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GENETIC ALGORITHMS 229 When necessary, we can also apply other decoding techniques, such as Gray coding (Caruana and Schaffer, 1988). Using decoded values of x and y as inputs in the mathematical function, the GA calculates the fitness of each chromosome. To find the maximum of the ‘peak’ function, we will use crossover with the probability equal to 0.7 and mutation with the probability equal to 0.001. As we mentioned earlier, a common practice in GAs is to specify the number of generations. Suppose the desired number of generations is 100. That is, the GA will create 100 generations of 6 chromosomes before stopping. Figure 7.6(a) shows the initial locations of the chromosomes on the surface and contour plot of the ‘peak’ function. Each chromosome here is represented by a sphere. The initial population consists of randomly generated individuals that are dissimilar or heterogeneous. However, starting from the second generation, crossover begins to recombine features of the best chromosomes, and the population begins to converge on the peak containing the maximum, as shown in Figure 7.6(b). From then until the final generation, the GA is searching around this peak with mutation, resulting in diversity. Figure 7.6(c) shows the final chromosome generation. However, the population has converged on a chromosome lying on a local maximum of the ‘peak’ function. But we are looking for the global maximum, so can we be sure the search is for the optimal solution? The most serious problem in the use of GAs is concerned with the quality of the results, in particular whether or not an optimal solution is Figure 7.6 Chromosome locations on the surface and contour plot of the ‘peak’ function: (a) initial population; (b) first generation; (c) local maximum solution; (d) global maximum solution
230 EVOLUTIONARY COMPUTATION being reached. One way of providing some degree of insurance is to compare results obtained under different rates of mutation. Let us, for example, increase the mutation rate to 0.01 and rerun the GA. The population might now converge on the chromosomes shown in Figure 7.6(d). However, to be sure of steady results we must increase the size of the chromosome population. Figure 7.7 Performance graphs for 100 generations of 6 chromosomes: (a) local maximum solution and (b) global maximum solution of the ‘peak’ function
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MICHAEL NEGNEVITSKY Artificial Inte
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We work with leading authors to dev
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Pearson Education Limited Edinburgh
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Contents Preface Preface to the sec
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CONTENTS ix 7 Evolutionary computat
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Preface ‘The only way not to succ
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PREFACE xiii In Chapter 3, we prese
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Prefacetothesecondedition The main
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Introduction to knowledgebased inte
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INTELLIGENT MACHINES 3 Figure 1.1 T
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THE HISTORY OF ARTIFICIAL INTELLIGE
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SUMMARY 17 Although fuzzy systems a
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SUMMARY 19 Table 1.1 Period A summa
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QUESTIONS FOR REVIEW 21 or fuzzy se
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REFERENCES 23 Kosko, B. (1997). Fuz
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Rule-based expert systems 2 In whic
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RULES AS A KNOWLEDGE REPRESENTATION
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THE MAIN PLAYERS IN THE EXPERT SYST
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STRUCTURE OF A RULE-BASED EXPERT SY
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FUNDAMENTAL CHARACTERISTICS OF AN E
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FORWARD AND BACKWARD CHAINING INFER
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MEDIA ADVISOR: A DEMONSTRATION RULE
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MEDIA ADVISOR: A DEMONSTRATION RULE
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MEDIA: A DEMONSTRATION RULE-BASED E
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CONFLICT RESOLUTION 47 Does MEDIA A
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CONFLICT RESOLUTION 49 . Fire the m
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SUMMARY 51 . Dealing with incomplet
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QUESTIONS FOR REVIEW 53 . Expert sy
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Uncertainty management in rule-base
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BASIC PROBABILITY THEORY 57 Table 3
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BASIC PROBABILITY THEORY 59 single
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BAYESIAN REASONING 61 Figure 3.1 Th
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BAYESIAN REASONING 63 places an eno
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FORECAST: BAYESIAN ACCUMULATION OF
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BIAS OF THE BAYESIAN METHOD 73 Doma
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CERTAINTY FACTORS THEORY AND EVIDEN
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FORECAST: AN APPLICATION OF CERTAIN
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SUMMARY 83 team also could assume t
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REFERENCES 85 . Both Bayesian reaso
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Fuzzy expert systems 4 In which we
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FUZZY SETS 89 Range of logical valu
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FUZZY SETS 91 Figure 4.2 Crisp (a)
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FUZZY SETS 93 Figure 4.3 Crisp (a)
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LINGUISTIC VARIABLES AND HEDGES 95
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OPERATIONS OF FUZZY SETS 97 Table 4
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OPERATIONS OF FUZZY SETS 99 Similar
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OPERATIONS OF FUZZY SETS 101 Figure
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FUZZY RULES 103 Example: NOT (tall
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FUZZY RULES 105 Figure 4.9 Monotoni
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FUZZY INFERENCE 107 determined by f
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FUZZY INFERENCE 109 However, the OR
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FUZZY INFERENCE 111 Step 4: Defuzzi
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FUZZY INFERENCE 113 Figure 4.15 The
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BUILDING A FUZZY EXPERT SYSTEM 115
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SUMMARY 125 4.8 Summary In this cha
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BIBLIOGRAPHY 127 9 What is clipping
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BIBLIOGRAPHY 129 Zadeh, L.A. (1975)
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132 FRAME-BASED EXPERT SYSTEMS Figu
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134 FRAME-BASED EXPERT SYSTEMS of a
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136 FRAME-BASED EXPERT SYSTEMS - -
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140 FRAME-BASED EXPERT SYSTEMS and
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142 FRAME-BASED EXPERT SYSTEMS such
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146 FRAME-BASED EXPERT SYSTEMS valu
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150 FRAME-BASED EXPERT SYSTEMS In a
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156 FRAME-BASED EXPERT SYSTEMS illu
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158 FRAME-BASED EXPERT SYSTEMS Area
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160 FRAME-BASED EXPERT SYSTEMS ) On
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162 FRAME-BASED EXPERT SYSTEMS The
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164 FRAME-BASED EXPERT SYSTEMS Bibl
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166 ARTIFICIAL NEURAL NETWORKS What
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168 ARTIFICIAL NEURAL NETWORKS Tabl
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170 ARTIFICIAL NEURAL NETWORKS Figu
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172 ARTIFICIAL NEURAL NETWORKS Step
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174 ARTIFICIAL NEURAL NETWORKS In F
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176 ARTIFICIAL NEURAL NETWORKS Why
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Page 201 and 202: 182 ARTIFICIAL NEURAL NETWORKS Then
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Page 205 and 206: 186 ARTIFICIAL NEURAL NETWORKS Figu
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Page 217 and 218: 198 ARTIFICIAL NEURAL NETWORKS In t
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Page 223 and 224: 204 ARTIFICIAL NEURAL NETWORKS Here
Page 225 and 226: 206 ARTIFICIAL NEURAL NETWORKS The
Page 233 and 234: 214 ARTIFICIAL NEURAL NETWORKS phys
Page 235 and 236: 216 ARTIFICIAL NEURAL NETWORKS 10 D
Page 238 and 239: Evolutionary computation 7 In which
Page 240 and 241: SIMULATION OF NATURAL EVOLUTION 221
Page 242 and 243: GENETIC ALGORITHMS 223 Figure 7.2 A
Page 244 and 245: GENETIC ALGORITHMS 225 Figure 7.3 T
Page 246 and 247: GENETIC ALGORITHMS 227 Figure 7.5 T
Page 250 and 251: GENETIC ALGORITHMS 231 A surface of
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Page 264 and 265: GENETIC PROGRAMMING 245 Which metho
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Page 268 and 269: GENETIC PROGRAMMING 249 Figure 7.15
Page 274 and 275: QUESTIONS FOR REVIEW 255 . Evolutio
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280 HYBRID INTELLIGENT SYSTEMS How
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282 HYBRID INTELLIGENT SYSTEMS In t
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284 HYBRID INTELLIGENT SYSTEMS Figu
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292 HYBRID INTELLIGENT SYSTEMS word
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294 HYBRID INTELLIGENT SYSTEMS Step
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296 HYBRID INTELLIGENT SYSTEMS Step
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298 HYBRID INTELLIGENT SYSTEMS 4 De
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Knowledge engineering and data mini
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INTRODUCTION, OR WHAT IS KNOWLEDGE
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WILL AN EXPERT SYSTEM WORK FOR MY P
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WILL A FUZZY EXPERT SYSTEM WORK FOR
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WILL A NEURAL NETWORK WORK FOR MY P
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WILL GENETIC ALGORITHMS WORK FOR MY
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WILL A HYBRID INTELLIGENT SYSTEM WO
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DATA MINING AND KNOWLEDGE DISCOVERY
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SUMMARY 361 9.8 Summary In this cha
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REFERENCES 363 7 Why are fuzzy syst
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Glossary The glossary entries are c
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GLOSSARY 367 Back-propagation see B
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GLOSSARY 369 Clipping A common meth
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GLOSSARY 371 amounts of data in ord
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GLOSSARY 373 Evolution strategy A n
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GLOSSARY 375 Fuzzy rule A condition
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GLOSSARY 377 Heuristic search A sea
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GLOSSARY 379 Knowledge base A basic
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GLOSSARY 381 Method A procedure ass
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GLOSSARY 383 Output layer The last
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GLOSSARY 385 Roulette wheel selecti
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GLOSSARY 387 the network differs fr
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GLOSSARY 389 determines the strengt
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392 AI TOOLS AND VENDORS EXSYS, Inc
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394 AI TOOLS AND VENDORS M.4 A powe
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396 AI TOOLS AND VENDORS CynapSys,
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398 AI TOOLS AND VENDORS 215 Parkwa
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400 AI TOOLS AND VENDORS text files
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402 AI TOOLS AND VENDORS TransferTe
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404 AI TOOLS AND VENDORS La Jolla,
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406 AI TOOLS AND VENDORS Fax: +1 (3
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408 INDEX belongs-to 137-8 Berkeley
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410 INDEX fuzzification 107 fuzzifi
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412 INDEX Mamdani, E. 20, 106 Mamda
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INDEX 415 unsupervised learning 200
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