Design And Application Of Fixed Point Iterative Evolution Algorithm

Evolutionary algorithms based on a mathematical model are a promising branch of meta-heuristic algorithms.Its reproduction operator is derived from a mathematical model through rigorous theory.There is a close relationship between the optimization algorithm and mathematical model.Therefore,this kind of algorithm has a more rigorous theoretical basis than other evolutionary algorithms,and has attracted more and more attention in the academic circle.Although existing evolutionary algorithms based on a mathematical model and the variants of these algorithms have shown strong competitiveness,the design of novel evolutionary algorithms based on a mathematical model is still in its infancy and has enough room for development.Fixed point iteration is a kind of practical and effective method to find the root of equation.The optimization process of evolutionary algorithms can be regarded as the gradual display process of the fixed point of equation under the iterative framework.Therefore,it is reasonable and feasible to design a novel evolutionary algorithm based on a mathematical model by using the iterative idea of solving equation.In this paper,polynomials derived from the fixed point iteration model are used as the reproduction operator,and two new algorithms are proposed and applied to solve the phase equilibrium calculation problem.The main research work of this paper is as follows:1.A fixed point evolution algorithm based on Aitken rapid iteration method(FPEA)is proposed.The design idea of FPEA is to regard the optimization process of evolutionary algorithms as the gradual display process of the solution of equations,that is,the fixed point is taken as the optimal value point of an optimization problem,and the approximate solution of an equation is taken as the individual in a population.The quadratic polynomial derived from the fixed point iteration model is used as the reproduction operator of the algorithm.In order to verify the feasibility of FPEA,comparative tests were conducted on CEC2014,CEC2019 benchmark function sets and four engineering constraint design problems respectively.The experimental results show that the average ranking of the optimal value of FPEA ranks first among all comparison algorithms on CEC2014 and CEC2019 benchmark function sets.For the four engineering constraint design problems,the proposed algorithm can obtain the highest accuracy with less computational cost compared with some state-of-the-art algorithms.2.A fixed point evolution algorithm based on expanded Aitken rapid iteration method(FPEea)is proposed.Firstly,A fixed point evolution model based on expanded Aitken rapid iteration method is established.Then,three polynomials are derived from this model,and the reproduction operator of FPEea are given.In order to verify the feasibility and effectiveness of FPEea,the proposed algorithm is compared with some classical evolutionary algorithms and the state-of-the-art algorithms on CEC2019,CEC2020 benchmark function sets and four engineering constraint design problems.The experimental results show that FPEea has good comprehensive performance.On CEC2019 and CEC2020 benchmark function sets,the average ranking of the mean value of this algorithm ranks first among all comparison algorithms.On the four engineering constraint design problems,the proposed algorithm has the highest accuracy among all comparison algorithms.3.A constrained Fixed point evolution algorithm(CFPEA)for phase equilibrium calculation of NVT-flash is proposed.CFPEA takes the total Helmholtz free energy as the objective function,and takes the molar vector and volume of a phase as the decision variables.The direct search method and outer point method are used to deal with the constraints of NVT-flash problem.The experimental results are consistent with the existing literatures.The proposed algorithm satisfies the energy attenuation characteristics.The effectiveness of this algorithm in solving NVT-flash problems is verified.CFPEA is the first example of successfully applying evolutionary algorithms to solve NVT-flash problems,which shows the application prospect of evolutionary algorithms in the field of phase equilibrium computation.