技术领域technical field
本发明属于道路路线方案比选领域，具体涉及一种考虑前景理论的高速公路路线方案不确定多属性优选方法。The invention belongs to the field of comparison and selection of road route schemes, and in particular relates to an uncertain multi-attribute optimization method for expressway route schemes considering prospect theory.
背景技术Background technique
公路作为重要的基础设施项目，而路线方案的比选是公路路线方案优化的核心。高速公路建设线路方案的综合比选，是在公路建设前期需要解决的重要问题，其基本走向方案选择的是否合理，直接影响到项目建成后能否满足国家经济建设需要，影响到线路设计的质量，工程造价和运营条件的好坏，并最终决定一条高速公路的经济效益。尤其在我国公路运输承担着国家客货运的主要运输任务，对国家的政治、经济、国防以及公路沿线所经区域的政治、经济、文化的发展都有着重要作用。因此，作为高速公路建设宏观决策的线路方案综合比选工作具有举足轻重的作用。Highway is an important infrastructure project, and route scheme comparison is the core of highway route scheme optimization. The comprehensive comparison and selection of highway construction route schemes is an important problem that needs to be solved in the early stage of highway construction. Whether the selection of the basic direction scheme is reasonable will directly affect whether the project can meet the needs of national economic construction after the completion of the project, and affect the quality of line design , project cost and operating conditions, and ultimately determine the economic benefits of an expressway. Especially in our country, road transportation undertakes the main transportation task of national passenger and cargo, and plays an important role in the country's politics, economy, national defense and the political, economic and cultural development of the areas along the road. Therefore, the comprehensive comparison and selection of route schemes as a macro-decision for expressway construction plays a pivotal role.
路线方案比选是一个涉面大、涉及因素众多、影响范围广而复杂的系统综合选优问题。不仅要满足国家和当地政府的政治、经济、文化、卫生等方面的需要，而且要考虑路线方案的可行性和使所选择的路线指标具有最优性。传统的路线方案比选方法主要有两类：一是主观性太强，基于方案的经济指标，决策者对社会及环境等主观判断后确定最优方案；二是过分追求客观性，生搬硬套数学方法，未考虑实际项目特点，不能很好的决策者多年实际经验用于方案比选决策中。The comparison and selection of route schemes is a comprehensive and complex system selection problem involving a large area, many factors, and a wide range of influences. Not only to meet the political, economic, cultural, health and other needs of the country and local governments, but also to consider the feasibility of the route plan and make the selected route indicators optimal. There are two main types of traditional route scheme comparison and selection methods: one is too subjective, based on the economic indicators of the scheme, decision makers determine the optimal scheme after making subjective judgments on society and the environment; the other is excessive pursuit of objectivity and mechanically applying mathematical methods , does not consider the characteristics of the actual project, and cannot use the years of practical experience of the decision-maker in the decision-making of program comparison and selection.
发明内容Contents of the invention
针对现有技术的不足，本发明目的在于提出一种考虑前景理论的高速公路路线方案不确定多属性优选方法，综合考虑了决策祝主观经验与客观条件对路线方案的影响，将路线方案中定量指标与定性指标转化成不同的数学语言，借助前景理论与多属性决策理论将路线方案优选过程科学合理化。Aiming at the deficiencies in the prior art, the purpose of the present invention is to propose an uncertain multi-attribute optimization method for highway route schemes considering prospect theory, which comprehensively considers the influence of decision-making and subjective experience and objective conditions on the route scheme, and quantifies the route scheme The indicators and qualitative indicators are converted into different mathematical languages, and the route selection process is scientifically rationalized with the help of prospect theory and multi-attribute decision-making theory.
为实现上述目的，本发明采用如下方案：To achieve the above object, the present invention adopts the following scheme:
考虑前景理论的高速公路路线方案不确定多属性优选方法，包括以下步骤：An uncertain multi-attribute optimization method for highway route schemes considering prospect theory, including the following steps:
首先、将方案集S＝{S1,S2,…,Si,…,Sm}中的路线方案指标按实数型、区间型与语言型进行分类并进行数据规范化处理，语言型状态集为L＝{L0,L1,…,Lk,…,Lt}，属性值集为V＝[Vij]m×n；其中Si为第i个备选方案，Lk为语言型指标第k个状态值，L0…Lt为从差到好逐步变化的状态值，Vij为第i个备选方案的第j个属性值；First, classify the route plan indicators in the plan set S={S1 ,S2 ,…,Si ,…,Sm } by real number type, interval type and language type and perform data normalization processing, and the language type state set is L={L0 ,L1 ,…,Lk ,…,Lt }, and the attribute value set is V=[Vij ]m×n ; where Si is the i-th alternative, and Lk is the language The k-th state value of the type index, L0 ... Lt is the state value gradually changing from bad to good, and Vij is the j-th attribute value of the i-th alternative;
其次、路线方案指标属性集为A＝{A1,A2,…,Aj,…,An}，Aj为第j个属性；依据决策者对各指标属性的偏好信息P＝{P1,P2,…,Pj,…,Pn}，Pj为决策者据主观经验对第j个属性的偏好信息，将规范化后的路线方案指标属性值转化为前景决策矩阵D＝[Dij]m×n，Dij为第i个备选方案的第j个属性决策初始值，各属性相互独立；Secondly, the index attribute set of the route scheme is A={A1 ,A2 ,…,Aj ,…,An }, Aj is the jth attribute; according to the decision maker’s preference information for each index attribute P={P1 ,P2 ,...,Pj ,...,Pn }, Pj is the decision maker's preference information for the jth attribute according to subjective experience, and the normalized route plan index attribute value is transformed into the prospect decision matrix D=[ Dij ]m×n , Dij is the initial decision value of the jth attribute of the i-th alternative, and each attribute is independent of each other;
然后、构建价值函数计算指标前景值，基于指标属性出现的不确定性，用熵权来描述指标属性在路线方案优化中贡献率的大小；Then, construct the value function to calculate the prospect value of the index, and use the entropy weight to describe the contribution rate of the index attribute in the route plan optimization based on the uncertainty of the index attribute;
最后、基于指标的初始属性值、前景值与熵权，建立综合优度评价模型，并依据综合优度值的大小进行方案排序，确定最优方案。Finally, based on the initial attribute value, prospect value and entropy weight of the index, the comprehensive goodness evaluation model is established, and the schemes are sorted according to the comprehensive goodness value to determine the optimal scheme.
进一步，将路线方案指标分为实数型(A1)、区间型(A2)与语言型(A3)三类，具体描述如下：Further, the route scheme indicators are divided into three types: real number type (A1 ), interval type (A2 ) and language type (A3 ), which are specifically described as follows:
实数型(A1)：指标的属性值能够定量计算，是精确数字，即属性值为Vj；Real number type (A1 ): the attribute value of the index can be quantitatively calculated, and it is an accurate number, that is, the attribute value is Vj ;
区间型(A2)：指标能够定量分析难以用精确数字描述，用区间来表述指标属性的不确定性，即属性值为[Vj-,Vj+]；Interval type (A2 ): The index can be quantitatively analyzed and difficult to describe with precise numbers, and the uncertainty of the index attribute is expressed by the interval, that is, the attribute value is [Vj- ,Vj+ ];
语言型(A3)：指标只能定性分析，属性值只能用例如“好、中、差”的语言描述，即属性值为[Vj-,Vj0,Vj+]＝(max{(Lk-1)/t,0},Lk/t,max{(Lk+1)/t,0})。Language type (A3 ): indicators can only be analyzed qualitatively, and attribute values can only be described in language such as "good, medium, and poor", that is, the attribute value is [Vj- ,Vj0 ,Vj+ ]=(max {(Lk -1)/t,0},Lk /t,max{(Lk +1)/t,0}).
进一步，将实数型、区间型与语言型路线方案指标进行数据规范化处理，具体如下：Further, the real number type, interval type, and language type route scheme indicators are subjected to data normalization processing, as follows:
对路线方案属性值数据进行规范化处理，属性值分为成本型和效益型，分别记作Aτ,Aθ其中成本型的属性值越小越好，效益型的属性值越大越好，处理方式如下：Standardize the attribute value data of the route plan. The attribute values are divided into cost type and benefit type, which are respectively recorded as Aτ , Aθ . as follows:
实数型(A1)：设Xj+＝max{max{Vij},Pj}，Xj-＝min{min{Vij},Pj}，规范化公式为：Real number type (A1 ): Let Xj+ ＝max{max{Vij },Pj }, Xj- ＝min{min{Vij },Pj }, the normalized formula is:
区间型(A2)：设规范化公式为：Interval type (A2 ): set The normalization formula is:
语言型(A3)：语言型指标属性值的确定即为规范化的过程，故语言型指标规范化值直接采用三角模糊数；Linguistic (A3 ): The determination of the attribute value of the linguistic index is the process of normalization, so the normalized value of the linguistic index directly adopts the triangular fuzzy number;
数据规范化处理后得到偏好向量P’＝{P1’,P2’,…,Pj’,…,Pn’}与决策矩阵V’＝[Vij’]m×n。After data normalization, the preference vector P'={P1 ',P2 ',...,Pj ',...,Pn '} and the decision matrix V'=[Vij ']m×n are obtained.
进一步，将规范化后的指标属性值转化为前景决策矩阵具体如下：Further, the normalized index attribute value is transformed into a prospect decision matrix as follows:
将决策者主观经验确定偏好向量作为参照点来衡量各个方案属性的“收益”或“损失”，对各方案的属性值Vij’与偏好属性Pj’的大小关系来衡量方案属性，采用欧式距离来计算属性值与偏好属性间距离，作为不同路线方案综合考虑主观经验与客观实际的初始属性值Dij，构建前景决策矩阵D，公式如下：The preference vector determined by the subjective experience of the decision-maker is used as a reference point to measure the "gain" or "loss" of each program attribute, and the relationship between the attribute value Vij ' of each program and the preference attribute Pj ' is used to measure the program attributes. To calculate the distance between the attribute value and the preferred attribute, as different route schemes, the initial attribute value Dij of subjective experience and objective reality is comprehensively considered, and the prospect decision matrix D is constructed. The formula is as follows:
进一步，构建价值函数计算指标前景值具体为：Further, constructing the value function to calculate the prospect value of the indicator is specifically:
前景理论假设价值函数在参考点以上是凹的，在参考点以下是凸的，来反映敏感性递减原理；前景理论还假设价值函数在损失区域比在收益区域更陡，来体现损失厌恶；Prospect theory assumes that the value function is concave above the reference point and convex below the reference point to reflect the principle of diminishing sensitivity; prospect theory also assumes that the value function is steeper in the loss area than in the gain area to reflect loss aversion;
根据上述假设提出以下价值函数C(Vij‘)：According to the above assumptions, the following value function C(Vij ') is proposed:
其中，α、β分别表征收益和损失区域价值幂函数的凹凸程度，即反映决策者敏感性递减的速度，λ系数用来表征损失区域比收益区域更陡的特征，即反映损失厌恶程度。Among them, α and β respectively represent the concavity and convexity of the value power function of the gain and loss areas, which reflect the speed of the decision-maker’s decreasing sensitivity.
进一步，α＝β＝0.88； λ＝2.25。Further, α=β=0.88; λ=2.25.
进一步，基于指标属性的不确定性确定指标熵权，熵与熵权的计算公式如下：Further, the entropy weight of the index is determined based on the uncertainty of the index attribute, and the calculation formula of entropy and entropy weight is as follows:
k为正的常数，当所有的pi对于任意给定的i相等时，pi＝1/n，Ei(pl,p2,…,pi,…,pm)取得最大值。k is a positive constant. When all pi are equal to any given i, pi =1/n, and Ei (pl , p2 ,...,pi ,...,pm ) takes the maximum value.
进一步，综合优度评价模型的构建具体如下：Further, the construction of the comprehensive goodness evaluation model is as follows:
综合考虑初始属性值与前景值提出综合优度评价模型，如下：Considering the initial attribute value and prospect value comprehensively, a comprehensive goodness evaluation model is proposed, as follows:
当Ui＞0时，表示评价方案整体为“收益”状态，当Ui＜0表示评价方案整体为“损失”，对所有方案的优度进行比较，若则方案Sr为最优方案，与决策者偏好信息偏离的程度与前景状态综合最优。When Ui > 0, it means that the overall evaluation plan is in a "benefit"state; when Ui <0, it means that the overall evaluation plan is in a "loss"state; compare the superiority of all the plans, if Then the scheme Sr is the optimal scheme, and the degree of deviation from the decision maker's preference information and the prospect state are optimal comprehensively.
本发明的创新点主要有以下方面：The innovations of the present invention mainly contain the following aspects:
1、通过引入经济学理论中的“前景理论”将决策者主观经验作为参考，利用客观的数学方法对各路线方案进行优选。1. By introducing the "prospect theory" in economic theory and taking the subjective experience of decision makers as a reference, use objective mathematical methods to optimize each route plan.
2、基于指标属性已有的信息量，考虑熵与熵权，从人类在处理未知事情的随机性和客观世界的概率性分析各指标在竞争意义上的相对激烈程度，使公路路线方案优选过程更加客观合理。2. Based on the existing information of index attributes, considering entropy and entropy weight, analyze the relative intensity of each index in the sense of competition from the randomness of human beings in dealing with unknown things and the probability of the objective world, so as to make the road route plan optimization process more objective and reasonable.
3、针对路线方案优选指标进行分类，不同类型的指标通过科学、客观的数学方法统一分析，结果更加合理可信。3. Classify the optimal indicators of the route plan. Different types of indicators are analyzed through scientific and objective mathematical methods, and the results are more reasonable and credible.
4、将决策者偏好与路线方案属性的欧式距离整合为前景决策矩阵，作为该发明的数据基础。4. Integrate the Euclidean distance between the decision maker's preference and the attribute of the route plan into a prospect decision matrix, which is used as the data basis of the invention.
本发明的优点主要有以下方面：Advantage of the present invention mainly contains the following aspects:
1、将决策者的主观经验作为一个属性进行客观的分析，避免了主观性强，也避免了优选过程不能结合实际完全客观的分析。1. The subjective experience of the decision-maker is analyzed objectively as an attribute, which avoids strong subjectivity and avoids completely objective analysis that the optimization process cannot be combined with reality.
2、将前景理论与熵权的思想引入公路路线方案优选的多属性决策方法中，构建了综合优度评价模型。为公路路线优选提供一种客观、可行的评价方法。2. Introduce the idea of prospect theory and entropy weight into the multi-attribute decision-making method of highway route scheme optimization, and build a comprehensive goodness evaluation model. Provide an objective and feasible evaluation method for highway route optimization.
3、从数学表达出发，将路线方案指标分为实数型、区间型与语言型。几乎涵盖了路线方案全部指标，解决了传统方法指标无法量化的难题。3. Starting from the mathematical expression, the route plan indicators are divided into real number type, interval type and language type. It covers almost all the indicators of the route plan, and solves the problem that the indicators of the traditional method cannot be quantified.
4、本发明被应用于实际项目，优选方案与实际项目建设条件、决策者期望一致，具有很强的实用性。4. The present invention is applied to actual projects, and the optimal scheme is consistent with the actual project construction conditions and the expectations of decision makers, and has strong practicability.
5、本发明指标处理清晰，计算流程简单，计算结果易懂，适合广泛应用于路线方案优选。5. The present invention has clear index processing, simple calculation process, and easy-to-understand calculation results, and is suitable for being widely used in route scheme optimization.
附图说明Description of drawings
图1为本发明设计方法的流程图Fig. 1 is the flowchart of design method of the present invention
图2为对于7个等级所对应的语言型指标用三角模糊数进行模糊化处理函数Figure 2 is the fuzzification processing function of the linguistic indicators corresponding to the 7 levels using triangular fuzzy numbers
图3为前景理论中图价值函数在不同参数下的模拟曲线Figure 3 is the simulation curve of graph value function under different parameters in prospect theory
图4为公路路线方案优选问题的实例Figure 4 is an example of the optimization problem of highway route scheme
具体实施方式Detailed ways
下面结合附图对本发明做进一步说明。The present invention will be further described below in conjunction with the accompanying drawings.
本发明一种考虑前景理论的高速公路路线方案不确定多属性优选方法，包括一下步骤：A kind of expressway route scheme uncertain multi-attribute optimization method considering prospect theory of the present invention comprises following steps:
首先、将路线方案指标按实数型、区间型与语言型进行分类并进行数据规范化处理；First, classify the route plan indicators according to real number type, interval type and language type and perform data normalization processing;
其次、依据决策者对各指标属性的偏好，将规范化后的指标属性值转化为前景决策矩阵；Secondly, according to the decision maker's preference for each index attribute, the normalized index attribute value is transformed into a prospect decision matrix;
然后、建立累积泛函计算指标属性的前景值，基于指标属性出现的不确定性，用熵权来描述指标属性在路线方案优化中贡献率的大小；Then, the cumulative functional calculation of the prospect value of the index attribute is established, and based on the uncertainty of the index attribute, the entropy weight is used to describe the contribution rate of the index attribute in the route plan optimization;
最后、基于指标的初始属性值、前景值与熵权，建立综合优度评价模型，并依据综合优度值的大小进行方案排序，确定最优方案。Finally, based on the initial attribute value, prospect value and entropy weight of the index, the comprehensive goodness evaluation model is established, and the schemes are sorted according to the comprehensive goodness value to determine the optimal scheme.
所述的路线方案优选方法用数学语言描述为：设存在一个路线方案优选问题，其方案集S＝{S1,S2,…,Si,…,Sm}，属性集为A＝{A1,A2,…,Aj,…,An}，语言型状态集为L＝{L0,L1,…,Lk,…,Lt}，属性值集为V＝[Vij]m×n，，前景决策矩阵为D＝[Dij]m×n，决策者偏好信息P＝{P1,P2,…,Pj,…,Pn}。其中Si为第i个备选方案；Aj为第j个属性；Lk为语言型指标第k个状态值，L0…Lt为从差到好逐步变化的状态值；Vij为第i个备选方案的第j个属性值，Dij为第i个备选方案的第j个属性决策初始值，各属性相互独立；Pj为决策者据主观经验对第j个属性的偏好信息。The route scheme optimization method described in mathematical language is as follows: Suppose there is a route scheme optimization problem, its scheme set S={S1 , S2 ,...,Si ,...,Sm }, and the attribute set is A={ A1 ,A2 ,…,Aj ,…,An }, the linguistic state set is L={L0 ,L1 ,…,Lk ,…,Lt }, and the attribute value set is V=[Vij ]m×n , the foreground decision matrix is D=[Dij ]m×n , and the decision maker's preference information P={P1 ,P2 ,…,Pj ,…,Pn }. Among them, Si is the i-th alternative; Aj is the j-th attribute; Lk is the k-th state value of the linguistic index, L0 ... Lt is the state value gradually changing from bad to good; Vij is The value of the jth attribute of the i-th alternative, Dij is the initial decision-making value of thej -th attribute of the i-th alternative, and each attribute is independent of each other; preference information.
这种路线方案优选方法具体步骤如下：The specific steps of this route scheme optimization method are as follows:
步骤1：评价指标分类与属性值确定Step 1: Classification of evaluation indicators and determination of attribute values
根据路线方案优选指标可定量计算、定量分析与定性分析的描述特点，将优选指标分为实数型(A1)、区间型(A2)与语言型(A3)三类，具体描述如下：According to the descriptive characteristics of quantitative calculation, quantitative analysis and qualitative analysis of the optimal index of the route plan, the optimal index is divided into three types: real number type (A1 ), interval type (A2 ) and language type (A3 ). The specific description is as follows:
(1)实数型(A1)：指标的属性值可定量计算，是精确数字，即属性值为Vj。如“费用”。(1) Real number type (A1 ): the attribute value of the index can be calculated quantitatively and is an accurate number, that is, the attribute value is Vj . Such as "fee".
(2)区间型(A2)：指标可定量分析但很难用精确数字描述，用区间来表述指标属性的不确定性，即属性值为如“超高”。(2) Interval type (A2 ): The index can be quantitatively analyzed but it is difficult to describe it with precise numbers. The uncertainty of the index attribute is expressed by the interval, that is, the attribute value is Such as "super high".
(3)语言型(A3)：指标只能定性分析，属性值只能用例如“好、中、差”之类的语言描述，即属性值为Lk/t,max{(Lk+1)/t,0})。如“路线方案引发的地质灾害”。(3) Linguistic type (A3 ): indicators can only be analyzed qualitatively, and attribute values can only be described in languages such as "good, medium, and poor", that is, the attribute value is Lk /t,max{(Lk +1)/t,0}). Such as "geological disasters caused by route plan".
步骤2：数据规范化处理Step 2: Data normalization processing
在混合型多属性决策问题中，为了消除不同物理量纲对决策结果的影响，需要对属性值数据进行规范化处理。属性值分为成本型和效益型，分别记作Aτ,Aθ其中成本型的属性值越小越好，效益型的属性值越大越好。处理方式如下：In the mixed multi-attribute decision-making problem, in order to eliminate the influence of different physical dimensions on the decision-making results, it is necessary to normalize the attribute value data. Attribute values are divided into cost-type and benefit-type, which are recorded as Aτ and Aθ respectively. The smaller the attribute value of the cost type, the better, and the larger the attribute value of the benefit type, the better. It is handled as follows:
(1)实数型(A1)：设Xj-＝min{min{Vij},Pj}，规范化公式为：(1) Real number type (A1 ): set Xj- ＝min{min{Vij },Pj }, the normalized formula is:
(2)区间型(A2)：设规范化公式为：(2) Interval type (A2 ): set The normalization formula is:
(3)语言型(A3)：语言型指标属性值的确定即为规范化的过程，故语言型指标规范化值直接采用三角模糊数。(3) Language type (A3 ): The determination of the attribute value of the language type index is the process of normalization, so the normalized value of the language type index directly adopts the triangular fuzzy number.
数据规范化处理后得到偏好向量P’＝{P1’,P2’,…,Pj’,…,Pn’}与决策矩阵V’＝[Vij’]m×nAfter data normalization, the preference vector P'={P1 ',P2 ',...,Pj ',...,Pn '} and decision matrix V'=[Vij ']m×n
步骤3：前景决策矩阵的确定Step 3: Determination of Prospect Decision Matrix
在前景理论中，将决策者主观经验确定偏好向量作为参照点来衡量各个方案属性的“收益”或“损失”，因此需要对各方案的属性值Vij’与偏好属性Pj’比较，并依据其之间的大小关系来衡量方案属性。该优选方法针对上述三种指标采用欧式距离来计算属性值与偏好属性间距离，作为不同路线方案综合考虑主观经验与客观实际的的初始属性值Dij，构建前景决策矩阵D，公式如下：In prospect theory, the decision-maker’s subjective experience determines the preference vector as a reference point to measure the “gains” or “losses” of the attributes of each option, so it is necessary to compare the attribute value Vij ' of each option with the preference attribute Pj ', and The scheme attributes are measured according to the size relationship among them. This optimization method uses the Euclidean distance to calculate the distance between the attribute value and the preferred attribute for the above three indicators. As the initial attribute value Dij of subjective experience and objective reality for different route schemes, the prospect decision matrix D is constructed. The formula is as follows:
步骤4：构建价值函数计算指标前景值Step 4: Construct a value function to calculate the prospect value of the indicator
前景理论假设了价值函数在参考点以上是凹的，在参考点以下是凸的，来反映敏感性递减原理；前景理论还假设了价值函数在损失区域比在收益区域更陡，来体现损失厌恶。根据上述假设提出以下价值函数C(Vij‘)：Prospect theory assumes that the value function is concave above the reference point and convex below the reference point to reflect the principle of diminishing sensitivity; prospect theory also assumes that the value function is steeper in the loss area than in the gain area to reflect loss aversion . According to the above assumptions, the following value function C(Vij ') is proposed:
其中，α、β分别表征收益和损失区域价值幂函数的凹凸程度，即反映决策者敏感性递减的速度，λ系数用来表征损失区域比收益区域更陡的特征，即反映损失厌恶程度。Among them, α and β respectively represent the concavity and convexity of the value power function of the gain and loss areas, which reflect the speed of the decision-maker’s decreasing sensitivity.
另一方面，Kahneman和Tversky通过实验得出了人们在面对收益和损失时的决策参数取值，即：α＝β＝0.88；λ＝2.25，研究表明上述取值能较准确的反应决策者的敏感性与损失厌恶程度，且大量学者也得出了相似的参数并将上述参数应用于实际研究。On the other hand, Kahneman and Tversky obtained the value of decision-making parameters when people face gains and losses through experiments, namely: α = β = 0.88; λ = 2.25, the research shows that the above values can more accurately reflect the decision-makers Sensitivity and loss aversion, and a large number of scholars have also obtained similar parameters and applied the above parameters to actual research.
步骤5：基于指标属性的不确定性，确定指标熵权Step 5: Determine the index entropy weight based on the uncertainty of index attributes
熵的概念最初产生于热力学，主要用来描述在某一给定时刻一个系统可能出现的有关状态的不确定程度，用于描述不同评价指标对路线优选的影响程度。基于指标Aj提供的m个客观属性信息V1j,V2j,…,Vij,…,Vmj，假设出现这些结果具有概率pl,p2,…,pi,…,pm，借助信息概率测度获取熵E(pl,p2,…,pi,…,pm)，通过熵的大小客观地确定事件发生的不确定性，即熵权ω。熵与熵权的计算公式如下：The concept of entropy originated from thermodynamics, and it is mainly used to describe the degree of uncertainty about the possible state of a system at a given moment, and it is used to describe the degree of influence of different evaluation indicators on route selection. Based on the m objective attribute information V1j , V2j ,…,Vij ,…,Vmj provided by the index Aj , assuming that these results have the probability pl ,p2 ,…,pi ,…,pm , with The information probability measure obtains entropy E(pl ,p2 ,…,pi ,…,pm ), and objectively determines the uncertainty of event occurrence through the size of entropy, that is, the entropy weight ω. The calculation formula of entropy and entropy weight is as follows:
k为正的常数，当所有的pi对于任意给定的i相等时，pi＝1/n，Ei(pl,p2,…,pi,…,pm)取得最大值。k is a positive constant, when all pi are equal to any given i, pi =1/n, and Ei (pl , p2 ,...,pi,...,pm ) takes the maximum value.
由此可见，熵权代表该指标在该问题中能提供有用信息量的多少程度。熵权本身并不只是表明某指标实际意义上的重要性，还表明各指标在竞争意义上的相对激烈程度。熵权充分利用了己知的属性信息，反映了人类在处理未知事情的随机性和客观世界的概率性，符合公路路线方案客观决策的要求。It can be seen that the entropy weight represents the extent to which the index can provide useful information in the problem. The entropy weight itself not only indicates the importance of a certain indicator in the actual sense, but also indicates the relative intensity of each indicator in the sense of competition. The entropy weight makes full use of known attribute information, reflects the randomness of human beings in dealing with unknown things and the probability of the objective world, and meets the requirements of objective decision-making of road route schemes.
步骤6：综合优度评价模型的构建Step 6: Construction of comprehensive goodness evaluation model
初始属性值Dij可以判断各个方案的属性值与决策者偏好信息偏离的程度，前景值Cij则判断各个方案的属性值是“收益”或“损失”的程度，只有当方案的初始属性值越小，且前景值越大方案才能最优，因此，本文综合考虑初始属性值与前景值提出综合优度评价模型，如下：The initial attribute value Dij can judge the degree of deviation between the attribute value of each plan and the preference information of the decision maker, and the prospect value Cij can judge the degree of "income" or "loss" of the attribute value of each plan. Only when the initial attribute value of the plan Therefore, this paper proposes a comprehensive goodness evaluation model considering the initial attribute value and the prospect value, as follows:
当Ui＞0时，表示评价方案整体为“收益”状态，当Ui＜0表示评价方案整体为“损失”。对所有方案的优度进行比较，若则方案Sr为最优方案，与决策者偏好信息偏离的程度与前景状态综合最优。When Ui >0, it means that the evaluation scheme as a whole is in a "profit" state, and when Ui <0, it means that the evaluation scheme as a whole is in a "loss" state. Compare the superiority of all schemes, if Then the scheme Sr is the optimal scheme, and the degree of deviation from the decision maker's preference information and the prospect state are optimal comprehensively.
以下结合具体实施例说明本发明方案：The scheme of the present invention is illustrated below in conjunction with specific examples:
为与原方案进行对比，首先选取传统评价中选取的指标，对指标进行分类与属性值的确定，综合考虑指标属性与决策者偏好属性的偏离程度、属性本身的前景状态，用综合优度评价模型对各方案进行计算与排序，最终依据优度值确定最优方案。In order to compare with the original plan, first select the indicators selected in the traditional evaluation, classify the indicators and determine the attribute value, comprehensively consider the degree of deviation between the index attribute and the decision maker's preferred attribute, and the prospect status of the attribute itself, and use the comprehensive goodness evaluation The model calculates and ranks each scheme, and finally determines the optimal scheme based on the goodness value.
本实例的原始数据是青藏高原多年冻土区秀水河至雅玛尔河段路线方案资料，如图4，该区域共包含4条路线方案S＝{S1,S2,S3,S4}，评价指标有平均每公里的建安费A1，桥隧比例A2，单位长度含冰量A3，地理环境A4，线形干扰A5等5项。图1为本实例应用本发明的示意图，图2和图3为实例应用中用要的函数与参数。The original data of this example is the route plan data of the section from Xiushui River to Yamar River in the permafrost region of the Qinghai-Tibet Plateau, as shown in Figure 4. This area contains a total of 4 route plans S={S1 , S2 , S3 , S4 }, the evaluation indicators include the average construction fee per kilometer A1 , bridge-tunnel ratio A2 , ice content per unit length A3 , geographical environment A4 , and linear interference A5 . Fig. 1 is a schematic diagram of the application of the present invention in this example, and Fig. 2 and Fig. 3 are functions and parameters used in the example application.
步骤1：评价指标分类与属性值确定Step 1: Classification of evaluation indicators and determination of attribute values
基于上述资料，A1与A2为实数型指标，A3为区间型指标，A4与A5为语言型指标，设该实例中语言为“非常差、差、较差、中、较好、好、非常好”7个等级分别记作VP,P,MP,M,MG,G,VG，设语言状态集为L＝{0,1,2,3,4,5,6}。经相关踏勘设计人员的汇报，决策者提出了期望目标，转化为偏好向量为P＝{14000,50,[60,80],M,MG}，方案初始属性值如表1。Based on the above data, A1 and A2 are real-number indicators, A3 is an interval-type indicator, A4 and A5 are language-type indicators, and the language in this example is set as "very poor, poor, relatively poor, medium, and good" , good, very good" are recorded as VP, P, MP, M, MG, G, VG respectively, and the language state set is L={0,1,2,3,4,5,6}. According to the reports of relevant survey designers, the decision-makers put forward the expected goals, which are converted into preference vectors as P={14000,50,[60,80],M,MG}, and the initial attribute values of the scheme are shown in Table 1.
表1各方案指标属性值Table 1 Index attribute values of each scheme
步骤2：数据规范化处理Step 2: Data normalization processing
指标A1、A2与A3属性值均为成本型，即越小越好，依据Aτ规范化公式进行处理，得到规范化属性值，见表2。The attribute values of indicators A1 , A2 , and A3 are all cost-type, that is, the smaller the better, they are processed according to the Aτ normalization formula, and the normalized attribute values are obtained, as shown in Table 2.
表2各方案指标规范化后的属性值Table 2. Attribute values after normalization of indicators of each scheme
步骤3：前景决策矩阵的确定Step 3: Determination of Prospect Decision Matrix
采用欧式距离来计算属性值与偏好属性间距离，作为不同路线方案综合考虑主观经验与客观实际的的初始属性值，构建前景决策矩阵，见表3。The Euclidean distance is used to calculate the distance between the attribute value and the preferred attribute, which is used as the initial attribute value of different route schemes to comprehensively consider subjective experience and objective reality, and construct a prospect decision matrix, as shown in Table 3.
表3前景决策矩阵(初始属性值)Table 3 Foreground decision matrix (initial attribute value)
步骤4：构建价值函数计算指标前景值Step 4: Construct a value function to calculate the prospect value of the indicator
依据价值函数C(Vij‘)，其中决策参数取值取α＝β＝0.88；λ＝2.25，如图3。计算各属性值的前景值，见表4。According to the value function C(Vij '), the value of the decision parameter is α=β=0.88; λ=2.25, as shown in Fig. 3 . Calculate the foreground value of each attribute value, see Table 4.
表4各属性值的前景值Table 4 Foreground value of each attribute value
步骤5：基于指标属性的不确定性，确定指标熵权Step 5: Determine the index entropy weight based on the uncertainty of index attributes
基于各方案提供的客观属性信息，计算概率测度，见表5。依据熵权理论计算熵权为ω＝(0.224,0.109,0.116,0.349,0.202)T。Based on the objective attribute information provided by each scheme, the probability measure is calculated, see Table 5. According to the entropy weight theory, the entropy weight is calculated as ω=(0.224,0.109,0.116,0.349,0.202)T .
表5属性值的概率测度Table 5 Probability measures of attribute values
步骤6：综合优度评价模型的构建Step 6: Construction of comprehensive goodness evaluation model
将步骤3～5中的计算结果代入综合优度评价模型，求得优度为U＝(0.12,-0.08,-0.49,0.05)，即U3(-0.49)＜U2(-0.08)＜U4(0.05)＜U1(0.12)。评价结果与传统评价结果一致。此外由结果可以进一步看出：方案A2与方案A3整体为“损失”状态，与方案实际建设条件差等息息相关，符合实际。而方案A1与方案A4为整体为“收益”状态，且方案A1收益的同时更接近决策者期望。因此，本发明综合考虑了决策者的经验和路线方案客观实际，将优选过程科学合理化，具有很强的实用性。Substitute the calculation results in steps 3 to 5 into the comprehensive goodness evaluation model, and obtain the goodness as U=(0.12,-0.08,-0.49,0.05), that is, U3 (-0.49)<U2 (-0.08)< U4 (0.05) < U1 (0.12). The evaluation results are consistent with the traditional evaluation results. In addition, it can be further seen from the results that scheme A2 and scheme A3 are in a state of "loss" as a whole, which is closely related to the poor actual construction conditions of the scheme and conforms to reality. However, plan A1 and plan A4 are in the state of "revenue" as a whole, and plan A1 is closer to the decision maker's expectation while benefiting. Therefore, the present invention comprehensively considers the experience of the decision maker and the objective reality of the route plan, scientifically rationalizes the optimization process, and has strong practicability.
以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明，不能认定本发明的具体实施方式仅限于此，对于本发明所属技术领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干简单的推演或替换，都应当视为属于本发明由所提交的权利要求书确定专利保护范围。The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments. It cannot be determined that the specific embodiments of the present invention are limited thereto. Under the present invention, some simple deduction or replacement can also be made, all of which should be regarded as belonging to the scope of patent protection determined by the submitted claims of the present invention.
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| CN201711039215.4ACN107784394A (en) | 2017-10-30 | 2017-10-30 | Consider that the highway route plan of prospect theory does not know more attribute method for optimizing |
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| CN201711039215.4ACN107784394A (en) | 2017-10-30 | 2017-10-30 | Consider that the highway route plan of prospect theory does not know more attribute method for optimizing |
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| RJ01 | Rejection of invention patent application after publication | Application publication date:20180309 | |
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