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Yuan-Ze University A Genetic Algorithm with Injecting Artificial Chromosomes for Single Machine Scheduling Problems Pei-Chann Chang, Shih-Shin Chen, Qiong-Hui.

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Presentation on theme: "Yuan-Ze University A Genetic Algorithm with Injecting Artificial Chromosomes for Single Machine Scheduling Problems Pei-Chann Chang, Shih-Shin Chen, Qiong-Hui."— Presentation transcript:

1 Yuan-Ze University A Genetic Algorithm with Injecting Artificial Chromosomes for Single Machine Scheduling Problems Pei-Chann Chang, Shih-Shin Chen, Qiong-Hui Ko, Chin-Yuan Fan.

2 http://ppc.iem.yzu.edu.tw Evolutionary Algorithm with Probability Models Single Machine Scheduling (Ei+Ti) Injecting Artificial Chromosome Parameter Selection and Method Comparisons The EAPM might be effective  Introduction  Problem Statement  Methodology  Empirical Results  Conclusions Contents

3 http://ppc.iem.yzu.edu.tw Introduction Research Framework Scheduling Single Machine Earliness/ Tardiness Problem Exact Algorithm Heuristics Meta-Heurisitc Genetic Algorithm Algorithm

4 http://ppc.iem.yzu.edu.tw Introduction Mutation exploits local information of current chromosomes. Crossover mates two individuals into two new offspring so that it explores the solution space. Selection is to preserve better chromosomes to be survived. Selection Crossover Mutation

5 http://ppc.iem.yzu.edu.tw Introduction ProblemAlgorithms  Continuous  Combinatorial  Single/Multi Objective  Nature Behavior Probability Model Improvements EAPM Memetic GAs Sexual VEGA NSGA II SPEA 2

6 http://ppc.iem.yzu.edu.tw EAPM Primary Steps Main Procedures Three general steps Selection is required Characteristics Crossover is not used. Mutation is not used. An explicit probability model Step 3 generates a population of chromosomes by probability model. Step 2 extracts gene information from population. Step 1 is to evaluate chromosomes’ fitness and to select better chromosomes.

7 http://ppc.iem.yzu.edu.tw Evolutionary Algorithm with Probability Models Ackley Bajula & Davies Muhlenbein and Paaß 1987 Feedback from population Voting Population-Base Incremental Learning (PHIL) Combining Optimizers with Mutual Information Tree (COMIT) 1999 Compact Genetic Algorithm (cGA) Replace crossover and mutation operator Zhang et al. Chang et al. Zhang classified these algorithms into EDA. For extensive review of evolutionary algorithm base on probability models, please refer to Larrañaga and Lozano. 2005 and 2007 Artificial Chromosome Single/Multi Objective problem 2005 Guided Mutation or Mutation Matrix

8 http://ppc.iem.yzu.edu.tw Problem Statement n i=1 Min Z = Σ(α i E i +β i T i ) s.t. Σx ij =1 j =1 to n Σx ij =1 i =1 to n C i － d i － E i + T i = 0 x ij {0,1} n i=1 n j=1 A A 20 Jobs 30 Jobs 40 Jobs 50 Jobs 60 Jobs 90 Jobs Testing instances: Sourd (2005) http://www-poleia.lip6.fr/~sourd/

9 http://ppc.iem.yzu.edu.tw Main Procedure Population: The population used in the Genetic Algorithm Generations: The number of generations startingGen: It determines when does the AC works interval: The frequency to generate artificial chromosomes 1.Initiate Population 2.ConstructInitialPopulation(Population) 3.RemovedIdenticalSolution() 4.counter  0 5.while counter < generations do 6. Evaluate Objectives and Fitness() 7. FindEliteSolutions(i) 8. if counter < startingGen or counter % interval != 0 do 9. Selection with Elitism Strategy() 10. Crossover() 11. Mutation() 12. TotalReplacement() 13. else 14. CalculateAverageFitness() 15. CollectGeneInformation() 16. GenerateArtificialChromsomomes() 17. Replacement(μ+λ) 18. End if 19. counter  counter + 1 20.end while

10 http://ppc.iem.yzu.edu.tw Genetic Operators  Selection:  tournament selection has better convergence and computational time-complexity properties than others. (Goldberg Deb, 1991)  Crossover:  Murata and Ishibuchi (1994) reported that two- point crossover is effective in scheduling problems.  Mutation:  Swap mutation operator is used because of its simplicity.

11 http://ppc.iem.yzu.edu.tw Artificial Chromosome  Extract Chromosome Information  Proportional Selection  Replacement

12 http://ppc.iem.yzu.edu.tw Step 1  To extract the population information.  A data structure called dominance matrix store it.

13 http://ppc.iem.yzu.edu.tw Step 2  Job assignment by probability selection

14 http://ppc.iem.yzu.edu.tw Empirical Results  Sourd (2005) provided single machine Ei/Ti instances.  Parameter settings: By Design of Experiment (DOE)  Replications: 30 times Hybrid Algorithm Artificial Chromosomes Genetic Algorithm with Dominance Properties (ACGADP) Simple Genetic Algorithm (SGA) Artificial Chromosome Genetic Algorithm (ACGA) Genetic Algorithm with Dominance Properties (GADP)

15 http://ppc.iem.yzu.edu.tw Parameter settings Population Size: 100 Crossover Rate: 0.9 Mutation Rate: 0.5 SGA Starting Generation: 250 Interval: 50 ACGA

16 http://ppc.iem.yzu.edu.tw Convergence Diagram

17 http://ppc.iem.yzu.edu.tw Results: The average objective of 20 jobs InstanceSGAGADPACGAACGADP sks222a5402529152895288.7 sks225a417439593958 sks228a21562085 sks252a4195394739793947 sks255a2489237223802372.5 sks258a1250124212001192.7 sks282a4435435343514353.8 sks285a46434452 sks288a35183421

18 http://ppc.iem.yzu.edu.tw Results: The average objective of 30 jobs InstanceSGAGADPACGAACGADP sks322a12066115721157711570 sks325a815277037587 sks328a35563164 sks352a8203739573947394.2 sks355a6849606860656057.5 sks358a3283307430733072.5 sks382a11319111521114911142 sks385a92129148 sks388a1149911317

19 http://ppc.iem.yzu.edu.tw Results: The average objective of 40 jobs InstanceSGAGADPACGAACGADP sks422a26211256582565925657 sks425a13592126041260612601 sks428a77417129 sks452a12634113671140611367 sks455a7566640564276405 sks458a5587430343214300.4 sks482a20122195801957319562 sks485a16023153091533815350 sks488a179991688116863

20 http://ppc.iem.yzu.edu.tw Summary Relative Average Error Ratio SGA ACGA GADP ACGADP 9.971% 0.251% 0.173% 0.109%

21 http://ppc.iem.yzu.edu.tw Results: The average objective of 50 jobs InstanceSGAGADPACGAACGADP sks522a4.4830.0440.0100.003 sks525a2.6740.0120.0200.004 sks528a11.470.2130.3700.056 sks552a8.5900.0000.1360.000 sks555a20.080.5500.2850.216 sks558a39.400.5450.000 sks582a4.3490.6370.0290.168 sks585a4.1650.0080.0440.089 sks588a6.3520.0080.004

22 http://ppc.iem.yzu.edu.tw Results: The average objective of 60 jobs InstanceSGAGADPACGAACGADP sks622a4.5760.0000.1670.000 sks625a5.7200.0950.1230.095 sks628a8.1190.0590.0700.047 sks652a7.2110.0000.2270.000 sks655a18.440.0000.3710.000 sks658a32.130.0010.3290.002 sks682a2.6040.5840.0900.540 sks685a4.3590.0320.0500.016 sks688a6.7810.3070.2620.283

23 http://ppc.iem.yzu.edu.tw Results: The average objective of 90 jobs InstanceSGAGADPACGAACGADP sks922a5.7690.8610.0600.534 sks925a6.1080.0100.0370.024 sks928a23.810.4940.4380.574 sks952a12.790.0560.2020.043 sks955a32.250.2680.3300.265 sks958a53.730.1350.4010.336 sks982a3.7840.4340.0310.475 sks985a8.5190.1860.1510.190 sks988a11.510.0110.0220.013

24 http://ppc.iem.yzu.edu.tw ANOVA SourceDFSeq SSAdj SSAdj MSFP instance2135.52E+12 2.59E+10211672.20.000 method36.52E+09 2.17E+0917755.570.000 instance*me thod6391.16E+10 18218808148.750.000 Error248243.04E+09 122476 Total256795.54E+12

25 http://ppc.iem.yzu.edu.tw Pair-wise Comparison Duncan Grouping Mean N Method A 13982.894 6420 SGA B 12827.096 6420 GADP B C B 12816.471 6420 ACGADP C C 12813.276 6420 ACGA ACGA The worst solution quality GADPSGA Better than SGA and works efficiently Outperform other algorithms.

26 http://ppc.iem.yzu.edu.tw Conclusions Artificial Chromosomes Genetic Operators Probability Model Genetic Algorithm with injecting artificial chromosomes

27 http://ppc.iem.yzu.edu.tw Conclusions Effective Simple Hybrid Methods The benefits of ACGA ACGA outperform others It is easy to implement It can be applied with other meta-heuristic

28 Yuan-Ze University

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