Robustness And Application Of A Class Of Multi-objective Optimization Problems

It is of great theoretical significance and application value to research on the ro-bustness of multi-objective optimization problems and the application of multi-objective optimization models.At present,stochastic programming methods and robust optimization methods are common and very effective methods for dealing with practical problems with uncertainties,and there are a lot of research results.In this paper,the solution of a class of robust multi-objective optimization problems is studied by using the scalar quantization method.Some properties of robust efficient solutions and robust weakly efficient solutions are obtained.In addition,the multi-objective optimization model is applied to study the optimal performance evaluation scheme considering incentive and fairness,and we obtain some properties of the established model.Chapter 1,mainly gives some main progress and some basic concepts of the solution properties of vector optimization problems.Chapter 2,extends the scalar model proposed by Burachik et al.for deterministic multi-objective optimization problem to the robust case,and a new class of robust scalar problem is proposed.For the concept of a class of robust efficient solutions and robust weakly efficient solutions,a necessary and sufficient condition of robust weakly solutions is established by using the scalar method.A sufficient condition for the robust effective solutions is obtained.The relationship between this class of robust scalar problems and the optimal solutions of two classical robust scalar problems is discussed.Some examples are also given to explain the main results.Chapter 3,applies the multi-objective optimization model to the study of performance allocation problem,and fully considers the impact of individual differences on performance distribution satisfaction.The workload completed by the assessment object is divided into basic workload and performance workload involved in performance allocation.First,we use the score conversion function to transform the actual score of the assessment object.Then we use the K-means clustering method to classify the assessment objects;Secondly,it discusses the optimal solution to the most favorable and unfavorable basic workload of the assessment object,and obtains the most favorable and unfavorable performance distribution ratio for the assessment object.Then the satisfaction function of the assessment object is constructed.On this basis,the multi-objective performance allocation model is established and the Pareto optimal solution is obtained.Finally,the actual evaluation scores of a university teacher are brought into the model established in this paper for numerical experiments.The results show that the multi-objective performance allocation model constructed in this paper has a good effect on improving the satisfaction of performance allocation.