Research On Differential Evolution Algorithm And Its Application In Path Synthesis Of A Four-bar Mechanism

Four-bar mechanism is a kind of mechanism which is very important.Many working processes require the point on the coupler to track along different paths,they can be straight lines or very complex shapes.Regardless of the shape of the path,it is difficult to design a mechanism that can accurately achieve the desired trajectory.The main purpose of path synthesis is to obtain a four-bar linkage so that the point on the coupler can track along a target path.Optimizing methods can effectively solve the path synthesis problem.The main advantage of optimizing methods is that they are easy to implement and do not require in-depth knowledge of the problem’s search space.The quality and effectiveness of optimization are directly related to the manufacturing cost and production efficiency of mechanical equipment.Therefore,how to design an efficient optimization algorithm has become a hot issue commonly focused in academia and engineering.Differential Evolution algorithm(DE)performs well in solving path synthesis problem of a four-bar mechanism.However,DE also has some problems,such as stagnation in the iteration process,premature convergence when solving multimode problems,and weak local search ability,etc.Aiming at the problems existing in the differential evolution algorithm,the basic and application research of the differential evolution algorithm are systematically studied in this dissertation,and three improved differential evolution algorithms are proposed.In the research background of four classical cases of path synthesis of planar four-bar mechanisms and one path synthesis of manipulator,the application of three proposed algorithms are studied.The main work of this dissertation is summarized as follows:1.Considering DE may suffers from stagnation problem in iteration process.Thus,the author propose an enhancing Dierential Evolution with a Rank-up Selection(RUSDE).First,the rank-up individuals in current population are selected and stored into a new archive;second,a debating mutation strategy is adopt in terms of the updating status of current population to decide the parents selection.Both of the two methods can improve the performance of DE.To verify the feasibility and effectiveness of RUSDE,this study conducted numerical experiments based on two different dimensions functions from CEC2014,where the results demonstrated the RUSDE is significantly better than other ten algorithms in most cases.2.Considering that the traditional DE algorithm is easy to fall into local optimum and premature convergence when solving multi-modal problems,the author proposes a Repellency Evolutionary Algorithm(REA),which includes two repellency search behaviors:the first one is that two parent individuals are repellency sources,and repel the offspring individual;the other is that one individual in parent is the source of repellency and repels another individual in parent,then the current offspring learn their behavior.The common characteristics of these two behaviors are:first,the population no longer learns from the current global optimum to avoid population falling into the local extremum region;second,the offspring search in any direction except the location of the parent.Obviously,this will be more effective to solve the multimode function problem.To verify the feasibility and effectiveness of REA,this study conducted numerical experiments based on 57 different functions from CEC2014 and CEC2017,where the results demonstrated the REA is significantly better than other eight algorithms in most multi-modal functions.3.In order to improve the local search ability and accelerate the convergence of DE,a new improved DE algorithm called Adaptive Lagrange Interpolation Differential Evolution algorithm(ADELI)is proposed.In ADELI,the author use Lagrange interpolation for local search(LSLI)to accelerate the convergence of DE algorithm.In addition,the author proposes an adaptive discussion strategy,which performs LSLI near the neighborhood of the best solution to prevent the algorithm from falling into local optimum.This mechanism can balance the local search and global search ability of the algorithm.To verify the feasibility and effectiveness of ADELI,30 test functions in CEC2014 benchmark sets with different dimensions were simulated.Besides,the performance of ADELI was compared with twelve algorithms based on 30 numerical functions of 30 dimensions and 50 dimensions.Results demonstrated that ADELI considerably outperforms other algorithms in most functions.4.In the background of four classical path synthesis cases of planar four-bar mechanisms,the applications of RUSDE,REA and ADELI algorithms are studied.The task of the four cases is to trace the point on coupler to track the desired points on four different shapes under the condition that the length of the four-bar meets the Grashof constraint and the input angle of the link meets the order constraint.The goal is to minimize the error between the desired points and the coupler point.The goal is to minimize the error between the desired trajectory points and the tracing points.The numerical experiments demonstrate the effectiveness of three proposed algorithms in solving optimal path synthesis,especially the REA algorithm,which greatly improves the previous research results in case 1 and case 4.5.Application research of RUSDE,REA and ADELI algorithms for the path synthesis problem of a manipulator is studied.The task of this problem is to minimize the Linearity Error of the manipulator when it enters the mould area.This problem is belong to the optimal path synthesis of a four-bar mechanism,and the mathematical model of the manipulator is established.The three proposed algorithms are used to solve the problem.The experimental results show that the three proposed algorithms are fast and effective.