EE4047_Part7 - Part 7: Advanced Designs in GA (I) Hybrid...

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1 City University of Hong Kong City University of Hong Kong Part 7: Advanced Designs in GA (I) Hybrid Design Example: Cloth Cutting r1 r2 r3 r4 Used length fabric Rectangular pieces
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2 Objective s Fabric – in a long roll s Cloth cutting = 2-D strip packing s Objective: Allocate rectangular pieces into a strip (of infinite length) such that h Pieces are not overlapped h No piece is outside the boundary of the strip h The used length is minimized Genetic Approach s Direct approach h complex chromosome structures, eg. tree h Specially designed genetic operations s Hybrid approach h Genetic algorithm for permutation problem + heuristic placement approach
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3 Flow Diagram of Hybrid Approach Order Crossover s Swap the segment and fill up the other genes by sliding through the parents starting from the segment 1 8 4 9 7 6 5 10 3 2 4 8 9 1 10 3 2 7 6 5 s Two crossover points are randomly selected 6 4 5 9 10 3 2 1 7 8 10 2 3 1 7 6 5 4 8 9
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4 Heuristic approach: LFLA s Lowest First, Left-Aligned s Heuristic Placement strategy s Allocates the rectangular pieces one by one onto the strip: h according to the order governed by the chromosome h a rectangular piece is to be placed at the lowest fitting position with left-aligned Example of LFLA r3 r5 r2 r4 r1 r3 r5 r2 r4 r1
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5 Result b Before optimizing Result (cont.) b After optimizing
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6 Convergence b Fitness VS Generation for 50 rectangular pieces Fitness VS Generations 95 100 105 110 115 120 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Generations Fitness (Height) best fitness value average fitness value Result 410sec 97sec 36msec Total execution time 2378.24 294.6 19 Low bound 2609 330 19 Obtained minimum length 200 50 18 Number of pieces
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7 City University of Hong Kong City University of Hong Kong Advanced GA Designs (II) Hierarchical Chromsome Structure Biological Inspiration s Regulatory Sequences and Structural Genes A B C structural genes promoter DNA transcription initiation site tran-acting factor mRNA polypeptide transcription translation
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8 Biological Inspiration s Exon and Intron TRANSCRIPTION intron loop SPLICING coding sequence TRANSLATION protein intron exon exon promoter Hierarchical Chromosome s A fixed chromosome structure s Consists of two types of genes: Control Genes and Parametric Genes s Provide different phenotype structures Parametric genes First level Control genes Second level Control genes
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9 Example 1 s Chromosome A X1 = (4,1,3,8) s Chromosome B X2 = (3,9) 4 7 1 3 8 9 1 0 1 1 1 0 4 7 1 3 8 9 0 0 0 1 0 1 1 0 1 1 1 0 4 7 1 3 8 9 0 0 0 1 0 1 4 7 1 3 8 9 Example 2 s Chromosome A X1 = (4,1) 4 7 1 3 8 9 1 0 1 1 1 0 1 0 4 7 1 3 8 9 1 0 1 1 1 0 1 0
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10 Multiobjective s Consider the structure as an objective s Selection with Preferable ranking s Replacement in group: compete with others in the same group f1 f2 1 1 2 4 Example 1: IIR Filter Design s determination of lowest filter order; s the filter must be stable (the poles must lie inside the unit circle) ; and s the filter must meet the prescribed tolerance settings
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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_Part7 - Part 7: Advanced Designs in GA (I) Hybrid...

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