Research And Application Of Genetic Algorithm In The Weights Calculation In The AHP

With the development of society, the decision problems are becoming more and more complicated. On one side, the decision makers need to make decisions rapidly, on the other side, they need to analyze the decision-making with the difficult owing to the uncertainty of the decision-making problems. As one important constitutive part of the decision-making problem, the multi attribute decision-making problem exists widely in our life. The analytic hierarchy process (AHP) is widely used in many fields as a classical multi attribute decision-making approach.The core step of multi attribute decision-making problem is to determine the comparison matrix and calculate the attribute weights in the AHP. However, it’s of great importance whether the given comparison matrix is consistency or not, which has direct influence on if or not the weights can reflect the realistic orders of the attribute. Therefore, the test and modification approach on the consistency of comparison matrix and calculating the attribute weights are very important aspects in the AHP. The following aspects about the AHP theories and approaches are concerned.First, this article provides nonlinear models to figure out the weights in the AHP from two perspectives. They can calculate the proper results when the comparison matrix consistency of the comparison is the best. Then standards are provided to evaluate the weights calculated in different methods and the genetic algorithm is designed to solve the problem.We propose two new models to improve consistency of the comparison matrix. One is local modification in comparison matrix, by which we modify elements in comparison matrix one by one. The other is the whole modification in comparison matrix, by which we have to modify all the elements at one time. Also the genetic algorithm is design to solve the problem.A lot of simulation results manifest that the models are feasibility and the algorithmic is efficient comparing with the data in some other paper. It is meaningful exploration for AHP based genetic algorithm to calculate weights and is further popularization and application.