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Introduction

8th IMACS Seminar on Monte Carlo Methods August 29–September 2, 2011, Borovets, Bulgaria. Introduction. Generalized Nets, Ant Colony Optimization Algorithms and Genetic Algorithms Vassia Atanassova Stefka Fidanova Ivan Popchev Panagiotis Chountas. Metaheuristics:

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Introduction

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  1. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Generalized Nets,Ant Colony Optimization Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to deliver satisfactory solutions to large and complex problems in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization

  2. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Generalized Nets Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to deliver satisfactory solutions to large and complex problems in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time

  3. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time

  4. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem

  5. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions

  6. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN models of ACO Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • ACO search procedure – in terms of GNs • A GN was constructed, describing the ACO algorithm. • On this basis, the opportunity arose for modification and improvement of the ACO algorithm. • GN models realizing the new modified versions of ACO were built. • The test samples proved that these modifications, resulting from the application of GNs, yield better results according to time.

  7. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN models of ACO GN for hybrid ACO/GA Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • ACO search procedure – in terms of GNs • A GN was constructed, describing the ACO algorithm. • On this basis, the opportunity arose for modification and improvement of the ACO algorithm. • GN models realizing the new modified versions of ACO were built. • The test samples proved that these modifications, resulting from the application of GNs, yield better results according to time. • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved.

  8. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in Gproc. • Both GACO and GGA have one input and one output places:

  9. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in Gproc. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P.

  10. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Constructing the GN model Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in GPROC. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P. • The -tokens from places l2 or l5 enter place iACO without a new characteristic. It transfers through GN GACO and going out of it (through place oACO) obtains the characteristic • “current solutions of ACO-algorithm”.

  11. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in GPROC. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P. • The -tokens from places l2 or l5 enter place iACO without a new characteristic. It transfers through GN GACO and going out of it (through place oACO) obtains the characteristic • “current solutions of ACO-algorithm”. • whereWACO,4 = “The end-condition is satisfied”,WACO,5 = ¬WACO,5 • When the truth-value of WACO,4 is “true”, token  enters place l4 with the characteristic“representation of the current solutions (populations) in appropriate form of the GA”. • Otherwise, it enters place l5 without a new characteristic.

  12. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in GPROC. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P. • The -tokens from places l2 or l5 enter place iACO without a new characteristic. It transfers through GN GACO and going out of it (through place oACO) obtains the characteristic • “current solutions of ACO-algorithm (population generations)”. • whereWACO,4 = “The end-condition is satisfied”,WACO,5 = ¬WACO,5 • When the truth-value of WACO,4 is “true”, token  enters place l4 with the characteristic“representation of the current solutions (populations) in appropriate form of the GA”. • Otherwise, it enters place l5 without a new characteristic. • Token from place l4 enters place iGA with the characteristic • “current population (solutions) of the GA”.

  13. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Thank youfor your attention! Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas Acknowledgment to Grants DID-02-29 “Modeling Processes with Fixed Development Rules” and DTK-02-44 “Effective Monte Carlo Methods for Large-Scale Scientific Problems” by National Science Fund of Bulgaria, and Grant JP 100372 by Royal Society, UK Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in GPROC. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P. • The -tokens from places l2 or l5 enter place iACO without a new characteristic. It transfers through GN GACO and going out of it (through place oACO) obtains the characteristic • “current solutions of ACO-algorithm (population generations)”. • whereWACO,4 = “The end-condition is satisfied”,WACO,5 = ¬WACO,5 • When the truth-value of WACO,4 is “true”, token  enters place l4 with the characteristic“representation of the current solutions (populations) in appropriate form of the GA”. • Otherwise, it enters place l5 without a new characteristic. • Token from place l4 enters place iGA with the characteristic • “current population (solutions) of the GA”.

  14. 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria 8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria Introduction Genetic Algorithms Generalized Nets GN models of GAs Ant Colony Optimization GN for hybrid ACO/GA Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Constructing the GN model Thank youfor your attention! Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas Acknowledgment to Grants DID-02-29 “Modeling Processes with Fixed Development Rules” and DTK-02-44 “Effective Monte Carlo Methods for Large-Scale Scientific Problems” by National Science Fund of Bulgaria, and Grant JP 100372 by Royal Society, UK Generalized Nets,ACO Algorithmsand Genetic Algorithms Vassia AtanassovaStefka FidanovaIvan PopchevPanagiotis Chountas • Metaheuristics: • increasingly popular in research and industry • mimic natural metaphors to solve complex optimization problems • efficient and effective to solve large and complex problems • allow to tackle large-size problems by delivering satisfactory solutions in a reasonable time • some of the most successful metaheuristics: • Genetic Algorithms • Ant Colony Optimization • Parallel global search technique that emulates natural genetic operators • GAs are stochastic search methods for exploring complex problem space in order to find optimal solutions using minimal information • Population of individuals (tentative solutions) • Fitness function (individual’s suitability to problem) • Operators: selection, crossover and mutation • Stop criterion (# iterations, finding of individual) • Convergence towards a global solution • No problem-specific info required in GAs, hence they’re more flexible and adaptable • Extension of Petri Nets and their modifications • Apparatus for description of parallel processes • Static structure: • Transitions • Places • Dynamic structure: • Tokens • Predicate index matrices • Memory • Time • 1. GA search procedure - in terms of GNs • The GN model simultaneously evaluates several fitness functions, ranks the individuals per their FF and chooses the best FF regarding the problem • 2. Selection and tuning of GA operators • The GN model has the possibility to test different groups of the defined genetic algorithm operators and choose the mostappropriate combination among them. • The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitnessfunction, regarding to the considered problem • ACO is a new metaheuristic method inspired by the social behaviour of ants in nature. • It finds good solutions for optimization problems with restrictive constraints • Low level interaction between single agents results in a complex behaviour of the whole ant colony • Shortest path from food source to formicary • Communication via pheromone (distributed numerical information), which ants use to probabilistically construct solutions • Usually metaheuristics are combined with local search procedureor an exact method. Our idea is to combine two metaheuristics. • The GA starts with population whichis closer to optimal solution. Sometimes after a number of iterations the GA goes to stagnation, the population stop to be improved. • Next, the GA solutions are provided as input for the ACO algorithm and the pheromone isupdated accordingly. • ACO with updated pheromone is run and thus a new population for GA is generated • Any ACO / GA version can be used, depending on the problem solved. • We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GAalgorithm. The problem is coded in GPROC. • Both GACO and GGA have one input and one output places: • Let tokenof GN Gproc enter place l1 of the GN with initial characteristic“current problem description(graph of the problem, problem constraints, etc.” • whereWGA,2 = “a next iteration is necessary”,WGA,3 = ¬WGA,2,where ¬P is the negation of predicate P. • The -tokens from places l2 or l5 enter place iACO without a new characteristic. It transfers through GN GACO and going out of it (through place oACO) obtains the characteristic • “current solutions of ACO-algorithm (population generations)”. • whereWACO,4 = “The end-condition is satisfied”,WACO,5 = ¬WACO,5 • When the truth-value of WACO,4 is “true”, token  enters place l4 with the characteristic“representation of the current solutions (populations) in appropriate form of the GA”. • Otherwise, it enters place l5 without a new characteristic. • Token from place l4 enters place iGA with the characteristic • “current population (solutions) of the GA”.

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