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GENETIC ALGORITHMS 223 Figure 7.2 A basic genetic algorithm Are any conventional termination criteria used in genetic algorithms? Because GAs use a stochastic search method, the fitness of a population may remain stable for a number of generations before a superior chromosome appears. This makes applying conventional termination criteria problematic. A common practice is to terminate a GA after a specified number of generations
224 EVOLUTIONARY COMPUTATION and then examine the best chromosomes in the population. If no satisfactory solution is found, the GA is restarted. A simple example will help us to understand how a GA works. Let us find the maximum value of the function ð15x x 2 Þ where parameter x varies between 0 and 15. For simplicity, we may assume that x takes only integer values. Thus, chromosomes can be built with only four genes: Integer Binary code Integer Binary code Integer Binary code 1 0001 6 0110 11 1011 2 0010 7 0111 12 1100 3 0011 8 1000 13 1101 4 0100 9 1001 14 1110 5 0101 10 1010 15 1111 Suppose that the size of the chromosome population N is 6, the crossover probability p c equals 0.7, and the mutation probability p m equals 0.001. (The values chosen for p c and p m are fairly typical in GAs.) The fitness function in our example is defined by f ðxÞ ¼15x x 2 The GA creates an initial population of chromosomes by filling six 4-bit strings with randomly generated ones and zeros. The initial population might look like that shown in Table 7.1. The chromosomes’ initial locations on the fitness function are illustrated in Figure 7.3(a). A real practical problem would typically have a population of thousands of chromosomes. The next step is to calculate the fitness of each individual chromosome. The results are also shown in Table 7.1. The average fitness of the initial population is 36. In order to improve it, the initial population is modified by using selection, crossover and mutation, the genetic operators. In natural selection, only the fittest species can survive, breed, and thereby pass their genes on to the next generation. GAs use a similar approach, but Table 7.1 The initial randomly generated population of chromosomes Chromosome label Chromosome string Decoded integer Chromosome fitness Fitness ratio, % X1 1 1 0 0 12 36 16.5 X2 0 1 0 0 4 44 20.2 X3 0 0 0 1 1 14 6.4 X4 1 1 1 0 14 14 6.4 X5 0 1 1 1 7 56 25.7 X6 1 0 0 1 9 54 24.8
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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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Page 193 and 194: 174 ARTIFICIAL NEURAL NETWORKS In F
Page 195 and 196: 176 ARTIFICIAL NEURAL NETWORKS Why
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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
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Page 238 and 239: Evolutionary computation 7 In which
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Page 244 and 245: GENETIC ALGORITHMS 225 Figure 7.3 T
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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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274 HYBRID INTELLIGENT SYSTEMS Figu
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278 HYBRID INTELLIGENT SYSTEMS sets
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280 HYBRID INTELLIGENT SYSTEMS How
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282 HYBRID INTELLIGENT SYSTEMS In t
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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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