CN102542354B - Optimal decision method based on situation analysis and hierarchy analysis - Google Patents
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Abstract
The invention provides an optimal decision method based on situation analysis and hierarchy analysis. The optimal decision method based on situation analysis and hierarchy analysis comprises the following steps of: first, establishing a multi-decision target index system on the basis of a situation analysis method; dividing decision targets into quantitative decision targets and non-quantitative decision targets; if the total quantitative decision targets play a dominant role in the total decision targets, determining a representative situation according to different states and constraint conditions of a decision variable; determining the weight of each quantitative target; calculating optimization values of different situations; sequencing the situations from small optimization value to big optimization value; selecting a plurality of former situations as initial optimal situations; and then decomposing the initial optimal situations into different hierarchy structures according to a hierarchy analysis method in a sequence of the total decision target, each sub decision target and the initial optimal situation; constructing a pairwise-compared weight judging matrix according to expert evaluation suggestions; calculating characteristic vector and matrix consistency of the judging matrix; figuring out a situation weight characteristic vector and a corresponding target weight characteristic vector; and finally, selecting an optimal situation. The method provided by the invention is simple and practical in technical realization.
Description
Technical Field
The invention relates to an optimization decision method for determining an optimal scenario scheme, in particular to an optimization decision method based on scenario analysis and hierarchical analysis.
Background
Since many quantifiable and non-quantifiable objects and variables are involved in the decision management process, many disciplines and different departments need to be considered, some relatively important objects need to be maximized, and other objects need to be balanced. The decision process is therefore quite complex. However, the current single decision support model at home and abroad has many defects both from the theory and the application, and the balance between quantifiable and unquantizable targets cannot be considered completely, so that the application of the model algorithm cannot guide the actual development and utilization, and cannot be used as a scientific and reliable decision basis to guide the decision-making department to form the final decision.
The scenario analysis method is also called scenario simulation analysis technology, and is used for analyzing actual problems encountered in management decision on the basis of speculation, describing scenarios possibly generated in the actual problems, and integrating scenario prediction sets of other aspects related to the scenarios to form a total integrated prediction. The whole process of the scenario analysis is to identify external factors influencing the research decision target or the development of the target, define decision variables, simulate various cross scenarios possibly generated by the external factors and analyze and predict various possible scenarios through the research of the related fields related to the decision target. This has the advantage that the decision can be made after a detailed analysis of the decision target environment. When setting the scenes, the problems need to be thoroughly considered and the scenes need to be flexible, various situations and various different environmental factors which can appear in the future are considered as much as possible, and all the situations are displayed as much as possible, so that the problems which can appear in the future can be found in time, actions are taken to eliminate or reduce the influence of the situations, and a decision maker can analyze and make final decisions.
However, on the premise of multi-decision-making target, many decision variables are difficult to be calculated quantitatively, and even if the decision variables can be calculated quantitatively, the dimensions of the decision variables are difficult to be unified, so that the scenario analysis method needs to be used in combination with other evaluation methods.
An Analytic Hierarchy Process (AHP) is a method of performing scenario analysis on decision targets, decision variables and corresponding constraints involved in management decisions, dividing decision targets, constraint conditions and multivariate scenarios related to the decisions into several levels, and performing qualitative and quantitative analysis on the basis. The analytic hierarchy process is suitable for the system evaluation of multiple decision targets and multiple limiting conditions without clear structural characteristics. Its advantages are simple and clear structure. The influence of each factor on the result is not cut off, and the thinking process of decision analysis is also mathematized and systematized. However, if the analytic hierarchy process is directly applied to the decision support system with multiple decision targets and multiple decision variables in the generation process of the management decision, the problem that the data statistics is huge due to too many indexes and the weight is difficult to determine is caused. Because of the need to construct multiple levels, large numbers and large scale decision matrices. Even the consistency of the single rank ordering and the total rank ordering is affected, so that the consistency check cannot pass.
The above-mentioned defects of the two algorithms of the scenario analysis method and the analytic hierarchy method become a problem to be solved urgently by researchers in the field.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art and provides an optimization decision method based on scenario analysis and hierarchical analysis. The method can select simple and practical optimal scenes for a multi-decision-making target system with quantized and unquantized targets coexisting.
The technical solution of the invention is as follows: the invention provides an optimization decision method based on scenario analysis and hierarchical analysis, which comprises the steps of firstly establishing a multi-decision-target index system based on a scenario analysis method, dividing decision targets into a quantifiable decision target and an unquantizable decision target, if the quantifiable decision target is dominant in the total decision target, determining reasonable representative scenarios according to different states and constraint conditions of decision variables, determining the weight of each quantifiable target, calculating the figure of merit of different scenarios, sequencing the scenarios from small to large according to the figure of merit, and selecting the first few scenarios as initial selection optimization scenarios; and then decomposing the sub-decision targets into different hierarchical structures according to the sequence of the total decision target, the sub-decision targets and the initially selected optimized scene based on an analytic hierarchy process, wherein each sub-decision target is positioned at the same layer in the hierarchical structures and comprises the total quantifiable decision target and each unquantizable decision target, constructing a weight judgment matrix which is compared in pairs according to expert evaluation opinions, calculating the characteristic vector and the matrix consistency of the judgment matrix, solving the scene weight characteristic vector and the corresponding target weight characteristic vector, and finally selecting the optimal scene according to the weight judgment matrix.
The optimization decision method based on the scene analysis and the hierarchical analysis comprises the following steps:
(1) establishing a multi-decision-target index system, identifying a decision target, a decision variable and a constraint condition thereof, and dividing the decision target into a quantifiable decision target and a non-quantifiable decision target according to the quantification attribute of the decision target; if the total quantifiable decision target is dominant in the total decision target, continuing the step (2);
(2) analyzing possible value states of decision variables in the index system and constraint conditions of the decision variables, arranging and combining different value states of the decision variables, and excluding unrealizable scenes to obtain a scene set to be optimized;
(3) for each quantifiable decision target, calculating the goodness of each scene in the scene set to be optimized to obtain the goodness value of each scene;
(4) sequencing all scenes in the scene set to be optimized from small to large according to the goodness value, selecting N-bit scenes before ranking, wherein N is more than 1 and less than the total number of the scenes to be optimized, and obtaining a primarily selected optimized scene set;
(5) decomposing the total decision-making target, each sub-decision-making target and the initially selected optimization scenario into different hierarchical structures according to the sequence, wherein each sub-decision-making target is positioned at the same layer in the hierarchical structures and comprises the total quantifiable decision-making target and each unquantizable decision-making target;
(6) according to the expert evaluation opinions, a weight judgment matrix for pairwise comparison is constructed:
wherein A isnnRepresenting the contrast weight between the targets or the scenes;
(7) calculating the eigenvector of the weight judgment matrix, and solving the scenario weight eigenvector and the corresponding target weight eigenvector;
(8) solving the maximum eigenvalue of the weight judgment matrix, and calculating the consistency of the matrix according to the obtained maximum eigenvalue;
if the consistency of the matrix is less than 0.1, the calculation of the matrix is effective, and the step (9) is continued;
if the consistency of the matrix is greater than or equal to 0.1, requiring the expert to reevaluate, and turning to the step (6);
(9) and determining the optimal scene according to the scene weight characteristic vector and the corresponding target weight characteristic vector.
Preferably, the method for calculating the goodness value of each scene in step (3) is as follows:
when the decision target is maximized to be optimal,
② when the decision target is minimized to be optimal,
wherein n represents the total quantifiable decision target, K represents the total number of scenes, and RkRepresenting the goodness value, alpha, of the kth sceneiRepresents the weight, λ, of the ith quantifiable decision targetkiRepresenting a scene goodness value of an ith quantifiable decision target in a kth scene; t isiRepresents the ith quantized decision target scenario optimum, MkiAnd indicating the scene actual value of the ith decision target in the kth scene.
Further, the method for constructing the weight judgment matrix a in step (6) is as follows:
(a) comparing every two sub-decision-making targets with respect to the upper layer of the total decision-making target, and assigning a weight value to obtain a weight judgment matrix between every two sub-decision-making targets with respect to the upper layer of the total decision-making target;
(b) and comparing every two scenes relative to each sub-decision target of the previous layer, and assigning a weight value to obtain a weight judgment matrix between every two scenes relative to each sub-decision target of the previous layer.
Further, the step (7) specifically comprises the following steps:
(a) the judgment matrix A is equal to (a)ij)n×nThe elements are normalized according to columns to obtain <math>
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(b) Will matrixAre added in rows to obtain vectorsWherein
(c) For vectorNormalization processing is carried out to obtain the scene weight characteristic vector and the target weight characteristic vector W ═ omega1，ω2，…，ωn)TWherein
Further, the method for determining the optimal scene in step (9) comprises the following steps: and multiplying the scene weight characteristic vector by the corresponding target weight characteristic vector, and summing to obtain the scene corresponding to the maximum value in the vectors, namely the optimal scene.
Compared with the prior art, the invention has the following advantages: the invention fully considers the fact that the quantization target and the unquantized target coexist in the complex multi-target decision and is difficult to optimize, adopts a layer-by-layer progressive method, firstly considers the dominant total quantization target, screens out few primary selection optimization scenes by simple calculation and analysis of numerous scene quantization targets, and applies a structured AHP weight evaluation method to greatly increase the feasibility of the complex scene evaluation of each unquantized decision sub-target, particularly effectively improves the operability of the scene optimization method in a computer optimization decision support system, and provides a new simple and practical decision method for optimizing a multi-decision target scheme with the coexistence of the quantization target and the unquantized target.
Drawings
Hereinafter, a specific embodiment of the present invention will be described with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of a scenario analysis AHP method framework according to an embodiment.
FIG. 2 is a hierarchy of total quantifiable targets and unquantizable targets.
Detailed Description
In the embodiment, the coal bed methane field produced water environment pollution prevention and control treatment is taken as an example to explain the optimal scenario integration selection method which adopts the scenario simulation analysis method and the hierarchical analysis method to be coupled.
Of course, any control decision system for the situation may be used as long as the optimization decision method based on the situation analysis and the hierarchical analysis provided by the present invention is used.
The main research area of the subject is the east edge willow demonstration engineering area of the E ' erdos basin, the structure position of the area is the east edge of the E ' erdos area, and the south-north structure zone where the Lu Liang mountain block Longand the E ' erdos broken block are connected is on the west side. The willow demonstration project area is located in the district of Lulian city, Shanxi province and in the middle of coal field in Hedong province. The block is an area with relatively mature coal bed gas exploration and development conditions, has higher exploration degree and detailed and reliable discharge and mining data, and preliminarily forms the capacity with a certain scale. The content of Total Dissolved Solids (TDS), NH4+, F-, Cl-in the water sample in the test area is seriously exceeded according to the measurement of pre-production sampling. The technical scheme of the invention is explained in detail by taking the four types of overproof pollutants as cases.
The contaminants first selected by the user to be primarily removed are Total Dissolved Solids (TDS), NH4+, F-, Cl-. Through monitoring, the TDS concentration in a water sample is 4650.00mg/L, the ammonia nitrogen concentration is 5.80mg/L, the concentration of F ions is 5.33mg/L when the F ions are not treated, the Cl ions reach 1917.00mg/L, the discharge mode of a test area after sewage treatment is required to be surface water discharge, and the discharge water quality standard must meet the requirements of three types of water in the surface water environment quality standard GB3838, namely, the Total Dissolved Solids (TDS) concentration is required to reach 1000.00mg/L, the ammonia nitrogen concentration is required to reach 1.00mg/L, the F ion concentration is required to reach 1.00mg/L, and the Cl ion concentration is required to reach 250.00 mg/L. As shown in table 1:
table 1: comparing the emission standard of main pollutants with the measured value
The corresponding treatment methods for various main pollutants are shown in table 2:
table 2: summary of pollutant treatment modalities
The age limit is set to 10 years, and 50 tons of wastewater are treated every day. According to the basic information, an optimization decision method based on scene analysis and AHP (advanced Analytic Hierarchy Process, Chinese name: Analytic Hierarchy Process) coupling is adopted to integrate and select the optimal scene, and the steps are as follows:
step 1: establishing a water treatment system scheme scenario analysis based on state variables (i.e. local geological conditions, water source conditions, service life, tonnage of produced water, etc.) according to pollutant types and emission requirements.
Identifying two quantifiable targets in the decision targets, wherein the two quantifiable targets are equipment and material consumption cost and operation maintenance cost in the wastewater treatment cost; two unquantized targets are provided, namely a ecosystem security target and a technical practicability target. In the selection of the wastewater treatment scheme, the wastewater treatment cost is taken into consideration as a leading factor.
Decision variables are different treatment techniques for the contaminants. The constraints are emission standards for different emission regimes selected by the user. The detailed data have already been listed above.
Step 2: aiming at several main pollutants, different emission indexes are used as constraint conditions, the treatment modes related to the complex coal bed gas produced water pollution treatment environmental problems are analyzed and arranged and combined, the same treatment mode is adopted for different pollutants in the same scheme to carry out scene combination, unreasonable schemes (namely unrealizable scenes) are deleted, and a possible scene set to be optimized for the water treatment scheme is obtained, as shown in table 3.
Table 3: aggregate of treatment plans
And step 3: for a quantifiable decision target, the goodness calculation is performed for each scenario in the total set of treatment recipes, the quantifiable decision target in this example is the equipment and consumables cost and the operation and maintenance cost in the wastewater treatment cost, and the goodness value of each scenario is calculated according to the following formula, and the results are shown in table 4:
wherein, <math>
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here, by expert evaluation, α1Assigned value of 0.6, α2The value is assigned to 0.4; according to Table 4, T1Value 960000, T2The value is 2012625. Of course, other methods may be sought to calculate the goodness value of each scene.
And 4, step 4: and (4) sorting the processing schemes from small to large according to the goodness values to obtain a sorted initial selection optimization scenario set, wherein the top five results are shown in table 4.
Table 4: initially selected optimized scenario set
And according to the obtained sequencing scene set, taking the first five scene schemes with the highest ranking, namely the water treatment schemes with the numbers of 1, 4, 3, 5 and 39 as an initial selection optimization scene result set.
And 5: and (2) according to the total quantifiable decision target and the non-quantifiable decision target determined in the step (1), regarding the total quantifiable decision target and the non-quantifiable decision target as sub-targets of the same layer, and decomposing the total decision target (the total target for short), the sub-decision targets (the sub-decision targets for short) and the initially selected optimization scenario into different hierarchical structures in sequence, as shown in fig. 2.
The total target is that the quantifiable target and the unquantizable target are integrally optimized, and the sub-decision targets comprise the total quantifiable target, the ecosystem safety target and the technical practicability target.
Step 6: and (4) performing secondary evaluation on different scenes under different targets by using a hierarchical analysis algorithm on the initially selected optimized scene set on the basis of expert evaluation. Meanwhile, AHP is also utilized to carry out weight value analysis among all targets. The following initial weight value table can be obtained by expert analysis, where table 5 is a target weight value table (also called a target weight matrix, where the row-column intersection point values in the table are the element values of the corresponding positions in the matrix), and table 6 is a scenario weight value table (also called a scenario weight matrix, where the row-column intersection point values in the table are the element values of the corresponding positions in the matrix). And (3) performing AHP analysis according to the initial weight value table:
table 5: target weight table
Table 6: scene weight value table
And 7: normalizing the target weight matrix and the context weight matrix (the normalization method is as described in the summary of the invention, and is not described here again), and finally obtaining a context weight eigenvector matrix and a corresponding target weight eigenvector matrix as follows:
wherein W0Is calculated by normalizing the target weight matrix (Table 5), W1W2W3Respectively calculated from the scene weight matrix (table 6).
And 8: calculating the maximum eigenvalue of the weight judgment matrix:respectively obtaining corresponding judgment values CR as follows:
CR0＝0.046，CR1＝0.035，CR2＝0.031，CR3＝0.052
since the matrix consistency is less than 0.1, the matrix calculation is valid, and step (9) is continued.
It should be noted that if the matrix consistency is greater than or equal to 0.1, the expert is required to re-evaluate, go to step (6) and continue.
And step 9: multiplying the obtained scene weight feature vector by the corresponding target weight feature vector, and summing to obtain a scene optimization final weight vector OPT:
and the scene corresponding to the maximum value in the vector is the optimal scene. The analysis result shows that the first value in the vector is the largest, so that the scheme 1 corresponding to the first value has the best benefit, the strongest technical practicability and the simple process while achieving the purification standard, and is the most suitable water pollution treatment technology for an experimental area.
In the invention, the analytic hierarchy process utilizes less quantitative information to make decision thinking process mathematical on the basis of deeply analyzing the essence, influence factors, internal relation and the like of the scene generated by complex water treatment, thereby providing a simple and convenient decision method for complex decision problems with multiple targets, multiple criteria or no structural characteristics. The method is particularly suitable for analyzing the decision result aiming at the target which is difficult to directly and accurately quantify after the current scene is analyzed. The analytic hierarchy process is to decompose the decision problem into different hierarchical structures according to the sequence of the total target, each sub target and the situation, then to use the method of solving and judging the characteristic vector of the matrix to obtain the priority weight of each element of each hierarchy to a certain element of the previous hierarchy, and finally to use the method of weighting (summation or integration) to hierarchically merge the final weights of each alternative scheme to the total target, wherein the situation with the maximum final weight is the optimal situation. The term "priority weight" as used herein is a relative measure indicating the relative measure of how superior each scheme is under a particular evaluation criterion or sub-goal, and how important each sub-goal is to the target of the previous level.
Those skilled in the art will appreciate that the details of the invention not described in detail in this specification are well within the skill of those skilled in the art.
The present invention is not limited to the contents described in the claims and the above embodiments, and any invention created based on the idea of the present invention should fall within the protection scope of the present invention.
Claims (2)
1. An optimization decision method based on scenario analysis and hierarchical analysis is characterized in that a multi-decision-target index system is established based on a scenario analysis method, decision targets are divided into a quantifiable decision target and an unquantizable decision target, if the quantifiable decision target is dominant in the total decision target, reasonable representative scenarios are determined according to different states and constraint conditions of decision variables, the weight of each quantifiable target is determined, and the goodness values of different scenarios are calculated, wherein the goodness value calculation method of each scenario comprises the following steps:
when the decision target is maximized to be optimal,
② when the decision target is minimized to be optimal,
wherein n represents the total quantifiable decision target, K represents the total number of scenes, and RkRepresenting the goodness value, alpha, of the kth sceneiRepresents the weight, λ, of the ith quantifiable decision targetkiRepresenting a scene goodness value of an ith quantifiable decision target in a kth scene; t isiRepresents the ith quantized decision target scenario optimum, MkiA scene actual value representing an ith decision target in the kth scene;
sorting the scenes according to the goodness value from small to large, and selecting the first few scenes as the primary selection optimization scenes; then decomposing the data into different hierarchical structures according to the sequence of a total decision-making target, each sub-decision-making target and the initially selected optimization scene based on an analytic hierarchy process, wherein each sub-decision-making target is positioned at the same layer in the hierarchical structures and comprises the total quantifiable decision-making target and each unquantizable decision-making target, and constructing pairwise comparison according to expert evaluation opinions
Weight judgment matrix:
wherein A isnnRepresenting the contrast weight between the targets or the scenes; the construction method of the weight judgment matrix A comprises the following steps:
(a) comparing every two sub-decision-making targets with respect to the upper layer of the total decision-making target, and assigning a weight value to obtain a weight judgment matrix between every two sub-decision-making targets with respect to the upper layer of the total decision-making target;
(b) comparing every two scenes relative to each sub-decision target of the previous layer, and assigning a weight value to obtain a weight judgment matrix between every two scenes relative to each sub-decision target of the previous layer;
calculating the eigenvector of the weight judgment matrix, and solving the scenario weight eigenvector and the corresponding target weight eigenvector:
(a) the judgment matrix A is equal to (a)ij)n×nThe elements are normalized according to columns to obtainWherein
(b) Will matrixAre added in rows to obtain vectorsWherein
(c) For vectorNormalization processing is carried out to obtain the scene weight characteristic vector and the target weight characteristic vector W ═ omega1，ω2，...，ωn)TWherein
Calculating the consistency of the eigenvector and the matrix of the judgment matrix, multiplying the scenario weight eigenvector by the corresponding target weight eigenvector, and summing to obtain the scenario corresponding to the maximum value in the vectors, namely the optimal scenario; and finally selecting the optimal scene according to the optimal scene.
2. The method for optimizing decision based on context analysis and hierarchical analysis according to claim 1, comprising the steps of:
(1) establishing a multi-decision-target index system, identifying a decision target, a decision variable and a constraint condition thereof, and dividing the decision target into a quantifiable decision target and a non-quantifiable decision target according to the quantification attribute of the decision target; if the total quantifiable decision target is dominant in the total decision target, continuing the step (2);
(2) analyzing possible value states of decision variables in the index system and constraint conditions of the decision variables, arranging and combining different value states of the decision variables, eliminating unachievable scenes and obtaining a scene set to be optimized;
(3) for each quantifiable decision target, calculating the goodness of each scene in the scene set to be optimized to obtain the goodness value of each scene;
(4) sequencing all scenes in the scene set to be optimized from small to large according to the goodness value, selecting N-bit scenes before ranking, wherein N is more than 1 and less than the total number of the scenes to be optimized, and obtaining a primarily selected optimized scene set;
(5) decomposing the total decision-making target, each sub-decision-making target and the initially selected optimization scenario into different hierarchical structures according to the sequence, wherein each sub-decision-making target is positioned at the same layer in the hierarchical structures and comprises the total quantifiable decision-making target and each unquantizable decision-making target;
(6) according to the expert evaluation opinions, a weight judgment matrix for pairwise comparison is constructed:
wherein A isnnRepresenting the contrast weight between the targets or the scenes;
(7) calculating the eigenvector of the weight judgment matrix, and solving the scenario weight eigenvector and the corresponding target weight eigenvector;
(8) solving the maximum eigenvalue of the weight judgment matrix, and calculating the consistency of the matrix according to the obtained maximum eigenvalue;
if the consistency of the matrix is less than 0.1, the calculation of the matrix is effective, and the step (9) is continued;
if the consistency of the matrix is greater than or equal to 0.1, requiring the expert to reevaluate, and turning to the step (6);
(9) and determining the optimal scene according to the scene weight characteristic vector and the corresponding target weight characteristic vector.
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| CN106599555B (en) * | 2016-12-01 | 2018-10-30 | 南通大学 | A kind of multi-expert Collaborative Decision Making Method for epilepsy E.E.G case history feature selecting |
| CN107256445B (en) * | 2017-04-27 | 2018-05-01 | 清华大学 | Analysis method, the device and system of production environment security |
| CN107180306A (en) * | 2017-05-24 | 2017-09-19 | 西安科技大学 | A kind of technical method of coal resources payable area block weighted superposition identification |
| CN111914831B (en) * | 2019-05-10 | 2023-06-02 | 杭州海康威视数字技术股份有限公司 | Target detection method, device and storage medium |
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