📄 chapter2.ps
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(the knowledge base or generalized into an analytical solution.) 108 436.94 T0.77 (W) 126 406.94 P0.77 (eak methods are algorithms that are broadly applicable and extendable to all prob-) 136.36 406.94 P1.35 (lem solving instances. AI uses weak methods as general algorithmic shells in which to) 108 388.94 P-0.28 (place knowledge as it is identi\336ed and codi\336ed. Interactive re\336nement and/or analytic gen-) 108 370.94 P0.91 (eralization of the knowledge base is intended to lead to a strong method for the task. In) 108 352.94 P-0.23 (order to be general, weak methods make no commitments to speci\336c operators that manip-) 108 334.94 P0.4 (ulate a speci\336c representation \050W) 108 316.94 P0.4 (inston 1983; Rich 1982\051 and thus make no commitment) 269.64 316.94 P0.35 (to credit assignment. At most, they supply a general algorithm for traversing the problem) 108 298.94 P0.85 (space in an orderly manner) 108 280.94 P0.85 (. T) 240.62 280.94 P0.85 (ask-speci\336c knowledge speci\336es how to traverse the prob-) 253.95 280.94 P2.27 (lem space \322intelligently\323 \050W) 108 262.94 P2.27 (inston 1983; Rich 1982\051. T) 251.88 262.94 P2.27 (o understand AI\325) 389.71 262.94 P2.27 (s reliance on) 474.85 262.94 P(explicit knowledge it is \336rst important to understand the limitations of weak methods.) 108 244.94 T1 F(2.4.1 W) 108 208.94 T(eak Methods) 149.32 208.94 T0 F0.27 (W) 126 182.94 P0.27 (eak methods are problem solving and search techniques inspired by observations of) 136.36 182.94 P2.28 (human performance \050Rich 1982; W) 108 164.94 P2.28 (inston 1983\051. They include) 287.18 164.94 P2 F2.28 (generate and test) 428.55 164.94 P0 F2.28 (,) 515.72 164.94 P2 F2.28 (hill) 524 164.94 P3.26 (climbing) 108 146.94 P0 F3.26 (,) 149.98 146.94 P2 F3.26 (means-ends analysis) 159.23 146.94 P0 F3.26 (,) 261.42 146.94 P2 F3.26 (constraint satisfaction) 270.67 146.94 P0 F3.26 (,) 380.88 146.94 P2 F3.26 (pr) 390.13 146.94 P3.26 (oblem r) 400.35 146.94 P3.26 (eduction) 440.14 146.94 P0 F3.26 (,) 481.44 146.94 P2 F3.26 (depth-\336rst) 490.7 146.94 P0.26 (sear) 108 128.94 P0.26 (ch) 128.21 128.94 P0 F0.26 (,) 139.53 128.94 P2 F0.26 (br) 145.79 128.94 P0.26 (eadth-\336rst sear) 156.01 128.94 P0.26 (ch) 228.78 128.94 P0 F0.26 ( and) 240.1 128.94 P2 F0.26 (best-\336rst sear) 263.94 128.94 P0.26 (ch) 329.39 128.94 P0 F0.26 ( among others. In this section, I present a) 340.71 128.94 P108 480.94 540 702 C219.7 692.44 219.7 575.44 2 L0.5 H0 Z0 X0 KN0 12 Q(Ef) 0 -270 212.47 611.44 TF(fectiveness) 0 -270 212.47 622.54 TF219.7 575.44 381.7 575.44 2 LN(Space of T) 264.7 560.05 T(asks) 315.81 560.05 T90 450 4.5 4.5 292.4 686.67 A287.9 682.17 296.9 686.67 R7 XVN180 270 63 104.91 359.9 688.08 G0 X180 270 63 104.91 359.9 688.08 A7 X270 360 63 104.91 224.9 688.08 G0 X270 360 63 104.91 224.9 688.08 A(Strong Method) 369.04 581.57 T225.6 634.65 M 241.18 642.52 258.98 632.31 276.46 630.66 D 295.45 628.88 317.33 636.53 337.96 633.84 D 351.35 632.09 364.3 629.7 377.71 630.38 D1 XN0 X(W) 386.62 628.17 T(eak Method) 396.98 628.17 T127.12 507.52 523.69 540.56 R7 XV1 10 Q0 X1.23 (Figur) 127.12 533.9 P1.23 (e 1: Comparison of the effectiveness of weak and str) 150.82 533.9 P1.23 (ong methods over the variety of) 382.92 533.9 P1.82 (tasks that can be attempted. Str) 127.12 523.9 P1.82 (ong methods ar) 271.53 523.9 P1.82 (e specialized for a set of tasks and mor) 341.07 523.9 P1.82 (e) 519.25 523.9 P(effective while weak methods ar) 127.12 513.9 T(e general acr) 262.95 513.9 T(oss tasks but less effective.) 317.72 513.9 T0 0 612 792 CFMENDPAGE%%EndPage: "18" 5%%Page: "19" 5612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(19) 528.01 712 T108 90 540 702 R7 XV0 X0.55 (few representative weak methods with typical properties. In order to simplify the discus-) 108 533.69 P(sion, the operators for the task are assuemd to connect the search space as a tree.) 108 515.69 T1 F(2.4.1.1 Generate and T) 108 479.69 T(est) 226.49 479.69 T0 F0.38 (Generate and test \050Nerwell and Simon 1972\051 is the weakest of the weak methods. All) 126 453.69 P0.5 (other weak methods can be considered specializations of this one method by virtue of its) 108 435.69 P0.89 (minimal commitments. The algorithm for a generate and test is shown in Figure 2. T) 108 417.69 P0.89 (wo) 525.34 417.69 P0.51 (components are needed to de\336ne a generate and test search: a generator and a tester) 108 399.69 P0.51 (. The) 514.84 399.69 P0.02 (generator is a function that returns one objects from the search space) 108 381.69 P2 F0.02 (S) 440.67 381.69 P0 F0.02 ( at each invocation.) 446.67 381.69 P1.55 (A generator) 108 363.69 P1.55 (\325) 166.94 363.69 P1.55 (s properties are typically dependent on the problem and the quality of the) 170.28 363.69 P1.05 (operators that or) 108 345.69 P1.05 (ganize the set of objects. W) 188.5 345.69 P1.05 (inston \0501983\051 suggests that good generators) 325.86 345.69 P(should possess the following properties:) 108 327.69 T(1.) 162 297.69 T2 F2.44 (Completeness:) 180 297.69 P0 F2.44 ( they eventually produce all positions in a search) 250.62 297.69 P(space.) 180 279.69 T(2.) 162 249.69 T2 F1.89 (Non-r) 180 249.69 P1.89 (edundancy) 208.21 249.69 P0 F1.89 (: they never damage ef) 260.16 249.69 P1.89 (\336ciency by proposing the) 376.74 249.69 P(same solution twice.) 180 231.69 T(3.) 162 201.69 T2 F1.6 (Informedness) 180 201.69 P0 F1.6 (: they use possibility limiting information to restrict) 244.62 201.69 P(the solutions they propose accordingly) 180 183.69 T(.) 364.43 183.69 T0.64 (Random search, the weakest generator possible, selects a single element of) 108 153.69 P2 F0.64 (S) 477.11 153.69 P0 F0.64 ( with a uni-) 483.11 153.69 P-0.24 (form probability) 108 135.69 P-0.24 (. It therefore does not require an operator set to traverse the space and thus) 185.94 135.69 P0.57 (the set of operators,) 108 117.69 P2 F0.57 (O,) 207.87 117.69 P0 F0.57 ( is null. Note that random search only embodies the completeness) 219.52 117.69 P0.19 (principle for good generators but neither of the other two. Because of this minimal ability) 108 99.69 P143.68 541.69 504.32 702 C159.99 602.16 489.75 693.56 R7 X0 KV5 12 Q0 X(function Generate-and-Test;) 159.99 685.56 T(begin) 159.99 670.56 T(obj := Generate\050\051;) 179.82 655.56 T(while not\050Tester\050obj\051\051) 179.82 640.56 T(obj := Generate\050\051;) 345.33 640.56 T(return obj;) 179.82 625.56 T(end;) 159.99 610.56 T156.61 567 490.6 582.75 R7 XV1 10 Q0 X(Figur) 156.61 576.08 T(e 2: Algorithm for Generate and T) 180.31 576.08 T(est weak method.) 326.51 576.08 T0 0 612 792 CFMENDPAGE%%EndPage: "19" 6%%Page: "20" 6612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(20) 528.01 712 T108 90 540 702 R7 XV0 X0.02 (to reach everything in the space, random search is often used as a comparison to proposed) 108 416.69 P-0.24 (methods since if a search performs better than random, then some characteristic of the task) 108 398.69 P(environment must be present in the generator) 108 380.69 T(.) 324.52 380.69 T0.37 (The tester in a generate and test method is very simple. Often it is just a function that) 126 350.69 P0.4 (takes an object returned by the generator and uses the evaluation function to determine if) 108 332.69 P0.12 (the object is an acceptable solution. This may involve transforming the object returned by) 108 314.69 P0 (the generator into a more appropriate representation for evaluation. How integrated a gen-) 108 296.69 P1.66 (erator and tester are determines their ef) 108 278.69 P1.66 (\336ciency for solving the problem or locating an) 305.55 278.69 P0.49 (acceptable solution from the search space. Some of the other weak methods specify their) 108 260.69 P0.19 (traversal of the search space more explicitly to improve performance while still maintain-) 108 242.69 P(ing a general applicability) 108 224.69 T(.) 232.13 224.69 T1 F(2.4.1.2 Hill Climbing) 108 188.69 T0 F0.12 (In hill climbing, the evaluation function plays an important role in the search. Given a) 126 162.69 P-0.25 (current object, this weak method, shown in Figure 3, evaluates each child of the object and) 108 144.69 P0.81 (selects the one that the evaluation function judges to be best. Thus, it is always the case) 108 126.69 P0.13 (that the progression of current positions leads to a series of values returned by the evalua-) 108 108.69 P116.1 424.69 531.9 702 C122.29 503.58 524.48 696.94 R7 X0 KV5 12 Q0 X(function Hill-Climber\050obj\051;) 122.29 688.94 T(begin) 122.29 673.94 T(best := null;) 142.12 658.94 T(while \050not \050Tester\050obj\051\051 and not\050best = obj\051 do) 142.12 643.94 T(begin) 142.12 628.94 T(best := obj;) 160.12 613.94 T(for opr in) 160.12 598.94 T6 F(O) 239.27 598.94 T5 F( do) 246.47 598.94 T(if \050evaluate\050opr\050obj\051\051 >= evaluate\050best\051\051 then) 178.12 583.94 T(best := opr\050obj\051;) 196.12 568.94 T(switch\050obj, best\051;) 160.12 553.94 T(end;) 142.12 538.94 T(return obj;) 142.12 523.94 T(end;) 122.29 508.94 T125.52 462.94 522.79 488.25 R7 XV1 10 Q0 X0.05 (Figur) 125.52 481.58 P0.05 (e 3: Algorithm for hill climbing weak method. the switch function switches the values of) 149.22 481.58 P(its arguments so that each has the others value.) 125.52 471.58 T0 0 612 792 CFMENDPAGE%%EndPage: "20" 7%%Page: "21" 7612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(21) 528.01 712 T108 90 540 702 R7 XV0 X1.97 (tion function that never decreases. Consider the landscape model of the search space.) 108 510.06 P2.77 (Assuming a maximal value from the evaluation function is preferred, a hill climber) 108 492.06 P0.14 (traverses the terrain of the landscape so that each step it takes is either up a hill or along a) 108 474.06 P1.25 (plateau, hence its name. Because the evaluation function determines which child of the) 108 456.06 P-0 (current object is the most pro\336table to investigate next, this weak method has the property) 108 438.06 P0.61 (of informedness. However) 108 420.06 P0.61 (, if the evaluation function de\336nes a non-monotonic landscape) 236.31 420.06 P2.19 (over the search space, then, depending on the initial position in the space, this weak) 108 402.06 P(method halts on some local extrema of the space. Thus, this generator is not complete.) 108 384.06 T1 F(2.4.1.3 Depth First Sear) 108 348.06 T(ch) 232.04 348.06 T0 F0.78 (Depth-\336rst search, described in Figure 4, is a stronger form of search that assumes a) 126 322.06 P-0.14 (generator that traverses the search space in a particular manner) 108 304.06 P-0.14 (. The generator begins at an) 407.48 304.06 P0.4 (initial position in the search space and expands all of the children of the current structure) 108 286.06 P0.28 (by calling the algorithm recursively for each child before returning to its parent. Thus the) 108 268.06 P1.5 (generator moves away from the initial object until the boundary of the search space is) 108 250.06 P0.66 (seen. Then the algorithm backs up a single operator application and continues. Note that) 108 232.06 P0.73 (this generator ful\336lls the completeness and non-redundancy principles of a good genera-) 108 214.06 P1.19 (tor) 108 196.06 P1.19 (. However) 120.67 196.06 P1.19 (, it doesn\325) 171.33 196.06 P1.19 (t possess a mechanism for integrating information learned in the) 221.14 196.06 P0.29 (search to curb future choices. This is because this weak method only uses the tester func-) 108 178.06 P2.04 (tion to determine if the current structure is a solution. Thus no information is passed) 108 160.06 P0.38 (between the tester and the generator since the tester is a simple binary function. On aver-) 108 142.06 P0.44 (age, when searching for a single position in the space, depth-\336rst search visits half of the) 108 124.06 P(positions in the search space before identifying the desired object.) 108 106.06 T112.21 518.06 535.79 702 C120.37 595.41 526.77 698.06 R7 X0 KV5 12 Q0 X(function Depth-First\050obj\051;) 120.37 690.06 T(begin) 120.37 675.06 T(if Tester\050obj\051 then) 140.2 660.06 T(return obj;) 158.2 645.06 T(else) 140.2 630.06 T(for opr in) 158.2 615.06 T6 F(O) 237.35 615.06 T5 F( do Depth-First-Search\050opr\050obj\051\051;) 244.55 615.06 T(end;) 120.37 600.06 T120.93 556.45 524.53 581.06 R7 XV1 10 Q0 X0.58 (Figur) 120.93 574.4 P0.58 (e 4: Recursive algorithm for depth-\336rst sear) 144.63 574.4 P0.58 (ch. O is the set of operators that de\336nes the) 335.55 574.4 P(connectivity of the sear) 120.93 564.4 T(ch space. The connectivity of the space is assumed to be a tr) 219.29 564.4 T(ee.) 472.56 564.4 T0 0 612 792 CFMENDPAGE%%EndPage: "21" 8%%Page: "22" 8612 792 0 FMBEGINPAGE108 63 540 702 R7 X0 KV108 711 540 720 RV0 12 Q0 X(22) 528.01 712 T108 90 540 702 R7 XV1 F0 X(2.4.1.4 Br) 108 381.81 T(eadth-First Sear) 160.09 381.81 T(ch and Beam Sear) 243.48 381.81 T(ch) 336.21 381.81 T0 F0.52 (Breadth \336rst search also traverses the search space in an orderly fashion, as in depth-) 126 355.81 P0.34 (\336rst search, but does so in a dif) 108 337.81 P0.34 (ferent manner) 259.42 337.81 P0.34 (. In this weak method, all of the positions in) 326.04 337.81 P0.36 (the space at the same depth away from the initial structure are expanded and evaluated at) 108 319.81 P1.52 (the same time. If a desired solution is found among them, the search is ended and the) 108 301.81 P0.08 (object is returned. If not, all objects at the next depth are investigated. Note that this weak) 108 283.81 P1.49 (method also possesses the properties of completeness and non-redundancy) 108 265.81 P1.49 (, but as with) 476.89 265.81 P(depth \336rst search, its operation can not be ef) 108 247.81 T(fected by previously rejected.) 319.96 247.81 T0.71 (One disadvantage to breadth-\336rst search is that it can require a signi\336cant amount of) 126 217.81 P0.6 (space. Consider a set of) 108 199.81 P2 F0.6 (b) 227.59 199.81 P0 F0.6 ( operators in the set of operators,) 233.59 199.81 P2 F0.6 (O) 398.36 199.81 P0 F0.6 (. In this space, breadth-\336rst) 407.01 199.81 P0.49 (search would need to evaluate) 108 181.81 P2 F0.49 (b) 258 181.81 P2 10 Q0.41 (i) 263.99 186.61 P0 12 Q0.49 (positions at depth) 270.26 181.81 P2 F0.49 (i) 359.36 181.81 P0 F0.49 (, an exponential growth of space. T) 362.69 181.81 P0.49 (o) 534 181.81 P0.17 (avoid this, a variant of this weak method, called) 108 163.81 P2 F0.17 (beam sear) 342.4 163.81 P0.17 (ch) 391.76 163.81 P0 F0.17 ( \050Lowerre and Reddy 1980\051,) 403.08 163.81 P1.27 (allows at most a \336xed number) 108 145.81 P1.27 (,) 258.1 145.81 P2 F1.27 (n) 265.37 145.81 P
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