Research On Multi-Objective Programming Methods Based On Satisfaction Degree

Considering multiple objectives is an inevitable decision-making problem in actual life,production practice,policy-making and other activities.Multi-objective programming is an effective mathematical model for dealing with multiple targets.A large number of scholars have combined many different decision-making environments and theories to construct many multi-objective programming models.But existing multi-objective programming methods either focus on the existence of decision results or on the reliability of decision-making results,and have not systematically considered the two together.Therefore,it is of great theoretical and practical significance to study the multi-objective decision-making method which takes into account the existence and reliability of decision results in complex environments.This paper constructs more efficient multi-objective programming models by formal description and feature analysis of the commonly used multi-objective decision-making models.1)To overcome the shortcomings of a multi-objective programming model with priority factors,relative deviation is introduced to describe the degree of deviation of objective function from the objective value,which reflects the satisfactory state of decision-making results.At the same time,different weights are given to each objective,and a multi-objective programming model based on relative deviation(i.e.MOPM-RD)is established.The effectiveness of the method is analyzed with a specific case.2)Aiming at the numerical multi-objective programming problem in stochastic environment,a two-stage multi-objective programming model based on reliability(i.e.TS-MOPM based on reliability)is established,in which the decision objective is regarded as a fuzzy event,and the expected value and the probability of the fuzzy event are taken as the quantitative indexes of randomness.Combining the probability calculation methods of fuzzy events under several common distributions,the specific solving steps of TS-MOPM are given,and the effectiveness and practicability of TS-MOPM are analyzed with a specific case.Theoretical analysis and practice show that: MOPM-RD and TS-MOPM based on reliability both can ensure the existence of decision results,also can measure the reliability of decision results,indirectly reflect the satisfaction degree of decision makers to the results,and have good operability and interpretability.To a certain extent,they enrich the existing multi-objective decision theory,and have wide application value in complex system optimization,portfolio analysis,management decision analysis and other fields.