Multi-objective Optimization Method And Applications

This paper consists of three parts.First, we introduce the history and mathematical model of multi-objective optimization, and present the definition of multi-objective optimization solution.Second, we systematically introduce several common methods about multi-objective optimization, including component weighted legitimate, selection of weights, component optimization and objective programming. One component optimization method is divided into primary objective method and the appropriate constraint method. Objective programming is divided into the ideal point method, max-min principle method, the purpose and objectives of objective programming.Component weighted legitimate is defined as follows:Every component f_i(x) of the multi-objective function F(x) = (f₁(x₁), f₂(x₁)…f_n(x₁))^T is weighted by the respective law. Then f_i (x) is summed by some principles. In what follows the new evaluate function is obtained. At last, the new evaluate function is single-objective minimized .Weight coefficients can be obtained by theα-method.Component optimization methods' main aim is that first one of the multi-objective functions is considered as the main objective function, other component functions are estimated. Upper limit and low limit are obtained. We consider multi-objective optimization as resolution of single-objective minimizedprobiems. The appropriate constraint method considers one of the definite multi-objective functions as the objective functions. Then choose the appropriate constant c, for other functions. Let f_i (x) = c_i (i≠p) ,in the sequel, resolve the component function minimized problems. Objective programming method obtains the objective values of all of the component functions by the different principle. After that we let the components be close to the respective objective values by some norms. Objective programming is divided into max-min principle method etc which follows from the different objective functions.Multi-objective minimized problem is defined as follows: the objective functions' maximum value can be chose to structure the evaluate function. In the following . This means that multi-objective minimized problem can be considered as resolving the function value minimized problem:which is called as the max-min principle method.Finally, we apply multi-objective method to the actual case. Partition point of bus routes to optimize settings, due to traffic conditions in cities in various regions of the country is different from other cities, public transport vehicles is the full price of 1 yuan. But this approach is not feasible in many lines because of Daqing special geographical traffic situation. We establish multi-objective decision-making model and make use of the component weighted method and Matlab programming to analyze and establish the mathematics models, obtain the solutions.This paper consists of three parts.First, we introduce the history and Mathematical model of Multi-objcetive Optimization, and present the definition of Multi-objcetive Optimization solution. Second, we systematically introduce several common methods about Multi-objective Optimization, including component weighted legitimate, selection of weights, component optimization and objective programming. One component optimization method is divided into primary objective method and the appropriate constraint method. Objective programming is divided into the ideal point method, max-min principle method, the purpose and objectives of objective programming.Finally, we apply multi-objective method to the actual case. Partition point of bus routes to optimize settings, due to traffic conditions in cities in various regions of the country is different from other cities, public transport vehicles is the full price of 1 yuan. But this approach is not feasible in many lines because Daqing special geographical traffic situation. So far very a few people on the issue of domestic research. I establish of multi-objective decision-making model and make use of goal programming method for solving it.