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98 Assignments with ab =
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represent the objective to select routes with minimum congestion, where Bab denotes the blocking probability on the link between switches a and b, fUtil (xi ) = min {1 Uab } + ab
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maximizes utilization, where Uab quanti es the level of utilization of the link between a and b, and
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ensures that minimum cost routes are selected, where Cab represents the nancial cost of carrying a call on the link between a and b The constants 1 to 4 control the in uence of each criterion 4 Use any selection operator 5 Use any crossover operator 6 Mutation: Mutation consists of replacing selected genes with a uniformly random selected switch in the range [1, nx ] This example is an illustration of a GA that uses a numeric representation, and variable length chromosomes with constraints placed on the structure of the initial individuals
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Assignments
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1 Discuss the importance of the crossover rate, by considering the e ect of di erent values in the range [0,1] 2 Compare the following replacement strategies for crossover operators that produce only one o spring: (a) The o spring always replaces the worst parent (b) The o spring replaces the worst parent only when its tness is better than the worst parent (c) The o spring always replaces the worst individual in the population (d) Boltzmann selection is used to decide if the o spring should replace the worst parent 3 Show how the heuristic crossover operator incorporates search direction 4 Propose a multiparent version of the geometrical crossover operator 5 Propose a marker initialization and update strategy for gene scanning applied to order-based representations 6 Propose a random mutation operator for discrete-valued decision variables 7 Show how a GA can be used to train a FFNN
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9 Genetic Algorithms
8 In the context of GAs, when is a high mutation rate an advantage 9 Is the following strategy sensible Explain your answer Start evolution with a large mutation rate, and decrease the mutation rate with an increase in generation number 10 Discuss how a GA can be used to cluster data 11 For oating-point representations, devise a deterministic schedule to dynamically adjust mutational step sizes Discuss the merits of your proposal 12 Suggest ways in which the competitive template can be initialized for messy GAs 13 Discuss the consequences of migrating the best individuals before islands have converged 14 Discuss the in uence that the size of the comparison set has on the performance of the niched Pareto GA
10
Genetic Programming
Genetic programming (GP) is viewed by many researchers as a specialization of genetic algorithms Similar to GAs, GP concentrates on the evolution of genotypes The main di erence between the two paradigms is in the representation scheme used Where GAs use string (or vector) representations, GP uses a tree representation Originally, GP was developed by Koza [478, 479] to evolve computer programs For each generation, each evolved program (individual) is executed to measure its performance within the problem domain The result obtained from the evolved computer program is then used to quantify the tness of that program This chapter provides a very compact overview of basic GP implementations to solve speci c problems More detail about GP can be found in the books by Koza [482, 483] The chapter is organized as follows: The tree-based representation scheme is discussed in Section 101 Section 102 discusses initialization of the GP population, and the tness function is covered in Section 103 Crossover and mutation operators are described in Sections 104 and 105 A building-block approach to GP is reviewed in Section 106 A summary of GP applications is given in Section 107