流域可持续评价的最大熵原理——投影寻踪耦合模型

在传统投影寻踪方法的基础上,综合考虑投影向量优化中的不确定性,提出基于最大熵原理的多准则投影寻踪方法,利用加速遗传算法对多准则目标函数进行优化求解.根据投影值与标准等级值的散点图趋势关系,建立了三次趋势曲线评价模型.淮河流域可持续性评价的实例结果表明了该模型在求解评价问题中的有效性.该模型同样适用于其它领域的综合评价问题.

Pursuit Projection Evaluation Model Based on Principle of Maximum Entropy for River Basin Sustainability Evaluation

Along with the gradual implementation of river basins sustainability development strategy,establishing a sustainability evaluation method based on the entire basin evaluation indexes system especially important.Correct appraisement of the sustainability status of river basins is the foundation of basins sustainability development policy's formulation,implementation,and management.However,basin sustainability evaluation is still at exploration stage,and some existing methods have various shortcomings,such as subjectivity,less differentiation,low computation precision and so on.Therefore an effective evaluation method should be urgently discovered. Aiming to these disadvantages and on the basis of traditional pursuit projection method,we proposed a multi-criterion evaluation model based on maximum entropy principal(ME-PP).The basic idea of traditional projection pursuit method is to project high dimension data to projective values in low dimension space, to describe some structure using a projective index function,to search optimal projective directions according to the projective index function,and to analyze the structure character of the high dimension data using the projective values.However,sometimes we can not obtain enough information for evaluation,and the evaluation system itself has randomness,fuzziness in original evaluation data.So,the results of projection vector gained by pursuit projection method have more uncertain factors called uncertainty,which can be resolved by information theory.According to Jaynes's maximum entropy principle,it thinks that we should take maximum entropy distribution when we just know partly information about the evaluation problem,which is the only choice that we can make,and any other choices mean that we have added other restraint or assumption,which can't be acquired according to the information that we have grasped.So in this paper,we present ME-PP model,which considered the uncertainty in projection vector quantity optimization,and used accelerate genetic algorithm(AGA) to optimize the multi-criterion object function. The modeling of ME-PP includes five steps as following: the first step is to standardize each index of the basin sustainability evaluation system to eliminate the dimension of each index and to unify the change range of each index.The second step is to construct a multi-criterion object function,which includes projective index function and maximum entropy function.The third step is the optimization of above multi-criterion object function by AGA.The projection direction vector and each sample's projective values can be acquired by AGA optimization.In the forth step,according to the tendency relationship of each sample's projection values and standard grades in scatter dots figure,a cubic tendency curve evaluation model is established,and in the same way we use AGA to optimize the curve model parameters.In the last step,we can evaluate the basin sustainability sample after data standardization,and then we could conclude the basin sustainable status and make suggestions for the basin sustainability.In case study,we appraised Huaihe River basin sustainability and the evaluation results show the efficiency of ME-PP.As an evaluation method,it is also suitable for other comprehensive evaluation problems.