Research On Efficient Algorithms For Many-objective Optimization Problems

The practical application problems in many fields can be modeled as optimization prob-lems with four or more objectives,which are called many-objective optimization problems,and the optimization problems with two or three objectives are called multi-objective opti-mization problems.Compared with multi-objective optimization problem,many-objective optimization problem is more difficult to solve.The main reasons are as follows:1)With the number of objectives increases,the number of Pareto optimal solutions increases expo-nentially.However,the selection pressure of the existing dominance methods is often in-sufficient,and it is unable to efficiently select representative solution sets with real potential from a large number of Pareto optimal solutions.2)As the number of objectives increases,the objective space increases exponentially.How to design an efficient algorithm to find a set of finite representative solutions with good convergence,uniform distribution and wide-ness in a huge objective space is a great challenge.Focusing on these two difficulties,this dissertation is devoted to researching and designing efficient many-objective evolutionary algorithms to solve these two difficult problems.The main work and innovations of this dissertation are as follows:Aiming at the shortcomings in the fitness evaluation mechanism of SPEA/R algorithm,namely,its local convergence strength interferes with the global convergence strength and diversity measure method cannot distinguish the difference of the contribution of the solu-tions with the same reference direction angle,a new fitness evaluation mechanism adapting to many-objective optimization problem is proposed.Firstly,a new convergence measure based on the global convergence strength is designed,which can effectively avoid the inter-ference of the local convergence strength of the solution to the global convergence strength of the solution,and the measured convergence is more reasonable and objective.At the same time,a new angle-distance based diversity measure method is designed,which can not only accurately measure the contribution of solutions with different reference directions to diversity,but also distinguish the contribution of solutions with the same reference direc-tion to diversity.Furthermore,in order to balance the proportion of convergence measure and diversity measure in the fitness evaluation mechanism,the convergence measure and the diversity measure are normalized to the same order of magnitude.Finally,a new fitness evaluation mechanism is designed based on the normalized convergence measure and diver-sity measure.The SPEA/R algorithm using the new fitness evaluation mechanism(denoted as ISPEA/R)is compared with the other five well-performing multi-objective evolutionary algorithms.The results show that ISPEA/R algorithm not only overcomes the defects of SPEA/R and reduces the computational complexity by an order of magnitude,but also has better convergence and diversity of the obtained solution setsAiming at the shortcomings of the existing dominance methods in solving many-objective optimization problem,namely,the selection pressure is insufficient and the diversity of so-lutions cannot be well maintained,a new dominance method-C?-dominance method based on expanding dominated area is designed.Different from the existing dominance method-s that expand the dominated area by using linear function transformation,this dominance method performs nonlinear transformation on the objective function,which not only ex-pands the dominated area of each solution to increase the selection pressure,but also re-moves the solutions that impede convergence,thus improving convergence and maintaining diversity.Furthermore,the superiority of C?-dominance method over the existing dominant method is proved theoretically.Finally,C?-dominance method and other four existing well dominance methods are used for NSGA-?,respectively,and experimental comparisons are made in DTLZ test suite.The results show that the solution sets obtained by C?-dominance method have better convergence and diversity than those obtained by other four dominance methods.In order to improve the performance of many-objective optimization algorithm,firstly,a double association strategy is designed.Different from the existing association method,af-ter the association between the population and each subspace,the association strategy is further related to the empty subspace,and the closest solution to the empty subspace is as-sociated with this empty subspace,increasing the probability of searching for the solution of the empty subspace.Then,a C?-dominance method with parameter adaptive adjustmen-t scheme is proposed.This scheme adaptively adjusts the parameter ? according to the number of objectives and iterations.On this basis,a fitness evaluation mechanism for si-multaneously evaluating convergence and diversity is designed.Combined with the above strategies,a new environmental selection strategy is designed,which can select a new pop-ulation with both convergence and diversity.Finally,a new many-objective evolutionary algorithm DSEA is proposed based on these techniques.A large number of simulation ex-periments show that DSEA has greater advantages in convergence and diversity compared with other five popular many-objective evolutionary algorithm.