The Improvement Of Differential Evolution Algorithm And It's Application In Constrained Optimization

Optimization is a common problem in mathematics,engineering,operations research,computer science and other fields.The traditional methods for solving optimization problems include simplex method,steepest descent method,two programming,cauchy newton method and other traditional methods.Most of these traditional methods have limitations,which require that the objective function has some characteristics,such as continuous,differentiable and derivable.It is also limited in dealing with large scale complex problems.Compared with the traditional algorithms,evolution algorithms do not require continuous,differentiable,differentiable and so on,and can't be easily trapped into local optima.Differential evolution algorithm uses differential mutation operator and crossover operator to generate new individuals.Because of its simplicity and high efficiency,it has attracted more and more scholars' attention and research.In addition to solving the single objective optimization problem,the differential evolution algorithm has been widely used in solving complex optimization problems such as multi-objective optimization,constrained optimization problem,dynamic optimization and so on.In this article,the improvement of the differential evolution algorithm is studied from two aspects:the improvement of the algorithm itself and the improvement of the algorithm.Then,the application of differential evolution algorithm in constrained optimization is studied,and two kinds of constrained differential evolution algorithm are proposed.The main research contents are as follows:1.The differential mutation strategy often fails to balance the relationship between "exploration" and "exploitation" when selecting an individual,making the algorithm vulnerable to trap into local optimization or slow down the convergence speed.This paper proposes an adaptive controlled strategy for stochastic ranking based selection method.The mutation operators use stochastic ranking method to sort individuals according to fitness and diversity measures.And then compute the individual selection probability.The comparative probability in stochastic ranking determines the relation between "exploration" and "exploitation" in the sorting process.In this paper,the comparative probability is adaptive controlled by the population success rate.When the rate of population success is high,it tends to "exploration " so as to avoid the population falling into the local optimum.When the population success rate is lower,it tends to "exploitation" to accelerate the convergence rate of the population.Compared with the other two methods,the experimental results show that the performance has been improved significantly.And since the selection strategy does not require manual tuning of parameters,it is easy to be used in various differential evolution algorithms.2.Opposite based learning strategy is an external strategy to improve differential evolution algorithm.By generating the opposite population,the method make the population has a greater probability to approach the global optimum.Because the exploitation ability of the strategy in dimension level is not strong,when solving multidimensional problems,the population may be far away from the optimal solution in some dimensions.To solve this problem,an orthogonal opposite based learning strategy is proposed in this paper.This strategy uses the orthogonal design method to generate a small number of uniformly distributed partial opposite individuals to strengthen the exploitation ability of the opposite based learning strategy in dimension level.At the same time,only a small number of partial opposite individuals need to be generated,so the number of function evaluations of the opposite based learning strategy is not significantly increased.We propose a differential evolution algorithm using orthogonal opposite based learning strategy,experimental results show that the perfonnance of the proposed algorithm is better than that of other kinds of opposite learning differential evolution algorithm.3.According to the "no free lunch" theorem,no single differential mutation strategy is suitable for solving all optimization problems.Therefore,it is one of the important methods to improve the differential evolution algorithm by the adaptive method to select the appropriate mutation strategy from several differential mutation strategies.The adaptive operator selection method is a method to select the mutation strategy by calculating the credit value of each mutation strategy.In this paper,the method is first used in differential evolution algorithm to solve the constrained optimization problem.In order to assign the appropriate credit value to the differential mutation strategy in the adaptive operator selection method,a credit assignment strategy based on mixed population fitness is proposed.The strategy divides the population into three types:infeasible,semi feasible and feasible.In each state,the credit value of the differential mutation strategy is calculated according to different penalty functions.The probability matching method is used as the strategy selection mechanism.In addition,the algorithm uses the mechanism of JADE algorithm to adaptive set the parameter of CR,F.Experiments show that the adaptive mechanism can effectively improve the perfonnance of differential evolution algorithm for solving constrained optimization problems.4.Combining multi-objective optimization with differential evolution is a kind of constrained differential evolution algorithm,which uses multi-objective optimization technique as constraint processing method.The algorithm randomly selects several individuals to perform differential mutation operation,so the selection pressure is weaker.Because the feasible region in the constrained optimization problem is often very small,the search of the algorithm in the infeasible region is too much to accelerate the convergence speed.We propose an accelerated combining multi-objective optimization with differential evolution for solving this problem.The algorithm presents a method of adaptive ranking based grouping selection.The population is divided into elite group and normal group according to their ranking.The individuals of elite group carry out random selection,and the individuals of common group implement greedy selection.Then it can accelerate the convergence speed of the algorithm and the selection pressure of the algorithm is also balanced so that it is not easy to fall into local optimum.And the method is analyzed theoretically in the paper.In addition,The algorithm presents a Individuals update assistant strategy,which improves the disadvantage of the CMODE algorithm of easily losing excellent offspring in the small scale population updating.The experimental results show that the improved algorithm maintains the high success rate of the original algorithm and accelerates the convergence speed of the algorithm.