![]() ![]() Initially, solutions are randomly generated to form an initial population. Usually it returns the cost of the candidate solution, and thus it is referred to as the cost function (to be minimized). This objective function is determined by the user. ![]() The fitness of each chromosome is determined by the corresponding objective function value. The PermGA so uses permutations of integers, namely from 1 to D, where D is the number of design variables. Repeat steps (2–5) until some condition is satisfied.Copy the best (elite) individual to the new population.Perform crossover and mutation to form a new population.Select individuals to form a new population according to each one’s fitness.Calculate the fitness of each individual in the population.Initialize randomly the population of individuals (chromosomes).The PermGA algorithm can be described by the following pseudo-code: Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the elite (best) member of the population. The new population is then used in the next iteration of the algorithm. Their genetic material is recombined, and possibly randomly mutated, to produce offspring and form a new population. Next, multiple individuals are stochastically selected from the current population (according to their fitness) to become parents. This is a measure of the quality of the solution, and it is depended on the objective function value corresponding to the solution. In each generation, the fitness of every individual in the population is evaluated. The evolution starts from a population of randomly generated individuals. A population of candidate solutions is evolved, generation by generation, using techniques inspired by natural evolution such as selection, mutation and crossover. The algorithm mimics the process of natural selection. There are two sub-cases of problems the first includes problems in which the absolute order is important (such as the Job Shop Scheduling problem) while in the second only adjacency is important (a typical example is the Traveling Salesman Problem - TSP). The permutation problems naturally take the form of deciding on the order in which a sequence of events should occur for these problems, a natural representation is a permutation of a set of integers. These are included in a solver named PermGA. XlOptimizer implements many variants of Genetic Algorithms for permutation problems. ![]()
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