A method, apparatus, and medium for generating a portfolio solution

Abstract

This invention relates to a method, apparatus, and medium for generating project portfolio solutions. The method first identifies four types of relationships between projects: synergy, mutual exclusion, temporal sequence, and conflict, and then constructs a four-layer multiplexing network for modeling. Based on the network, it identifies synergistic and conflicting project portfolios, quantifying their resulting value emergence, cost-sharing effect, value inhibition, and resource competition effect. Based on this, a multi-objective optimization model is constructed, using project selection as a variable to simultaneously minimize total cost and maximize total value. The model constraints include temporal sequence, mutual exclusion, and strategic objective support requirements. An improved genetic algorithm based on temporal chain encoding is used to solve the model, generating a Pareto optimal solution set, from which the final solution is extracted. This method can systematically quantify the combination effects generated by inter-project interactions, thereby generating a project portfolio solution with optimal cost and value under multiple constraints, assisting in scientific decision-making.

Description

Technical Field

[0001] This invention relates to the field of project portfolio management and optimization technology, specifically to a method, device, and medium for generating project portfolio solutions. Background Technology

[0002] Against the backdrop of diversified strategic objectives and rapidly evolving business needs, construction or investment projects implemented by various organizations (such as large enterprises and institutions) are exhibiting significant "high complexity." This complexity is not only reflected in the technical difficulty and scale of individual projects, but more importantly, in the intricate relationships between multiple projects. Traditional project review and selection methods typically focus on evaluating and weighing individual project metrics (such as cost, value, and schedule). While this approach is simple and direct, its fundamental flaw lies in treating the entire project portfolio as independent entities, neglecting the complex interactions among projects, including resource synergy, goal competition, implementation timing, and technical conflicts.

[0003] In practical project portfolio management, neglecting these interrelationships can lead to decision-making biases and resource misallocation. On the one hand, some projects that perform well individually may experience internal friction due to competition for key resources or conflicting objectives if pursued simultaneously, resulting in a "1+1<2" overall benefit reduction. On the other hand, some projects with mediocre individual indicators but strong synergistic effects can generate a "1+1>2" value emergence through resource sharing and complementary advantages if rationally combined, thereby significantly improving the overall effectiveness of the project portfolio. Therefore, how to systematically characterize the multi-dimensional relationships between projects, scientifically quantify the non-linear combination effects (including gain and loss effects) caused by these relationships, and on this basis, generate project portfolio solutions that can balance strategic goal support, resource constraints, and optimal overall benefits has become a core challenge in complex project portfolio decision-making.

[0004] Existing portfolio optimization methods are mostly based on simple resource constraints or priority ranking, failing to establish sophisticated models to characterize various types of project relationship networks, such as synergy, mutual exclusion, temporal relationships, and conflicts. They also lack quantitative analysis modules for the resulting portfolio effects, such as value emergence, cost sharing, value suppression, and resource competition. This leads to solutions that are often locally optimal, but fail to maximize the overall and long-term comprehensive benefits of the portfolio.

[0005] Therefore, there is an urgent need for a new method for generating project portfolio solutions that can construct a structured model that fully reflects the complex relationships between projects from a holistic system perspective, accurately quantify the combined effects of these relationships, and integrate strategic guidance and multi-objective optimization techniques to provide decision-makers with a scientific and efficient set of optimal project portfolio solutions. Summary of the Invention

[0006] This invention provides a method, apparatus, and medium for generating project portfolio schemes. Its purpose is to solve the technical problem that traditional project evaluation methods cannot systematically handle the complex relationships and combination effects between projects due to isolated analysis of individual projects, thus resulting in the inability to optimize the overall benefits of the project portfolio.

[0007] To achieve the above objectives, the first aspect of the present invention provides a method for generating a portfolio of projects, comprising the following steps:

[0008] Identify the relationships between any two construction projects in the set of candidate construction projects; each candidate construction project is a project unit corresponding to the entity to be constructed, and each project unit has independent engineering cost and technical efficiency indicators; the relationships include synergistic relationships, mutually exclusive relationships, temporal relationships, and conflicting relationships; wherein synergistic and conflicting relationships are used to characterize the interaction between different construction projects in terms of physical resources, technical paths, or schedule arrangements.

[0009] Based on the identified cooperative relationships, mutually exclusive relationships, temporal relationships, and conflict relationships, a four-layer multiplexing network is constructed; each layer of the four-layer multiplexing network independently corresponds to a type of association relationship;

[0010] Using the four-layer multiplexing network, project portfolios with cooperative relationships and project portfolios with conflicting relationships are identified;

[0011] To identify a portfolio of projects with synergistic relationships, the value emergence effect and cost sharing effect are calculated. The value emergence effect quantifies the technological efficiency gain resulting from technological synergy, and the cost sharing effect quantifies the engineering cost savings resulting from resource sharing.

[0012] To identify a portfolio of projects with conflicting relationships, the value suppression effect and the resource competition effect are calculated. The value suppression effect quantifies the loss of technical efficiency caused by technical conflict, and the resource competition effect quantifies the increase in engineering costs caused by resource competition.

[0013] A multi-objective optimization model is constructed, which takes project selection as the decision variable and aims to minimize the total engineering cost of the project portfolio and maximize the total technical efficiency of the project portfolio. The calculation of the total engineering cost and total technical efficiency incorporates the value emergence effect, cost sharing effect, value inhibition effect, and resource competition effect. The constraints of the multi-objective optimization model include temporal constraints defined based on the temporal relationship layer in the four-layer multiplexing network, mutual exclusion constraints defined based on the mutual exclusion relationship layer, and engineering technical indicator support constraints based on the degree of support of the project for engineering technical indicators.

[0014] A genetic algorithm based on temporal chain encoding is used to solve the multi-objective optimization model to generate a Pareto optimal solution set;

[0015] Extract at least one project combination scheme from the Pareto optimal solution set.

[0016] Furthermore, methods for constructing a four-layer multiplexing network include:

[0017] Establish a four-layer network structure containing the same set of nodes, where each layer corresponds to one of the aforementioned association types;

[0018] The first layer of the network is defined as the collaboration relationship layer, and connections are established between construction projects that have collaboration relationships in this collaboration relationship layer;

[0019] The second layer of the network is defined as a mutual exclusion layer, and edges are established in this mutual exclusion layer for construction projects that have mutual exclusion relationships.

[0020] The third layer network is defined as the temporal relationship layer, and directed edges are established in this temporal relationship layer for construction projects that have temporal relationships. The direction of the directed edges is from the previous construction project to the subsequent construction project.

[0021] The fourth layer of the network is defined as the conflict relationship layer, and connections are established between construction projects that have conflict relationships in this conflict relationship layer.

[0022] The cooperative relationship layer, the mutual exclusion relationship layer, the temporal relationship layer, and the conflict relationship layer are integrated to form the four-layer multiplexing network, where each layer is an unweighted network.

[0023] Furthermore, methods for calculating the value emergence effect and cost sharing effect include:

[0024] Based on the collaborative relationship layer in the four-layer multiplexing network, all pairs of construction projects with collaborative relationships are identified;

[0025] For each pair of construction projects with a collaborative relationship, obtain the preset value emergence coefficient and cost sharing coefficient respectively;

[0026] Based on the value emergence coefficient, the increment of the synergistic relationship on the total technical efficiency of the project portfolio is calculated as the value emergence effect value;

[0027] Based on the cost allocation coefficient, the reduction in the total project cost of the project portfolio due to this collaborative relationship is calculated as the cost allocation effect value.

[0028] Furthermore, methods for calculating the value suppression effect and the resource competition effect include:

[0029] Based on the conflict relationship layer in the four-layer multiplexing network, all pairs of construction projects with conflict relationships are identified.

[0030] For each pair of construction projects with conflicting relationships, obtain the preset value inhibition coefficient and resource competition coefficient respectively;

[0031] Based on the value inhibition coefficient, the amount by which the conflict relationship reduces the overall technical effectiveness of the project portfolio is calculated, and this is taken as the value inhibition effect value.

[0032] Based on the resource competition coefficient, the increase in the total engineering cost of the project portfolio due to this conflict relationship is calculated as the resource competition effect value.

[0033] Furthermore, prior to the step of constructing the multi-objective optimization model, the method also includes a step of determining the degree of support of the construction project for engineering and technical indicators, the step of which includes:

[0034] Construct a composite fuzzy element matrix, where the rows of the composite fuzzy element matrix correspond to construction projects, the columns correspond to engineering and technical indicators, and the matrix elements are the fuzzy values ​​of the support capabilities of the corresponding construction projects for the corresponding engineering and technical indicators.

[0035] The composite fuzzy element matrix is ​​defuzzified to obtain the corresponding composite element matrix;

[0036] Based on the composite element matrix, calculate the optimal membership degree of each construction project to each engineering technical indicator;

[0037] Based on the weight of each engineering technical indicator and the preferred membership degree of each construction project, the Euclidean proximity of each construction project to each engineering technical indicator is calculated.

[0038] The Euclidean proximity of each construction project is compared with a preset proximity threshold. When the Euclidean proximity is greater than or equal to the proximity threshold, the construction project is determined to support the corresponding engineering and technical indicators. When the Euclidean proximity is less than the proximity threshold, the construction project is determined to not support the corresponding engineering and technical indicators.

[0039] Furthermore, a method for solving the multi-objective optimization model using a genetic algorithm based on temporal chain encoding to generate a Pareto optimal solution set includes:

[0040] Preprocessing stage: Based on the time sequence relationship layer in the four-layer multiplexing network, one or more time sequence chains are generated. Each time sequence chain is a sequence of construction projects arranged in chronological order, and it is ensured that the construction projects in the chain do not violate mutual exclusion relationships and loop constraints.

[0041] Encoding stage: Based on the time sequence chain, chromosome encoding is performed on the project combination scheme, where each gene position corresponds to a time sequence chain, and the value of the gene position is an integer, indicating the selection of the first few projects from the time sequence chain;

[0042] Operator operation phase: Perform selection, crossover, and mutation operations on the encoded chromosome population to generate offspring population;

[0043] Fitness assessment phase: Decode the individuals in the population to obtain the actual combination of construction projects, and calculate the total engineering cost and total technical efficiency according to the multi-objective optimization model, which are used as fitness values;

[0044] Iterative optimization phase: Repeat the operator operation phase and fitness evaluation phase, and use an elite strategy to retain excellent individuals until the termination condition is met, and output the final Pareto optimal solution set.

[0045] Furthermore, the decoding process in the encoding phase and the fitness evaluation phase is as follows:

[0046] The encoding is a real number encoding, and the chromosome is a fixed-length vector whose length is equal to the total number of time chains;

[0047] During decoding, based on the integer value of each gene locus on the chromosome, a corresponding number of construction projects are selected from the starting position in the corresponding time sequence chain. The set of all selected construction projects constitutes a construction project combination scheme.

[0048] Furthermore, before calculating the fitness of an individual, the fitness assessment stage also includes a constraint processing step, which includes:

[0049] Check whether the project combination scheme obtained by decoding violates the mutual exclusion constraint: if projects with mutual exclusion relationship are selected at the same time, the chain pruning mechanism is activated to truncate the relevant time chain to eliminate mutual exclusion;

[0050] Check whether the project combination scheme obtained by decoding meets the engineering and technical indicator support constraints: if the number of supporting projects for any engineering and technical indicator in the project combination is lower than the preset ratio, then mark the fitness of that individual as invalid.

[0051] To achieve the above objectives, a second aspect of the present invention provides an electronic device including a memory and a processor, the memory being used to store a program supporting the processor in executing the method for generating the project portfolio scheme, and the processor being configured to execute the program stored in the memory.

[0052] To achieve the above objectives, a third aspect of the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of the method for generating a project portfolio scheme.

[0053] The beneficial effects of this invention are:

[0054] Compared with existing technologies, this invention provides a method, device, and medium for generating project portfolio schemes. It systematically characterizes four types of relationships among projects—coordination, mutual exclusion, temporal sequence, and conflict—by constructing a four-layer multiplexing network. Based on this network, it accurately quantifies the value emergence and cost-sharing effects brought about by coordination, as well as the value inhibition and resource competition effects caused by conflict. Furthermore, it establishes a cost-value multi-objective optimization model that incorporates the aforementioned quantified portfolio effects and strategic goal support constraints. Finally, it designs an improved genetic algorithm based on temporal chain encoding. This algorithm explicitly handles the temporal and mutual exclusion constraints among projects through a temporal chain structure and employs dynamic chain pruning and constraint handling mechanisms to ensure the feasibility of the solution. This enables it to efficiently search and generate a set of Pareto-optimal project portfolio schemes that balance total cost and total value while satisfying complex relationship constraints and strategic requirements. From model construction to algorithm solution, it completely solves the problem that traditional methods cannot optimize the overall portfolio benefits due to isolated project evaluation. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for generating a project portfolio scheme disclosed in an embodiment of the present invention.

[0056] Figure 2 This is a multiplexing network construction diagram disclosed in an embodiment of the present invention.

[0057] Figure 3 This is a flowchart of a non-dominated sorting genetic algorithm based on a time-series chain, as disclosed in an embodiment of the present invention.

[0058] Figure 4 This is a decoding schematic diagram disclosed in an embodiment of the present invention.

[0059] Figure 5 This is a schematic diagram of a chain pruning mechanism driven by mutual exclusion disclosed in an embodiment of the present invention.

[0060] Figure 6 This is a combination of trend curves showing the proportion of effective solutions changing with the number of iterations under different population sizes, as provided in the embodiments of the present invention.

[0061] Figure 6 (a) is the curve showing the change in the proportion of effective solutions when the population size is 30.

[0062] Figure 6(b) is the curve showing the change in the proportion of effective solutions when the population size is 50.

[0063] Figure 6 (c) is the curve showing the change in the proportion of effective solutions when the population size is 70.

[0064] Figure 6 (d) is the curve showing the change in the proportion of effective solutions when the population size is 100.

[0065] Figure 7 This is a combination diagram of Pareto front curves under different parameter settings disclosed in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the method for generating project portfolio solutions provided by this invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this invention.

[0067] The core of the technical solution provided by this invention lies in proposing a systematic and quantifiable model and algorithm framework to solve the problem of how to scientifically select and combine the optimal solution from a batch of candidate construction projects with complex interrelationships under the conditions of limited resources and multiple objectives.

[0068] In this invention, the term "construction project" refers to a project unit corresponding to the physical entity of the project to be constructed, i.e., a specific engineering construction object with clear physical boundaries and independently calculable engineering costs and technical efficiency. For example, new highway bridge projects, regional substation and power transmission and transformation facility projects, large-scale cloud computing data center park projects, 5G communication base station network projects, and industrial park infrastructure projects all fall under the category of "construction projects" in this invention. Each construction project has independent engineering costs (such as building material costs, construction equipment rental costs, and labor costs) and technical efficiency indicators (such as bridge load-bearing capacity, substation power supply capacity, data center processing capacity, and communication network bandwidth). Furthermore, there may be complex engineering relationships between construction projects, such as technology route selection, construction sequence dependence, equipment resource sharing, or competition for key resources. This invention targets these construction projects with physical entities by systematically identifying synergistic, mutually exclusive, temporal, and conflicting relationships between projects, quantifying the combined effect, and using a multi-objective optimization model to generate a project combination scheme that achieves the best balance between engineering costs and technical efficiency. This solves the problem of misallocation of engineering resources and loss of overall technical benefits caused by traditional project review methods neglecting the interactions between projects. The specific implementation methods of each step of the present invention will be described below based on such typical application backgrounds.

[0069] According to an embodiment of the present invention, it should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions. And although the logical order is shown in the following method, in some cases, the steps shown or described can be executed in a different order than here.

[0070] As Figure 1 shown, the present invention provides a method for generating a project portfolio plan, the method comprising:

[0071] Step S100, identifying the association relationship between any two construction projects in the set of candidate construction projects; the candidate construction projects are project units corresponding to the to-be-built engineering entities, and each project unit has independent engineering cost and technical efficiency indicators; the association relationship includes a synergistic relationship, a mutually exclusive relationship, a time sequence relationship, and a conflict relationship; wherein the synergistic relationship and the conflict relationship are used to characterize the interaction between different construction projects in terms of physical resources, technical paths, or construction period arrangements;

[0072] In the specific implementation process of the method of the present invention, this step aims to systematically explore and define various possible interaction modes between candidate construction projects, exceeding the limitation of traditional methods that only focus on the independent attributes of projects. Specifically, it is necessary to analyze and identify four types of association relationships: synergistic relationship, mutually exclusive relationship, time sequence relationship, and conflict relationship.

[0073] The "synergistic relationship" means that when there is a synergistic relationship between two construction projects, it means that the two can achieve an efficiency superposition through mutual cooperation and promotion, achieving an overall benefit that exceeds the sum of individuals. This synergistic effect can promote the efficient integration of projects in aspects such as resource allocation, technical research, and achievement transformation, thereby significantly enhancing the comprehensive benefit of the project and improving the quality of the final result. It should be noted that the synergistic relationship may not exhibit a symmetric characteristic: if construction project A is identified as a synergistic project of construction project B, it does not necessarily mean that construction project B is also a synergistic project of construction project A. In a specific scenario of optimizing the annual construction investment project portfolio of an enterprise.

[0074] The "mutually exclusive relationship" means that when there is a mutually exclusive relationship between two construction projects, it means that there are incompatible situations between the two in terms of time planning, resource allocation, etc., and the resulting contradiction lacks room for reconciliation, so they cannot be included in the same construction project portfolio plan at the same time. It should be noted that the mutually exclusive relationship exhibits a symmetric characteristic: if construction project A and construction project B form a mutually exclusive relationship, then construction project B must also form a mutually exclusive relationship with construction project A.

[0075] "Sequential relationship" refers to the sequential relationship between two construction projects. It means that they follow a predetermined order in time, with the earlier project laying the foundation for the subsequent ones, and the implementation of the later projects relying on the progress of the earlier one. This sequential arrangement ensures the continuity and rationality of the project process, preventing resource waste and progress stagnation caused by a reversal of the order, thus strongly supporting the smooth progress of the overall project and the achievement of its ultimate goals. It is worth noting that the sequential relationship has a clear directional attribute: if construction project A is a preceding project of construction project B, then construction project B must be a subsequent project of construction project A.

[0076] "Conflict relationship" refers to a situation where two construction projects are in conflict, meaning they interfere with or compete with each other in terms of technical execution and resource allocation. However, unlike mutually exclusive relationships, these projects can be included in the same construction project portfolio simultaneously. Conflict relationships can cause mutual constraints and limitations on resources between projects, thus adversely affecting the regular progress and final outcome of the projects. It is worth noting that conflict relationships exhibit symmetrical characteristics: if construction project A conflicts with construction project B, then project B must also conflict with construction project A.

[0077] In the specific implementation scenario of an enterprise's annual construction portfolio planning, step S100 aims to identify four types of relationships between candidate construction projects through expert discussions, historical data analysis, or dependency matrix tools. For example, "synergistic relationships" can be manifested as follows: Construction Project A (building a new highway bridge) and Construction Project B (widening an adjacent section of the highway) can form strong complementarity in terms of construction equipment sharing, material allocation, and traffic organization, jointly promoting the improvement of the overall road network connectivity technical efficiency, and achieving collaborative cost sharing through sharing survey data and construction access roads. "Mutual exclusion relationships" exist between Construction Project C (using suspension bridge technology to cross a canyon) and Construction Project D (using cable-stayed bridge technology to build in the same canyon location), because they represent two fundamental and incompatible main structural technology routes, and due to geological conditions and project budget constraints, the two cannot be included in the same construction portfolio plan at the same time. "Temporal relationships" have a clear logical sequence. For example, project E (construction of a regional substation and supporting power transmission and transformation facilities) must be a prerequisite for project F (infrastructure construction for the development of the regional industrial park). The latter depends on the stable power supply provided by the former to carry out subsequent construction and equipment commissioning. "Conflicting relationships" are different from mutual exclusion. For example, project G (construction of a large-scale cloud computing data center park) and project H (construction of a 5G communication base station network in the same region) can coexist in the same regional development plan, but they will compete for limited power capacity, fiber optic pipeline resources, and professional construction teams. This may lead to mutual constraints on their construction periods, resulting in resource competition and increased project costs.

[0078] Step S200: Based on the identified cooperative relationships, mutually exclusive relationships, temporal relationships, and conflict relationships, construct a four-layer multiplexing network; each layer of the four-layer multiplexing network independently corresponds to a type of association relationship;

[0079] In the specific implementation process, to systematically support the four heterogeneous associations identified in step S100, this invention introduces a multiplexed network as a modeling tool. A multiplexed network is a complex network with multiple layers, its core being the sharing of the same set of nodes (i.e., candidate projects), while each layer independently characterizes a specific type of node connection pattern. This hierarchical architecture of homogeneous nodes and heterogeneous connections can clearly define the essential differences between different association forms.

[0080] According to the general theory of multiplexed networks, a network with... A layered multiplexing network can be represented as ,in, Indicates a multiplexed network. This indicates the total number of layers in the multiplexing network. For the first in a multiplexed network Layered network ( ), each layer It contains three elements: a shared set of nodes Each node here is numbered (e.g., Each project corresponds to a single candidate construction project. It is the first The set of edges connecting layers (if the layer is a directed layer, then...) Indicates from node Pointing to node Directed edges; if it is an undirected layer, it represents a node. With nodes (There are connecting edges between them). Indicates the first The set of weights in the layer, if the first layer... The layer is an unweighted network layer, and its connection state is represented by an adjacency matrix. It means that, among them, This indicates that there is a connection. This indicates that no edges exist. Specifically:

[0081] Indicates construction project It is a construction project Collaborative projects; Indicates construction project It is a construction project Mutually exclusive items; Indicates construction project It is a construction project Time sequence items; Indicates construction project It is a construction project Conflict projects.

[0082] Based on this, and according to the four types of relationships identified in step S100, the present invention constructs a specific multiplexing network with four layers, represented as follows: Its structure is as follows Figure 2 As shown, each layer is a directed unweighted network, specifically defined as follows:

[0083] First floor ( Collaboration Relationship Layer: This layer describes the collaborative relationships between construction projects. In this layer, if a node... It is a node For collaborative projects, the adjacent matrix elements It should be noted that collaborative relationships are directional. It does not contain .

[0084] Second floor ( Mutual Exclusion Layer: This layer describes the mutual exclusion relationships between construction projects. In this layer, if a node... With nodes Mutually exclusive, then Since the mutual exclusion relationship is symmetric, the adjacency matrix of this layer satisfies... .

[0085] The third floor ( Temporal Dependency Layer: This layer is used to characterize the temporal dependencies between construction projects. In this layer, if a node... It is a node The preceding item, then This layer clearly expresses the sequence of steps that must be followed in the project implementation.

[0086] Fourth floor ( (Conflict Relationship Layer): This layer is used to characterize the conflict relationships between construction projects. In this layer, if nodes... With nodes If a conflict exists, then The conflict relationship is also symmetrical, hence... .

[0087] By constructing this four-layer multiplexing network, the four association types of cooperation, mutual exclusion, timing, and conflict are decoupled and mapped to independent network layers; thus, this model overcomes the limitation of traditional single networks in being unable to accurately express multiple connection attributes at the same time.

[0088] Step S300: Using the four-layer multiplexing network, identify project portfolios with cooperative relationships and project portfolios with conflicting relationships;

[0089] In the actual implementation process, each layer of the network is traversed and analyzed:

[0090] Identifying combinations of collaborative relationships: Traversing the adjacency matrix of the collaborative relationship layer (first layer) For any element in the matrix If its value is 1, then the node is identified. Corresponding construction projects and nodes The corresponding construction projects constitute a pair of construction projects with a collaborative relationship. All satisfying... of The set of combinations constitutes all the collaborative project combinations in the entire set of candidate projects that require calculation of positive (gain) combination effects.

[0091] Identifying conflicting relationship combinations: Traversing the adjacency matrix of the conflicting relationship layer (fourth layer) For any element in the matrix If its value is 1, then the node is identified. Corresponding construction projects and nodes The corresponding construction projects constitute a pair of construction projects with a conflicting relationship. All satisfying of The set of combinations constitutes all conflicting project combinations within the entire set of candidate projects that require calculation of negative (reduced) combination effects.

[0092] Through the above-described retrieval operation based on the network adjacency matrix, all relevant cooperative and conflict pairs in the construction project can be systematically and comprehensively identified. This process transforms the complex interactions implicit in the construction project into a clear, structured data list that can be directly processed by subsequent mathematical models.

[0093] Step S400: For the identified project portfolios with synergistic relationships, calculate the emergence effect of technical efficiency and the cost-sharing effect of engineering.

[0094] This step quantifies the positive synergistic effects of all identified collaborative project pairs, specifically the technology efficiency emergence effect and engineering cost sharing effect under the gain mode. In practice, firstly, for each identified collaborative project pair, pre-defined project technology efficiency emergence coefficients and project engineering cost sharing coefficients under the collaborative relationship are obtained. These coefficients can be pre-set through domain expert evaluation, historical data analysis, or specific business rules to characterize the strength of the synergy between that particular project pair.

[0095] The calculation of the emergent effect of technical effectiveness is used to quantify the additional technical effectiveness gain resulting from synergy. Specifically, for a pair of synergistic projects, if they are both selected into a portfolio, their combined effect will bring an increment to the total technical effectiveness of the portfolio that exceeds the sum of their individual technical effectiveness. Therefore, in a portfolio of projects, the sum of the emergent effects of technical effectiveness contributed by all selected projects that have synergistic relationships constitutes the synergistic gain portion of the total technical effectiveness of the portfolio.

[0096] The calculation of the cost-sharing effect is used to quantify the cost savings achieved through resource sharing and integration. For the same pair of collaborative projects, when they are implemented together, their individual implementation costs can be reduced by sharing equipment, manpower, technology platforms, or management resources. This effect will be deducted from the total project cost of the combined projects, thereby reducing the overall project cost.

[0097] Step S500: For the identified project portfolios with conflicting relationships, calculate the technical efficiency inhibition effect and resource competition effect;

[0098] This step quantifies the negative combined effects of all identified conflicting project pairs, specifically the technical efficiency suppression effect and resource competition effect under the loss-inducing model. In practice, for each identified conflicting project pair, pre-defined project technical efficiency suppression coefficients and project resource competition coefficients under the conflicting relationship are obtained. These coefficients are typically pre-set based on expert experience or historical conflict case analysis to quantify the severity of mutual interference or competition between the specific project pairs.

[0099] The calculation of the technical effectiveness suppression effect is used to quantify the reduction in project technical effectiveness caused by conflict. When a pair of conflicting construction projects are simultaneously incorporated into a portfolio and promoted concurrently, they may interfere with each other in terms of technical routes, business processes, or target markets, resulting in their respective expected technical effectiveness not being fully realized. This effect value will be deducted from the total technical effectiveness of the project portfolio.

[0100] The calculation of the resource competition effect is used to quantify the additional engineering costs caused by conflict. When conflicting construction projects are combined, they compete fiercely for limited key resources (such as expert teams in specific fields, specialized equipment, and budget funds), leading to difficulties in resource coordination and inefficient allocation. This can result in project delays or the need for additional investment, thereby increasing the overall engineering cost. This effect is added to the total engineering cost of the project combination.

[0101] Step S600: Construct a multi-objective optimization model. The multi-objective optimization model takes the selection of construction projects as the decision variable and aims to minimize the total engineering cost of the construction project combination and maximize the total technical efficiency of the construction project combination. The calculation of the total engineering cost and total technical efficiency includes the emergence effect of technical efficiency, the engineering cost amortization effect, the technical efficiency inhibition effect, and the resource competition effect. The constraints of the multi-objective optimization model include the temporal constraints defined based on the temporal relationship layer in the four-layer multiplexing network, the mutual exclusion constraints defined based on the mutual exclusion relationship layer, and the engineering technical indicator support constraints based on the degree of support of the construction project for the engineering technical indicators.

[0102] In its implementation, this step aims to integrate the relationships identified in the preceding steps, the calculated effects, and the supporting requirements for engineering and technical indicators into a formalized mathematical optimization problem. This provides a clear optimization objective and a framework of rules that must be followed for subsequent algorithmic solutions. The core of this model lies in the fact that decision-making no longer considers the original engineering costs and technical efficiency of each project in isolation, but rather places them within a combinatorial context, systematically incorporating the nonlinear gains and losses generated by the interactions (cooperation and conflict) between construction projects.

[0103] First, the model defines the decision variables as the selection states of the construction project. Let there be... The candidate construction projects constitute a set For each construction project ( Introduce a 0-1 decision variable :when When, it indicates a construction project. The selected combination of options for the current evaluation; when When, it indicates a construction project. Not selected. All The values ​​of these factors collectively determine a specific project combination scheme.

[0104] Secondly, model construction constraints ensure that the generated solution conforms to business logic and engineering requirements. These constraints are mainly divided into three categories:

[0105] The first type is time-series constraints, which originate from the time-series relation layer in multiplexing networks. This constraint stipulates that if the construction project... It is a construction project Pre-construction projects (i.e.) ), then when subsequent construction projects Selected ( When ), its preceding construction projects It must also be selected ( The mathematical expression is:

[0106]

[0107] The second type is mutual exclusion constraints, which originate from the mutual exclusion relation layer. It stipulates that if the construction project With construction projects Mutually exclusive (i.e.) Therefore, they cannot both appear in the same combination, that is:

[0108]

[0109] The third category is engineering and technical indicator constraints. This constraint requires that, for each engineering and technical indicator... (belongs to the set of engineering technical indicators) The number of selected construction projects that can effectively support this indicator must be no less than a minimum proportion of the total number of projects that can support this indicator among all candidate construction projects. .set up In order to support engineering technical indicators If the set of construction projects is a subset, then the mathematical expression for this constraint is:

[0110]

[0111] This constraint ensures that the final project portfolio can comprehensively and adequately cover all engineering and technical intentions.

[0112] Finally, the model establishes two competing objective functions. The first objective is to minimize the total engineering cost of the project portfolio, which consists of three parts: the original engineering costs of all selected projects. The sum of costs is calculated as follows: first, the cost savings resulting from collaborative relationships (through cost-sharing effects); second, the cost increases resulting from conflict relationships (through resource competition effects). Its mathematical expression is:

[0113]

[0114] in, To minimize the total engineering cost of the project portfolio, For construction projects The original cost; This refers to the cost-sharing coefficient for engineering projects under a collaborative relationship. Indicates construction project It is a construction project Collaborative construction projects (originating from the collaborative relationship layer) ); This represents the resource competition coefficient under conflicting relationships. Indicates construction project It is a construction project Conflict-related construction projects (originating from conflict relations layer) ); For construction projects The original engineering cost; For each construction project ( We introduce a 0-1 decision variable. The second part of the formula (negative term) reflects the reduction in engineering costs brought about by collaboration, while the third part (positive term) reflects the increase in engineering costs brought about by conflict.

[0115] The second objective is to maximize the overall technical effectiveness of the project portfolio, which also consists of three parts: first, the original technical effectiveness of all selected projects. The sum of the three factors is: first, the technical efficiency gains resulting from synergistic relationships (through the emergent effect of technical efficiency); and second, the technical efficiency losses resulting from conflict relationships (through the inhibitory effect of technical efficiency). Its mathematical expression is:

[0116]

[0117] in, To maximize the overall technical efficiency of the project portfolio, For construction projects The original value; The emergent coefficient of technical effectiveness under collaborative relationships; The technical effectiveness inhibition coefficient under conflict conditions; and The meaning is the same as above; For construction projects The original value. The second part of the formula (positive term) reflects the improvement in technical efficiency brought about by collaboration, while the third part (negative term) reflects the loss of technical efficiency brought about by conflict.

[0118] Through these two objective functions, the model directly integrates the four combined effects quantified in steps S400 and S500 into the evaluation system of the overall performance of the scheme. This enables the optimization process to automatically weigh the two usually conflicting objectives of "reducing total engineering costs" and "improving total technical efficiency," and intelligently utilize synergistic gains while avoiding or mitigating conflict losses.

[0119] Step S700: A genetic algorithm based on temporal chain encoding is used to solve the multi-objective optimization model to generate a Pareto optimal solution set;

[0120] In the field of multi-objective optimization research, the NSGA series of algorithms, based on the Pareto dominance criterion, has become a classic method for handling multi-objective optimization problems. Multiple experimental results confirm that the multi-objective optimization performance of this series of algorithms is superior to traditional multi-objective genetic algorithms. Among them, the NSGA II algorithm, based on the original NSGA algorithm architecture, incorporates strategies such as fast non-dominated sorting, crowding assessment, and elite selection, significantly enhancing the optimization effect and improving computational efficiency, becoming a high-performance multi-objective optimization method. Given the complex mechanism of coupling project relationships and combination effects in complex construction project portfolio systems, this method, based on the NSGA II algorithm framework, proposes an improved multi-objective optimization algorithm—a non-dominated sorting genetic algorithm based on time-series chains—that integrates temporal constraints, mutual exclusion rules, and engineering technical indicator support requirements modeling. This algorithm is specifically designed to solve multi-objective optimization problems of construction project portfolio schemes considering combination effects. This algorithm constructs a time-series chain to explicitly encode chromosomes, and combines constraint processing mechanisms with crossover and mutation operators designed specifically for the encoding characteristics, forming a sequence of chromosomes. Figure 3 The complete algorithm system is shown.

[0121] In the data preprocessing stage, a relationship graph is first constructed based on the temporal correlation between construction projects. Then, a depth-first search (DFS) algorithm is used to construct a complete temporal chain structure starting from each initial node. A temporal chain refers to a set of construction project sequences arranged in chronological order. Its generation logic starts with all nodes with an in-degree of 0 as starting points and generates all potential temporal chain paths by calling the DFS function.

[0122] To ensure the effectiveness of the time-series chain, two core constraints must be met: First, there must be no circular structure within the chain, meaning that no direct or indirect preceding project of any construction project can become its subsequent project; second, the same time-series chain must not contain construction projects with mutually exclusive relationships. This is because the mutual exclusion attribute between projects implies compatibility conflicts, and such conflicts are inherently incompatible with indirect time-series relationships. Based on these constraints, a loop detection mechanism and a mutual exclusion relationship verification module are specifically set up in the preprocessing stage to ensure the accuracy and rationality of the generated time-series chain data.

[0123] In the encoding and decoding stages, the proposed encoding mechanism uses a temporal chain as its basic framework and employs real-number encoding, where the gene bits are integers. Each gene unit corresponds to a temporal chain, and the value at the gene bit represents the selection depth of that temporal chain, i.e., the number of construction projects selected sequentially from the starting node of the temporal chain, and its value must be limited to a specific interval. A chromosome, as a vector structure composed of multiple genes, corresponds to a specific combination of construction projects, and the length of the chromosome's gene sequence is consistent with the total number of temporal chains. In the population initialization stage, based on the preset population size, a random integer sampling strategy is used to generate random integer values ​​for all genes of each individual, thereby providing a diverse initial solution set for subsequent iterative operations of the genetic algorithm.

[0124] The decoding process is a crucial step in transforming the encoded chromosome into a practical project selection scheme; essentially, it's a reverse deduction of the encoded logic. For example, if the preprocessing stage generates five complete time-series chains, such as... Figure 4 As shown, their lengths are 3, 3, 1, 2, and 2, respectively. When an individual's encoding is [3,3,1,2,2], the value 3 of the first gene means selecting the first 3 projects from the first temporal chain to be included in the combination scheme. The interpretation of other gene positions follows the same principle. This decoding mechanism can accurately adapt to the characteristics of optimization problems that require maintaining temporal correlation between projects, ensuring the effective implementation of temporal constraints in scheme generation.

[0125] During the operator operation phase, this method employs a binary tournament mechanism, randomly selecting two individuals from the population for performance comparison each time. By evaluating non-dominance level and crowding indices, the individual with the better performance is selected as the parent to participate in subsequent crossover and mutation processes. This approach not only helps preserve high-quality gene fragments but also maintains the overall diversity of the population.

[0126] The crossover operation employs a traditional two-point crossover strategy. First, two crossover locations are randomly determined. Then, the two parent chromosomes exchange gene segments located between these two locations, and the remaining genes are directly copied to the corresponding locations in the offspring. Because the gene exchange occurs at the same location, this design ensures that the offspring resulting from the crossover always fall within a valid temporal chain index range.

[0127] The mutation operation employs a basic bit mutation method adapted to the encoding rules. The process first obtains the mutation probability for each gene bit, then independently determines whether to trigger mutation. When a gene bit needs to be mutated, a new valid value is randomly generated within a preset range. This design also ensures that the mutation operation does not exceed the legal temporal chain index boundary.

[0128] It is worth noting that during the implementation of a series of genetic operations such as selection, crossover, and mutation, there is no need to additionally check whether individuals violate the constraints. The constraint verification of all individuals will be centrally processed before the fitness assessment phase.

[0129] During the fitness assessment phase, even though individuals within the population have met temporal constraints through selection, crossover, and mutation, they may still violate mutual exclusion constraints and engineering technical indicator support constraints before their fitness is assessed. Therefore, a reasonable constraint handling mechanism needs to be constructed to dynamically adjust gene values ​​until these two types of constraints are met before calculating individual fitness.

[0130] (1) Dynamic chain length gene decoding: Based on the value of the gene position, a truncation operation is performed to convert the real number encoding into a truncated item selection time chain, thereby ensuring that the time association between items is strictly followed.

[0131] (2) Mutual Exclusion Constraint-Driven Chain Pruning: The system traverses all chain pairs to check for mutual exclusion relationships. If a mutual exclusion relationship exists, the first mutual exclusion point of each chain is located, and a bidirectional mutual exclusion-driven chain pruning mechanism is initiated. If no mutual exclusion relationship is found, it indicates that the chain pair combination meets the mutual exclusion constraint requirements. The bidirectional mutual exclusion-driven chain pruning mechanism compares the positions of the first mutual exclusion points of the chain pair combination and truncates the time-series chain with the greater distance between the mutual exclusion points. If the positions of the first mutual exclusion points are the same, the longer chain is retained and the shorter chain is pruned based on the principle of retaining the most items. See the relevant schematic diagram. Figure 5 After this step, the timing chains can satisfy the mutual exclusion constraint condition.

[0132] (3) Extreme value penalty driven by engineering technical indicators: Unlike the gradual penalty method adopted by soft constraints, the engineering technical indicators support constraints are hard constraints. When a project in a certain project combination scheme violates the engineering technical indicators constraint, the solution will be mapped to the extreme region of the target space, specifically, the engineering cost is set to positive infinity and the technical efficiency is set to negative infinity, thereby ensuring that the solution is excluded in the subsequent screening process.

[0133] (4) Calculation of objective function value: Based on the comprehensive consideration of the combined effect, calculate the increase in technical efficiency and reduction in engineering cost of the selected project under the gain mode, and the decrease in technical efficiency and increase in engineering cost under the loss mode. Finally, the total technical efficiency and total engineering cost of the scheme are obtained as the core basis for fitness assessment.

[0134] During the iterative optimization phase, this algorithm, based on the framework of the standard NSGA-II algorithm, uses three core mechanisms—fast non-dominated sorting, crowding calculation, and elite strategy—to efficiently approximate the Pareto optimal frontier of the problem. It also makes key improvements to address the complex temporal, mutual exclusion, and engineering technical constraints in the combinatorial optimization of construction projects.

[0135] 1. Fast Non-Dominated Sorting and Population Stratification: Fast non-dominated sorting is the core of the algorithm's efficiency, used to divide individuals in the population into multiple non-dominated levels (frontiers) based on their dominance relationships according to their objective function values ​​(total project cost and total technical efficiency). Its core idea is to maintain a dominance counter (recording the number of individuals that dominate it) and a dominated set (recording the individuals it dominates) for each individual. The algorithm first identifies all individuals with a dominance counter of 0, classifying them as the first non-dominated layer; then, it removes the "dominance" influence of these individuals on the individuals they dominate, updates the counters, and iteratively identifies subsequent non-dominated layers. This process optimizes the algorithm's complexity to [missing information - likely a time complexity range]. ( For the target number, (Based on population size), it enables efficient stratification of the population, providing a clear priority order for subsequent selection operations.

[0136] 2. Crowding Degree Calculation and Diversity Preservation: To further differentiate the quality of individuals within the same non-dominated level and maintain the diversity of the solution set distribution, the algorithm introduces crowding degree calculation. The core idea is to calculate the normalized distance between an individual and its neighbors along each objective function dimension, and use the sum of the distances across dimensions as the crowding distance for that individual. Boundary individuals are assigned infinitely large crowding distances to ensure their preservation. By prioritizing individuals with large crowding distances (i.e., those distributed in sparse regions), the algorithm effectively prevents the solution set from prematurely converging to local regions, thus obtaining a more uniformly distributed non-dominated solution set on the Pareto front. The complexity of this calculation process is O(n log n). .

[0137] 3. Elite Strategy and Intergenerational Succession: The elite strategy involves merging parent and offspring populations (at a scale of...). ), and select the best from them. Individuals constitute the next generation, thus ensuring that superior individuals are not lost during evolution. The specific operation involves: performing a rapid non-dominated sort on the merged population, and then adding individuals from the entire non-dominated level to the new population in descending order of non-dominated level, until the new population reaches or is about to exceed this level. For the last non-dominated layer that cannot be fully incorporated, individuals in that layer are sorted in descending order of their crowding distance, and the highest-ranking individuals are selected until the new population is filled. This strategy accelerates convergence while maintaining population diversity.

[0138] 4. Improved Adaptability to Project Portfolio Constraints: The core innovation of this algorithm lies in its deep adaptation of its encoding and constraint processing mechanisms to the project portfolio problem.

[0139] Temporal chain coding: Employing real-number coding based on temporal chains, the project selection problem is transformed into an optimization of the selection depth of temporal chains, ensuring the automatic satisfaction of temporal constraints from the coding level.

[0140] Dynamic constraint handling: Before fitness evaluation, the coding value is automatically adjusted to eliminate the simultaneous selection of mutually exclusive items through the "mutually exclusive constraint-driven chain pruning" mechanism; through the "engineering technical index constraint-driven extreme value penalty" mechanism, solutions that violate the engineering technical index support constraints are assigned an extreme fitness value (infinite engineering cost, infinitely small technical efficiency) to ensure that they are naturally eliminated.

[0141] By combining the aforementioned standard mechanisms with customized improvements, the algorithm can efficiently and robustly search for high-quality Pareto optimal solutions for project portfolios under complex relationships and hard constraints.

[0142] This process is repeated iteratively (selection, crossover, mutation, evaluation, non-dominated sorting, elite retention) until the preset number of iterations or convergence condition is reached. The final set of individuals at the highest non-dominated level in the population is the Pareto optimal solution set.

[0143] Step S800: Extract at least one project combination scheme from the Pareto optimal solution set.

[0144] This step aims to transform the Pareto optimal solution set, representing the trade-offs obtained by the algorithm, into a clear solution that decision-makers can review and choose from. In practice, the Pareto front output by the algorithm contains a set of mutually exclusive solutions. Each solution corresponds to a combination of construction projects that satisfies all time-series, mutual exclusion, and engineering technical indicator constraints, and has a pair of calculated total engineering cost and total technical efficiency target values. These solutions are distributed on the "engineering cost-technical efficiency" plane, forming the optimal trade-off boundary. Different strategies can be adopted when implementing this step depending on the actual decision-making needs: one approach is to directly submit the entire Pareto optimal solution set to experts or decision-makers, using visualization charts (such as...). Figure 7The scatter plot shown clearly illustrates the cost-benefit trade-offs of different options, allowing decision-makers to make the final selection based on preferences or higher-level judgments. Another approach is to automatically filter one or more options that best meet specific conditions from the solution set based on pre-defined decision rules (such as setting a maximum budget ceiling, requiring a minimum technical efficiency threshold, or maximizing cost-effectiveness). For example, a cost constraint can be set, and then the option with the highest technical efficiency can be selected from the solutions that satisfy the constraint. Ultimately, the extracted project portfolio will be presented as a clear project list, explicitly indicating which projects have been selected for implementation, along with the overall estimated project cost and technical efficiency of the portfolio, thus providing direct and quantitative evidence for scientific decision-making regarding project portfolios.

[0145] Preferably, before constructing the multi-objective optimization model, this method also includes a preliminary step of quantifying the degree of support of each candidate construction project for various engineering and technical indicators. In this step, this method will use the support degree to determine the correspondence of each construction project. The main steps for calculating the support degree of engineering and technical indicators are as follows:

[0146] Construct a composite fuzzy element matrix. Since the supporting capabilities of engineering and technical indicators in the actual implementation of construction projects are often uncertain and difficult to describe with precise numerical values, fuzzy theory is introduced for processing:

[0147]

[0148] in, This represents a matrix of composite fuzzy elements, where the composite elements are arrays. , Indicates the first in the set of construction projects Projects ( ); Indicates the first in the set of construction projects One engineering technical indicator ( ); Indicates the first The construction project is for the first Fuzzy values ​​representing the supporting capabilities of various engineering and technical indicators.

[0149] Construction projects often exhibit unstable characteristics during their actual implementation, making it difficult to describe the uncertainty of their support capabilities using precise numerical values. Fuzzy theory, however, has the advantage of handling such uncertainties. Given this uncertainty in the data, in practice, domain experts are typically invited to conduct fuzzy assessments based on their accumulated experience. After defuzzifying the composite fuzzy element matrix, the corresponding composite element matrix can be obtained. .

[0150] Deblurring:

[0151]

[0152] in, This is the deblurred composite element matrix, where the deblurred composite elements are arrays. , The first one obtained after deblurring The construction project is for the first The precise value of the supporting capability of each engineering and technical indicator.

[0153] This method uses median value deblurring. Assume two experts... support The abilities of the individuals were scored, with one expert giving a score of [3,4] and another giving a score of [5,6]. Therefore, the two experts gave scores of 3.5 and 5.5 respectively. It is the average of the scores from two experts. Similarly, the composite element matrix... All other elements in the equation are derived in the same way.

[0154] Calculate the preferred membership degree:

[0155] ;

[0156] The optimal membership matrix can be obtained from the above formula. .in, Indicates the first The maximum supporting capacity of each engineering and technical indicator; Indicates the first The construction project is for the first The optimal membership degree of each engineering technical indicator takes a value between [0,1].

[0157] Calculate Euclidean proximity:

[0158] ;

[0159] in, Indicates the first A set of proximity to each construction project; Indicates the first The construction project is for the first The degree of similarity between the engineering technical indicators; Indicates the weight of engineering and technical indicators; This indicates that each construction project is related to the first... The optimal membership value of each engineering technical indicator.

[0160] Finally, the support relationship is determined based on proximity. A threshold is set. (For example, the average of all proximity scores could be taken). For each construction project... For each indicator proximity Compare with this threshold: If Then determine the construction project For engineering technical indicators It plays a supporting role; if If the support is not provided, it will be deemed to have no supporting function. This determination will clearly define the technical specifications of each supporting structure. Project Collection This set will be directly used as the input data for constructing the "engineering technical indicator support constraints" in step S600, ensuring that each project in the final optimized solution is adequately supported by the corresponding engineering technical indicators.

[0161] Preferably, when calculating various effects in steps S400 and S500, the quantification model is based on a deep understanding of the underlying mechanism of the combined effect.

[0162] Specifically: For the loss-reduction pattern (conflict relationship):

[0163] Technological efficiency inhibition effect: When conflicting projects (such as those with generational differences in technical approaches, conflicting business processes, or significantly overlapping service goals) are implemented together, their mutual interference can prevent the full realization of their respective expected technological efficiencies, resulting in a "1+1<2" outcome. Quantitatively, this effect manifests as a reduction in the technological efficiency of the conflicting projects.

[0164] Resource competition effect: Conflicting construction projects compete for limited funds, specific human resources, specialized equipment, and other key resources. This competition leads to increased costs of resource coordination, reduced allocation efficiency, and even project delays, thus significantly increasing the overall implementation cost of the project portfolio.

[0165] For gain mode (cooperative relationship):

[0166] Emergent technological effectiveness: A combination of projects with synergistic relationships can generate excess technological effectiveness, where "1+1>2". For example, in the technological dimension, the technological advantages of different projects can complement each other through knowledge sharing and integration, giving rise to new solutions; in the resource dimension, sharing data, platforms, or market channels can optimize resource allocation, thereby breaking through the technological effectiveness boundaries of individual projects and creating additional combined technological effectiveness.

[0167] Cost-sharing effect: Collaborative projects can effectively reduce unit project costs through sharing mechanisms. For example, multiple projects can share the same testing equipment, software licenses, experimental sites, or administrative services, avoiding redundant investment, achieving economies of scale, and thus reducing the total project cost of the project portfolio.

[0168] In the annual construction investment plan of a large infrastructure construction group, the method of this invention was applied as follows: First, four types of relationships were identified among the 100 candidate construction projects. For example, "the construction of a new expressway section A" and "the bridge project of the same expressway section B" are collaborative (they can share construction equipment, precast beam yards, and material supply chains); "the canyon bridge project using suspension bridge technology" and "the bridge project in the same location using cable-stayed bridge technology" are mutually exclusive (due to incompatibility of geological conditions and technical routes); "the construction of a regional core substation project" is a prerequisite project for "the development of infrastructure projects in adjacent industrial parks" (the latter depends on the former's power supply); "the construction of a large cloud computing data center park" and "the construction of a 5G communication backbone network in the same region" have a conflicting relationship of resource competition (they compete for limited power capacity, fiber optic pipelines, and professional construction teams). Based on these relationships, a four-layer multi-path multiplexing network was constructed to systematically quantify the technical efficiency improvement and engineering cost savings brought about by the combination of collaborative construction projects, as well as the technical efficiency loss and resource competition engineering costs caused by the combination of conflicting construction projects. Subsequently, a multi-objective optimization model was constructed, using project selection as the decision variable and simultaneously pursuing the minimization of total project cost and the maximization of total technical efficiency. Constraints were incorporated, including time-series constraints, mutual exclusion constraints, and support ratios for 12 engineering technical indicators (including road network capacity, power supply reliability, data transmission bandwidth, and project schedule achievement rate). An improved genetic algorithm based on time-series chain coding was used to solve the model, ultimately generating multiple Pareto optimal solutions that balance project cost and technical efficiency under given constraints for the decision-making level to choose from. This method effectively solves the problem of misallocation of engineering resources and loss of overall technical benefits caused by neglecting the combination effect in traditional review methods by specifically quantifying the complex interactions between construction projects.

[0169] To verify the feasibility and effectiveness of the project combination scheme generation method proposed in this invention, this section demonstrates the application process of the method through a specific embodiment and compares and analyzes the performance of the algorithms:

[0170] This paper selects the project portfolio generation stage in a construction project management process as an example to illustrate how the designed algorithm is applied to generate project selection schemes that conform to the overall plan. The data used in this example comes from a statistical fit of a dataset of all approved major investment planning projects in a certain country from 1996 to 2012. This dataset has a high degree of fit with the construction project studied by this method. To achieve accurate simulation, the data generation method draws on relevant research results from the literature.

[0171] Based on the generated project dataset, and considering the combined effect of construction projects, a detailed explanation of the inter-project relationships and supporting relationships of engineering and technical indicators is provided. This example includes fields describing project relationships and fields related to supporting engineering and technical indicators; the specific basic attribute configurations can be found in Table 1.

[0172] Table 1 Basic Attribute Data of the Project

[0173]

[0174] Columns 4-7 in Table 1 represent the projects with four different relationships to the corresponding projects. These can be empty sets or sets containing several projects. Columns 8-18 represent whether all engineering and technical indicators are supported by the corresponding projects. This is calculated based on the support level assessment of engineering and technical indicators, with the proximity threshold set to the average value. The support level of each project for different indicators is represented by 0-1, where 1 indicates that the project supports the engineering and technical indicator, and 0 indicates that the project does not support the engineering and technical indicator.

[0175] This method was tested in an environment with an 11th Gen Intel(R) Core(TM) i5-1135G7 processor, 8GB RAM, and Windows 11. To study the algorithm's performance by controlling variables in the comparative experiment, the experimental parameters and the parameters of the comparison algorithm were set as follows:

[0176] Table 2 Experimental Fixed Parameter Settings

[0177]

[0178] Table 3 Comparison of Algorithm Parameter Settings

[0179]

[0180] To investigate the impact of population size on algorithm performance, a set of comparative experiments was designed. In the experiments, except for the population size parameter, all other parameters remained consistent with the settings in Tables 2 and 3, thus identifying the population size parameter that optimizes the overall performance of the algorithm.

[0181] This experiment used two metrics, HV and IGD, to evaluate the convergence performance and solution diversity of the algorithm under different population size parameters. The results of the relevant experiments are presented in [link to experimental data]. Figure 6 In Table 4.

[0182] Figure 6Figures (a) to (d) show the trend curves of the percentage of effective solutions changing with the number of iterations when the population size is 30, 50, 70, and 100, respectively. Specific statistical data can be found in Table 4. It can be clearly observed from the figures that when the population size is set to 50 and 70, the percentage of effective solutions consistently fluctuates above 90%. Figure 6 (a) and Figure 6 (b) The average effective solution ratio is close to that of the curves, but the fluctuation range of curve 6(a) in the figure is significantly greater. Figure 6 (c); and Figure 6 Although the average effective solution ratio of (d) is the highest, there are numerical points below 85%, indicating that the stability of the algorithm is poor at this population size.

[0183] Table 4. Experimental results data under different population sizes

[0184]

[0185] Table 4 presents the impact of population size parameters on the performance of the improved NSGA II algorithm. Although the effective solution ratio exceeded 95% in all experimental groups, further in-depth analysis is needed, combining the HV and IGD indices. Data shows that for medium and small populations, the HV index increases with population size, while the IGD index decreases. When the population size is too large, the HV index declines, and the IGD index rebounds. At a population size of 70, the HV index reaches its maximum value, and the IGD index drops to its minimum value, indicating that the algorithm performs optimally in balancing solution set diversity and convergence at this point. The experiment also observed diminishing marginal returns due to population size; when the population size increases to 100, the marginal benefit even turns negative. This suggests that algorithm parameter optimization should focus on the inflection point of marginal benefit. In this experiment, a population size of 70 is precisely this inflection point, where the marginal benefit is close to zero. Considering the robustness, solution set quality, and time cost of the algorithm, a population size of 70 results in significantly better overall performance. Therefore, subsequent experiments will use 70 as the population size parameter.

[0186] This section's experiments aim to investigate how the combination of crossover rate and mutation rate affects algorithm performance. To this end, a comparative experiment was designed with nine different parameter combinations to screen for the optimal crossover rate and mutation rate combination for subsequent experiments. In the experiments, the crossover rate was set at three levels: 0.7, 0.8, and 0.9, and the mutation rate was set at three levels: 0.1, 0.2, and 0.3.

[0187] Figure 7The Pareto fronts obtained by the algorithm under different parameter combinations are visually presented on a two-dimensional coordinate plane as scatter points of different colors and shapes: the shape differences of the scatter points correspond to different values ​​of the variation rate, and the color differences under the same shape correspond to different values ​​of the crossover rate.

[0188] As shown in the figure, the overall improvement in technical efficiency is accompanied by an increase in engineering costs, which is consistent with the "benefit-cost" trade-off logic of multi-objective optimization. Under different parameter combinations, the distribution density and coverage of the Pareto front scatter points vary. Some combinations result in denser scatter points that are evenly distributed along the front, indicating that the algorithm generates richer and more reasonable non-dominated solutions; conversely, this reflects insufficient solution set diversity or convergence. Further analysis, with fixed parameters... (Circular scatter plot) The scattered points are more densely and evenly distributed in the "technical efficiency-engineering cost" plane, resulting in better solution set diversity; The data points are sparse, indicating insufficient gene exchange due to a low crossover rate. Scattered points show slightly weaker coverage in high-performance regions, or their convergence may be affected by excessively high crossover rates that disrupt desirable genes. Fixed When (green scatter), The scatter distribution is the most uniform, and it has a better balance between convergence and diversity. Scattered clusters of low-tech efficiency indicate that the mutation rate is too low, resulting in insufficient population evolutionary vitality. The scattered data points are generally dispersed and lack coverage of low-tech efficiency segments, indicating excessive mutation of superior genes due to excessive mutation rate. In summary, , The combined performance is better, and its scatter points have the most comprehensive coverage and the most uniform distribution on the "technical efficiency-engineering cost" frontier. The algorithm can fully explore the solution space and effectively approximate the real Pareto frontier, and its multi-objective optimization performance is better.

[0189] In the experiments of this method, the present invention used the improved NSGA II, C-TAEA, and MOEA / D algorithms to solve the problem, and compared the performance of the improved NSGA II algorithm with other multi-objective optimization algorithms. The experimental results are shown in Table 5.

[0190] Table 5. Algorithm Comparison Results

[0191]

[0192] The average engineering cost index presented in Table 5 is obtained by further averaging the 30 single-operation average engineering costs obtained from 30 independent calculations; the average technical efficiency index is the average of the technical efficiency results obtained from each of the 30 independent calculations. Analysis of the data in the table shows that the MOEA / D and C-TAEA algorithms have significant advantages in computational efficiency, but the improved NSGAII algorithm has the lowest cost-efficiency ratio. This result indicates that although the improved NSGAII algorithm consumes relatively more computation time, it can find a higher quality solution and exhibits the strongest optimization efficiency under the same number of iterations.

[0193] From the perspective of data support, both the stability of the algorithm during operation and the quality of the final output solution fully verify the effectiveness of the proposed improved NSGA II algorithm. This algorithm is particularly suitable for optimization scenarios where solution quality is the primary goal and computational efficiency requirements are relatively relaxed. Its advantages are even more significant in high-value optimization problems that allow for longer computation times.

[0194] This method focuses on the problem of project portfolio selection and emphasizes the portfolio effect. Given the shortcomings of traditional project portfolio decision-making methods in systematically characterizing the multi-dimensional relationships between projects and the transmission mechanism of portfolio effects, this method attempts to innovate from both theoretical and algorithmic perspectives.

[0195] In terms of theoretical construction, a project association model based on a four-layer multiplexing network was developed, which quantifies the emergence of technical effectiveness and the engineering cost sharing effect in collaborative scenarios, as well as the inhibition of technical effectiveness and the resource competition effect in conflict scenarios. At the same time, combined with goal orientation, an engineering technical indicator support degree calculation model integrating fuzzy evaluation and Euclidean closeness was created, thereby building a multi-objective optimization mathematical model that considers relational constraints and engineering technical indicator support.

[0196] At the level of methodological innovation, a chain-based encoding mechanism and a dynamic constraint processing mechanism oriented towards temporal relationships were designed, and an improved NSGA II algorithm that fits the characteristics of the model was developed, successfully overcoming the problem of searching the feasible solution space under complex relationships.

[0197] The innovations of this study are mainly in three aspects: First, a system modeling framework for multi-dimensional project relationships was constructed, which breaks away from the limitations of the traditional binary relationship model; second, a quantitative model of the transmission of combined effects was established, which accurately describes the nonlinear interaction between projects; and finally, an evolutionary algorithm based on time-series chains was proposed, which greatly enhances the ability to find the Pareto front under complex constraints.

[0198] Experimental results show that the proposed algorithm outperforms traditional multi-objective optimization algorithms in both solution set quality and stability. This verifies the effectiveness of the model and method, and provides a solution with both theoretical depth and practical value for project portfolio selection.

[0199] According to another aspect of the embodiments of this application, an electronic device is also provided, including a processor and a memory, wherein the processor is configured to implement the steps of the method when executing a computer program stored in the memory.

[0200] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0201] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0202] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0203] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0204] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method of generating a portfolio solution, characterized by, Includes the following steps: Identify the relationships between any two construction projects in the set of candidate construction projects; each candidate construction project is a project unit corresponding to the entity to be constructed, and each project unit has independent engineering cost and technical efficiency indicators; the relationships include synergistic relationships, mutually exclusive relationships, temporal relationships, and conflicting relationships. Among them, synergistic and conflict relationships are used to characterize the interaction between different construction projects in terms of physical resources, technical paths, or schedule arrangements; Based on the identified cooperative relationships, mutually exclusive relationships, temporal relationships, and conflict relationships, a four-layer multiplexing network is constructed; each layer of the four-layer multiplexing network independently corresponds to a type of association relationship; Using the four-layer multiplexing network, project portfolios with cooperative relationships and project portfolios with conflicting relationships are identified; To identify a portfolio of projects with synergistic relationships, the value emergence effect and cost sharing effect are calculated. The value emergence effect quantifies the technological efficiency gain resulting from technological synergy, and the cost sharing effect quantifies the engineering cost savings resulting from resource sharing. To identify a portfolio of projects with conflicting relationships, the value suppression effect and the resource competition effect are calculated. The value suppression effect quantifies the loss of technical efficiency caused by technical conflict, and the resource competition effect quantifies the increase in engineering costs caused by resource competition. A multi-objective optimization model is constructed, which takes project selection as the decision variable and aims to minimize the total engineering cost of the project portfolio and maximize the total technical efficiency of the project portfolio. The calculation of the total engineering cost and total technical efficiency incorporates the value emergence effect, cost sharing effect, value inhibition effect, and resource competition effect. The constraints of the multi-objective optimization model include temporal constraints defined based on the temporal relationship layer in the four-layer multiplexing network, mutual exclusion constraints defined based on the mutual exclusion relationship layer, and engineering technical indicator support constraints based on the degree of support of the project for engineering technical indicators. A genetic algorithm based on temporal chain encoding is used to solve the multi-objective optimization model to generate a Pareto optimal solution set; Extract at least one project combination scheme from the Pareto optimal solution set; A method for solving the multi-objective optimization model using a genetic algorithm based on temporal chain encoding to generate a Pareto optimal solution set includes: Preprocessing stage: Based on the time sequence relationship layer in the four-layer multiplexing network, one or more time sequence chains are generated. Each time sequence chain is a sequence of construction projects arranged in chronological order, and it is ensured that the construction projects in the chain do not violate mutual exclusion relationships and loop constraints. Encoding stage: Based on the time sequence chain, chromosome encoding is performed on the project combination scheme, where each gene position corresponds to a time sequence chain, and the value of the gene position is an integer, indicating the selection of the first few projects from the time sequence chain; Operator operation phase: Perform selection, crossover, and mutation operations on the encoded chromosome population to generate offspring population; Fitness assessment phase: Decode the individuals in the population to obtain the actual combination of construction projects, and calculate the total engineering cost and total technical efficiency according to the multi-objective optimization model, which are used as fitness values; Iterative optimization phase: Repeat the operator operation phase and fitness evaluation phase, and use an elite strategy to retain excellent individuals until the termination condition is met, and output the final Pareto optimal solution set; The decoding process in the encoding and fitness evaluation phases is as follows: The encoding is a real number encoding, and the chromosome is a fixed-length vector whose length is equal to the total number of time chains; During decoding, based on the integer value of each gene locus on the chromosome, a corresponding number of construction projects are selected from the starting position in the corresponding time sequence. The set of all selected construction projects constitutes a construction project combination scheme. Before calculating the fitness of an individual, the fitness assessment phase also includes a constraint processing step, which includes: Check whether the project combination scheme obtained by decoding violates the mutual exclusion constraint: if projects with mutual exclusion relationship are selected at the same time, the chain pruning mechanism is activated to truncate the relevant time chain to eliminate mutual exclusion; Check whether the project combination scheme obtained by decoding meets the engineering and technical indicator support constraints: if the number of supporting projects for any engineering and technical indicator in the project combination is lower than the preset ratio, then mark the fitness of that individual as invalid.

2. The method of generating a portfolio solution of claim 1, wherein, Methods for constructing a four-layer multiplexing network include: Establish a four-layer network structure containing the same set of nodes, where each layer corresponds to one of the aforementioned association types; The first layer of the network is defined as the collaboration relationship layer, and connections are established between construction projects that have collaboration relationships in this collaboration relationship layer; The second layer of the network is defined as a mutual exclusion layer, and edges are established in this mutual exclusion layer for construction projects that have mutual exclusion relationships. The third layer network is defined as the temporal relationship layer, and directed edges are established in this temporal relationship layer for construction projects that have temporal relationships. The direction of the directed edges is from the previous construction project to the subsequent construction project. The fourth layer of the network is defined as the conflict relationship layer, and connections are established between construction projects that have conflict relationships in this conflict relationship layer. The cooperative relationship layer, the mutual exclusion relationship layer, the temporal relationship layer, and the conflict relationship layer are integrated to form the four-layer multiplexing network, where each layer is an unweighted network.

3. The method of generating a portfolio solution of claim 2, wherein, Methods for calculating the value emergence effect and cost sharing effect include: Based on the collaborative relationship layer in the four-layer multiplexing network, all pairs of construction projects with collaborative relationships are identified; For each pair of construction projects with a collaborative relationship, obtain the preset value emergence coefficient and cost sharing coefficient respectively; Based on the value emergence coefficient, the increment of the synergistic relationship on the total technical efficiency of the project portfolio is calculated as the value emergence effect value; Based on the cost allocation coefficient, the reduction in the total project cost of the project portfolio due to this collaborative relationship is calculated as the cost allocation effect value.

4. The method of generating a portfolio solution of claim 2, wherein, Methods for calculating the value suppression effect and the resource competition effect include: Based on the conflict relationship layer in the four-layer multiplexing network, all pairs of construction projects with conflict relationships are identified. For each pair of construction projects with conflicting relationships, obtain the preset value inhibition coefficient and resource competition coefficient respectively; Based on the value inhibition coefficient, the amount by which the conflict relationship reduces the overall technical effectiveness of the project portfolio is calculated, and this is taken as the value inhibition effect value. Based on the resource competition coefficient, the increase in the total engineering cost of the project portfolio due to this conflict relationship is calculated as the resource competition effect value.

5. The method of generating a portfolio solution of claim 1, wherein, Before constructing the multi-objective optimization model, the process also includes determining the degree of support the construction project provides for engineering and technical indicators. This step includes: Construct a composite fuzzy element matrix, where the rows of the composite fuzzy element matrix correspond to construction projects, the columns correspond to engineering and technical indicators, and the matrix elements are the fuzzy values ​​of the support capabilities of the corresponding construction projects for the corresponding engineering and technical indicators. The composite fuzzy element matrix is ​​defuzzified to obtain the corresponding composite element matrix; Based on the composite element matrix, calculate the optimal membership degree of each construction project to each engineering technical indicator; Based on the weight of each engineering technical indicator and the preferred membership degree of each construction project, the Euclidean proximity of each construction project to each engineering technical indicator is calculated. The Euclidean proximity of each construction project is compared with a preset proximity threshold. When the Euclidean proximity is greater than or equal to the proximity threshold, the construction project is determined to support the corresponding engineering and technical indicators. When the Euclidean proximity is less than the proximity threshold, the construction project is determined to not support the corresponding engineering and technical indicators.

6. An electronic device comprising a memory and a processor, characterized in that The memory is used to store programs that support the processor in executing the method for generating project combination schemes according to any one of claims 1-5, the processor being configured to execute the programs stored in the memory.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program, when run by a processor, performs the steps of the method for generating a project portfolio scheme according to any one of claims 1-5.

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