The Application of an Improved Genetic Algorithm to the Initial Wavelength Calibration

In the initial wavelength calibration for the processing of two-dimensional spectral data from the LAMOST and SDSS, searches are usually performed to find the optimum coefficients to fit the dispersion relation.These are achieved by giving a set of initial coefficient values, and then searching the optimum solution in the proximity of the multidimensional space of the relevant coefficients.The calibration is actually a global optimization problem.The method now used for the LAMOST and SDSS is the enumerative search.Since such a method lacks the prior information of optimum solution, the search checks the entire space of coefficients and spends a large amount of time to pin down the global optimum solution.As a genetic algorithm uses the heuristic search, it is efficient in global optimization and is being increasingly applied in different research areas.Under the framework of a standard genetic algorithm, which is very simple, there are usually some practical disadvantages of premature convergence-the algorithm does not converge to the global optimum solution but to a local optimum solution.To overcome the problems, we design an improved genetic algorithm with suitable coding, fitness functions, and genetic operators.We apply the algorithm to the initial wavelength calibration.Specifically, the float-point coding is used to encode the individual genes, which is more exact for the solution than the binary coding.The genetic operators consist of fitness-proportional reproduction, elitist selection, heuristic crossover operator, mutation operator, and cataclysm operator, all of which are originally introduced for the research of biological evolution.We use Shaffer's F6 function to test the convergence of the improved genetic algorithm by letting the algorithm search the global maximum of the function.It is shown that the improved algorithm can converge to the global optimum solution via enough searches.Subsequently, the improved algorithm is applied to the simulated initial wavelength calibration for the LAMOST.The simulation results show the efficiency and effectiveness of the improved algorithm.According to the convergence of the improved genetic algorithm, the number of evolution generations can be chosen to be small to reach the global optimum solution.In other words, an approximate optimum solution can be derived with a small computational time, which is reasonable in practical applications.