EE4047_Part4 - 1 City University of Hong Kong City...

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Unformatted text preview: 1 City University of Hong Kong City University of Hong Kong City University of Hong Kong City University of Hong Kong Part 4 : Modifications on Simple GA Simple Genetic Algorithm • Binary representation • Roulette Wheel Selection • Single Point Crossover • Bit Mutation • High crossover rate and low mutation rate • Generational Replacement Policy 2 City University of Hong Kong City University of Hong Kong City University of Hong Kong City University of Hong Kong Chromosome Representation Binary and Gray Code • Gray code – followed after Frank Gray (1953) • Each number in the sequence of integers [0, 2 N-1] as a binary string of length N in an order such that adjacent integers differ in only one bit position ● start with all bits zero and successively flip the right- most bit that produces a new string 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111 3 Advantages of using Gray code • Adjacent integers only lie a single-bit flips apart • Improve the mutation operator's chances of making incremental improvements • Flip of a single bit will make only small changes in most of the cases, while it effects a truly big change in a small chance (EXPLORATION & EXPLOITATION) Real-coded Chromosome • Use of high cardinality alphabet instead of low cardinality • Example: Integer representation, float number representation 4 Low cardinality alphabet • An alphabet of cardinality K eg. the cardinality of a hexadecimal is 16 (0-F), the cardinality of a binary is 2 (0 or 1) • K+1 schemata per position • Each position represents log 2 K bits • (K+1) 1/log 2 K schemata per bit • Strings coded with smaller alphabets are representatives of larger numbers of schemata than strings coded with larger alphabets Simple Example 3 7 111 11 5 101 8 3 011 22 000 Function Value Octal Binary • For octal representation, we can make no inferences regarding which of the structures might be promising • For binary representation, many hypotheses can be formulated regarding the association between string values and high fitness ⇒ information for recombination 5 High cardinality alphabet • One-gene-one-variable correspondence • Avoidance of Hamming cliffs • Fewer generations to population conformity • Reduction of normal-mode deception D.E. Goldberg, “Real-code Genetic algorithms, virtual alphabets, and blocking” Tree Representation • Generation of Equation • Binary tree representation • Inorder traversal: 1. Traverse the left subtree 2. Visit the root 3. Traverse the right subtree '+' 3 5 '+' 3 '/' '*' '-' 4 7 6 3+4*(6-7)/5+3 * This is also known as Genetic Programming. 6 City University of Hong Kong City University of Hong Kong City University of Hong Kong City University of Hong Kong Crossover Operations Two-point crossover • Two random crossover points are selected • A segment is swapped with that from parents • 2-point crossover is generally better than 1-point crossover 7 Two-point crossover...
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This note was uploaded on 05/01/2011 for the course ELECTRICAL EE5602 taught by Professor Xuequan during the Spring '11 term at City University of Hong Kong.

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EE4047_Part4 - 1 City University of Hong Kong City...

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