convergence time of GA procedures is very important to be pre-calculated or estimated to know for how long your procedure will run to get results. this time is based on the complexity of the algorithm that solves the cognitive function model equations also it depends on the processing speed. So, I need to calculate it in terms of the number of cycles multiplied by the cycle running time.
Equation 1 in the following paper (attached file ) gives the time to convergence for a genetic algorithm on a flat function and is therefore an upper bound for any static function.
Louis, S. J., & Rawlins, G. J. (1993). Predicting convergence time for genetic algorithms. Foundations of Genetic Algorithms, 2, 141-161.
Convergence time depends on many variables:
1) complexity of fitness function. How much does it to calculate the objective function. for example in nonlinear Finite element analysis, we are dealing with expensive objective functions.
2). GA parameters ( Population size, mutation rate, ...)
3) Landscape of objective function (number of local minimums, basin of attractions,.?
4) Number of design variables
5) number and type of constraints.
For a particular problem, GA parameters can be selected by trial error or experimental design methods (taguchi, ...) So that the number of function evaluations (NFEs) is minimized.
Dear Yasser E Abueldahab
There is no mathematical equation which can describe time complexity of genetic algorithm. It depends on many factor as discussed above by Behrouz Ahmadi-Nedushan. IT is also dependent of the objective function used, constraints, number of variables etc.
Dear Yasser, computation time of any optimization algorithm purely depends on population size, dimension of the problem, number of iterations, type of objective function, type of constraints etc.
Equation 1 in the following paper (attached file ) gives the time to convergence for a genetic algorithm on a flat function and is therefore an upper bound for any static function.
Louis, S. J., & Rawlins, G. J. (1993). Predicting convergence time for genetic algorithms. Foundations of Genetic Algorithms, 2, 141-161.
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