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(simply allowing a lar) 108 208 T(ger amount of space for storing information about the search.) 209.39 208 T2.1 (Recall from Equation 5, the expected number of population members at time) 126 178 P2 F2.1 (t+1) 522.57 178 P0 F(which contain feature) 108 160 T3 F(m) 214.91 160 T0 F( is given by:) 221.82 160 T0 10 Q(\050EQ 6\051) 512.53 120.97 T204.27 101.21 416.25 138 C2 12 Q0 X0 K(m) 205.27 120.97 T3 F(m) 219.35 120.97 T2 F(t) 230.68 120.97 T0 F(1) 243.81 120.97 T3 F(+) 234.87 120.97 T0 F(\050) 214.64 121.97 T(,) 225.54 121.97 T(\051) 250.45 121.97 T2 F(n) 273.03 120.97 T0 F(1) 286.83 120.97 T3 F(e) 304.7 120.97 T(-) 295.83 120.97 T(m) 314.67 120.97 T2 F(t) 327.58 120.97 T3 F(,) 321.58 120.97 T(\050) 310.68 120.97 T(\051) 330.92 120.97 T([) 281.73 120.97 T(]) 335.52 120.97 T(s) 357.2 120.97 T2 F(i) 372.23 120.97 T(t) 381.57 120.97 T3 F(,) 375.57 120.97 T(\050) 367.13 120.97 T(\051) 385.51 120.97 T2 9 Q(i) 340.34 108.67 T3 F(L) 350 108.67 T(m) 359.16 108.67 T2 F(t) 368.83 108.67 T3 F(,) 364.33 108.67 T(\050) 356.16 108.67 T(\051) 371.33 108.67 T(\316) 343.84 108.67 T3 18 Q(\345) 342.79 117.77 T3 12 Q(=) 260.45 120.97 T0 0 612 792 CFMENDPAGE%%EndPage: "48" 9%%Page: "49" 9612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(49) 528.01 712 T108 90 540 702 R7 XV0 X-0.27 (where) 108 694 P2 F-0.27 (n) 140.03 694 P0 F-0.27 ( is the population size and) 146.03 694 P3 F-0.27 (e) 272.34 694 P0 F-0.27 (\050) 277.61 694 P3 F-0.27 (m) 281.6 694 P0 F-0.27 (,) 288.51 694 P2 F-0.27 (t) 294.24 694 P0 F-0.27 (\051 is the probability that the feature is disrupted dur-) 297.57 694 P(ing reproduction. Equation 6 can be rewritten as follows:) 108 676 T0 10 Q(\050EQ 7\051) 512.53 634.99 T(\050EQ 8\051) 512.53 578.05 T0 12 Q0.63 (where) 108 541.88 P148.16 551.49 140.93 551.49 2 LV0.65 H0 ZN3 F0.63 (s) 140.93 541.88 P0 F0.63 (\050) 148.16 541.88 P3 F0.63 (m) 152.15 541.88 P0 F0.63 (,) 159.06 541.88 P2 F0.63 (t) 165.68 541.88 P0 F0.63 (\051 is the average probability of selection for a member of) 169.02 541.88 P3 F0.63 (L) 446.7 541.88 P0 F0.63 (\050) 454.93 541.88 P3 F0.63 (m) 458.92 541.88 P2 F0.63 (, t) 465.83 541.88 P0 F0.63 (\051. Notice that) 475.79 541.88 P-0.3 (when) 108 523.88 P3 F-0.3 (m) 136.68 523.88 P0 F-0.3 ( is a schema,) 143.59 523.88 P213.91 533.49 206.68 533.49 2 LVN3 F-0.3 (s) 206.68 523.88 P0 F-0.3 ( is de\336ned in accordance with \336tness proportionate reproduction and) 213.91 523.88 P3 F-0.13 (e) 108 505.88 P0 F-0.13 ( is de\336ned to adjust for crossover and point mutation then the lower bound expression for) 113.26 505.88 P(the schema theorem of Holland \0501975\051 shown in Equation 3 is recovered.) 108 487.88 T-0.03 (The interest in Equation 8 for abstract feature propagation stems from its characteriza-) 126 457.88 P1.48 (tion of the properties of reproduction as the relative \336tness of the population members) 108 439.88 P0.2 (with and without) 108 421.88 P3 F0.2 (m) 192.89 421.88 P0 F0.2 ( change. As long as) 199.8 421.88 P304.63 431.49 297.4 431.49 2 LVN3 F0.2 (s) 297.4 421.88 P0 F0.2 (\050) 304.63 421.88 P3 F0.2 (m) 308.62 421.88 P0 F0.2 (,) 315.53 421.88 P2 F0.2 (t) 321.73 421.88 P0 F0.2 (\051 > 1) 325.06 421.88 P2 F0.2 (/\050n - n) 348.21 421.88 P3 F0.2 (e) 377.93 421.88 P0 F0.2 (\050) 383.19 421.88 P3 F0.2 (m) 387.18 421.88 P0 F0.2 (,) 394.09 421.88 P2 F0.2 (t) 400.29 421.88 P0 F0.2 (\051\051, the number of population) 403.62 421.88 P-0.11 (members with the feature is likely to be lar) 108 403.88 P-0.11 (ger in the next generation. On the other hand, if) 312.79 403.88 P115.23 395.49 108 395.49 2 LVN3 F0.39 (s) 108 385.88 P0 F0.39 (\050) 115.23 385.88 P3 F0.39 (m) 119.23 385.88 P0 F0.39 (,) 126.13 385.88 P2 F0.39 (t) 132.52 385.88 P0 F0.39 (\051 < 1) 135.85 385.88 P2 F0.39 (/\050n - n) 159.38 385.88 P3 F0.39 (e) 189.47 385.88 P0 F0.39 (\050) 194.73 385.88 P3 F0.39 (m) 198.73 385.88 P0 F0.39 (,) 205.63 385.88 P2 F0.39 (t) 212.02 385.88 P0 F0.39 (\051\051 then the number of population members containing) 215.35 385.88 P3 F0.39 (m) 478.28 385.88 P0 F0.39 ( is likely to) 485.19 385.88 P0.18 (decrease. In other words, as long as) 108 367.88 P3 F0.18 (m) 282.75 367.88 P0 F0.18 ( presents a suf) 289.66 367.88 P0.18 (\336cient selection advantage to the sub-) 358.25 367.88 P1.87 (population that contains it, additional population members tend to acquire the feature.) 108 349.88 P0.55 (When) 108 331.88 P3 F0.55 (m) 140.19 331.88 P0 F0.55 ( is no longer an advantage, the feature is removed from the population automati-) 147.1 331.88 P(cally by the natural dynamics of the evolutionary weak method.) 108 313.88 T0.97 (Equation 8 characterizes the empirical power of the reproductive process used in all) 126 283.88 P0.09 (evolutionary weak methods. It is this strength that separates evolutionary algorithms from) 108 265.88 P0.3 (other search and optimization techniques and provides the adaptive capacity that separate) 108 247.88 P0.28 (them from standard weak methods. Of equal importance is the generality and exploitabil-) 108 229.88 P0.19 (ity of this reproductive process. For example, Davis \0501991\051 and Schwefel \0501981\051 describe) 108 211.88 P1.05 (dif) 108 193.88 P1.05 (ferent methods for evolving the parameters for manipulating population members for) 121.11 193.88 P(two dif) 108 175.88 T(ferent evolutionary weak methods.) 142.1 175.88 T-0.11 (The necessity of a population for empirical credit assignment does not imply that stan-) 126 145.88 P2.86 (dard weak methods that use populations, such as best-\336rst search and beam search,) 108 127.88 P2.83 (embody empirical credit assignment: a population is necessary but not suf) 108 109.88 P2.83 (\336cient. In) 491.2 109.88 P179.83 615.23 440.7 654 C2 12 Q0 X0 K(m) 180.83 634.99 T3 F(m) 194.9 634.99 T2 F(t) 206.24 634.99 T0 F(1) 219.37 634.99 T3 F(+) 210.43 634.99 T0 F(\050) 190.19 635.99 T(,) 201.1 635.99 T(\051) 226.01 635.99 T2 F(n) 255.46 634.99 T0 F(1) 269.27 634.99 T3 F(e) 287.13 634.99 T(-) 278.26 634.99 T(m) 297.11 634.99 T2 F(t) 310.01 634.99 T3 F(,) 304.01 634.99 T(\050) 293.11 634.99 T(\051) 313.35 634.99 T([) 264.17 634.99 T(]) 317.95 634.99 T2 F(m) 323.77 643.57 T3 F(m) 340.24 643.57 T2 F(t) 353.14 643.57 T3 F(,) 347.15 643.57 T(\050) 335.14 643.57 T(\051) 357.09 643.57 T2 F(m) 323.77 627.37 T3 F(m) 340.24 627.37 T2 F(t) 353.14 627.37 T3 F(,) 347.15 627.37 T(\050) 335.14 627.37 T(\051) 357.09 627.37 T(s) 381.64 634.99 T2 F(i) 396.68 634.99 T(t) 406.01 634.99 T3 F(,) 400.01 634.99 T(\050) 391.58 634.99 T(\051) 409.95 634.99 T2 9 Q(i) 364.79 622.69 T3 F(L) 374.44 622.69 T(m) 383.6 622.69 T2 F(t) 393.27 622.69 T3 F(,) 388.78 622.69 T(\050) 380.61 622.69 T(\051) 395.77 622.69 T(\316) 368.28 622.69 T3 18 Q(\345) 367.24 631.78 T3 12 Q(=) 242.88 634.99 T323.77 637.58 362.83 637.58 2 L0.33 H0 ZN0 0 612 792 C201.84 573.88 418.68 591.23 C2 12 Q0 X0 K(m) 202.84 580.05 T3 F(m) 216.92 580.05 T2 F(t) 228.25 580.05 T0 F(1) 241.38 580.05 T3 F(+) 232.44 580.05 T0 F(\050) 212.21 581.05 T(,) 223.11 581.05 T(\051) 248.02 581.05 T2 F(n) 270.6 578.05 T0 F(1) 281.98 578.05 T3 F(e) 299.84 578.05 T(-) 290.97 578.05 T(m) 309.82 578.05 T2 F(t) 322.72 578.05 T3 F(,) 316.73 578.05 T(\050) 305.82 578.05 T(\051) 326.06 578.05 T([) 276.88 578.05 T(]) 330.66 578.05 T2 F(m) 339.79 578.05 T3 F(m) 354.38 578.05 T2 F(t) 367.29 578.05 T3 F(,) 361.29 578.05 T(\050) 349.28 578.05 T(\051) 371.23 578.05 T(s) 379.8 578.05 T(m) 392.96 578.05 T2 F(t) 405.87 578.05 T3 F(,) 399.87 578.05 T(\050) 387.86 578.05 T(\051) 409.81 578.05 T(=) 258.02 578.05 T380.8 586.04 387.03 586.04 2 L0.33 H0 ZN0 0 612 792 CFMENDPAGE%%EndPage: "49" 10%%Page: "50" 10612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(50) 528.01 712 T108 90 540 702 R7 XV0 X1.4 (empirical credit assignment, the reproduction operators must map between members of) 108 694 P1.22 (the problem space independent of task-speci\336c knowledge. Evolutionary weak methods) 108 676 P0.29 (accomplish this by de\336ning representation-speci\336c operators for manipulation rather than) 108 658 P0.29 (task-speci\336c operators as in standard weak/strong methods. T) 108 640 P0.29 (o the extent that best \336rst or) 404.33 640 P0.57 (beam search algorithms use representation speci\336c operators and not task-speci\336c opera-) 108 622 P0.37 (tors, then these weak methods use a form of empirical credit assignment. However) 108 604 P0.37 (, if the) 508.29 604 P0.53 (operators that create new population members from old employ task-speci\336c knowledge,) 108 586 P(as is intended in beam search and best-\336rst search, then the assignment of credit is strong.) 108 568 T0.72 (In short, evolutionary weak methods gather a degree of information about the search) 126 538 P0.5 (space by modifying the content of the population so that it contains abstract features that) 108 520 P-0.15 (consistently associate with objects of better than average \336tness. Evolutionary weak meth-) 108 502 P1.23 (ods become informed about the search space and the features important for solving the) 108 484 P0.28 (problem during the run by manipulating the contents of the population. Informedness is a) 108 466 P0.45 (quality consistently missing from the standard weak methods described above. The types) 108 448 P0.69 (of features preserved and passed on to subsequent populations are determined chie\337y by) 108 430 P0.61 (the reproduction operators and the method of selecting which objects in a population are) 108 412 P(used to create the next.) 108 394 T1 F(3.2  Emergent Intelligence) 108 358 T0 F-0.21 (Empirical credit assignment uses the \336tness function as an integral part of its computa-) 126 334 P1.75 (tion. Unlike stronger forms of credit assignment, empirical credit assignment does not) 108 316 P0.1 (deduce the validity of representational components but empirically determines an abstract) 108 298 P2.51 (feature\325) 108 280 P2.51 (s validity though modi\336cation and retesting. This sets up a strong interaction) 144.63 280 P1.12 (between the evolutionary weak method and the task environment. Through this interac-) 108 262 P0.14 (tion, solution constraints that are implicit within the task environment become manifested) 108 244 P2.39 (in the population as they are discovered. V) 108 226 P2.39 (iewing the system at the knowledge-level) 329.19 226 P1.12 (\050Newell 1982\051, an observer would deduce that the evolutionary weak method possesses) 108 208 P0.94 (task-speci\336c knowledge that lead to the solution\325) 108 190 P0.94 (s structure. Given that there is no task-) 348.19 190 P-0.13 (speci\336c knowledge in the problem solver) 108 172 P-0.13 (, the interaction of the evolutionary weak method) 304.41 172 P0.32 (with the task environment allows knowledge to emer) 108 154 P0.32 (ge at the knowledge-level that is not) 364.19 154 P(available to the problem solver as explicit knowledge.) 108 136 TFMENDPAGE%%EndPage: "50" 11%%Page: "51" 11612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(51) 528.01 712 T108 90 540 702 R7 XV1 F0 X(3.2.1  Emergence and Emergent Computation) 108 694 T0 F0.14 (Emer) 126 668 P0.14 (gent intelligence is a direct generalization from the properties of empirical credit) 151.76 668 P2.23 (assignment and evolutionary weak methods that exploits the task environment during) 108 650 P2.41 (problem solving. Emer) 108 632 P2.41 (gent intelligence suggests that interaction of a simple problem) 222.88 632 P0.58 (solver with a task environment can remove the need for task-speci\336c knowledge internal) 108 614 P1.74 (to the problem solver) 108 596 P1.74 (. Before a more adequate explanation of emer) 214.82 596 P1.74 (gent intellige

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