Two-stage Adaptive Differential Evolution Algorithm For Constrained Problems And Its Application

There are a lot of constrained optimization problems(COPs)in industrial production and engineering practice.The traditional mathematical method is very difficult to solve this kind of problem,so the heuristic algorithm is quickly concerned by related researchers because of its simple design structure and easy implementation.Constraint-handling technique is a key technique to solve the constrained optimization problem.Due to the existence of constraint conditions,the solution space of constrained optimization problem is faced with challenges such as discontinuous and non-convex solution space.The main purpose of constraint-handling technique is how to balance the relation between feasible solution and infeasible solution so that the constraint optimization problem can find the global optimal solution.At present,the four most widely used constraint-handling techniques are penalty function method,objective and constraint separation method,multi-objective optimization method and ensemble of constraint-handling techniques.Differential evolution(DE)algorithm is a heuristic algorithm proposed by Storn and Price in 1995.It is favored by researchers because of its simplicity and efficiency in solving optimization problems.In this paper,six mutation operators of differential evolution are analyzed and three DE algorithms for COPs based on differential evolution,FROFI,CMAD and e-DE,are briefly described.Based on the analysis of the characteristics of constrained optimization problems,an adaptive differential evolution algorithm based on freedom-governance stage(FG-ADE)is proposed.The traditional DE optimization algorithm to solve COPs is improved by using the two-phase strategy and the self-adaptive parameter strategy.First,the strategy of Freedom and Governance is adopted to divide the whole constraint optimization algorithm into two stages:bias to objective function and bias to constraint condition.In the Freedom stage,the swarm only takes the objective function value as the direction of evolution without considering the constraint restriction,so that the swarm can quickly distribute in the region with better fitness.In the Governance stage,constraints are added,and the first criterion for individual comparison is the degree constraint violation,which aims to enable individuals to quickly enter the feasible region.Secondly,a self-adaptive method is used to select appropriate parameters for different problems or different stages of the same problem to improve the robustness of the algorithm.At the same time,we compare and analyze the key parameters of FG-ADE algorithm.The results from 18 benchmark test functions of CEC 2010 show that FG-ADE has a significant advantage over other similar constrained optimization algorithms in performance.In addition,FG-ADE algorithm is used to solve the portfolio problem in the field of economics,and the performance of FG-ADE is tested on the improved mean-variance model.The test results show that FG-ADE is better than other optimization algorithms in the economic portfolio problem,and FG-ADE algorithm is far more effective than other algorithms.