Evolutionary Computation versus Classical Optimization in .NET

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88 Evolutionary Computation versus Classical Optimization
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Evolutionary Computation versus Classical Optimization
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While classical optimization algorithms have been shown to be very successful (and more e cient than EAs) in linear, quadratic, strongly convex, unimodal and other specialized problems, EAs have been shown to be more e cient for discontinuous, non-di erentiable, multimodal and noisy problems EC and classical optimization (CO) di er mainly in the search process and information about the search space used to guide the search process: The search process: CO uses deterministic rules to move from one point in the search space to the next point EC, on the other hand, uses probabilistic transition rules Also, EC applies a parallel search of the search space, while CO uses a sequential search An EA search starts from a diverse set of initial points, which allows parallel search of a large area of the search space CO starts from one point, successively adjusting this point to move toward the optimum Search surface information: CO uses derivative information, usually rstorder or second-order, of the search space to guide the path to the optimum EC, on the other hand, uses no derivative information The tness values of individuals are used to guide the search
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Assignments
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1 Discuss the importance of the tness function in EC 2 Discuss the di erence between genetic and phenotypic evolution 3 In the case of a small population size, how can we ensure that a large part of the search space is covered 4 How can premature convergence be prevented 5 In what situations will a high mutation rate be of advantage 6 Is the following statement valid A genetic algorithm is assumed to have converged to a local or global solution when the ratio f /fmax is close to 1, where fmax and f are the maximum and average fitness of the evolving population respectively 7 How can an EA be used to train a NN In answering this question, focus on (a) the representation scheme, and (b) tness function 8 Show how an EA can be used to solve systems of equations, by illustrating how (a) solutions are represented, and (b) the tness is calculated What problem can be identi ed in using an EA to solve systems of equations 9 How can the e ect of a high selective pressure be countered
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8 Introduction to Evolutionary Computation
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10 Under which condition will stochastic universal sampling behave like tournament selection 11 Identify disadvantages of tness-based selection operators 12 For the nonlinear ranking methods given in equations (812) and (813), indicate if these assume a minimization or maximization problem 13 Critisize the following stopping condition: Stop execution of the EA when there is no signi cant change in the average tness of the population over a number of consecutive generations
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Genetic Algorithms
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Genetic algorithms (GA) are possibly the rst algorithmic models developed to simulate genetic systems First proposed by Fraser [288, 289], and later by Bremermann [86] and Reed et al [711], it was the extensive work done by Holland [376] that popularized GAs It is then also due to his work that Holland is generally considered the father of GAs GAs model genetic evolution, where the characteristics of individuals are expressed using genotypes The main driving operators of a GA is selection (to model survival of the ttest) and recombination through application of a crossover operator (to model reproduction) This section discusses in detail GAs and their evolution operators, organized as follows: Section 91 reviews the canonical GA as proposed by Holland Crossover operators for binary and oating-point representations are discussed in Section 92 Mutation operators are covered in Section 93 GA control parameters are discussed in Section 94 Di erent GA implementations are reviewed in Section 95, while advanced topics are considered in Section 96 A summary of GA applications is given in Section 97
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