Tournament selection

Selection From the ranked population, create a parent pool of candidate solutions with high fitness scores using selection methods such as Roulette-wheel selection , tournament selection , elitist mutation , etc. 

Tournament selection This selection type chooses two or more chromosomes to compete with one another. The best chromosome is determined and selected. 

Several alternative methods of selection exist in this example, we shall use Binary Tournament Selection. Later we shall encounter other methods. Two... 

The selection of strings for the tournament is random, thus the results may vary each time the process is performed on a given starting population. This unpredictable selection of strings is the second time that random numbers have been used in the algorithm (the first was in the construction of the strings in the initial population) and random numbers will return shortly. It may seem surprising that random numbers are needed when the problem to be solved has a definite (albeit, still unknown) solution, but their use is a common feature in AI methods and, in fact, is fundamental to the operation of several of them. 

Strings Chosen by Binary Tournament Selection to Participate in the First Parent Pool... 

A weakness of both roulette wheel selection and tournament selection is that although both are biased in favor of fitter strings as the algorithm requires, neither guarantees that the best string in one generation will be chosen as a parent for the next. 

The ball might never fall into the widest slot in the roulette wheel. In fact, it is possible, though unlikely, that the roulette wheel will select only the poorest strings from a population to act as parents. Tournament selection cannot select the worst string, but it is only able to choose the best string from among... 

After a number of new solutions are produced by crossover (or more generally, recombination) and mutation operations, improved solutions must be incorporated into the population. The best solution found thus far is almost always retained. A common strategy replaces a certain fraction of the remaining individuals, either with improved offspring or with new individuals chosen to maintain diversity. Another strategy is tournament selection, in which new solutions and current population members compete in a tournament. Each solution competes with K other solutions, which may be randomly selected, and, in each pairwise comparison, the solution with best fitness value wins. If P is the population size, the P solutions with the most wins become the new population. 

Further procedures, such as tournament selection (in which pairs of parent strings are chosen at random and the string of higher fitness is copied into the child population), are also widely used and are discussed in standard texts on the subject. 

As a population of solutions now exists, two variations are opened up which we can use to select members of the next population. In both methods, the members of the child population are chosen deterministically, in other words, through a type of tournament selection in which the better of two solutions always wins. 

D. E. Goldberg, A note on Boltzmann tournament selection for genetic algorithms and population-oriented simulated annealing. Complex Systems, 4 (1990) 445. 

Now that we know how to compare chromosomes in P, we start to copy them in a gene pool (box P", having Np locations). We use the tournament selection procedure. We take any two members from P randomly, and make a copy of the better of these two chromosomes into P". We then put both the chromosomes back into P. This is repeated till P" has Np members. Crossover and mutation are now carried out on the chromosomes in P", as in SGA, finally giving Np daughters in box D. These are then copied in box D for further processing. 

The procedure for selection of parents is the same as that of NSGA-II. Binary tournament is used to select a parent from two individuals. Binary tournament between two candidate solutions x and x is performed as follows ... 

Four solutions are chosen at random from the population. Prom the first two solutions, parent 1 is selected and from the last two individuals, parent 2 is selected using binary tournament. To ensure that all the solutions in the population take part in the selection process, a shuffled list of IDs (1 to M) is created and individuals are picked up 4 at a time from this list. 

In this step, a selection method is used in order to fill the mating pool, P(t-tl)). A variety of selection methods can be used in EAs. Two classical selection schemes are the roulette wheel selection and the tournament selection. In the first scheme, chromosomes are chosen according to a given probability, which is a function of their fitness . In the second scheme, a number of chromosomes are randomly chosen from the previous generation. 

In our MOEA methodology, we use a combination of roulette wheel and tournament selection approaches according to ... 

Harik GR. Finding multimodal solutions using restricted tournament selection. In Eshelman LJ, ed. Proceedings of the Sixth International Conference on Genetic Algorithms. San Francisco, CA, USA Morgan Kaufmann Publishers, Inc., 1995 24-31. 

A third scheme is called tournament selection. Here, pairs of individuals are selected from the population, and the better of the two enters the breeding pool, whereas the poorer does not. For the SGA, this offers little advantage over roulette wheel selection, but it does allow the population to be replaced incrementally in a clean manner, as discussed next. 

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