The Optimization Method And Application Research Of Interval Multi-objective Programming Problems

Multi-objective optimization problem has been widely applied into various fields. However, the complexity and uncertainty of collected information will lead to the ambiguity of the obtained data. So the general method to solve such problems is using the interval number and building interval multi-objective programming model. Interval multi-objective programming problem is a relatively new non-deterministic optimization method, which is also a common method for practical decision problems. The characteristic of such method is using interval number to represent uncertainty information. Therefore, it just need to get the upper and lower bounds of variables, which reflects good convenience in uncertainty modeling field.At present, there are many methods to solve the interval multi-objective programming problem. Most of them are converting the multi-objective programming problem into a single objective programming problem, that is to say converting the uncertain problem into deterministic problem. However, the previous studies for the methods to solve interval multi-objective programming problem, the different importance of each objective function of the interval of multi-objective problem were not taken into account, which refer to the weights. Therefore, taking into account the different importance of each objective function’s weights, this paper proposes fuzzy geometric weighting method.Firstly, the general model of interval multi-objective programming problems is put forward. Secondly, According to the properties of interval numbers, the interval multi-objective programming problem is converted into identified multi-objective programming problem. Through solving the membership function of the conversed multiobjective programming’s objective function. After geometrically weighting that membership function, a fuzzy geometric weighting single objective programming model is constructed. Using the maximum and minimum operator method constructs the equivalent model of fuzzy geometric weighting single objective programming problems, and following the corresponding proof. Solving the best model and worst model of the equivalent model gets the non-inferior solution and method to solve optimal value interval of the objective function, under the condition of the objective function getting different weights. Finally, the study of multi-objective decision programming model, which is related to dispatching emergency supplies in one area, verifies the feasibility and effectiveness of the method.