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By Ascheuer N., Junger M., Reinelt G.

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Extra resources for A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints

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6 Populations Fig. 3 Representation of a gene 41 1 0 1 0 1 1 1 0 1 1 1 1 Gene 1 Gene 2 Gene 3 0 1 0 1 Gene 4 into the number of intervals that can be expressed by the gene’s bit string. A bit string of length ‘n’ can represent (2n -1) intervals. The size of the interval would be (range)/(2n-1). The structure of each gene is defined in a record of phenotyping parameters. The phenotype parameters are instructions for mapping between genotype and phenotype. It can also be said as encoding a solution set into a chromosome and decoding a chromosome to a solution set.

The actual mapping depends upon the decoding scheme used. The objective function values can be scalar or vectorial and are necessarily the same as the fitness values. Fitness values are derived from the object function using scaling or ranking function and can be stored as vectors. 8 Search Strategies The search process consists of initializing the population and then breeding new individuals until the termination condition is met. There can be several goals for the search process, one of which is to find the global optima.

2 Genetic Algorithms World Genetic Algorithm raises a couple of important features. First it is a stochastic algorithm; randomness as an essential role in genetic algorithms. Both selection and reproduction needs random procedures. A second very important point is that genetic algorithms always consider a population of solutions. Keeping in memory more than a single solution at each iteration offers a lot of advantages. The algorithm can recombine different solutions to get better ones and so, it can use the benefits of assortment.

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A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints by Ascheuer N., Junger M., Reinelt G.

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