Refined gray-encoded evolution algorithm for parameter optimization in convection-diffusion equations

摘要

Purpose - The purpose of this paper is to reduce the computational burden and improve the precision of the parameter optimization in the convection-diffusion equation, a new algorithm, the refined gray-encoded evolution algorithm (RGEA), is proposed. Design/methodology/approach - In the new algorithm, the differential evolution algorithm (DEA) is introduced to refine the solutions and to improve the search efficiency in the evolution process; the rapid cycle operation is also introduced to accelerate the convergence rate. The authors apply this algorithm to parameter optimization in convection-diffusion equations. Findings - Two cases for parameter optimization in convection-diffusion equations are studied by using the new algorithm. The results indicate that the sum of absolute errors by the RGEA decreases from 74.14 to 99.29 percent and from 99.32 to 99.98 percent, respectively, compared to those by the gray-encoded genetic algorithm (GGA) and the DEA. And the RGEA has a faster convergent speed than does the GGA or DEA. Research limitations/implications - A more complete convergence analysis of the method is under investigation. The authors will also explore the possibility of adapting the method to identify the initial condition and boundary condition in high-dimension convection-diffusion equations. Practical implications - This paper will have an important impact on the applications of the parameter optimization in the field of environmental flow analysis. Social implications - This paper will have an important significance for a sustainable social development. Originality/value - The authors establish a new RGEA algorithm for parameter optimization in solving convection-diffusion equations. The application results make a valuable contribution to the parameter optimization in the field of environmental flow analysis.