Mahfoud, S. W . 1995b. Population size and genetic drift in fitness sharing. In Foundations of genetic algorithms, vol. 3, eds. L. D. Whitley and M. D. Vose, 185223. San Francisco, Calif.: Morgan Kaufmann.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of population size is essential in Genetic Algorithms; a small population may result in local convergence, while larger ones will result in slow convergence. To chose the suitable population size, several trial case studies are needed, and there are rules regarding proper choice of population size [17], 18] In some cases, local optimal solutions are also of interest in system planning and control besides the global one. In such cases, a Genetic Algorithm with sharing function method can be employed to locate both the global and the local optima [11] 17] 19] 20] III. Objective ....

....proper choice of population size [17] 18] In some cases, local optimal solutions are also of interest in system planning and control besides the global one. In such cases, a Genetic Algorithm with sharing function method can be employed to locate both the global and the local optima [11] [17], 19] 20] III. Objective Functions for VAR Planning The VAR optimal planning problem is aimed at improving the system performance, and enhancing voltage profile as well as reducing the system operational cost. To achieve the best performance under the minimum costs, the objective function ....

S. W. Mahfoud, "Population Size and Genetic Drift in Fitness Sharing", L. D. Whitile and M. D. Vose edt. Foundations of Genetic Algorithms ffl 3, Morgan Kaufmann Publishing, Inc. 1995, pp. 185--223.

....of population size is essential in Genetic Algorithms; a small population may result in local convergence, while larger ones will result in slow convergence. To chose the suitable population size, several trial case studies are needed, and there are rules regarding proper choice of population size [4, 9, 10]. In our simulation, the population size in the range from 100 to 600 was selected. It has been discovered that this population size is sufficient to locate the global solution for the problem. 11 5 An Illustrative Example In this section, we will use the GAs to solve the minimum order predictor ....

S. W. Mahfoud, "Population size and genetic drift in fitness sharing", L. D. Whitile and M. D. Vose edt. Foundations of Genetic Algorithms ffl 3, Morgan Kaufmann Publishing, Inc. 1995, pp. 185--223.

....and all individuals j in generation, see Eqn. 16) The similarity of individuals is evaluated by the distance, d(i; j) from each other, see Eqn. 15) The resulting shared fitness Phi 0 is changed through dividing the original fitness Phi by the corresponding niche count, see Eqn. 17) 21] [23]. d(i; j) d(x i ; x j ) 15) m 0 (i) n X j=1 sh[d(i; j) 16) Phi 0 (i) Phi(i) P n j=1 sh[d(i; j) 17) The sharing function is defined so that it fulfills, sh(d) 8 : 0 sh(d) 1 sh(0) 1 lim d 1 sh(d) 0 (18) For example the sharing function can have the form, sh(d) ....

....to ensure GA to locate the multiple maxima of the fitness function, and to avoid the noise induced by genetic draft, sufficient population size should be considered. However, too large population size will result in slow convergence. Techniques for choosing the population size can be found in [23]. In our test systems, the population size in the range from 30 to 160 was selected. It has been discovered that this population size is sufficient to locate the maxima in the space of power system variables. 3.3. Fitness Function Formulation The fitness function plays an important role in ....

[Article contains additional citation context not shown here]

S. W. Mahfoud, "Population size and genetic drift in fitness sharing", L. D. Whitile and M. D. Vose edt. Foundations of Genetic Algorithms ffl 3, Morgan Kaufmann Publishing, Inc. 1995, pp. 185-- 223.

....will be derived here assuming that fitness proportional selection is used. The result should be comparable under tournament selection, but the analysis is more difficult. A similar, far more extensive analysis has been done for fixed fitness functions with conventional fitness sharing [61]. First, assume that competitive fitness sharing is being used. The total fitness received by the host population is O, since each defeatable parasite contributes a total of 1 fitness to the host population, divided evenly among those hosts able to defeat it. So, a host with fitness f has ....

S.W. Mahfoud. Population size and genetic drift in fitness sharing. In L.D. Whitley and M.D. Vose, editors, Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1995.

....and all individuals j in generation, see Eqn. 10) The similarity of individuals is evaluated by the distance, d(i; j) from each other, see Eqn. 9) The resulting shared fitness Phi 0 is changed through dividing the original fitness, Phi by the corresponding niche count, see Eqn. 11) 20] [22]. d(i; j) d(x i ; x j ) 9) m 0 (i) n X j=1 sh[d(i; j) 10) Phi 0 (i) Phi(i) P n j=1 sh[d(i; j) 11) The sharing function is defined so that it fulfills, sh(d) 8 : 0 sh(d) 1 sh(0) 0 lim d 1 sh(d) 0 (12) For example the sharing function can have the form, sh(d) ....

....to ensure GA to locate the multiple maxima of the fitness function, and to avoid the noise induced by genetic draft, sufficient population size should be considered. However, too large population size will result in slow convergence. Techniques for choosing the population size can be found in [22]. In our test systems, the population size in the range from 30 to 160 was selected. It has been discovered that this population size is sufficient to locate the maxima in the space of power system variables. 5 The Optimum Operation Direction By using the methods addressed here, it is possible to ....

S. W. Mahfoud, "Population Size and Genetic Drift in Fitness Sharing", L. D. Whitile and M. D. Vose edt. Foundations of Genetic Algorithms ffl 3, Morgan Kaufmann Publishing, Inc. 1995, pp. 185-- 223.

....it. Probabilities will be derived here assuming that roulette wheel selection is used. The result should be comparable under tournament selection, but the analysis is more difficult. A similar, far more extensive analysis has been done for fixed fitness functions with conventional fitness sharing (Mahfoud, 1995). First, assume that competitive fitness sharing is being used. The total fitness received by the host population is O, since each defeatable parasite contributes a total of 1 fitness to the host population, divided evenly among those hosts able to defeat it. So, a host with fitness f has ....

Mahfoud, S.W. (1995) Population size and genetic drift in fitness sharing. Foundations of Genetic Algorithms 3. Morgan Kaufmann.

....be something of a waste of effort, especially in the Lamarckian case, as we would have two copies of the same local optimum in the population. There are several possible ways to select a diverse set from the population. This is very similar to the diversity enforcement [60, 59] and fitness sharing [28, 61, 77] schemes which are often used for reproductive selection in EA practice. This case is 46 different, however, in that we are selecting a small subset of the population (without replacement) In contrast, selection for reproduction typically chooses a set as large as or larger than the population, ....

S.W. Mahfoud. Population size and genetic drift in fitness sharing. In L.D. Whitley and M.D. Vose, editors, Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1995.

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Mahfoud, S. W . 1995b. Population size and genetic drift in fitness sharing. In Foundations of genetic algorithms, vol. 3, eds. L. D. Whitley and M. D. Vose, 185223. San Francisco, Calif.: Morgan Kaufmann.

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Mahfoud, S. W. (in press). Population size and genetic drift in fitness sharing. In L. D. Whitley (Ed.), FOGA, 3. Morgan Kaufmann. Muhlenbein, H. (1991). Evolution in time and space --- The parallel genetic algorithm. In G. J. E. Rawlins (Ed.), FOGA (pp. 316--337). Morgan Kaufmann.

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