JGA A Java tool for solving (single and multiobjective) ) optimization problems based on evolutionary algorithms

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1 JGA A Java tool for solving (single and multiobjective) ) optimization problems based on evolutionary algorithms Andrés s Medaglia, Ph.D. Eliécer Gutiérrez, M.Sc., M.E. Centro para la Optimización n y Probabilidad Aplicada (COPA( COPA) Departamento de Ingeniería a Industrial Universidad de los Andes Last update: June 2 nd, 2006

2 Outline Researchers Motivation Fundamentals Architecture Single-objective optimization examples applications Extension to multi-objective optimization Future work and concluding remarks 2

3 Researchers (brief)) background Andrés L. Medaglia Education Ph.D. in Operations Research (NC State U. USA, 2001) M.Sc. in Industrial Engineering (U. de los Andes-Colombia, 1996) B.Sc. in Industrial Engineering (U. Javeriana Colombia, 1992) Experience Assistant professor (IE Dept. - U. de los Andes, since 2002) Postdoctoral Fellow (IE Dept. NC State U.-USA, ) Funded by SAS Institute Inc. - ORD (Cary, NC) ORML Student internship (R&D) SAS Institute Inc. ORD ( ) Supply Chain Optimization initiative (Interfaces) Research Assistant (OR Dept. NC State, ) Eliécer Gutiérrez Education Ph.D. student in Engineering (U. de los Andes) M. E. in Industrial Engineering (U. de Puerto Rico) M.Sc. in Computer Science (U. de los Andes) B.Sc. in Computer Science (U. de los Andes) 3

4 JGA background Multiobjective matching (Medaglia & Fang, 2003) Scheduling (Gutiérrez et al., 2001) Vehicle routing Shortest path with turn prohibitions (AOR[s]-Medaglia & Gutiérrez, 2004) R&D: Mapas y Datos + Servinformación Bi-objective facility location Uncapacitated (AOR-Villegas, Palacios & Medaglia, 2004) Capacitated (Gutiérrez & Medaglia, 2004) Project Selection Noisy function with linearly constrained space (Kluwer- Medaglia, 2003; EJOR-Medaglia, Graves & Ringuest, 2004) Consulting with public utility company (SEPS[s]-Medaglia, Mendieta, Hueth & Sefair, 2005) 4

5 Medaglia, A. L., and Gutiérrez, E. JGA: An Object-Oriented Framework for Rapid Development of Genetic Algorithms. In Handbook of Research on Nature Inspired Computing for Economics and Management. Jean-Phillipe Rennard (Ed.), Medaglia, A. L., and Gutiérrez, E. Applications of JGA to Operations Management and Vehicle Routing. In Handbook of Research on Nature Inspired Computing for Economics and Management. Jean- Phillipe Rennard (Ed.), Medaglia, A. L., Gutiérrez, E., and Villegas, J.G. Solving Facility Location Problems using a Tool for Rapid Development of Multi- Objective Evolutionary Algorithms (MOEAs). In Handbook of Research on Nature Inspired Computing for Economics and Management. Jean-Phillipe Rennard (Ed.), Rodríguez, J. E., Medaglia, A. L. and Casas, J. P.. Approximation to the optimum design of a motorcycle frame using finite element analysis and evolutionary algorithms. Ellen J. Bass, (editor). In Proceedings of the 2005 IEEE Systems and Information Engineering Design Symposium, 2005 Rodríguez-Coca, D. M., Medaglia, A. L., and Villegas, J. G. Design of a hospital waste management network in the Department of Boyacà (Colombia). Sponsored talk given at INFORMS Annual Meeting, San Francisco, U.S.A,

6 Solution approach Mosel/Xpress-MP SAS/OR OPL/CPLEX GAMS Start Formulate MP Try MP solution approach Fails? Design heuristic Compare to MP approach Design computational experiments Report End 6

7 Metaheuristics Simulated annealing Tabu search Ant colony optimization Genetic (evolutionary) algorithms Single-objective optimization Multi-objective evolutionary optimization (MOEA) Approximate Pareto optimal front 7

8 Evolutionary algorithms An evolutionary algorithm is a stochastic search heuristic inspired by the evolution process in nature. 8

9 Example Source: : Gen & Cheng (1997) max s.a. f ( x 1, x 2 ) = x sen(4πx 1 1 ) + x 2 sen(20πx 2 ) -3.0 x 4.1 x

10 Example 21.5+x sin(4 π x)+y sin(20 π y) f = ['3*(1-x)^2*exp(-(x^2) - (y+1)^2)'... '- 10*(x/5 - x^3 - y^5)*exp(- x^2-y^2)' y '- 1/3*exp(-(x+1)^2 - y^2)']; ezmesh(f,[-pi,pi]) x >> f=['21.5+x*sin(4*pi*x)+y*sin(20*pi*y)']; >> ezsurfc(f,[-3,15,4.1,5.8]) 10

11 Evolutionary algorithms Population of individuals (chromosomes) representing solutions Generations (iterations) Fitness function Children of individuals are generated by crossover mutation Selection pressure Principle: The fitter ones have a better chance of survival At the end (several generations) we hope the population improves (in average), and throughout the process, we discover good individuals (hopefully the optimal) Key design issue: Balance between exploration and exploitation. 11

12 Evolutionary algorithm (BasicGeneticAlgorithm) 12

13 Evolutionary algorithm components Individual genotype phenotype Genetic operators mutation crossover Selection Evaluation Algorithm logic 13

14 JGA architecture myfitnessfunction mymutationoperator mycrossoveroperator myselectionoperator myapplication AppConfig.ini AppConfig.ini myconfig.ini Application layer mygenotype myphenotype FitnessFunction <<abstract>> GeneticAlgorithm Handler GASettings MutationOperator <<abstract>> GeneticAlgorithm <<abstract>> Individual Genotype <<abstract>> Phenotype <<abstract>> CrossoverOperator <<abstract>> BasicGeneticAlgorithm StatCollector 14 SelectionOperator <<abstract>> JGA framework layer Handlers JGA core Bult-in components: BinaryGenotype, IntegerGenotype, PermutationGenotype, ExchangeMutation, FlipMutation, PMXCrossover, SinglePointCrossover, TwoPointsCrossover,...

15 Solution representation Genotype newinstance(arraylist params):void initrandom():void tostring():string Phenotype setfitnessvalue(arraylist f):void getfitnessvalue(): ArrayList compare(phenotype pt):int tostring():string BinaryGenotype IntegerGenotype RealGenotype PermutationGenotype... SingleFitnessPhenotype MultipleFitnessPhenotype... Built-in components PermutationGenotype... User-defined components 15

16 Evaluation FitnessFunction evaluate(genotype gt):arraylist Ackley Branin Rosenbrock... Built-in components Branin... User-defined components 16

17 Genetic operators MutationOperator CrossoverOperator mutate(genotype gt):void crossover(genotype gt1,genotype gt2):arraylist ExchangeBinaryMutation InterchangeBinaryMutation RandomBinaryMutation... SinglePointBinaryCrossover TwoPointBinaryCrossover... Built-in components 17

18 Selection SelectionOperator select(arraylist population, int size):arraylist RouletteWheelSelection BestIndividualSelection TournamentSelection Built-in components 18

19 Typical main program myapplication.java GeneticAlgorithmHandler GeneticAlgorithmHandler( String ConfigFileName, ArrayList genotypeparams) run():arraylist 19

20 Single-objective JGA examples Ackley Uncapacitated lot sizing Routing TSP VRP 20

21 JGA example: Ackley ( x ) * * f = x = 0; [0,0] 21

22 JGA example: Ackley Output 1/2 22

23 JGA example: Ackley Output 2/2 23

24 JGA example: Ackley Implementation JGAConfigAckley.ini AckleySettingsVar3.ini AckleyMain AckleySettings.ini main(string args[]) FAckley extends FitnessFunction evaluate(genotype gt) AckleySettings RealGenotype RandomRealMutation SingleFitnessPhenotype BasicGeneticAlgorithm JGA SinglePointRealCrossover BestIndividualSelection 24

25 JGA example: Ackley Configuration files Problem-specific configuration file Instance 1 Main configuration file Instance 2 25

26 JGA example: Ackley AckleyMain.java 26

27 JGA example: Uncapacitated Lot Sizing (ULS) Given: planning horizon determininistic demand per period setup and inventory costs Find: How much to produce per period? Period Demand Setup Cost Inventory Cost 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 Source: Silver (1998) 27

28 JGA example: ULS T=4 Source: Wolsey (1998) Minimum cost flow problem with fixed charges Optimal solutions have a mathematical structure 28

29 JGA example: ULS MIP Source: Wolsey (1998) Xpress-MP solution 29

30 Ejemplo 2: ULS MIP (exact( exact) solution Units Production Inventory Demand Period 30

31 JGA example: ULS Representation Wagner & Whitin (1958) Period Demand Setup Cost Inventory Cost 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4 chromosome 31

32 JGA example: ULS Implementation ULSmain main(string args[]) JGAConfigULS.ini ULSSettings.ini ULSFitness extends FitnessFunction evaluate(genotype gt) ULSBinaryG extends BinaryGenotype tostring():string ULSSettings BinaryGenotype ExchangeBinaryMutation SingleFitnessPhenotype BasicGeneticAlgorithm JGA SinglePointBinaryCrossover RouletteWheelSelection 32

33 JGA example: ULS Class diagram 33

34 JGA example: ULS Configuration files Main configuration file Problem-specific configuration file 34

35 JGA example: ULS ULSmain.java import edu.uniandes.copa.jgalib.*; import java.util.*; public class ULSmain { public static void main (String args[]){ ArrayList genotypeparams = new ArrayList(); int numperiods = 12; genotypeparams.add(new Integer(numPeriods)); GeneticAlgorithmHandler ga; ga = new GeneticAlgorithmHandler( JGAConfigULS.ini,genotypeParams); ArrayList finalpopulation = ga.run(); } } 35

36 JGA example: ULS Output 1/2 36

37 JGA example: ULS Output 2/2 37

38 JGA example: TSP Travelling Salesman Problem (TSP) Given n nodes (clients) and their distances. Find a minimal distance tour which: departs from a depot (initial node), visits all the nodes, and returns to the depot. How many tours? (n-1)! 38

39 JGA example: TSP Instance: dantzig42 Source: 39

40 TSP: : echo 40

41 41

42 JGA example: CVRPC Capacitated Vehicle Routing Problem (CVRP) Given Find Complete graph Set of nodes Symmetric case: Cost of traveling from node i to node j : Node 0 is the depot Demand Vehicle capacity Number of vehicles G = ( N, E) N = { 0,1, K, n} E = (, i j) i, j N; i< j C { } The CVRP consists of finding a set of at most K vehicle routes of total minimum cost; such that every route starts and ends at the depot, each customer is visited exactly once, and the sum of the demands in each vehicle route does not exceed the vehicle s capacity c ij 42

43 JGA example: CVRPC 43

44 JGA example: CVRPC d 12 = C=6000 d 10 = d 3 =1500 d 5 = d 9 = vehicle 2 vehicle 3 6 d 6 = vehicle 4 0 d 1 =1200 d 8 = d 2 = vehicle 1 11 d 11 =1700 Instance S013-04e (Christofides & Eilon, 1969) d 7 = d 4 =1400

45 JGA example: CVRPC Instance S013-04e (Christofides & Eilon, 1969). 45

46 JGA example: CVRPC Genetic Vehicle Representation (GVR) proposed by Pereira, Tavares, Machado and Costa (2002)

47 JGA example: CVRPC Crossover operator temporary child parent insertion point parent 2 (donor) child 47

48 JGA example: CVRPC Reparation di i temporary child d i i split binpack insertion point d i i child 48

49 JGA example: CVRPC Insertion cost k l k l i j i j 0 0 s ( k, l ) = c + c c ij ik jl ij 49

50 JGA example: CVRPC Mutation (inversion) operator parent child 50

51 JGA example: CVRPC Implementation 51

52 JGA example: CVRPC Results Clarke & Wright (1964) 52

53 JGA example: CVRPC Results JGA/GVR GVR 53

54 Single-objective JGA applications Motorcycle frame design Speech perception post cochlear implant 54

55 JGA applications 55

56 Frame geometry and parameter illustration Discrete parameters: 10 Continuous 56 parameters: 12

57 JGA applications Motorcycle frame design Initial population of frame designs Frame parameters (discrete and continuous) F.E.A Evaluation of design criteria Evolutionary Algorithm Frame performance - Frame mass - Maximum Von Mises stress No Yes Convergence? 57 Approximation to the optimum design

58 Motorcycle frame design app Applicative layer FrameFitness RZMutation SinglePointRZCrossover BestIndividualSelection RZMain RZSettings.ini RZGenotype SingleFitnessPhenotype FitnessFunction <<abstract>> GeneticAlgorithm Handler JGASettings MutationOperator <<abstract>> GeneticAlgorithm <<abstract>> Individual Genotype <<abstract>> CrossoverOperator <<abstract>> GeneticAlgorithm StatCollector Phenotype <<abstract>> SelectionOperator <<abstract>> Handlers Library layer (JGA) 58

59 Computational Results EA parameters N 40 T 50 pc 0.6 pm 1/22 59

60 Frame A Max 60

61 Frame B Max 61

62 Frame C Max 62

63 JGA applications Predictive model for speech perception among children post cochlear implant Funded research (CEIS & BanRep) Universidad de los Andes (School of Medicine and Industrial Engineering Department) and FSFB Principal investigators: A.Peñaranda, MD (FSFB); O. L. Sarmiento, MD, MPH, Ph.D. (School of Medicine); and A. L. Medaglia, Ph.D. (IE Dept.) Student: J. Rodriguez-D allemann 63

64 JGA applications Predictive model for speech perception among children post cochlear implant decision support system prediction decision maker artificial neural network GUI new records automatic training historical data base 64

65 JGA applications JGA for ANN model selection Tipo de terapia del lenguaje Lugar del niño en la familia Tipo de rehabilitación Nivel educativo del padre Nivel educativo de la madre Promedio Tonal Suma de ingreso familiar mensual Edad de inicio de la terapia del lenguaje Estrategia de codificación del lengua Oído del implante coclear Edad del niño Tasa de Ap. 0.1 Porcentaje de sesiones de terapia a la semana (publicas) Momento 0.7 # of hidden nodes # of hidden layers 65

66 JGA applications Results model fit 66 Sensitivity: probability of predicting a good response to the cochlear implant, when the child had a good response to the implant. Specificity: probability of predicting a bad response to the cochlear implant, when the child indeed had a bad response. Positive Predictive Value: given that the model predicted a good response, the PPV is the probability that the child indeed will have a good response. Negative Predictive Value: given that the model predicted a bad response, the NPV is the probability that the child indeed will have a bad response.

67 JGA extension to multi-objective evolutionary optimization Villegas, Palacios, Medaglia (2004) 67

68 Biobjective location problem 68

69 Biobjective location problem 69

70 Biobjective location problem 70

71 Biobjective location problem 71

72 Multiobjective optimization terms 72

73 Multiobjective optimization terms 73

74 Multiobjective optimization terms 74

75 Multiobjective optimization terms 75

76 (Approximate) Efficient Frontier 76

77 Multiobjective Evolutionary Algorithms (MOEAs) A-priori articulation of preferences Aggregated functions VEGA (Schaffer,1985) 77 A-posteriori articulation of preferences MOGA: Multi Objective Genetic Algorithm (Fonseca & Fleming, 1993) Niched Pareto Genetic Algorithm (Horn, Nafpliotis, & Goldberg, 1993) NSGA: Non-dominated Sorting Genetic Algorithm (Deb & Srinivas, 1995) NSGA-II: Non-dominated Sorting Genetic Algorithm (Deb et. al, 2000) Micro-GA: Micro-Genetic Algorithm for Multiobjective Optimization (Coello and Toscano, 2001) SPEA: Strength Pareto Evolutionary Algorithm (Zitzler & Thiele, 1999)

78 NSGA II - NSGAGeneticAlgorithm 1: t 1 2: initialize P (t) 3: evaluate P (t) 4: while t T do 5: mutate P (t) and generate C m (t) 6: cross P (t) and generate C c (t) 7: C (t) C m (t) U C c (t) 8: evaluate C (t) 9: E (t) P (t) U C (t) 10: nondominated sort E (t) intor (t) 11: select P (t + 1) from the best in R (t) 12: t t : end while crowding distance 78

79 MO-JGA Architecture Application Extended Classes myapplication JGAConfig.ini Extended Classes MO-JGA/NSGA NSGASelection Operator NSGAGenetic Algorithm MONSGAIndividual MOPhenotype FitnessFunction <<abstract>> GeneticAlgorithm <<abstract>> Individual Genotype <<abstract>> MutationOperator <<abstract>> GeneticAlgorithm Handler Phenotype <<abstract>> CrossoverOperator <<abstract>> SelectionOperator <<abstract>> JGA core Built-in classes BinaryGenotype, IntegerGenotype, PermutationGenotype JGA 79

80 Biobjective capacitated facility location Given: -Set of depots D={1,2...,m} with fixed costs f i and capacity u i -Set of purchasing centers (customers) C={1,2...,n} with demand d j -Distances d ij and transportation costs c ij for each pair depot-customer. y i = 1, if depot i is open 0, otherwise x ij = 1, if depot i attendscustomer j 0, otherwise min f 1 = i D j C c ij x ij + i D fiy i max f 2 = dj j C i Qj x ij j C d j 80 subject to, i D j C x ij dix = 1, j C ij uiyi, i D (1) (2) where, Q j = { i D: h ij D max } for all j

81 Representation Binary representation (m) BOGAP <Greedy> ExchangeBinaryMutation UniformBinaryCrossover POPSIZE: 100 MAXGEN: 200 CROSSRATE: 0.8 MUTRATE:

82 Results Instance 1 (n=100, m=20) Población Final Solución de máxima cobertura S ' = S( PF) S( x*) 82 Dominated space metric (Zitzler & Thiele,1998)

83 Other (computational) resources at COPA Modeling languages AMPL (Dept. of Mathematics) GAMS Mosel (Dash Optimization) OPL (ILOG) Lingo Solvers CPLEX Xpress-MP SAS/OR Developer tools CVS UML: Visual Paradigm, Rational Rose Eclipse (open source IDE) Native compiler: JET/Excelsior Installer: install4j 83

84 Concluding Remarks Rapid application development and fast prototyping easy to embed in an application Flexible and extensible framework Allows single and multi-objective optimization Java inherited advantages portability existing libraries Eclipse IDE (and other open source development) Good performance 84

85 Contact info Andrés s Medaglia, Ph.D. url: Eliécer Gutiérrez, M.Sc.,., M.E. Centro para la Optimización n y Probabilidad Aplicada - COPA ://copa.uniandes.edu.co Departamento de Ingeniería a Industrial Universidad de los Andes 85

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