Chaos gray-coded genetic algorithm and its application for pollution source identifications in convection–diffusion equation

In order to reduce the computational amount and improve computational precision for nonlinear optimizations and pollution source identification in convection–diffusion equation, a new algorithm, chaos gray-coded genetic algorithm (CGGA) is proposed, in which initial population are generated by chaos mapping, and new chaos mutation and Hooke–Jeeves evolution operation are used. With the shrinking of searching range, CGGA gradually directs to an optimal result with the excellent individuals obtained by gray-coded genetic algorithm. Its convergence is analyzed. It is very efficient in maintaining the population diversity during the evolution process of gray-coded genetic algorithm. This new algorithm overcomes any Hamming-cliff phenomena existing in other encoding genetic algorithm. Its efficiency is verified by application of 20 nonlinear test functions of 1–20 variables compared with standard binary-coded genetic algorithm and improved genetic algorithm. The position and intensity of pollution source are well found by CGGA. Compared with Gray-coded hybrid-accelerated genetic algorithm and pure random search algorithm, CGGA has rapider convergent speed and higher calculation precision.