Simultaneously Locating Multiple Roots Of Nonlinear Equations Based On Differential Evolution

Many practical application problems,such as physics,chemistry,engineering research,can be converted into nonlinear equations.In recent years,Solving nonlinear equaitons has attracted widespread attentions,especially the requirement of locating multiple roots in a single run.However,it is a difficult task in numerical compuation.Differential evolution is a random real parameter optimization algorithm,which is widely used to solve many optimization problems.However,due to the global optimal property of differential evolution,only one optimal solution can be found.Therefore,it is difficult to obtain multiple roots of nonlinear equations in a single run.Based on the above considerations,the research work of this paper is to use differential evoluiton for simultaneously locating multiple roots of nonlinear equations.The main contents and innovations of this paper are as follows:(1)A hybrid artificial bee colony and differential evolutionSwarm intelligence algoritms have also been used in many practical optimization problems.A hybrid swarm intelligence with improved ring topology is proposed to locate multiple roots.(2)Dynamic repulsion-based differential evolutionThe repulsion method is an effective method to solve nonlinear equations,but it is difficult to set proper repulsion radius for different problems.Thus,a dynamic repulsion mechanism is proposed and combined with differential evolution.(3)Memetic niching-based differential evolutionMaintaining population diversity is an important factor in solving nonlinear equations.However,using diversity preserving mechanism in differential evoluiton will reduce the accuracy of the found roots.Based on the above considerations,we propose a generic framework of memetic niching-based differential evolution.(4)Decomposition-based differential evolution with reinitializationAlthough niche technology can effectively maintain population diversity,several parameters,such as crowding factor or species radius,need to be given in advance.To solve this issue,an improved decomposition technique is proposed to maintain population diversity.In addition,a sub-population control strategy is proposed to improve the search ability.Moreover,the sub-population re-initialization mechanism is used to enhance the population diversity and effectively use computational resources.