A method for selecting water environment governance project portfolio with multi-dimensional strategic fit

Abstract

The present invention discloses a method for selecting a water environment governance project portfolio for multi-dimensional strategic fit, including constructing a strategic indicator set of water environment governance, economic benefits and enterprise development strategic goals; establishing a nonlinear mapping relationship between strategic indicators and strategic fit, and realizing the evaluation of the fit degree between the project portfolio and strategic goals of multiple dimensions; constructing a project portfolio selection model considering multi-dimensional strategic fit under resource constraints, and using an intelligent algorithm to solve the Pareto solution set of the project portfolio selection model; for the cases of repeated solution sets and large solution sets, a PPSOS method is used to screen out representative Pareto solutions, so as to realize the refinement of the solution set output by the intelligent algorithm, reduce the complexity of decision-making, effectively balance the gap between theoretical models and practical applications, and ensure the scientificity and practicality of decision-making plans.

Description

Technical Field

[0001] The present invention relates to the technical field of water environment management, and in particular to a method for selecting a combination of water environment management projects oriented to multi-dimensional strategic fit. Background Art

[0002] my country's water environment governance industry has developed rapidly in recent years. The "China Environmental Protection Industry Development Status Report" shows that the scale of water environment governance in 2019 is about 630 billion yuan, and the scale of water environment governance will expand to 670.1 billion yuan in 2023. It is expected that the scale of water environment governance will reach 1.43 trillion yuan in 2025, and the market size will continue to grow. Water environment governance projects have unique strategic value, which is reflected in the need to focus not only on their ecological value, but also on their economic value such as return on investment. There is a complex interactive relationship between the two, and the pursuit of any value alone cannot achieve the long-term sustainable development of the enterprise. Water environment governance is a governance process with multiple strategic dimensions and large investment scale. A single water environment governance project is often difficult to fully meet all the strategic needs of the enterprise. How to scientifically select and combine multiple water environment governance projects under limited resource conditions to ensure that the implementation of the project portfolio is consistent with the strategic goals of water environment governance, promotes the healthy development of the enterprise's organization, and brings reasonable economic benefits to the enterprise to maintain sustainable development is a key issue facing enterprise managers.

[0003] As my country's economic development shifts from high speed to high quality, enterprises not only pursue economic benefits when formulating development strategies, but also consider environmental responsibility, social responsibility, corporate governance and other factors to achieve sustainable development. There are usually some conflicts and contradictions between these strategic goals, and it is necessary to further consider the fit between strategic goals and balance the conflicts between strategic goals through project portfolio selection. However, the current quantitative evaluation method of project portfolio strategic fit still has room for improvement. The strategic fit measurement method based on subjective evaluation is prone to deviation due to expert preference, while the objective evaluation method is too dependent on current data characteristics and it is difficult to draw on historical project experience, making the evaluation results lack of interpretability. Therefore, a water environment governance project portfolio selection method for multi-dimensional strategic fit is urgently needed to solve the above problems. Summary of the invention

[0004] The purpose of the present invention is to provide a water environment governance project portfolio selection method for multi-dimensional strategic fit, which combines an intelligent solution algorithm with a scheme optimization algorithm, thereby improving the quality and diversity of the solved project portfolio selection schemes, compressing the scale of the Pareto solution set, and reducing the decision-making difficulty of managers, thus providing a practical project portfolio selection model for improving the governance capacity of water environment governance projects.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a method for selecting a water environment management project portfolio for multi-dimensional strategic fit, comprising the following steps:

[0006] S1. Construct a set of strategic indicators for water environment management, economic benefits and corporate development strategic goals;

[0007] S2. Establish a nonlinear mapping relationship between strategic indicators and strategic fit, and evaluate the fit between the project portfolio and strategic goals in multiple dimensions;

[0008] S3. Construct a project portfolio selection model that considers multi-dimensional strategic fit under resource constraints, and use intelligent algorithms to solve the Pareto solution set of the project portfolio selection model;

[0009] S4. Based on the PPSOS method, representative Pareto solutions are screened out from the Pareto solution set.

[0010] Preferably, the strategic goals of water environment governance can be decomposed into: the improvement rate of Class I to III water quality in national control sections, the improvement rate of Class V water quality in national control sections, the improvement rate of sewage treatment capacity, the coverage rate of urban pipe networks, the improvement rate of naturalization of river banks and lakeshores, the treatment rate of river dredging sediment, the improvement rate of flood control and drainage capacity, the improvement rate of urban greening coverage, etc.; the strategic goals of enterprise development can be decomposed into: the improvement rate of industry competitiveness, the growth rate of senior technical and management personnel, the improvement rate of professional and technical capabilities, the growth rate of enterprise human resources and other indicators related to enterprise development; the economic benefit goals of enterprises can be reflected by net present value.

[0011] Preferably, in step S2, AP-NFIS (Arbitrary Power Neural Fuzzy Inference System) is used to establish a nonlinear mapping relationship between strategic indicators and strategic fit, so as to evaluate the fit between the project portfolio and strategic goals in multiple dimensions, specifically including:

[0012] S21: The strategic fit problem of the project portfolio is defined as: the strategic indicator set of the project portfolio in the water environment governance strategy (j=1) and the enterprise development strategy (j=2) is expressed as: In the formula, j is the number of strategic goal dimensions, n is the number of strategic indicators under the jth dimension, and N is the total number of strategic indicators under the jth dimension. Indicates the specific value of the nth strategic indicator under the jth dimension;

[0013] S22: Map the indicator value to strategic fit, the mathematical form is: Y j =f s (X j );where Y j represents the strategic fit, fs (·) represents the mapping relationship between the above strategic indicators and strategic fit;

[0014] The strategic indicator value of the project portfolio Input AP-NFIS network, use root mean square error to evaluate input space (strategic indicator) and output space (strategic fit) Y j The fitting error ε between ε and ε is expressed as:

[0015] The problem of measuring strategic fit can be expressed as: j =f AP-NFIS (X j |C1,C2,…,C m ), where A and B represent the NFIS parameter set, C is the bias, and m is the number of biases;

[0016] S23: In the constructed AP-NFIS network, the strategic indicator set Each indicator value in is first converted into a membership value through a membership function, expressed as: Among them, r (r = 1, 2, ..., R) is the index of the fuzzy set, so there are a total of N R fuzzy sets, and is the hyperparameter of the fuzzy set of the nth element in the rth fuzzy set, which is used to adjust the shape and width of the membership function to adapt to different data characteristics and fuzziness requirements;

[0017] According to the general paradigm of fuzzy computing, the strategic indicator set X can be further divided into j The activation degree is defined as the degree of adaptability of each rule to the input strategic indicator set. The activation degree can be calculated by the membership function corresponding to the fuzzy rule, which is specifically expressed as the product of the membership of the premise part of the rule or other synthetic operations. The calculation expression of the activation degree can be expressed as:

[0018]

[0019] The constructed AP-NFIS adopts fuzzy subdomains to fit the strategic indicator set and Y j The complex nonlinear relationship between the fuzzy subdomain can be expressed as: k =F(W k ,x j ,β k ), where W k (w 1,k ,…w N,k) represents the learnable network weight set in the forward and backward propagation processes of AP-NFIS; the calculation method of the fuzzy subdomain can be expressed as:

[0020] Finally, the fuzzy subdomain outputs the strategic fit of the project portfolio, realizing the comprehensive evaluation of the strategic fit of the project portfolio through AP-NFIS. This process is expressed as: Among them, Y j Indicates strategic fit, represents the specific value of the nth strategic indicator under the jth dimension, j = 1 represents the water environment governance strategic indicator set, j = 2 represents the enterprise development strategic indicator set, k represents the kth fuzzy set, N R represents the total number of fuzzy sets;

[0021] Preferably, in step S3, the resource limitation situation includes:

[0022] Updatable resource constraints: in, K represents the consumption of the nth type of renewable resources by the jth project in the t-period project portfolio. n,t It represents the stock of the nth type of renewable resources in period t;

[0023] Non-updatable resource constraints: Where T represents the interest period, t∈T, represents the consumption of the nth type of non-renewable resources by the jth project in the t-period project portfolio, Indicates the total amount of the nth type of non-renewable resources;

[0024] Constraints on water environment governance effects, urban sewage treatment volume (10,000 t / d), flood retention belt landscaping project area (m 2 ), riverside and lakeside ecological wetland restoration area (m 3 ), storage capacity (m 3 ) and the length of new and repaired sewage interception pipelines in towns (km) and other constraints: in, It represents the water environment governance index value, including the specific governance effect of the urban sewage treatment volume and the riverside and lakeside wetland restoration area that can be improved by the enterprise's project implementation, Θ s Indicates the standard value of water environment management;

[0025] The enterprise's organizational capacity constraints: the number of all projects that an enterprise can execute during the entire investment cycle is limited and determined by the enterprise's organizational capacity. Therefore, it is necessary to constrain the number of project selections. Assume that z j ∈{0,1}, indicating that if item j is selected, then z j =1, otherwise z j=0, then the project quantity constraint during the investment period can be expressed as: Among them, z j The number of items selected, N s It is the maximum number of projects that can be carried out simultaneously during the entire strategic cycle.

[0026] Preferably, when constructing a project portfolio selection model, first perform the following operations:

[0027] The strategic fit objective function constructed using AP-NFIS is:

[0028] Obj1 and Obj2 represent the strategic fit inference values ​​of water environment governance strategy and enterprise development strategy, respectively. represents the AP-NFIS network with a quadratic polynomial kernel function, represents the strategic indicator value of project portfolio j under the kth (k=1,,2}) dimension strategy (water environment governance strategy and enterprise development strategy), (A k ,B k ,C k ) represents the network parameter set learned by AP-NFIS under the k-th dimension strategy. The training dataset of AP-NFIS consists of historical data of experts’ evaluation of the strategic fit of project portfolios;

[0029] To construct the revenue target of the water environment governance project portfolio, we first need to clarify the capital items of the project portfolio in the entire investment cycle, including: financing cost FI, government subsidy SI, project construction investment CI, project operation and maintenance return OPR, project operation and maintenance fee OPI, and tax payable after subsidy TC; on the basis of clarifying the project capital items, the revenue target function of the water environment governance project portfolio can be constructed, which can be expressed as:

[0030]

[0031] The decision variable for project portfolio selection is defined as: P =(x1,…,x p ,…,x P ),p∈P, where X P Each element x in p Satisfy x p ∈{0,1}, when item p is selected, the corresponding x p =1, otherwise, if not selected, then x p =0;

[0032] Adding decision variables to the above constraints and further combining them with the optimization objectives of the model, the final project portfolio selection model is:

[0033]

[0034]

[0035] Among them, Obj1 and Obj2 represent the strategic fit inference values ​​of water environment governance strategy and enterprise development strategy respectively. represents the AP-NFIS network with quadratic polynomial kernel function, X P The decision variables for the project portfolio selection, A k ,B k ,C k represents the network parameter set learned by AP-NFIS under the k-th dimension strategy, FI is the financing cost, SI is the government subsidy, CI is the project construction investment, i c is the discount rate, P is the number of candidate projects in the project pool, CE t is the initial investment made by the enterprise in period t to implement the project portfolio, z p is the selection of candidate item p in the item pool. If item p is selected, then z p =1, otherwise z p =0, is the water environment management index value of project p, OPR t,j is the operation and maintenance return of the jth project in the t-cycle project portfolio, OPI t,j is the operation and maintenance cost of the jth project in the t-cycle project portfolio, and TC is the tax payable after subsidy.

[0036] Preferably, in step S3, the project portfolio selection model is solved using the HV-NSGA-III algorithm, and specifically:

[0037] Non-dominated solution stratification and sorting: First, the non-dominated sorting algorithm is applied to the initial generation population P t The (initial project portfolio selection scheme set) is classified to form several non-dominated layers. Then, the critical layer screening technology is used to retain only those non-dominated layers with high priority to the subsequent generations, so that the schemes in the new generation population are better than the initial population schemes;

[0038] Standardization operation of the objective function: First, the optimal value of all objective function values ​​(strategic fit values) in the current population is obtained to form an ideal point. Then, the ideal point is subtracted from the objective value of all individuals to achieve the transformation of the solution space coordinates. The ideal point is moved to the origin through translation operation, and then the extreme point and intercept are calculated.

[0039] Reference point setting: Using the boundary cross weight construction algorithm, the target of each dimension is evenly divided into p′ segments on the normalized reference plane, thereby uniformly generating reference points, connect the ideal points in the previous step and these reference points to form a reference line;

[0040] Calculate extreme points: Combined with the project portfolio objective function (strategic fit) constructed above, the ASF (Achievement Scalarizing Function) function is used to process the objectives of each dimension to identify those points that show extremely high values ​​on a certain objective but low values ​​on other objectives. Such points are regarded as extreme points. The intercept on the corresponding coordinate axis can be calculated based on the function value of the extreme point.

[0041] Reference line and association: The line connecting the reference point and the origin is used as the reference line of the reference point in the target space. For each population individual (possible optimal project portfolio selection plan), all reference point vectors are traversed to find the reference point closest to each project portfolio selection plan, and the position of the reference point and the corresponding shortest distance are recorded. Through continuous iteration, the optimal solution, that is, the optimal project portfolio selection plan, is finally obtained.

[0042] The Hypervolume Indicator measurement rule is introduced to improve the solution quality. The hypervolume measurement process is as follows:

[0043] Normalization of objective function value (strategic fit value): First, each objective function value (strategic fit value) is first linearly normalized to k=1,2,3; where represents the project portfolio selection decision variable, which corresponds one-to-one to the project portfolio selection scheme. is the verification value of target k, that is, the strategic fit value of the kth dimension of the verified project portfolio, which is obtained by AP-NFIS mapping and can be expressed as: is the value of the normalized objective function k, and are the minimum and maximum values ​​of the objective function k found in the feasible solution space;

[0044] Calculate the hypervolume contribution of non-dominated solutions: For each solution in the Pareto solution set The super volume contribution can be calculated as follows: In the formula, r k is the reference point coordinate of the kth target;

[0045] Calculate the cumulative hypervolume: add up the hypervolume contributions of all points to get the total hypervolume of the entire Pareto front: In the formula, represents the Pareto solution The higher the super volume index, the closer the solution set is to the Pareto optimal frontier and the more uniform the distribution of solutions is, that is, the higher the quality and diversity of solutions are.

[0046] Preferably, in step S4, in order to ensure the efficiency and practicality of the final solution set, in the PPSOS process, the project portfolio solution set output by the HV-NSGA-III algorithm is first optimized by the Pareto solution set pruning strategy, and the Pareto solution set screening includes:

[0047] Identify duplicate solutions: By comparing each solution in the solution set with other solutions, identify those solutions that are the same or very close in target value (strategic fit value);

[0048] Identify non-dominated solutions: Evaluate each solution (project portfolio selection plan) in the solution set to determine whether it is dominated by other solutions in the solution set. Specifically, if there is another solution that is not inferior to the current solution in all objectives (strategic fit) and is superior to the current solution in at least one objective, then the current solution is considered to be dominated;

[0049] Eliminate inferior and duplicate solutions: All solutions identified as duplicate or dominated are removed from the solution set, leaving only those non-dominated independent solutions.

[0050] Further preferably, considering that cluster analysis can effectively identify the commonalities of groups in the solution set and retain the diversity of solutions, the Pareto optimal solution set obtained by cluster analysis of the above steps is grouped by K-medoids algorithm, and the cluster center in each group is used as the representative solution. The core formula can be expressed as: Among them, m j′ represents the jth cluster in the Pareto solution set, is the cluster representative in the j′th cluster, that is, the representative project portfolio selection scheme; and

[0051] Quality evaluation of representative solutions based on joint metrics: To overcome the shortcomings of existing metrics, a joint metric based on relative Euclidean index and relative cosine index is proposed;

[0052] The relative Euclidean index can be defined as: In the formula, |C j′ | is the cluster C j′ The number of midpoints, m j′ is the cluster C j′ The center of the cluster, J′ is the total number of clusters, and the relative Euclidean index I REI The smaller the value of (J′), the better the clustering result, that is, the higher the similarity within the cluster and the better the separability between clusters;

[0053] The relative cosine index can be defined as: I RCI The larger the (J′) value is, the stronger the cosine similarity between the two values ​​is. RCIThe larger the (J′) value is, the more similar the central data point is to other data points in its cluster, that is, the more widely the representative solution is distributed along the original Pareto frontier, and the representative solution set well preserves the diversity of the original solution set, that is, the representative project portfolio selection scheme can preserve the diversity of all project portfolio selection schemes in the Pareto solution set.

[0054] I RCI The smaller the (J′) value, the opposite is true;

[0055] The joint metric of relative Euclidean index and relative cosine index can be expressed as:

[0056]

[0057] Where α represents an adjustment factor (0<α<1) used to balance the importance of intra-cluster similarity and inter-cluster separability.

[0058] Beneficial effects: The present invention provides a water environment governance project portfolio selection method for multi-dimensional strategic fit, uses AP-NFIS to evaluate the degree of fit of multi-dimensional strategic goals, and solves the Pareto solution set of the project portfolio selection model through the HV-NSGA-III algorithm to obtain a project portfolio plan with better diversity and higher quality. For repeated solution sets and large solution sets, the PPSOS method is used to screen out representative Pareto solutions, thereby refining the solution set output by the intelligent algorithm, reducing the decision-making difficulty of managers, and ensuring the scientificity and practicality of the decision-making plan.

[0059] Among them, the present invention combines the powerful machine learning ability of neural networks and the human-like reasoning and evaluation ability of fuzzy logic through arbitrary power neural fuzzy inference machine technology, increases the interpretability of the system, and provides managers with intuitive understanding and decision support; and in view of the limited dispersion and diversity of solution sets of classic algorithms such as NSGA-III algorithm and MOEA / D algorithm, further introduces hypervolume indicator measurement rules to improve the quality of solution sets, provides higher quality Pareto solution sets, and provides a more scientific and efficient selection plan for project portfolios under multi-dimensional strategic goals.

[0060] The present invention further refines and optimizes the project portfolio selection scheme generated by the HV-NSGA-III algorithm through a scheme optimization method based on Pareto pruning, reduces the complexity of decision-making, effectively balances the gap between theoretical models and practical applications, and ensures the scientificity and practicality of the decision-making scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0062] In the attached picture:

[0063] Figure 1 A schematic diagram of the multi-dimensional strategic composition of the method of the present invention and the process of selecting a project portfolio that is compatible with the multi-dimensional strategy;

[0064] Figure 2 A network structure diagram of the AP-NFIS method proposed in the present invention;

[0065] Figure 3 The present invention proposes an AP-NFIS network strategy fit reasoning process diagram;

[0066] Figure 4 A schematic diagram of multi-objective optimization of the project portfolio selection model of the present invention;

[0067] Figure 5 The solution flow chart of the HV-NSGA-III algorithm proposed by the present invention is as follows;

[0068] Figure 6 The principle diagram of the PPSOS method proposed by the present invention;

[0069] Figure 7 A flow chart showing the optimal selection of the project combination of the present invention;

[0070] Figure 8 FIG. 1 is a diagram of the training process of the AP-NFIS network parameter set of the present invention;

[0071] Fig. 9 A Pareto front graph solved by the HV-NSGA-III algorithm of the present invention;

[0072] Fig.10 This is a representative Pareto solution identification result diagram based on the PPSOS method of the present invention;

[0073] Fig.11 This is a representative Pareto solution identification process diagram based on the PPSOS method of the present invention. DETAILED DESCRIPTION

[0074] The embodiments of the present invention are described below in conjunction with the drawings in the embodiments of the present invention. The terms used in the implementation mode of the present invention are only used to explain the specific embodiments of the present invention, and are not intended to limit the present invention. The embodiments of the present application are described below in conjunction with the drawings.

[0075] Example: Figure 1-Figure 7 As shown in the figure, a method for selecting a water environment governance project portfolio with multi-dimensional strategic fit includes the following steps:

[0076] S1. Considering the strategic goal needs of enterprises in different dimensions, a strategic fit evaluation index system for water environment governance enterprises is constructed, and a measurement method for each evaluation index value is proposed. The specific evaluation indicators and their quantification methods are as follows:

[0077] First, an evaluation index system that considers water environment management, economic benefits and corporate development strategic goals is constructed. The strategic goals of water environment management can be decomposed into: the improvement rate of Class I to III water quality in national control sections, the improvement rate of Class V water quality in national control sections, the improvement rate of sewage treatment capacity, the coverage rate of urban pipe networks, the naturalization improvement rate of river banks and lakeshores, the treatment rate of river dredging sediment, the improvement rate of flood control and drainage capacity, the improvement rate of urban greening coverage, etc.; the strategic goals of corporate development can be decomposed into: the improvement rate of industry competitiveness, the growth rate of senior technical and management personnel, the improvement rate of professional and technical capabilities, the growth rate of corporate human resources and other indicators related to corporate development; the corporate economic benefit goals can be reflected by net present value;

[0078] Specifically: In the strategic objectives of water environment governance:

[0079] Improvement rate of Class I-III water quality in national controlled sections: Water Quality Assessment Indicator (WQI) was used to evaluate the improvement rate of Class I-III water quality in national controlled sections of rivers before and after the implementation of the water environment governance project portfolio. I-III) The specific calculation method is expressed as: In the formula, and They represent the number of national monitoring sections of Class I to III water quality in the later period t+Δt of the basin where the project portfolio is implemented, and Respectively represent the number of sections with water quality of Class I-III in the previous period t; NA s represents the total number of sections monitored, Δt represents the time difference between the previous and next periods, which is the implementation period of the project portfolio;

[0080] Improvement rate of Class V water quality in the state-controlled section: Improvement rate of Class V water quality in the river monitoring section before and after the implementation of the water environment governance project portfolio WQI (V) The specific calculation method is expressed as: In the formula, Indicates the number of sections with inferior V-class water quality in the later period t+Δt; Indicates the number of sections with inferior V-class water quality in the previous period t;

[0081] Sewage treatment capacity improvement rate: Urban sewage refers to the domestic sewage of urban residents, drainage from government agencies, schools, hospitals, commercial service agencies and various public facilities, as well as industrial wastewater and initial rainwater that are allowed to be discharged into the urban sewage collection system. The unit of measurement for the treatment capacity of urban sewage treatment plants is generally "10,000 m3 / day”, and the wastewater treatment capacity assessment indicator (WCI) was used to evaluate the improvement rate of wastewater treatment capacity before and after the implementation of the water environment governance project, expressed as: Where, WTC t+Δt It represents the sewage treatment capacity in the later period t+Δt (after the implementation of the project combination); WTC t It represents the sewage treatment capacity in the previous period t (before the implementation of the project combination);

[0082] Urban pipe network coverage rate: The Urban Stormwater and Sewage Network Coverage Ratio Assessment Indicator (UCI) is used to measure the improvement of the coverage rate of urban stormwater and sewage pipe networks by water environment governance projects, expressed as: In the formula, and They represent the urban built-up area covered by the rainwater and sewage pipe networks renovated and newly built by the project portfolio in period t, It represents the repeated calculation of the urban built-up area covered by the rainwater and sewage pipe network renovated and newly built in the t period, PV (S) It represents the total built-up area of ​​the town;

[0083] Riverbank and lakeshore naturalization improvement rate: The Riverbank and Lakeshore Naturalization Assessment Indicator (RLI) is used to measure the riverbank and lakeshore naturalization rate before and after the implementation of the water environment management project, expressed as: In the formula, and They represent the ecological areas of the river channel and lakeside belts restored in the later period (after the implementation of the project portfolio), and The ecological area of ​​river belt and lakeside belt in the later period (before the implementation of the project portfolio);

[0084] River dredging sediment treatment rate: The sewage treatment capacity evaluation index (Sediment Treatment Assessment Indicator, STI) is used to evaluate the river dredging sediment treatment rate before and after the implementation of the water environment management project, expressed as: In the formula, STC t+ΔtIt represents the volume of river dredged sediment treated as resource and harmless in the later period t+Δt (after the implementation of the project combination) (unit: 10,000 m 3 ), STC s It indicates the total volume of dredged sediment that needs to be processed in the current watershed;

[0085] Improvement rate of flood control and drainage capacity: Drainage pumping stations are the core components of urban flood control systems. The improvement of flood control and drainage capacity is evaluated by the scale of newly added drainage pumping stations in the region, expressed as: In the formula, FDI represents the improvement rate of flood control and drainage capacity, DSC t+Δt represents the installed capacity of the newly built or renovated drainage pump station in the later period t+Δt (after the implementation of the project combination) (unit: kilowatt), DSC t represents the installed capacity of the drainage pump station in the previous period t (before the implementation of the project portfolio);

[0086] Urban greening coverage improvement rate: The greening projects implemented in the water environment governance project are mainly garden greening projects that undertake flood storage and retention functions and are adjacent to water bodies. The urban greening coverage improvement rate is measured by the proportion of the urban built-up area covered by the new greening projects to the total urban built-up area, expressed as: In the formula, UGI represents the urban green coverage improvement rate, GCA t+Δt It represents the built-up area covered by the newly built greening project in the later period t+Δt (after the implementation of the project combination) (unit: 10,000 m 2 ), V (S) It represents the total built-up area of ​​the town;

[0087] In the enterprise development strategy goals:

[0088] Industry competitiveness improvement rate: The comprehensive wastewater treatment cost (CWC) is used to discount the water cost per ton of the project portfolio. If the calculated comprehensive wastewater treatment cost per ton is less than or equal to the market cost, the project portfolio is considered to be market competitive. The ratio of the average market cost to the comprehensive wastewater treatment cost per ton of the enterprise is used as the market competitiveness index CCI for judging the enterprise. The larger the value, the greater the market competitiveness of the enterprise. Otherwise, the competitiveness is smaller. The CCI index is free from the restrictions of project scale and type. It analyzes the main factors affecting the cost of sewage treatment. The calculation method of CCI is: In the formula, MWC represents the average cost per ton of water in the market, CI t,n represents the construction investment cost of the nth sewage treatment plant in the project portfolio in period t, OPI t,n Represents the operation and maintenance cost of the sewage treatment plant, FI t,nThe financing cost of the sewage treatment plant is the long-term and short-term interest generated by the loan during the construction period of the sewage treatment plant and the working capital loan during the operation period. t,n Indicates the amount of tax payable, including income tax, value-added tax, etc. Sewage treatment projects are generally affected by tax preferential policies and enjoy certain tax exemptions. WT t,n It represents the tons of sewage treated by the sewage treatment plant in period t;

[0089] Senior technical and management personnel growth rate: The growth rate of senior professional and technical personnel is used to evaluate the degree to which the implementation of the water environment governance project portfolio improves the professional and technical level and management capabilities of the lead enterprise, expressed as: In the formula, TMI represents the growth rate of senior technical and management personnel, TMN t+Δt It represents the number of technical and management personnel with the title of senior engineer or project manager (deputy manager) or above that are expected to be added in the later period t+Δt (after the implementation of the project portfolio), TMN t Indicates the total number of personnel at the above level in the previous period;

[0090] Professional and technical capability improvement rate: The number of invention and utility model patents is used as the main indicator to quantify the professional and technical capabilities of the lead enterprise, which can be expressed as: In the formula, PTI represents the rate of improvement of professional and technical capabilities, PN t+Δt Indicates the number of invention and utility model patents expected to be added after the implementation of the project portfolio, PN t Indicates the total number of invention and utility model patents in the field before implementation;

[0091] Enterprise human resource growth rate: The ratio of the number of new employees before and after the implementation of the project portfolio to the total number of employees before implementation is used as an indicator to measure the improvement of the organization's human resources, which can be expressed as: In the formula, HRI represents the growth rate of enterprise human resources, EN t+Δt Indicates the number of new employees added to the project portfolio implementation, EN t represents the total number of employees before implementation;

[0092] Economic benefit target: Net present value is used as the economic benefit target of the lead enterprise to implement the water environment governance project portfolio. Net present value (NPV) is a key financial indicator used to measure the overall economic benefits of the investment project portfolio. The net present value evaluates the value of the selected project portfolio by comparing the sum of the present value of the project's expected future cash flows with the initial investment cost. Considering the long construction and operation cycle of water environment governance projects, NPV is an extremely important tool for measuring the time value of money. The net present value is equal to the discounted value of the future cash flow generated by the investment minus the project investment cost. The calculation formula is: In the formula, CI represents cash inflow, CO represents cash outflow, CI-CO represents net cash flow, and i c Represents the discount rate.

[0093] S2. Use AP-NFIS (Arbitrary Power Neural Fuzzy Inference System) to model the complex nonlinear mapping relationship between strategic evaluation indicators and strategic fit, and evaluate the fit between the project portfolio and strategic goals in multiple dimensions, such as Figure 2 and Figure 3 As shown in Figure 2, the process of constructing a mathematical model to evaluate strategic fit is:

[0094] S21: The strategic fit problem of the project portfolio is defined as: the strategic indicator set of the project portfolio in the water environment governance strategy (j=1) and the enterprise development strategy (j=2) is expressed as: In the formula, j is the number of strategic goal dimensions, n is the number of strategic indicators under the jth dimension, and N is the total number of strategic indicators under the jth dimension. Indicates the specific value of the nth strategic indicator under the jth dimension;

[0095] S22: Map the indicator value to strategic fit, the mathematical form is: Y j =f s (X j );where Y j represents the strategic fit, f s (·) represents the mapping relationship between the above strategic indicators and strategic fit;

[0096] The strategic indicator value of the project portfolio Input AP-NFIS network, use root mean square error to evaluate input space (strategic indicator) and output space (strategic fit) Y j The fitting error ε between ε and ε is expressed as:

[0097] The problem of measuring strategic fit can be expressed as: j =f AP-NFI S(X j |C1,C2,…,C m ), where A and B represent the NFIS parameter set, C is the bias, and m is the number of biases;

[0098] S23: In the constructed AP-NFIS network, the strategic indicator set Each indicator value in is first converted into a membership value through a membership function, expressed as:

[0099] Among them, r (r = 1, 2, ..., R) is the index of the fuzzy set, so there are a total of N R fuzzy sets, and is the hyperparameter of the fuzzy set of the nth element in the rth fuzzy set, which is used to adjust the shape and width of the membership function to adapt to different data characteristics and fuzziness requirements;

[0100] According to the general paradigm of fuzzy computing, the strategic indicator set X can be further divided into j The activation degree is defined as the degree of adaptability of each rule to the input strategic indicator set. The activation degree can be calculated by the membership function corresponding to the fuzzy rule, which is specifically expressed as the product of the membership of the premise part of the rule or other synthetic operations. The calculation expression of the activation degree can be expressed as:

[0101]

[0102] The constructed AP-NFIS adopts fuzzy subdomains to fit the strategic indicator set and Y j The complex nonlinear relationship between the fuzzy subdomain can be expressed as: k =F(W k ,x j ,β k ), where W k (w 1,k ,…w N,k ) represents the learnable network weight set in the forward and backward propagation processes of AP-NFIS; the calculation method of the fuzzy subdomain can be expressed as:

[0103] Finally, the fuzzy subdomain outputs the strategic fit of the project portfolio, realizing the comprehensive evaluation of the strategic fit of the project portfolio through AP-NFIS. This process is expressed as:

[0104] S3. Construct a project portfolio selection model that considers multi-dimensional strategic fit under resource constraints, such as Figure 4 As shown in the figure, the HV-NSGA-III algorithm (Hypervolume Indicator-non-dominated sorting genetic algorithm-Ⅲ, a third-generation non-dominated sorting genetic algorithm that introduces hypervolume indicator measurement rules) is used to solve the Pareto solution set of the project portfolio selection model, so as to obtain a project portfolio solution set with diversity and higher quality; resource constraints include:

[0105] Updatable resource constraints: in, K represents the consumption of the nth type of renewable resources by the jth project in the t-period project portfolio. n,t It represents the stock of the nth type of renewable resources in period t;

[0106] Non-updatable resource constraints: Where T represents the interest period, t∈T, represents the consumption of the nth type of non-renewable resources by the jth project in the t-period project portfolio, Indicates the total amount of the nth type of non-renewable resources;

[0107] Constraints on water environment governance effects, urban sewage treatment volume (10,000 t / d), flood retention belt landscaping project area (m 2 ), riverside and lakeside ecological wetland restoration area (m 3 ), storage capacity (m 3 ) and the length of new and repaired sewage interception pipelines in towns (km) and other constraints: in, It represents the water environment governance index value, including the specific governance effect of the urban sewage treatment volume and the riverside and lakeside wetland restoration area that can be improved by the enterprise's project implementation, Θ s Indicates the standard value of water environment management;

[0108] The enterprise's organizational capacity constraints: the number of all projects that an enterprise can execute during the entire investment cycle is limited and determined by the enterprise's organizational capacity. Therefore, it is necessary to constrain the number of project selections. Assume that z j ∈{0,1}, indicating that if item j is selected, then z j =1, otherwise z j =0, then the project quantity constraint during the investment period can be expressed as: Among them, z j The number of items selected, N s It is the maximum number of projects that can be carried out simultaneously during the entire strategic cycle.

[0109] When building a project portfolio selection model, first do the following:

[0110] The strategic fit objective function constructed using AP-NFIS is:

[0111] Obj1 and Obj2 represent the strategic fit inference values ​​of water environment governance strategy and enterprise development strategy, respectively. represents the AP-NFIS network with a quadratic polynomial kernel function, represents the strategic indicator value of project portfolio j under the kth (k = {1,,2}) dimension strategy (water environment governance strategy and enterprise development strategy), (A k ,Bk ,C k ) represents the network parameter set learned by AP-NFIS under the k-th dimension strategy. The training dataset of AP-NFIS consists of historical data of experts’ evaluation of the strategic fit of project portfolios;

[0112] To construct the revenue target of the water environment governance project portfolio, we first need to clarify the capital items of the project portfolio in the entire investment cycle, including: financing cost FI, government subsidy SI, project construction investment CI, project operation and maintenance return OPR, project operation and maintenance fee OPI, and tax payable after subsidy TC; on the basis of clarifying the project capital items, the revenue target function of the water environment governance project portfolio can be constructed, which can be expressed as:

[0113]

[0114] The decision variable for project portfolio selection is defined as: P =(x1,…,x p ,…,x P ),p∈P, where X P Each element x in p Satisfy x p ∈{0,1}, when item p is selected, the corresponding x p =1, otherwise, if not selected, then x p =0;

[0115] Adding decision variables to the above constraints and further combining them with the optimization objectives of the model, the final project portfolio selection model is:

[0116]

[0117] Among them, Obj1 and Obj2 represent the strategic fit inference values ​​of water environment governance strategy and enterprise development strategy respectively. represents the AP-NFIS network with quadratic polynomial kernel function, X P The decision variables for the project portfolio selection, A k ,B k ,C k represents the network parameter set learned by AP-NFIS under the k-th dimension strategy, FI is the financing cost, SI is the government subsidy, CI is the project construction investment, i c is the discount rate, P is the number of candidate projects in the project pool, CE t is the initial investment made by the enterprise in period t to implement the project portfolio, z p is the selection of candidate item p in the item pool. If item p is selected, then z p =1, otherwise z p =0, is the water environment management index value of project p, OPR t,j is the operation and maintenance return of the jth project in the t-cycle project portfolio, OPI t,j is the operation and maintenance cost of the jth project in the t-cycle project portfolio, and TC is the tax payable after subsidy;

[0118] The HV-NSGA-III algorithm is used to solve the project portfolio selection model, such as Figure 5 as shown; and specifically:

[0119] Non-dominated solution stratification and sorting: First, the non-dominated sorting algorithm is applied to the initial generation population P t The (initial project portfolio selection scheme set) is classified to form several non-dominated layers. Then, the critical layer screening technology is used to retain only those non-dominated layers with high priority to the subsequent generations, so that the schemes in the new generation population are better than the initial population schemes;

[0120] Standardization operation of the objective function: First, the optimal value of all objective function values ​​(strategic fit values) in the current population is obtained to form an ideal point. Then, the ideal point is subtracted from the objective value of all individuals to achieve the transformation of the solution space coordinates. The ideal point is moved to the origin through translation operation, and then the extreme point and intercept are calculated.

[0121] Reference point setting: Using the boundary cross weight construction algorithm, the target of each dimension is evenly divided into p' segments on the normalized reference plane, thus uniformly generating reference points, connect the ideal points in the previous step and these reference points to form a reference line;

[0122] Calculate extreme points: Combined with the project portfolio objective function (strategic fit) constructed above, the ASF (Achievement Scalarizing Function) function is used to process the objectives of each dimension to identify those points that show extremely high values ​​on a certain objective but low values ​​on other objectives. Such points are regarded as extreme points. The intercept on the corresponding coordinate axis can be calculated based on the function value of the extreme point.

[0123] Reference line and association: The line connecting the reference point and the origin is used as the reference line of the reference point in the target space. For each population individual (possible optimal project portfolio selection plan), all reference point vectors are traversed to find the reference point closest to each project portfolio selection plan, and the position of the reference point and the corresponding shortest distance are recorded. Through continuous iteration, the optimal solution, that is, the optimal project portfolio selection plan, is finally obtained.

[0124] The Hypervolume Indicator measurement rule is introduced to improve the solution quality. The hypervolume measurement process is as follows:

[0125] Normalization of objective function value (strategic fit value): First, each objective function value (strategic fit value) is first linearly normalized to k=1,2,3; where represents the project portfolio selection decision variable, which corresponds one-to-one to the project portfolio selection scheme. is the verification value of target k, that is, the strategic fit value of the kth dimension of the verified project portfolio, which is obtained by AP-NFIS mapping and can be expressed as: is the value of the normalized objective function k, and are the minimum and maximum values ​​of the objective function k found in the feasible solution space;

[0126] Calculate the hypervolume contribution of non-dominated solutions: For each solution in the Pareto solution set The super volume contribution can be calculated as follows: In the formula, r k is the reference point coordinate of the kth target;

[0127] Calculate the cumulative hypervolume: add up the hypervolume contributions of all points to get the total hypervolume of the entire Pareto front: In the formula, represents the Pareto solution The higher the super volume index, the closer the solution set is to the Pareto optimal frontier and the more uniform the distribution of solutions is, that is, the higher the quality and diversity of solutions are.

[0128] S4, for repeated solutions and large solutions, such as Figure 6 As shown, the PPSOS method (ParetoPruning-based Solution Optimization Selection) is used to screen out representative Pareto solutions;

[0129] The specific algorithm flow of the solution optimization algorithm based on Pareto pruning is as follows:

[0130] In order to ensure the efficiency and practicality of the final solution set, in the PPSOS process, the project portfolio solution set output by the HV-NSGA-III algorithm is first optimized through the Pareto solution set pruning strategy. The Pareto solution set screening includes:

[0131] Identify duplicate solutions: By comparing each solution in the solution set with other solutions, identify those solutions that are the same or very close in target value (strategic fit value);

[0132] Identify non-dominated solutions: Evaluate each solution (project portfolio selection plan) in the solution set to determine whether it is dominated by other solutions in the solution set. Specifically, if there is another solution that is not inferior to the current solution in all objectives (strategic fit) and is superior to the current solution in at least one objective, then the current solution is considered to be dominated;

[0133] Eliminate inferior and duplicate solutions: All solutions identified as duplicate or dominated are removed from the solution set, leaving only those non-dominated independent solutions.

[0134] Further preferably, considering that cluster analysis can effectively identify the commonalities of the groups in the solution set and retain the diversity of solutions, Figure 7 As shown in the figure, the Pareto optimal solution set is obtained by clustering analysis of the above steps through K-medoids algorithm, and the cluster center in each group is used as the representative solution; the core formula can be expressed as: Among them, m j′ represents the jth cluster in the Pareto solution set, is the cluster representative in the j′th cluster, that is, the representative project portfolio selection scheme; and

[0135] Quality evaluation of representative solutions based on joint metrics: To overcome the shortcomings of existing metrics, a joint metric based on relative Euclidean index and relative cosine index is proposed;

[0136] The relative Euclidean index can be defined as: In the formula, |C j′ | is the cluster C j′ The number of midpoints, m j′ is the cluster C j′ The center of the cluster, J′ is the total number of clusters, and the relative Euclidean index I REI The smaller the value of (J′), the better the clustering result, that is, the higher the similarity within the cluster and the better the separability between clusters;

[0137] The relative cosine index can be defined as: I RCI The larger the (J′) value is, the stronger the cosine similarity between the two values ​​is. RCI The larger the (J′) value is, the more similar the central data point is to other data points in its cluster, that is, the more widely the representative solution is distributed along the original Pareto frontier, and the representative solution set well preserves the diversity of the original solution set, that is, the representative project portfolio selection scheme can preserve the diversity of all project portfolio selection schemes in the Pareto solution set.

[0138] I RCI The smaller the (J′) value, the opposite is true;

[0139] The joint metric of relative Euclidean index and relative cosine index can be expressed as:

[0140]

[0141] Where α represents an adjustment factor (0<α<1) used to balance the importance of intra-cluster similarity and inter-cluster separability.

[0142] Based on the above, in a specific embodiment:

[0143] Taking the CT Phase I project portfolio of water environment governance that CJ Environmental Protection Group plans to invest in as an example, the total investment is expected to be about 455 million yuan. Through preliminary investigations and evaluations of the market, resources and government policies, 21 projects have been included in the candidate project pool. Some of these projects come from government review projects, and the other part comes from corporate inspection projects. Projects from both sources are included in the candidate project pool. CJ Environmental Protection Group needs to evaluate the candidate projects based on their scale, implementation capabilities, etc. The main environmental governance indicators obtained through the investigation are shown in Table 3, specifically: ① Sewage treatment volume (10,000 t / d); ② Flood retention zone landscaping project area (m 2 );③ Riverbank and lakeside ecological wetland restoration area (m 2 );④ Storage capacity (m 3 ) ; ⑤ Length of newly built and repaired sewage interception pipelines (km). The first phase of the CT project portfolio for water environment governance involves sewage treatment plants, urban sewage pipe network projects, inner lake source control and sewage interception projects, ecological wetland restoration projects, tailwater purification projects, and live water quality improvement projects. Due to limited funds and organizational capacity, only some projects that best match the strategic goals can be selected from the pool of alternative projects for combined implementation. After market research and investigation, the information of the alternative projects to be implemented (the alternative project numbers are: P1~P21).

[0144] According to the above information, CJ Environmental Group plans to select several projects from the 21 candidate projects to form a water environment governance project portfolio for implementation. Project P1 is a government review project that the company must implement, and the remaining projects are company inspection projects that can be implemented selectively. Detailed project information and various parameters are shown in Tables 1 to 3:

[0145] Table 1 Information on the candidate projects for the first phase of CT water environment management of CJ Environmental Protection Group

[0146]

[0147]

[0148] Table 2 Parameters of alternative projects for the first phase of the CT water environment treatment project

[0149]

[0150] Table 3 Phased demand for water environment governance in the public sector

[0151]

[0152] Process analysis of multi-dimensional strategic fit assessment of water environment governance project portfolio;

[0153] According to the current strategic positioning of CJ Environmental Group and the characteristics of water environment governance projects, a strategic fit index system is constructed from three dimensions: water environment governance strategy, corporate development strategy and economic benefit goals, as shown in Table 4:

[0154] Table 4 Evaluation indicators of strategic fit of the first phase of the water environment governance CT project portfolio

[0155]

[0156]

[0157] The strategic fit assessment process for the first phase of the CJ Environmental Group water environment management project mainly includes the following two parts:

[0158] (1) Parameter set learning of the AP-NFIS network model: First, a post-evaluation of the strategic fit of 113 water environment governance projects that CJ Environmental Group is currently implementing and has completed is conducted. In order to integrate the advantages of subjective and objective evaluation methods, this study uses the analytic hierarchy process (AHP) and principal component analysis (PCA) to evaluate the strategic fit of CJ Environmental Group's historical projects based on water environment governance strategy and corporate development strategy, respectively. The indicator system for strategic fit evaluation is shown in Table 5. Subsequently, based on the post-evaluation results of historical data, subjective and objective evaluation data sets were constructed respectively. These two data sets were used to train the proposed arbitrary power neural fuzzy inference engine (AP-NFIS).

[0159] (2) Strategic fit reasoning of project portfolio: The AP-NFIS network model is trained using a mixed evaluation data set. The network parameter set obtained from the training represents the nonlinear relationship between the project strategic indicators and strategic fit. In the reasoning stage, by freezing the network parameter set and inputting the strategic indicator data of the first phase of the water environment management project of CJ Environmental Protection Group, the corresponding strategic fit evaluation can be obtained. This strategic fit reasoning process combines historical experience data and improves the modeling ability of complex nonlinear relationships, achieving a comprehensive evaluation of the strategic fit of candidate projects.

[0160] In order to further evaluate the inference performance of the proposed AP-NFIS model, the training and parameter learning process of the model is as follows: Figure 8As shown. Compared with the linear neuro-fuzzy inference system (NFIS), AP-NFIS has obvious advantages in the ability to understand subjective and objective evaluation data. Specifically, in the objective strategic fit evaluation dataset, the verification accuracy of AP-NFIS reached 82.23%, which is 6.60% higher than NFIS. In the subjective evaluation dataset, the verification accuracy of AP-NFIS was 71.92%, which was 8.71% better than NFIS. In the mixed dataset, the performance of AP-NFIS was relatively weak, but the reasoning accuracy could still reach 60.53%, which was 13.37% higher than NFIS. The verification results show that AP-NFIS can effectively understand the data characteristics of different evaluation methods. And compared with the linear NFIS, AP-NFIS exhibits stronger data processing capabilities. Thanks to the high-order power kernel function adopted, the proposed AP-NFIS can more accurately model the complex nonlinear relationship between the strategic indicators of the project portfolio and the strategic fit;

[0161] Analysis of the results of water environment governance project portfolio selection for multi-dimensional strategies:

[0162] The constructed project portfolio selection model is solved by the HV-HSGA-III algorithm to obtain the Pareto solution set of the water environment management project portfolio scheme; in order to avoid the situation where the strategic fit or the return is too low in the solution set, a minimum threshold is set for each target dimension; according to the opinions of the managers of CJ Environmental Protection Group, the strategic fit threshold of water environment management is set at 85%, the corporate development strategy fit threshold is 80%, and the net present value threshold is 500 million yuan. If the strategic fit and net present value of the project portfolio scheme are lower than these thresholds, it will be regarded as a portfolio failure and eliminated; under the same conditions, those project portfolio schemes that can take into account both strategic fit and project portfolio returns are preferred; after threshold screening, a Pareto solution set containing 83 project portfolio selection schemes is obtained;

[0163] The Pareto solution set is sorted according to the strategic fit of water environment governance, the fit of enterprise development strategy and the net present value, and the five best solutions are selected. The results are shown in Table 5, Table 6 and Table 7 respectively. From the results, it can be seen that the project combination with the largest net present value is: {P1-P3-P6-P7-P9-P10-P11-P13-P14-P15-P16-P17-P18-P20-P21}; its net present value of income is 559.3362 million yuan. In the Pareto solution set, the highest strategic fit of water environment governance is 98.32%, and the corresponding project combination is: {P1-P2-P3-P4-P7-P10-P11-P12-P13-P15-P16-P18-P19};

[0164] In addition, the highest degree of fit with the enterprise development strategy is 98.68%, and the corresponding project portfolio selection options are:

[0165] {P1-P3-P5-P7-P8-P10-P11-P12-P13-P15-P16-P17-P18-P20}.

[0166] Further analysis of the results of project portfolio selection shows that: compared with the project portfolio with the highest water environment governance strategy fit and the highest net present value, the water environment governance strategy fit increased by 9.89%, but at the same time the net present value decreased by 6.2794 million yuan, which shows that CJ Environmental Protection Group can maximize the water environment governance strategy undertaken (strategic fit is 98.32%) while giving up less economic benefits (relative to the total investment volume of 1.95 billion yuan). Similarly, compared with the project portfolio with the highest corporate development strategy fit and the highest return, the corporate development strategy fit is 13.25% higher, but at the same time the net present value is reduced by 5.5667 million yuan. In summary, there are certain conflicts and contradictions between the water environment governance strategy goals, corporate development strategy goals and the project portfolio's return goals, and compared with the maximum realization of the water environment governance strategy, the economic cost of realizing the corporate development strategy is relatively less.

[0167] Table 5 Pareto set of water environment governance CT phase I project portfolio selection (water environment governance strategy priority)

[0168]

[0169]

[0170] Table 6 Pareto set of water environment governance CT phase I project portfolio selection (enterprise development strategy priority)

[0171]

[0172] Table 7 Pareto set of project portfolio selection for the first phase of water environment governance CT (net present value priority)

[0173]

[0174] To further verify the effectiveness of the adopted HV-NSGA-III algorithm, the solution results of the HV-NSGA-III algorithm were compared with those of the classic NSGA-III and MOEA / D algorithms, and the average hypervolume metric method was used to evaluate the quality of the Pareto sets of different algorithms. To ensure the robustness of the results, each algorithm was run 15 times and the average value was recorded. The results are shown in Table 8:

[0175] Table 8 Average hypervolume metric results of the compared algorithms

[0176]

[0177] As shown in Table 8, for the solution problem of the constructed water environment governance project portfolio selection model, the average hypervolume metric (MHV) value of the Pareto solution set of the HV-NSGA-III algorithm is 60.80%~63.62%, which is better than the NSGA-III algorithm (61.13%~63.39%) and the MOEA / D algorithm (61.31%~63.05%). This shows that compared with the classic NSGA-III algorithm and the MOEA / D algorithm, the HV-NSGA-III algorithm can fully explore different areas of the Pareto frontier, so that the Pareto solution obtained has better dispersion, that is, the better the diversity of the solution. In addition, the average hypervolume metric results also show that the Pareto solution set obtained by the HV-NSGA-III algorithm is closer to the ideal Pareto frontier, that is, the higher the quality of the solution. In summary, the average hypervolume metric results prove the effectiveness of the HV-NSGA-III algorithm in solving the constructed project portfolio selection model, and the obtained water environment governance project portfolio has better diversity and higher quality.

[0178] Further observation shows that Fig. 9 As shown in the figure, although the HV-NSGA-III algorithm can obtain high-quality Pareto solutions, the solution set still contains many water environment governance project combination schemes, and there are still 83 schemes after threshold screening; for managers, it is still very difficult to judge the pros and cons of these 83 project combination schemes. In order to further reduce the scale of the Pareto solution set and reduce the decision-making difficulty of managers, a Pareto pruning-based optimization method is proposed to identify representative project combination schemes from the Pareto solution set, so that managers can choose the best solution from them, further reducing the decision-making difficulty of managers;

[0179] The Pareto pruning-based solution optimization (PPSOS) method was used to screen the Pareto solution set of the first phase of the water environment management project portfolio of CJ Environmental Protection Group. The T-SNE algorithm was used to visualize the clustering process in PPSOS. The results are as follows: Fig.10 As shown in the figure, the PPSOS method generates three solution clusters through the K-medoids clustering method. The solution clusters are distinguished by colors, and the cluster center of each cluster is marked with a "+" sign. Fig.10In the figure, CP, POP, MP and GN represent the crossover probability, population size, mutation probability and evolutionary generation of the HV-NSGA-III algorithm. The K-medoids clustering results show that when the evolutionary generation is 100, there is a certain mixture between different solution clusters, so the separability is not high. At this time, four cluster centers are identified by the K-medoids clustering method. When the evolutionary generation GN increases to more than 200 generations, the separability between solution clusters gradually improves, and the cluster centers stabilize at 3. When GN increases to 500 generations, the intra-class compactness of the same solution cluster is better, and the separability between different solution clusters is higher; the above results show that appropriately increasing the evolutionary generation of HV-NSGA-III can improve the performance of the K-medoids clustering method in the subsequent PPSOS method.

[0180] In addition, the results also show the effectiveness of combining K-medoids clustering with joint metrics in the proposed PPSOS method. In the PPSOS method, each cluster center corresponds to a representative project portfolio solution, so Fig.11 It can be seen that a total of three representative project portfolio selection schemes are obtained, and the results are shown in Table 9:

[0181] Table 9 Representative schemes of water environment governance CT phase I project portfolio

[0182]

[0183] Subsequently, managers can select the best solution from three representative project portfolio solutions based on their decision preferences (water environment governance strategy, corporate development strategy, and project portfolio benefits). The management decision-making level of CJ Environmental Group takes the water environment protection strategy formulated by the central government as the primary guide and refers to the recommendations in Table 9. The best project portfolio solution is:

[0184] {P1-P2-P3-P5-P7-P9-P10-P11-P12-P13-P16-P17-P18-P19-P21};

[0185] Compared with the scheme that only takes the project portfolio benefits as a single guide, the representative project portfolio scheme has improved its strategic fit with water environment governance by 8.72%, and has increased its benefits by 784,700 yuan compared with the scheme that only takes the water environment governance strategy as a single guide. Therefore, the PPSOS method can help managers achieve a balance between project portfolio benefits and strategic fit to a certain extent.

[0186] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. For ordinary technicians in this technical field, after knowing the contents recorded in the present invention, they can make several equivalent changes and substitutions without departing from the principle of the present invention. These equivalent changes and substitutions should also be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for selecting a water environment governance project portfolio with multi-dimensional strategic fit, characterized in that: The steps include: S1. Construct a set of strategic indicators for water environment management, economic benefits and corporate development strategic goals; S2. Establish a nonlinear mapping relationship between strategic indicators and strategic fit, and evaluate the fit between the project portfolio and strategic goals in multiple dimensions; S3. Construct a project portfolio selection model that considers multi-dimensional strategic fit under resource constraints, and use intelligent algorithms to solve the Pareto solution set of the project portfolio selection model; S4. Based on the PPSOS method, representative Pareto solutions are screened out from the Pareto solution set.

2. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 1 is characterized by: In step S1, the strategic goals of water environment management include: improvement rate of Class I to III water quality in national control sections, improvement rate of Class V water quality in national control sections, improvement rate of sewage treatment capacity, urban pipe network coverage rate, improvement rate of river bank and lakeside naturalization, river dredging sediment treatment rate, improvement rate of flood control and drainage capacity, and improvement rate of urban greening coverage; the strategic goals of enterprise development include: improvement rate of industry competitiveness, growth rate of senior technical and management personnel, improvement rate of professional and technical capabilities, and growth rate of enterprise human resources; the economic benefit goals of the enterprise are reflected in the net present value.

3. The method for selecting a water environment management project portfolio for multi-dimensional strategic fit according to claim 1 is characterized by: In step S2, a nonlinear mapping relationship is established using AP-NFIS, specifically including: The strategic indicator set is input into the AP-NFIS network, and the root mean square error is used to evaluate the fitting error between the strategic indicators and the strategic fit; In the AP-NFIS network, each indicator value is converted into a membership value through a membership function; and a fuzzy subdomain is used to fit the complex nonlinear relationship between strategic indicators and strategic fit; and The strategic fit of the project portfolio is output through the fuzzy subdomain: Among them, Y j Indicates strategic fit, represents the specific value of the nth strategic indicator under the jth dimension, j = 1 represents the water environment governance strategic indicator set, j = 2 represents the enterprise development strategic indicator set, k represents the kth fuzzy set, N R Represents the total number of fuzzy sets.

4. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 1 is characterized by: In step S3, resource limitation situations include: Updatable resource constraints: in, K represents the consumption of the nth type of renewable resources by the jth project in the t-period project portfolio. n,t It represents the stock of the nth type of renewable resources in period t; Non-updatable resource constraints: Where T represents the interest calculation period, t∈T, represents the consumption of the nth type of non-renewable resources by the jth project in the t-period project portfolio, Indicates the total amount of the nth type of non-renewable resources; Constraints on water environment governance effects: in, It represents the water environment governance index value, including the specific governance effect of the urban sewage treatment volume and the riverside and lakeside wetland restoration area that can be improved by the enterprise's project implementation, Θ s Indicates the standard value of water environment management; Constraints on enterprise organizational capabilities: Among them, z j The number of items selected, N s It is the maximum number of projects that can be carried out simultaneously during the entire strategic cycle.

5. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 4 is characterized by: The project portfolio selection model is: Among them, Obj1 and Obj2 represent the strategic fit inference values ​​of water environment governance strategy and enterprise development strategy respectively. represents the AP-NFIS network with quadratic polynomial kernel function, X P The decision variables for the project portfolio selection, A k ,B k ,C k represents the network parameter set learned by AP-NFIS under the k-th dimension strategy, FI is the financing cost, SI is the government subsidy, CI is the project construction investment, i c is the discount rate, P is the number of candidate projects in the project pool, CE t is the initial investment made by the enterprise in period t to implement the project portfolio, z p is the selection of candidate item p in the item pool. If item p is selected, then z p =1, otherwise z p =0, is the water environment management index value of project p, OPR t,j is the operation and maintenance return of the jth project in the t-cycle project portfolio, OPI t,j is the operation and maintenance cost of the jth project in the t-cycle project portfolio, and TC is the tax payable after subsidy.

6. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 5 is characterized by: X P =(x1,…,x p ,…,x P ),p∈P, where X P Each element x in p Satisfy x p ∈{0,1}, when item p is selected, the corresponding x p =1, otherwise, if not selected, then x p =0.

7. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 3 is characterized by: In step S3, the project portfolio selection model is solved using the HV-NSGA-III algorithm, and specifically: Apply the non-dominated sorting algorithm to select the solution set P for the initial project portfolio t Classify and form several non-dominated layers, and use critical layer screening technology to screen and retain high-priority non-dominated layers to subsequent generations; Obtain the optimal value of all objective function values ​​in the current population, that is, the optimal value of the strategic fit value, to form an ideal point, then subtract the ideal point from the objective value of all individuals to achieve the transformation of the solution space coordinates, move the ideal point to the origin through translation operation, and then calculate the extreme point and intercept; Using the boundary cross-weight construction algorithm, the target of each dimension is evenly divided into p' segments on the normalized reference plane, thus uniformly generating reference points, the connected ideal points and reference points form a reference line; The ASF function is used to process the targets of each dimension to identify points that show extremely high values ​​on a certain target but low values ​​on other targets, and the corresponding points are regarded as extreme points. The intercept on the corresponding coordinate axis is calculated according to the function value of the extreme point; The line connecting the reference point and the origin is used as the reference line of the reference point in the target space. For each individual in the population, all reference point vectors are traversed to find the reference point closest to each project combination selection plan, and the position of the reference point and the corresponding shortest distance are recorded. Through continuous iteration, the optimal solution is finally obtained, that is, the optimal project combination selection plan.

8. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 7 is characterized by: The hypervolume index measurement rule is introduced in the HV-NSGA-III algorithm: Each objective function value is first linearly normalized to in, represents the project portfolio selection decision variable, which corresponds one-to-one to the project portfolio selection scheme. is the verification value of target k, that is, the strategic fit value of the kth dimension of the verified project portfolio, which is obtained by AP-NFIS mapping and can be expressed as: is the value of the normalized objective function k, and are the minimum and maximum values ​​of the target k found in the feasible solution space, respectively; For each solution in the Pareto solution set The super volume contribution can be calculated as follows: Among them, r k is the reference point coordinate of the kth target; Adding up the hypervolume contributions of all points gives the total hypervolume of the entire Pareto front: in, represents the Pareto solution The super volume index.

9. A method for selecting a water environment management project portfolio for multi-dimensional strategic fit according to claim 7 or 8, characterized in that: In step S4, the Pareto solution set screened includes: Identify duplicate solutions: By comparing each solution in the solution set with other solutions, identify those that are the same or very close to the target value; Identify non-dominated solutions: Evaluate each solution in the solution set to determine whether it is dominated by other solutions in the solution set. If there is another solution that is not inferior to the current solution in all objectives and is superior to the current solution in at least one objective, the current solution is considered to be dominated. All solutions identified as duplicates or dominated are removed from the solution set, keeping only those independent solutions that are not dominated.

10. The method for selecting a water environment management project portfolio for multi-dimensional strategic compatibility according to claim 9, characterized in that: In step S4, the Pareto solution set selected by K-medoids algorithm cluster analysis is grouped, and the cluster center in each group is used as the representative solution: Among them, m j′ represents the jth cluster in the Pareto solution set, is the cluster representative in the j′th cluster, that is, the representative project portfolio selection scheme; and The joint metric based on relative Euclidean index and relative cosine index evaluates the quality of the representative solution: Among them, |C j′ | is the cluster C j′ The number of midpoints, m j′ is the cluster C j′ , J' is the total number of clusters, and α represents a regulation factor; 0<α<1.

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