0501990; 1991\051, Nolan and Hinton \0501991\051 and Jacob, Jordan, Hin-) 108 196 P0.3 (ton and Nolan \0501991\051 demonstrates techniques for problem decomposition in connection-) 108 178 P2.89 (ist networks. For instance, Jacob, Jordan and Barto \0501990; 1991\051 begin with a pre-) 108 160 P2.42 (determined architecture that has two parallel subnets and a mechanism for switching) 108 142 P0.26 (between them. Each of the two subnets is appropriate for one portion of their problem. In) 108 124 P0.43 (the end, the network learns to switch to the appropriate network based on which instance) 108 106 PFMENDPAGE%%EndPage: "105" 3%%Page: "106" 3612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(106) 522.01 712 T108 90 540 702 R7 XV0 X-0.16 (of the problem the input belongs. Jordan and Jacobs \0501993\051 extend this method to a hierar-) 108 694 P(chical or) 108 676 T(ganization of subnets and decision components.) 149.41 676 T-0 (In all of the above work, the decompositions of the problem are pre-determined by the) 126 646 P0.26 (programmer either completely or in part. In the case of SOAR, the discovered chunks are) 108 628 P0.36 (merely productions representing the transitive closure over the several levels of the prob-) 108 610 P-0.06 (lem space environment. A run of SOAR does not determine an appropriate decomposition) 108 592 P0.28 (but merely bene\336ts from one the programmer provides as explicit knowledge. In the con-) 108 574 P0.73 (nectionist work, the architectures determine the decomposition of the problem implicitly) 108 556 P0.91 (when the input to the network does not do so explicitly) 108 538 P0.91 (. The networks must only assign) 380.19 538 P-0 (appropriate roles to the subnets consistent to their architectural restrictions. While the net-) 108 520 P0.36 (work training method must determine the computational roles for the individual architec-) 108 502 P2.09 (tural components, this is far easier than automatically determining a suitable problem) 108 484 P(decomposition.) 108 466 T1 F(6.2 The Genetic Library Builder) 108 430 T0 F0.24 (The Genetic Library Builder \050GLiB\051 \050Angeline and Pollack 1993a; Angeline and Pol-) 126 406 P1.23 (lack 1992\051 is an extended genetic program that uses a form of emer) 108 388 P1.23 (gent intelligence to) 445.6 388 P0.95 (construct solutions with task-speci\336c decompositions without relying on explicit knowl-) 108 370 P0.36 (edge. As with the emer) 108 352 P0.36 (gence of task-speci\336c features of the last chapter) 220.13 352 P0.36 (, the only modi\336-) 455.63 352 P3.56 (cation to the evolutionary algorithm is the addition of weak representation-speci\336c) 108 334 P0.21 (operators. No explicit knowledge describing how to extract appropriate modules from the) 108 316 P(programming language representation is available.) 108 298 T2.06 (The Genetic Library Builder \050GLiB\051 is a dynamic genetic algorithm using Koza\325) 126 268 P2.06 (s) 535.33 268 P0.5 (genetic programming paradigm) 108 250 P0.5 (as the base evolutionary weak method. Individuals of the) 262.55 250 P0.25 (population in both GPP and GLiB represent programs in a task-speci\336c language that use) 108 232 P1.72 (a LISP expression tree syntax. Both also use a crossover operator that exchanges ran-) 108 214 P0.28 (domly selected subtrees between parents to create the novel genotypes. The principal dif-) 108 196 P-0.03 (ference between GPP and GLiB is the addition of two novel mutation operators that allow) 108 178 P0.8 (task decompositions to emer) 108 160 P0.8 (ge. These operators, named) 247.09 160 P2 F0.8 (compr) 384.84 160 P0.8 (ession) 415.04 160 P0 F0.8 ( and) 445.02 160 P2 F0.8 (expansion) 469.93 160 P0 F0.8 (, are) 518.56 160 P-0.13 (similar to the) 108 142 P2 F-0.13 ( fr) 171.04 142 P-0.13 (eeze) 181.47 142 P0 F-0.13 ( and) 202.11 142 P2 F-0.13 (unfr) 225.17 142 P-0.13 (eeze) 244.72 142 P0 F-0.13 ( operators of the last chapter) 265.36 142 P-0.13 (. Both are applied probabilis-) 400.28 142 P(tically to evolving individuals, as are all evolutionary operators.) 108 124 TFMENDPAGE%%EndPage: "106" 4%%Page: "107" 4612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(107) 522.01 712 T108 90 540 702 R7 XV1 F0 X(6.2.1 Compr) 108 485.88 T(ession of Modules) 174.41 485.88 T0 F1.72 (Compression begins by randomly selecting a subtree from the parent. This subtree) 126 459.88 P0.25 (becomes the body of a new function, called a) 108 441.88 P2 F0.25 (module) 330.06 441.88 P0 F0.25 (, that is added to the) 365.37 441.88 P2 F0.25 (genetic library) 466.46 441.88 P0.25 (,) 537 441.88 P0 F-0.19 (a logical storehouse for the de\336nitions of all modules in the system. This library associates) 108 423.88 P-0.29 (the chosen subtree with a unique identi\336er that becomes the module\325) 108 405.88 P-0.29 (s name. The subtree is) 434.23 405.88 P0.1 (then extracted from the parent and replaced by the newly de\336ned module\325) 108 387.88 P0.1 (s name. When a) 463.11 387.88 P0.94 (genetic program with a compressed module is evaluated, the de\336nition of the module is) 108 369.88 P0.41 (retrieved from the genetic library and executed as though the original subtree were in the) 108 351.88 P0.77 (genetic program at the point the module\325) 108 333.88 P0.77 (s name appears. Thus the compression operator) 307.86 333.88 P(performs only a syntactic modi\336cation to the genetic program rather than a semantic one.) 108 315.88 T0.66 (A compression operation begins with the selection of a random position in the geno-) 126 285.88 P-0.09 (type. This position identi\336es the root of the subtree to be compressed. When the module is) 108 267.88 P0.79 (de\336ned, the subtree is extracted from the genotype and replaced with a unique symbolic) 108 249.88 P0.61 (name as shown in Figure 24. GLiB binds the extracted subtree to the module\325) 108 231.88 P0.61 (s symbolic) 487.74 231.88 P-0.2 (name by entering the pair into the \322genetic library) 108 213.88 P-0.2 (.\323 This library is the collection of all cre-) 345.43 213.88 P0.33 (ated modules and serves only as a symbol reference table. During a genotype\325) 108 195.88 P0.33 (s execution) 485.37 195.88 P0.28 (GLiB retrieves the de\336nitions of compressed modules from the genetic library) 108 177.88 P0.28 (. This form) 485.8 177.88 P0.42 (of compression is identical to Koza\325) 108 159.88 P0.42 (s) 282.99 159.88 P2 F0.42 (encapsulation) 291.08 159.88 P0 F0.42 ( operator \050Koza 1992\051 although Koza) 358.37 159.88 P(takes this operator no further) 108 141.88 T(.) 245.9 141.88 T108 90 540 702 C132.77 493.88 515.23 702 C144.12 516.94 501.77 549 R7 X0 KV3 12 Q0 X1.59 (Figure 24:) 144.12 541 P2 F1.59 (Cr) 203.26 541 P1.59 (eation of a compr) 215.49 541 P1.59 (essed module fr) 304.75 541 P1.59 (om a randomly selected) 382.76 541 P(subtr) 144.12 529 T(ee of a genotype. Newfunc\325) 168.33 529 T(s de\336nition is added to the library) 297.02 529 T(.) 458.95 529 T
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