📄 chapter2.ps
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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 13 FMDOCUMENT0 0 /Times-Roman FMFONTDEFINE1 0 /Times-Bold FMFONTDEFINE2 0 /Times-Italic FMFONTDEFINE3 1 /Symbol FMFONTDEFINE4 0 /Times-BoldItalic FMFONTDEFINE5 0 /Courier FMFONTDEFINE6 0 /Courier-Oblique 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: "15" 1%%BeginPaperSize: Letter%%EndPaperSize612 792 0 FMBEGINPAGE108 72 540 81 R7 X0 KV0 12 Q0 X(15) 312.01 73 T108 90 540 648 R7 XV0 X(CHAPTER II) 291.19 640 T(BACKGROUND) 281.69 604 T1 F(2.0 Backgr) 108 562 T(ound) 166.08 562 T0 F-0.09 (This chapter describes background relating to weak methods, strong methods and evo-) 126 536 P0.24 (lutionary algorithms. It is ar) 108 518 P0.24 (gued that evolutionary algorithms consist a new type of weak) 243.01 518 P0.36 (method, called the evolutionary weak method, that adapts its task-independent method of) 108 500 P-0.16 (search based on information garnered in previous portions of the problem space. First, this) 108 482 P(chapter begins with a general discussion of search and intelligence.) 108 464 T1 F(2.1 Sear) 108 428 T(ch and Intelligence) 152.09 428 T0 F1.23 (Search has always been an integral part of machine intelligence from the \336rst com-) 126 404 P-0.21 (puter chess programs to the current sur) 108 386 P-0.21 (ge in learning methods. In general, search is used in) 293.06 386 P0.44 (two distinct ways. In a standard search, an object with speci\336c properties is to be located) 108 368 P0.86 (from a known set of objects. For problem solving search, an initial object, a goal object) 108 350 P0.22 (and a set of operators is provided with the objective being the identi\336cation of an ordered) 108 332 P1.92 (list of operators that transform the initial object into the goal object. Problem solving) 108 314 P0.04 (search can be equated as a standard search merely by realizing that the set of objects to be) 108 296 P(searched is all possible orderings of the operators.) 108 278 T-0.28 (Let the set of possible search objects be denoted by) 126 248 P2 F-0.28 (S) 372.31 248 P0 F-0.28 (.) 378.31 248 P2 F-0.28 (S) 384.02 248 P0 F-0.28 (, in and of itself, is unor) 390.02 248 P-0.28 (ganized) 502.7 248 P0.31 (and can contain any form of object from numbers or mathematical equations to computer) 108 230 P0.67 (programs. T) 108 212 P0.67 (o or) 166.45 212 P0.67 (ganize) 185.89 212 P2 F0.67 (S) 220.86 212 P0 F0.67 (, a set of operators,) 226.85 212 P2 F0.67 (O) 324.45 212 P0 F0.67 (, can be de\336ned so that) 333.11 212 P2 F0.67 (o) 450.03 212 P2 10 Q0.56 (i) 456.03 209 P3 12 Q0.67 (\316) 461.86 212 P2 F0.67 (O, o) 474.08 212 P2 10 Q0.56 (i) 495.4 209 P2 12 Q0.67 (: S) 498.18 212 P3 F0.67 (\256) 515.5 212 P2 F0.67 ( S) 527.34 212 P0 F0.67 (.) 537 212 P0.23 (These operators set up an ordering over the set of objects, usually called the) 108 194 P2 F0.23 (sear) 477.93 194 P0.23 (ch space) 498.14 194 P0 F2.21 (or) 108 176 P2 F2.21 (pr) 123.2 176 P2.21 (oblem space) 133.42 176 P0 F2.21 (. Selecting a set of bene\336cial operators is typically done with some) 195.24 176 P(understanding of the task and intended representation of the objects.) 108 158 T0.1 (Often, the search space is described as a Cartesian space, with each point representing) 126 128 P-0.1 (a single member of the set of objects and each operator of) 108 110 P2 F-0.1 (O) 387.18 110 P0 F-0.1 ( denoting a dimension orthog-) 395.84 110 PFMENDPAGE%%EndPage: "15" 2%%Page: "16" 2612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(16) 528.01 712 T108 90 540 702 R7 XV0 X0.58 (onal to the rest. Thus if |) 108 694 P2 F0.58 (O) 228.12 694 P0 F0.58 (| =) 236.78 694 P2 F0.58 (n) 253.1 694 P0 F0.58 (, the search space is an) 259.1 694 P2 F0.58 (n) 374.8 694 P0 F0.58 (-dimensional space. At times the) 380.79 694 P0.67 (connectivity of the search space is described as a graph or tree with operators serving as) 108 676 P0.92 (edges between nodes which represent the various objects. In either case, the) 108 658 P2 F0.92 (distance) 486.11 658 P0 F0.92 ( or) 526.09 658 P2 F1.25 (depth) 108 640 P0 F1.25 ( between objects is the number of operator applications required to transform one) 134.65 640 P0.17 (search space object into the other) 108 622 P0.17 (. In the event that more than one path through the search) 267.71 622 P(space connect two objects, their distance is the minimum path distance.) 108 604 T0.3 (Next, an) 126 574 P2 F0.3 ( evaluation function) 166.93 574 P0 F0.3 (,) 263.47 574 P2 F0.3 (f) 269.76 574 P0 F0.3 (: S) 273.1 574 P3 F0.3 (\256) 289.69 574 P2 F0.3 (I) 304.82 574 P4 F0.3 (R) 306.81 574 P0 F0.3 (, de\336nes the \322correctness\323 of each point in the) 316.81 574 P0.2 (search space. A threshold of this value identi\336es those points in the space that are consid-) 108 556 P0.16 (ered solutions. This function may be any computable function including a simple boolean) 108 538 P1 (function that returns something equivalent to TRUE when a desired object is evaluated.) 108 520 P1.18 (The evaluation function and the) 108 502 P2 F1.18 (n) 269.48 502 P0 F1.18 (-dimensional search space combine to de\336ne an) 275.47 502 P2 F1.18 (n+) 515.92 502 P0 F1.18 (1-) 530.01 502 P0.92 (dimensional space, often called a) 108 484 P2 F0.92 (landscape) 274.46 484 P0 F0.92 (, where the value returned by the evaluation) 323.09 484 P0.55 (function serves to de\336ne the height of each point in the search space. Often, descriptions) 108 466 P0.8 (of the operation of search methods are in terms of how they traverse the connectivity of) 108 448 P(the search space or the \322terrain\323 of the landscape.) 108 430 T1 F(2.2 Optimization and Satis\336cing) 108 394 T0 F0.77 (When a search is performed to locate global extrema of the evaluation function over) 126 370 P-0.07 (the search space with an extremely lar) 108 352 P-0.07 (ge number of solutions, such as the space of all pos-) 290.54 352 P0.77 (sible tours through a collection of cites in the T) 108 334 P0.77 (raveling Salesperson Problem \050TSP\051, the) 341.38 334 P0.06 (search is typically called an) 108 316 P2 F0.06 (optimization) 243.87 316 P0 F0.06 (. Finding the extrema of such lar) 303.84 316 P0.06 (ge space is often) 460.22 316 P0.09 (an NP-Hard problem \050Gurari 1989\051, requiring at least an exponentially increasing number) 108 298 P0.08 (of search space points to be investigated as the problem is scaled up. When the number of) 108 280 P0.09 (objects that must be investigated in order to \336nd the optimal element increases by a facto-) 108 262 P(rial, the situation is called) 108 244 T2 F( combinatorial explosion) 231.59 244 T0 F(.) 351.53 244 T-0 (Arti\336cial intelligence researchers combat combinatorial explosion in two ways. Often,) 126 214 P1.19 (a tractable subproblem can be de\336ned and solved more ef) 108 196 P1.19 (\336ciently that the original NP-) 394.64 196 P-0.24 (Hard problem. Another way to avoid combinatorial explosion is to settle for less than opti-) 108 178 P1.29 (mal solutions. In many cases,) 108 160 P2 F1.29 (near) 258.71 160 P0 F1.29 (optimal solutions, solutions within some reasonable) 284.99 160 P1.37 (percentage of optimal, can be found consistently and quickly) 108 142 P1.37 (. Simon \0501969\051 called this) 410.27 142 P1.02 (approach) 108 124 P2 F1.02 (satis\336cing) 155.98 124 P0 F1.02 ( to indicate that the solution satis\336es minimal requirements and suf-) 204.62 124 P(\336ces to solve the problem in the environment.) 108 106 TFMENDPAGE%%EndPage: "16" 3%%Page: "17" 3612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(17) 528.01 712 T108 90 540 702 R7 XV1 F0 X(2.3 The Cr) 108 694 T(edit Assignment Pr) 165.75 694 T(oblem) 263.47 694 T0 F1.74 (The problem solving ability of an algorithm is chie\337y determined by how \322intelli-) 126 670 P0.38 (gently\323 the algorithm traverses the possible solutions in the problem space. One possibil-) 108 652 P0.5 (ity is to perform) 108 634 P2 F0.5 (cr) 190.64 634 P0.5 (edit assignment) 200.18 634 P0 F0.5 ( \050Minsky 1963\051 on the representational components of) 275.65 634 P0.85 (each solution encountered and bias future solutions towards or) 108 616 P0.85 (ganizations of representa-) 414.4 616 P0.12 (tional pieces that perform well together) 108 598 P0.12 (. Credit assignment typically refers to the rating of) 296.83 598 P0.43 (a structure\325) 108 580 P0.43 (s components as being bene\336cial or harmful to solving the problem. The term) 162.05 580 P-0.05 (is most associated with machine learning programs, however) 108 562 P-0.05 (, a search algorithm also uses) 399.66 562 P0.02 (an implicit form of credit assignment when selecting which element in the search space to) 108 544 P1.28 (visit next. Poor search algorithms, such as random search, use inaccurate credit assign-) 108 526 P0.39 (ment, if any) 108 508 P0.39 (, to guide them through the search space. A more \322intelligent\323 search mecha-) 165.63 508 P1.75 (nism embodies an accurate credit assignment mechanism for the task and manipulates) 108 490 P(only problematic representational components to traverse the space.) 108 472 T-0.26 (Exactly how to assign credit to components of a particular representation is often a dif-) 126 442 P2.47 (\336cult problem. Occasionally) 108 424 P2.47 (, if enough assumptions are made, analytical solutions to) 248.41 424 P-0.19 (credit assignment for a particular problem type and representation can be de\336ned, as in the) 108 406 P(case of neural networks and back-propagation \050Rumelhart, Hinton and W) 108 388 T(illiams 1986\051.) 459.91 388 T1 F(2.4 W) 108 352 T(eak and Str) 140.32 352 T(ong Methods) 199.41 352 T0 F-0.12 (At a very high level, AI problem solving methods can be split into two distinct catego-) 126 328 P0.58 (ries:) 108 310 P2 F0.58 (weak) 132.23 310 P0 F0.58 (and) 160.46 310 P2 F0.58 ( str) 177.77 310 P0.58 (ong) 193.57 310 P0 F0.58 (. A strong method is one that contains a signi\336cant amount of task-) 211.57 310 P1.24 (speci\336c knowledge in order to solve it. In contrast, a weak method requires little or no) 108 292 P1.23 (knowledge about a task. As the name implies, strong methods are more powerful algo-) 108 274 P-0.27 (rithms than weak methods. Strong and weak methods dif) 108 256 P-0.27 (fer in their approach to task appli-) 378.43 256 P(cability and task ef) 108 238 T(fectiveness, as shown in Figure 1.) 198.72 238 T0.53 (Strong methods can take the form of an analytic solution or an expert system using a) 126 208 P0.46 (lar) 108 190 P0.46 (ge knowledge base. Because their content is directed toward solving a particular prob-) 120.44 190 P0.25 (lem, they tend to be narrowly applicable, as shown in the \336gure. However) 108 172 P0.25 (, their task-spe-) 465.23 172 P1.93 (ci\336c knowledge often allows these techniques to \336nd accurate solutions with minimal) 108 154 P0.18 (computational ef) 108 136 P0.18 (fort. Analytic methods and rulebases supply the same sort of strength for) 188.91 136 P0.86 (solving a particular task since they contain the same information at the knowledge-level) 108 118 P0.31 (\050Newell 1982\051. However) 108 100 P0.31 (, general analytic methods and lar) 227.7 100 P0.31 (ge rulebases are not easily cre-) 390.92 100 PFMENDPAGE%%EndPage: "17" 4%%Page: "18" 4612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(18) 528.01 712 T108 90 540 702 R7 XV0 X0 (ated with current techniques. Knowledge-based AI techniques requires the programmer to) 108 472.94 P0.27 (extract the task-speci\336c knowledge out of a domain or an expert so it can be inserted into) 108 454.94 P
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