General information Theoretic basis of evolutionary computing. The general scheme of evolutionary algorithms General information Theoretic basis of evolutionary computing. The general scheme of evolutionary algorithms (EA)

GENERAL INFORMATON  Title : Evolutionary computing and genetic algorithms  Course holder : Cătălina-Lucia Cocianu, Professor, PhD.  Activities:  lecture: Tuesday 9:00-10:20  seminaries: Wednesday 12:30-13:20 (1052)  Thursday15:00-16:20 (1053)  Thursday 16:30-17:50 (1054)  other activities  2301, Tuesday 13:30-15:00  address : o  Prerequisites  Computer programming fundamentals. Algorithms and programming techniques  Probabilities and statistics  Computer fundamentals

 References  Manual  C. Cocianu, C. Uscatu, Programare evolutivă i algoritmi genetici, Editura ASE Bucureti, 2015  Other recommended monographies  Eiben, A. E., Smith, J. E., Introduction to Evolutionary Computing, Springer-Verlag, 2003  Fulcher, J., Jain, L. C. (Eds.), Computational Intelligence: A Compendium,Springer-Verlag, 2008  Engelbrecht, A.P., Computational Intelligence. An Introduction, John Wiley & Sons, 2007  Evaluation  Seminary 50%  Practical test 20%  Project30%  Written exam 50%  online.ase.ro – use intranet ASE online.ase.ro  Course description, lecture presentations, other helpful notes

 Curricula:  Evolutionary algorithms (EA)  General scheme; examples  Classification  EA’s components  Direct search – stochastic search evolution  Genetic algorithms (GA)  Chromosome representation, population models  Fitness function  Variation operators  Mutation  Recombination (crossover)  Selection operators  GAs for solving problems in economics  Job shop scheduling  Portfolio optimization problems

I. EVOLUTIONARY COMPUTING (EC). BIOLOGIC SUPPORT OF EC  The evolutionary computing (EC) – computer science research area inspired by the process of natural evolution ; the core of this area is given by the trial and error-like problem solving technique  Being given an environment that supports a certain population of individuals and the basic reproduction instinct, the natural selection process advantages the most competitive members from both resources acquiring and environment adaptability points of view– survival of the fittest.  The fitness of individuals represents their chances of survival and producing offspring (multiplying)  During the reproduction process, some of the offspring suffer occasional mutations

 Intuitively, the process is similar to an adaptive 3D landscape, in the sense that an individual represented by p(x,y,z) is such that  the values of p in OXY plane correspond to its characteristics  the value of p on OZ axis represents the fitness of p.  The evolution – the population accession toward higher zones based on mutation, crossover and natural selection processes respectively → the connection to multimodal problems (local optimum points). High altitude stands for high fitness.

 The link between natural evolution and problem solving is represented in the following table EVOLUTION (genetic approach) PROBLEM SOLVING (standard, real-world approach) ENVIRONMENTPROBLEM INDIVIDUAL (GENOTYPE, CHROMOSOME, CANDIDATE SOLUTION) CANDIDATE SOLUTION (PHENOTYPE) FITNESSQUALITY (OPTIMUM)

II.THE CLASSES OF PROBLEMS SOLVED USING EC  Optimization problems: being given the model and outputs compute the inputs. Examples:  Travel salesman problem (TSP);  Job shop scheduling;  N queens problem.  Simulation problems: if the model and the input data are known, compute the corresponding output data. Example: what-if questions in evolving populations, where the evolution is assured by the variation and the selection operators respectively  System identification problems (modelling): being given the inputs and their corresponding outputs determine the model such that each pair (input, output) is correctly identified. Example: two-classes supervised classification problem

III. EA’S GENERAL COMPUTATION SCHEME

THE GENERIC EA

EA CLASSIFICATON  GENETIC ALGORITHMS (GAs) – THE MOST COMMONLY USED EVOLUTIONARY ALGORITHMS  EVOLUTIONARY STRATEGIES  EVOLUTIONARY PROGRAMMING  GENETIC PROGRAMING

IV. EXAMPLE - Solving an one dimensional optimization problem using EA

Example

Example – the variation of the population average fitness along 75 generations

Example – population distribution for dim=104, pc=0.5, pm=0.1, and no more than 100 generaions