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# EE4047_Part4 - Part 4 Modifications on Simple GA City...

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1 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

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2 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 0 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111 0 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

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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 0 000 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.

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6 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 Perform an exchange of a single segment More building blocks are possible Further increase the number of points multi-point crossover Three-point crossover

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8 Uniform crossover A random crossover mask is generated
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