introduction metaheuristics: increasingly popular in research and industry mimic natural metaphors...

IntroductionIntroduction

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

Generalized Nets,Generalized Nets,Ant Colony Optimization Ant Colony Optimization

AlgorithmsAlgorithmsand Genetic Algorithmsand Genetic Algorithms

Vassia AtanassovaVassia AtanassovaStefka FidanovaStefka Fidanova

Ivan PopchevIvan PopchevPanagiotis ChountasPanagiotis Chountas

8th IMACS Seminar on Monte Carlo MethodsAugust 29–September 2, 2011, Borovets, Bulgaria

•Extension of Petri Nets and their modifications

•Apparatus for descriptionof parallel processes

•Static structure:–Transitions–Places

•Dynamic structure:–Tokens–Predicate index matrices

•Memory•Time

Generalized NetsGeneralized NetsIntroductionIntroduction


optimization problems • efficient and effective to deliver satisfactory

solutions to large and complex problems in a reasonable time


Generalized Nets,Generalized Nets,ACO AlgorithmsACO Algorithms

and Genetic Algorithmsand Genetic Algorithms




http://ifigenia.org/wiki/Image:GN-transition-mxn.png

•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

Genetic AlgorithmsGenetic Algorithms





•Memory•Time



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








•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 most appropriate combination among them.

– The developed GN executes a genetic algorithm and implements tuning of the genetic operators, as well as the fitness function, regarding to the considered problem

GN models of GAsGN models of GAs





•Operators: selection, crossover and mutation

•Stop criterion (# iterations, finding of individual)

•Convergence towards a global solution






•Memory•Time













• 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

Ant Colony OptimizationAnt Colony Optimization











•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






•Memory•Time













• 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.

GN models of ACOGN models of ACO

























•Memory•Time













• Usually metaheuristics are combined with local search procedure or an exact method. Our idea is to combine two metaheuristics.

– The GA starts with population which is 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.

GN for hybrid ACO/GAGN for hybrid ACO/GA

• 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.

GN models of ACOGN models of ACO

























•Memory•Time













• We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GA algorithm. The problem is coded in Gproc.

• Both GACO and GGA have one input and one output places:

Constructing the GN model Constructing the GN model































•Memory•Time













• 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.


• We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GA algorithm. The problem is coded in Gproc.

































•Memory•Time













• 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”.





• We describe ACO and GA with GNs (GACO and GGA, respectively) and using them we prepare a GN describing the hybrid ACO/GA algorithm. The problem is coded in GPROC.

































•Memory•Time













• 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.



“current solutions of ACO-algorithm”.






































•Memory•Time












• Token from place l4 enters place iGA with the characteristic

“current population (solutions) of the GA”.







“current solutions of ACO-algorithm (population generations)”.






































•Memory•Time












Thank youThank youfor your attention!for your attention!



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


• Token from place l4 enters place iGA with the characteristic

“current population (solutions) of the GA”.







“current solutions of ACO-algorithm (population generations)”.






































•Memory•Time












introduction metaheuristics: increasingly popular in research and industry mimic natural metaphors...

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