Method for generating linear infrastructure construction path of structure evolvable energy field under multi-agent conflict

Abstract

The application provides a linear infrastructure path generation method of a structure evolvable energy field under multi-agent conflict, belongs to the cross technical field of civil construction engineering, traffic engineering and intelligent decision, and the method comprises the following steps: S1. multi-agent strategy game modeling and parameter solving; S2. structure evolvable energy field construction; S3. three-dimensional elastic band modeling and constraint force application; S4. multi-stage evolution convergence and three-dimensional linear path generation. The application aims at the technical pain points in the existing linear infrastructure planning, such as strategy-physical-geometric fragmentation, energy field static rigidity, field fragmentation and the need for a large number of post-corrections, and realizes the deep integration of society-physical-geometric by constructing the structure evolvable energy field and the multi-stage collaborative evolution mechanism, so that the optimal linearity naturally emerges, the planning cost is reduced, the decision efficiency is improved, and a unified solution is provided for the linear infrastructure planning under complex scenes.

Description

A method for generating linear infrastructure paths in structurally evolving energy fields under multi-subject conflict. Technical Field

[0001] This invention relates to the interdisciplinary fields of civil engineering, transportation engineering, and intelligent decision-making, and in particular to a method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict. Background Technology

[0002] The planning of linear infrastructure (such as railways, highways, pipelines, and power transmission lines) involves complex terrain, multiple engineering constraints, and trade-offs among various stakeholders, making it a typical socio-technical coupled spatial decision-making problem. Although this problem has been studied for decades, existing methods often separate strategic decision-making, physical modeling, and geometric linearity, making it difficult to characterize the overall generative logic of linearity formation and limiting the transferability of methods across different engineering types and policy scenarios.

[0003] Linear infrastructure (such as railways, highways, and energy networks) is not only the physical framework of modern civilization but also a key force reshaping the landform and social connections. With the acceleration of global urbanization and the advancement of sustainable development goals, the planning of such systems has evolved into a highly challenging planetary-scale spatial decision problem. These systems often traverse highly heterogeneous terrains and complex socio-political environments, and their planning process is not only constrained by rigid engineering physical constraints but also deeply entangled in the interplay of multiple interests and environmental uncertainties. Modern theory posits that infrastructure is no longer a simple static engineering object but a complex socio-technical system evolving amidst ever-increasing uncertainty.

[0004] Despite long-standing academic exploration, mainstream methodologies remain hampered by a significant structural dichotomy. First, in discrete decision-making, graph search or network flow-based methods suffer from the "curse of dimensionality." When continuous geometric constraints (such as curvature and slope) and multidimensional resource limitations are introduced, the problem degenerates into a nondeterministic polynomial-difficulty resource-constrained shortest path (RCSP) problem, making it difficult to guarantee computational scalability in large-scale real-world scenarios. Second, in engineering generation, while widely used rule-based heuristics are efficient, they exhibit high domain fragmentation—optimization models for roads, railways, and pipelines are often confined to specific modes, lacking a unified mathematical formulation. Furthermore, although emerging data-driven and deep learning methods have shown potential, their "black box" nature makes them unsuitable for meeting stringent compliance reviews and interpretability requirements in critical infrastructure involving public safety. More importantly, traditional multi-criteria decision making (MCDM) often simplifies complex conflicts of interest into static weights, making the planning results vulnerable to dynamic social preferences and often requiring extensive manual post-processing and ex-post correction.

[0005] A more fundamental epistemological crisis lies in the fact that existing paradigms isolate strategy, physics, and geometry into independent islands. Current approaches either abstractly "weight" preferences at the top level and then forcibly fit the geometry at the bottom; or they first generate physical paths and then "patchise" them with social constraints. This decoupling leads to a severe "semantic gap": the game equilibrium at the decision-making level cannot be accurately transmitted to the spatial form at the physical level, and the geometric constraints at the physical level are difficult to influence the strategy space at the upper level. Previous reviews have pointed out that the lack of a unified generative logic to characterize "how linearity naturally emerges from complex socio-physical constraints" is a long-standing theoretical gap in this field.

[0006] In fact, the form of infrastructure is not simply determined by topography, but rather a spatial projection of multi-stakeholder strategic interactions. Research on infrastructure governance shows that investors, regulators, and communities, in a non-cooperative game under uncertainty, do not directly draw the routes, but indirectly reshape the "feasibility landscape" of planning by changing risk-sharing boundaries and access costs. However, there is currently no mature mathematical framework for systematically "compiling" this discrete, game-theory-based strategic equilibrium into geometrically generative forces in continuous space.

[0007] In summary, existing technologies have significant drawbacks:

[0008] Strategy, physics, and geometry are separated: Traditional methods decouple multi-agent strategy decision-making, physical environment modeling, and geometric linear design, resulting in a "semantic gap." The game equilibrium at the decision-making level cannot be accurately transmitted to the engineering geometry, and physical constraints are difficult to influence strategy optimization.

[0009] The energy field method is static and rigid: Existing path generation techniques based on energy fields treat the energy field as a fixed cost background, which cannot adapt to dynamic engineering constraints. Furthermore, the energy gradient is prone to conflict with engineering geometric constraints, requiring a lot of manual correction.

[0010] Domain fragmentation and poor portability: Optimization models for different infrastructures such as roads, railways, and pipelines lack a unified mathematical form, are limited to specific modes, and are difficult to reuse across types.

[0011] Insufficient interpretability and robustness: Data-driven approaches suffer from a "black box" problem and cannot meet the compliance review requirements of critical infrastructure; traditional multi-criteria decision-making relies on static weights, which are vulnerable to dynamic social preferences and require frequent ex-post adjustments. Summary of the Invention

[0012] This invention provides a method for generating linear infrastructure paths in structurally evolvable energy fields under multi-agent conflict conditions. The aim is to address the technical pain points of existing linear infrastructure planning, such as the separation of strategy, physics, and geometry, static and rigid energy fields, fragmented domains, and the need for extensive post-hoc adjustments. This invention aims to provide a path generation method that is adaptable to multi-agent conflicts, transferable across different types, and combines engineering rationality and interpretability. By constructing a structurally evolvable energy field and a multi-stage collaborative evolution mechanism, it achieves deep integration of "social-physical-geometric" aspects, allowing the optimal linear shape to emerge naturally, reducing planning costs, improving decision-making efficiency, and providing a unified solution for linear infrastructure planning in complex scenarios.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A method for generating linear infrastructure paths in structurally evolving energy fields under multi-agent conflict conditions, including:

[0015] S1. Construct a multi-agent strategy decision-making model and solve for a set of strategy parameters describing the preferences and constraints of different stakeholders;

[0016] S2. Based on the set of strategy parameters, the continuous energy field in the planning space is structurally constructed to form a structurally evolvable energy field;

[0017] S3. In the structurally evolvable energy field, the planned target path is modeled as a three-dimensional elastic band, and during the path evolution process in the form of the three-dimensional elastic band, external forces generated by the gradient of the structurally evolvable energy field, smoothing constraint forces generated inside the elastic band, and geometric constraint forces generated by engineering geometric constraints are applied simultaneously.

[0018] S4. By adjusting the resolution and path evolution parameters of the structure's evolvable energy field in stages, the path in the form of the three-dimensional elastic band gradually converges during the continuous evolution process, generating a three-dimensional linear path that satisfies engineering geometric constraints.

[0019] The planar evolution and vertical evolution of the three-dimensional linear path are decoupled mechanically controlled.

[0020] In this specification, the structurally evolving energy field is a multi-stage evolving energy field. Different spatial smoothing scales and constraint strengths are used at different stages of the generation of the three-dimensional linear path to guide the global shaping and local geometric refinement of the three-dimensional linear path, respectively.

[0021] In this specification, the phased adjustment specifically refers to: in the initial stage, a low-resolution structurally evolvable energy field is constructed to suppress local terrain disturbances and quickly lock in a macroscopically reasonable path corridor; in the subsequent stage, a high-resolution structurally evolvable energy field is switched to accurately introduce local terrain features and engineering constraints and optimize the path details.

[0022] In this specification, the decoupled mechanical control method is specifically as follows: the planar displacement of the three-dimensional linear path is controlled by the terrain-related gradient of the structure's evolvable energy field, and the vertical displacement is jointly controlled by engineering geometric constraints and structural bias energy, so as to avoid path oscillation caused by mutual interference between planar and vertical constraints.

[0023] In this specification, the engineering geometric constraints include at least one or more of the following: maximum slope constraint, minimum slope length constraint, and curvature continuity constraint. All engineering geometric constraints are embedded in the evolution process of the three-dimensional linear path in the form of continuous constraint forces, without the need for post-processing correction after path generation.

[0024] In this specification, the structurally evolvable energy field includes two types of core energy terms: one is the surface repulsion energy term generated by the ground cost weight parameter in the strategy parameter set, and the other is the vertical bias energy term generated by the structural preference parameter in the strategy parameter set. The two types of energy terms work together to guide the three-dimensional linear path to adapt to the terrain and interest preferences.

[0025] In this specification, the strategy parameters in the set of strategy parameters are used to selectively modulate the spatial distribution of the structure's evolvable energy field, change the range and shape of the low-energy region in the energy field, so that the three-dimensional linear path avoids local low-energy traps during the evolution process, and improves the stability and convergence efficiency of the generation process.

[0026] In this specification, the low-resolution structure-evolvable energy field highlights the overall trend of the terrain by amplifying the spatial scale and enhancing the smoothing process; the high-resolution structure-evolvable energy field accurately captures local terrain differences and engineering constraint boundaries by reducing the smoothing degree and refining the spatial grid.

[0027] In this specification, the multi-agent strategy decision-making model is a Bayesian game model under incomplete information.

[0028] In this specification, the set of strategy parameters is obtained by solving the Nash equilibrium of the Bayesian game model, and includes at least the surface disturbance penalty parameter, tunnel cost parameter, and safety margin parameter. All of these parameters are directly used to regulate the energy distribution of the structurally evolving energy field, thereby directionally influencing the evolution direction and final form of the three-dimensional linear path.

[0029] In summary, the present invention has at least the following beneficial effects:

[0030] Breaking the "semantic gap": Establishing a mathematical bridge between discrete game strategies and continuous geometric generation, enabling the precise transmission of multi-agent strategy preferences to engineering linearity, and reflecting the trade-offs of interests without human intervention.

[0031] No need for post-hoc correction: Engineering constraints (maximum slope, minimum slope length, etc.) are embedded into the evolution process in an endogenous manner, and the path naturally meets the engineering specifications, avoiding the cost of forced corrections in traditional methods.

[0032] Engineering structures emerge naturally: engineering forms such as bridges, tunnels, and roadbeds are not preset discrete options, but rather the steady-state results of path evolution in the energy field, adaptively selected to suit terrain and strategy preferences.

[0033] Strong cross-domain versatility: The unified generation mechanism requires no structural modifications and can be adapted to various linear infrastructure types such as high-speed railways, highways, power transmission lines, and oil and gas pipelines.

[0034] Excellent robustness and interpretability: The multi-resolution energy field collaborative mechanism avoids the path from getting stuck in the local low-energy region, the evolution process is traceable, the results are highly consistent with the artificial expert design scheme, and meet the requirements of compliance review. Attached Figure Description

[0035] Figure 1 is a schematic diagram of the method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict involved in this invention.

[0036] Figure 2 is a schematic diagram of the Game–Field–Shape framework involved in this invention.

[0037] Figure 3 is a schematic diagram of the strategy weights of the equilibrium parameter Λ derived from Bayesian Nash equilibrium in this invention.

[0038] Figure 4 is a schematic diagram of the compilation energy landscape reshaped by strategy preferences involved in this invention.

[0039] Figure 5 is a schematic diagram of the energy gradient distribution and steering force analysis involved in this invention.

[0040] Figure 6 is a schematic diagram of the initial stage route plan involved in this invention.

[0041] Figure 7 is a schematic diagram of the longitudinal profile of the initial stage route involved in this invention.

[0042] Figure 8 is a schematic diagram of the fine-resolution stage route plan involved in this invention.

[0043] Figure 9 is a schematic diagram of the longitudinal section of the fine-resolution stage route involved in this invention.

[0044] Figure 10 is a schematic diagram of the fine-resolution stage route plan involved in this invention.

[0045] Figure 11 is a schematic diagram of the longitudinal section of the fine-resolution stage route involved in this invention.

[0046] Figure 12 is a schematic diagram of a high-speed railway engineering case involved in this invention.

[0047] Figure 13 is a schematic diagram of a highway engineering case involved in this invention.

[0048] Figure 14 is a schematic diagram of a transmission line example involved in this invention.

[0049] Figure 15 is a schematic diagram of an oil and gas pipeline example involved in this invention.

[0050] Figure 16 is a schematic diagram comparing the planar alignment results of the present invention, the artificial alignment, and the Hybrid A* method in the railway case involved in this invention.

[0051] Figure 17 is a schematic diagram of the artificial linear longitudinal section involved in this invention.

[0052] Figure 18 is a schematic diagram of the longitudinal section of the GFS line involved in this invention.

[0053] Figure 19 is a schematic diagram of the longitudinal section of the Hybrid A* line involved in this invention. Detailed Implementation

[0054] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0055] As shown in Figure 1, this embodiment provides a method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict, including:

[0056] S1. Construct a multi-agent strategy decision-making model and solve for a set of strategy parameters describing the preferences and constraints of different stakeholders;

[0057] S2. Based on the set of strategy parameters, the continuous energy field in the planning space is structurally constructed to form a structurally evolvable energy field;

[0058] S3. In the structurally evolvable energy field, the planned target path is modeled as a three-dimensional elastic band, and during the path evolution process in the form of the three-dimensional elastic band, external forces generated by the gradient of the structurally evolvable energy field, smoothing constraint forces generated inside the elastic band, and geometric constraint forces generated by engineering geometric constraints are applied simultaneously.

[0059] S4. By adjusting the resolution and path evolution parameters of the structure's evolvable energy field in stages, the path in the form of the three-dimensional elastic band gradually converges during the continuous evolution process, generating a three-dimensional linear path that satisfies engineering geometric constraints.

[0060] The planar evolution and vertical evolution of the three-dimensional linear path are decoupled mechanically controlled.

[0061] In some embodiments, the structurally evolvable energy field is a multi-stage evolvable energy field, employing different spatial smoothing scales and constraint strengths at different stages of the three-dimensional linear path generation, respectively used to guide the global shaping and local geometric refinement of the three-dimensional linear path.

[0062] In some embodiments, the phased adjustment specifically involves: in the initial stage, a low-resolution structurally evolvable energy field is constructed to suppress local terrain disturbances and quickly lock in a macroscopically reasonable path corridor; in the subsequent stage, a high-resolution structurally evolvable energy field is switched to accurately introduce local terrain features and engineering constraints and optimize the path details.

[0063] In some embodiments, the decoupled mechanical control method specifically means that the planar displacement of the three-dimensional linear path is controlled by the terrain-related gradient of the structurally evolving energy field, and the vertical displacement is jointly controlled by engineering geometric constraints and structural bias energy, so as to avoid path oscillation caused by mutual interference between planar and vertical constraints.

[0064] In some embodiments, the engineering geometric constraints include at least one or more of the following: maximum slope constraint, minimum slope length constraint, and curvature continuity constraint. All engineering geometric constraints are embedded in the evolution process of the three-dimensional linear path in the form of continuous constraint forces, without the need for post-processing correction after path generation.

[0065] In some embodiments, the structurally evolvable energy field includes two types of core energy terms: one is the surface repulsion energy term generated by the ground cost weight parameter in the strategy parameter set, and the other is the vertical bias energy term generated by the structural preference parameter in the strategy parameter set. The two types of energy terms work together to guide the three-dimensional linear path to adapt to the terrain and interest preferences.

[0066] In some embodiments, the strategy parameters in the strategy parameter set are used to selectively modulate the spatial distribution of the structurally evolvable energy field, change the range and shape of the low-energy region in the energy field, so that the three-dimensional linear path avoids local low-energy traps during the evolution process, and improves the stability and convergence efficiency of the generation process.

[0067] In some embodiments, low-resolution structure-evolvable energy fields highlight the overall terrain trend by amplifying the spatial scale and enhancing smoothing; high-resolution structure-evolvable energy fields accurately capture local terrain differences and engineering constraint boundaries by reducing the smoothing degree and refining the spatial grid.

[0068] In some embodiments, the multi-agent strategy decision-making model is a Bayesian game model under incomplete information.

[0069] In some embodiments, the set of strategy parameters is obtained by solving the Nash equilibrium of the Bayesian game model, and includes at least the surface disturbance penalty parameter, tunnel cost parameter, and safety margin parameter. These parameters are all directly used to regulate the energy distribution of the structurally evolving energy field, thereby directionally influencing the evolution direction and final form of the three-dimensional linear path.

[0070] The technical concept of this invention is as follows:

[0071] This invention proposes a novel perspective that deeply integrates "social-physical-geometry": the optimal linear shape of linear infrastructure should not be "designed," but rather "evolved." This invention proposes a unified Game-Field-Shape (GFS) planning paradigm, simulating the minimum action principle of path formation in nature. This paradigm contains three logical loops:

[0072] Game (Game Theory Layer): First, the planning is expressed as a Bayesian game, and the Nash equilibrium of each stakeholder establishes the system's inherent trade-off between risk and cost.

[0073] Field: Proposes a novel "policy-parameter compilation mechanism" to map abstract game equilibrium into continuous physical field parameters, thereby reshaping the energy landscape in three-dimensional space.

[0074] Shape: The linear shape is modeled as a three-dimensional elastic band in the energy field, evolving automatically according to gradient descent dynamics. In this process, bridges, tunnels, and roadbeds are no longer preset discrete options, but rather the morphogenesis results that naturally emerge as the path pursues vertical energy minimization.

[0075] The main contributions of this invention include: (1) establishing a mathematical bridge connecting discrete game strategies and continuous geometric generation, bridging the semantic gap between social decision-making and engineering design; (2) proposing a unified generation algorithm based on Elastic Band Dynamics, realizing the adaptive evolution of three-dimensional linear shapes under complex constraints; and (3) revealing the emergence mechanism of engineering structures (bridges / tunnels / roads) as stable states in the energy landscape.

[0076] Core innovation: Linear generation based on structurally evolvable energy fields.

[0077] I. Problems with Existing Energy Field Methods In existing technologies, methods based on energy field generation paths typically suffer from the following technical drawbacks:

[0078] 1. The energy field exists only as a static cost background.

[0079] Existing methods typically treat the energy field as a fixed spatial cost distribution, and the path is searched or descended only within this static energy field, making it difficult to adapt to complex engineering constraints.

[0080] 2. The energy gradient conflicts with engineering geometric constraints.

[0081] In real-world engineering scenarios, simple energy gradient descent often leads to excessive path bending, local oscillations, or violations of engineering specifications such as slope and curvature, requiring extensive manual correction.

[0082] 3. Difficulty in simultaneously handling planar and longitudinal coupling problems.

[0083] Traditional energy field methods are mostly designed for two-dimensional planar path optimization, making it difficult to simultaneously consider terrain adaptability and longitudinal profile engineering feasibility in three-dimensional space, resulting in a line shape that "can be calculated but cannot be constructed".

[0084] II. The fundamental innovation of this invention: the energy field is not a "background," but an "evolvable and generative structure."

[0085] (I) Innovation Point 1: Introduction of "Structurally Evolvable Energy Field"

[0086] This invention does not employ a static energy field for path search, but instead proposes a structurally evolving energy field construction scheme:

[0087] The spatial distribution structure of the energy field is determined by both the strategy parameters and the path evolution stage;

[0088] The energy field is not generated all at once, but is reconstructed in stages during the path generation process;

[0089] The energy field at different stages plays different roles in generation, rather than uniformly bearing all constraints.

[0090] (II) Innovation Point 2: Multi-resolution-multi-stage energy field collaborative generation mechanism

[0091] To resolve the conflict between global path search and local path shaping, this invention divides the energy field construction process into at least two stages:

[0092] 1. Global Guidance Phase (Coarse-Resolution Energy Field)

[0093] During this stage:

[0094] The energy field suppresses local terrain noise through spatial smoothing and scale amplification;

[0095] Energy gradient primarily reflects the overall trend of terrain;

[0096] The energy field at this stage is used to guide the path to form the overall direction and macroscopic structure.

[0097] The technological benefits at this stage are:

[0098] To avoid the path from falling into a local low-energy area too early, and to ensure global connectivity and corridor rationality.

[0099] 2. Fine-grained forming stage (high-resolution energy field)

[0100] During this stage:

[0101] The resolution of the energy field is gradually improving;

[0102] Local terrain features and engineering constraints are explicitly introduced;

[0103] The path undergoes fine geometric adjustments within the defined corridor.

[0104] The technological benefits of this stage are:

[0105] Ensure that the path evolves into a workable alignment while meeting macro-level rationality requirements.

[0106] (III) Innovation Point 3: Decoupling and Synergy of Energy Gradient and Engineering Geometric Constraints

[0107] This invention discovers that directly applying a uniform energy gradient descent to the path in three-dimensional space will inevitably lead to the following problems:

[0108] Planar energy gradient straightening path;

[0109] Feasibility of longitudinal section engineering under vertical return force failure;

[0110] The interaction between the two leads to path oscillations.

[0111] Therefore, the present invention employs the following technical means:

[0112] Mechanically decouple the planar direction from the vertical direction during the path evolution process;

[0113] The planar direction is mainly guided by the gradient of the terrain energy field;

[0114] The vertical direction is mainly constrained by engineering specifications and controlled by strategic bias forces;

[0115] The overall geometric continuity is maintained in both directions by internal constraints of the elastic band.

[0116] This step is the key reason why "linearity can be generated", rather than simple gradient descent.

[0117] (iv) Innovation Point 4: Engineering constraints are embedded in the energy evolution process in an endogenous manner

[0118] Unlike existing technologies that use engineering specifications as post-hoc filtering conditions, this invention incorporates engineering constraints:

[0119] In the form of continuous constraint forces;

[0120] Directly embedding the path evolution process;

[0121] Including but not limited to:

[0122] Maximum slope constraint;

[0123] Minimum slope length constraint;

[0124] Curvature continuity constraint.

[0125] In this way, the path is continuously projected into the engineering feasible region during the evolution process, thereby avoiding forced correction after generation.

[0126] IV. Innovation Point 5 (Very Important): The linear shape is "emergent," not "calculated."

[0127] In this invention, the path is not generated by enumerating rules or combining engineering units, but rather evolves gradually in a continuous energy landscape to form a stable structure.

[0128] Specifically, this manifests as follows:

[0129] When the ground cost is low, the path naturally follows the ground in a more natural and dynamic manner.

[0130] When surface costs increase, the path automatically shifts towards underground or elevated directions;

[0131] The emergence of bridges, tunnels, and roadbeds is not a discrete choice, but a natural result of energy balance.

[0132] In some embodiments, a multi-agent strategy decision-making model is constructed to obtain a set of strategy parameters Λ that describes the preferences and constraints of different stakeholders. The set of strategy parameters Λ includes at least ground cost weight parameters, structural preference parameters, and safety margin parameters.

[0133] Based on the set of strategy parameters Λ, the continuous energy field in the planning space is constructed in a structured manner. The strategy parameters are not directly superimposed on the cost function as scalar weights, but are compiled into physical control parameters for changing the spatial distribution structure of the energy field.

[0134] In the energy field, the planned path is modeled as a three-dimensional elastic band, and during the path evolution process, external forces generated by the energy field gradient, smoothing constraints generated by the elastic band, and geometric constraints generated by engineering specifications are applied simultaneously.

[0135] By adjusting the energy field resolution and path evolution parameters in stages, the path gradually converges during the continuous evolution process, generating a three-dimensional linear path that meets engineering geometric constraints.

[0136] The planar and vertical evolution of the path is decoupled and controlled by mechanical means, and bridges, tunnels or ground engineering forms naturally emerge as stable structures formed by the evolution of the path in a continuous energy field.

[0137] In some embodiments, the energy field is a multi-stage evolvable energy field, employing different spatial smoothing scales and constraint intensities at different stages of path generation to guide the global path formation and local geometric refinement of the path, respectively.

[0138] In some embodiments, a low-resolution energy field is constructed in the initial stage of path generation to suppress local terrain disturbances, and a high-resolution energy field is constructed in the subsequent stage of path generation to introduce local terrain and engineering constraints.

[0139] In some embodiments, during the path evolution process, the displacement in the planar direction is mainly controlled by the terrain-related energy gradient, while the displacement in the vertical direction is mainly controlled by engineering geometric constraints and structural bias energy, thereby avoiding path oscillations caused by mutual interference between planar and longitudinal constraints.

[0140] In some embodiments, the engineering geometric constraints include at least the maximum slope constraint, the minimum slope length constraint, or the curvature continuity constraint, and the engineering geometric constraints are embedded in the path evolution process in the form of continuous constraint forces, rather than being corrected after the path is generated.

[0141] In some embodiments, the energy field includes a surface repulsion energy term generated by a ground cost weighting parameter and a vertical bias energy term generated by a structural preference parameter, used to guide the adaptive evolution of the path among ground engineering, bridge engineering and tunnel engineering.

[0142] In some embodiments, the bridge, tunnel, or ground engineering form is not determined by discrete rule enumeration or manual specification, but rather is a stable structure formed by the evolution of the path under the combined action of a continuous energy field and engineering constraints.

[0143] In some embodiments, the energy field structure is modulated by the strategy parameters to prevent the path from getting trapped in local low-energy regions during the evolution process, thereby improving the stability and convergence of the path generation process.

[0144] Overview of the Game-Field-Shape Programming Paradigm:

[0145] Figure 2 illustrates the Game–Field–Shape unified planning paradigm proposed in this invention. This paradigm formulates the linear infrastructure routing problem as a continuous generative process from policy to physics to geometry, rather than a traditional path search or rule combination. Figure 2 reveals an overview of the Game–Field–Shape framework: policy preferences indirectly shape path emergence through energy fields.

[0146] In this framework, planning first occurs at the game layer. Different stakeholders, under conditions of incomplete information, form stable strategic interactions, and their equilibrium states characterize the system's preference structure across dimensions such as cost, risk, security, and social acceptability. This layer does not generate any spatial path decisions, but only generates abstract preference information.

[0147] Subsequently, the game equilibrium is mapped to the compilation layer (Game-to-Field compilation). As shown in Figure 2, this process transforms policy preferences into a continuous set of parameters Λ with explicit engineering semantics, such as surface disturbance penalty intensity, tunnel tolerance, and safety margin. These parameters do not directly constrain path morphology but serve as control variables for subsequent physical processes, reshaping the overall cost structure of the planning space.

[0148] In the field layer, the parameter set Λ is injected into a unified physical energy field. This energy field comprehensively describes the distribution characteristics of terrain adaptability, economic costs, and engineering constraints in continuous space, thereby defining the mechanical environment of path evolution.

[0149] Finally, in the shape layer, the path is modeled as an elastic band in the energy field, which naturally evolves and converges under the combined action of external energy gradient force and internal smoothing constraint, and is further transformed into a constructable line shape that meets engineering specifications.

[0150] The key point is that this paradigm does not limit the specific solution process, but rather describes the generative logic shared by linear infrastructure planning.

[0151] Balanced strategies reshape the planned energy landscape:

[0152] Figures 3, 4, and 5 illustrate a comparison of energy fields under the same terrain but different strategies. The core finding is that game equilibrium does not specify paths, but rather reshapes the energy landscape from which those paths emerge. Figure 3 demonstrates the compilation of game equilibrium strategies into planned energy landscapes, showing the equilibrium parameters derived from Bayesian Nash equilibrium. The strategy weights are shown in Figure 4, which depicts the compiled energy landscape reshaped by strategy preferences. Figure 5 shows the energy gradient distribution and steering force analysis. The red vector field represents the negative gradient force generated by the energy landscape. These forces act as external driving forces, guiding the three-dimensional elastic linear shape to migrate towards the low-energy region. This reveals how game equilibrium indirectly and systematically influences the final trajectory shape through the energy field.

[0153] The equilibrium strategies obtained under different game scenarios exhibit significant differences in preference structures, such as sensitivity to surface disturbances or acceptance of tunnel structures. However, these strategies are not interpreted as specific spatial decisions, but are uniformly compiled into a parameter set Λ, which acts on the energy field construction process. It is important to emphasize that these parameters are not optimized to match a specific route, but are entirely determined by the game equilibrium under uncertain conditions.

[0154] Under identical topographical conditions, the energy landscapes corresponding to different Λ configurations exhibit significant differences. The strategy change did not introduce discrete no-entry zones or forced passages, but rather altered the overall shape of energy distribution in a continuous manner, thereby reshaping the attraction structure of paths in space.

[0155] Further analysis shows that this change is globally consistent and interpretable in space, and the impact of different strategy parameters on the energy field is consistent with its engineering semantics.

[0156] Continuous path generation based on elastic band dynamics:

[0157] Figures 6, 7, 8, 9, 10, and 11 show the continuous evolution of the path from the initial state to the steady state in the energy field. Figure 6 is a plan view of the initial stage path. Figure 7 is a longitudinal section view of the initial stage path. Figure 8 is a plan view of the path in the fine-resolution stage, Figure 9 is a longitudinal section view of the path in the fine-resolution stage, Figure 10 is a plan view of the path in the fine-resolution stage, and Figure 11 is a longitudinal section view of the path in the fine-resolution stage. These figures demonstrate the gradual evolution and convergence of the path in the reshaped energy field through elastic band dynamics.

[0158] In the initial stage, the path is merely a rough geometric line, lacking any engineering or economic intelligence. As evolution progresses, the path, acting as an elastic band, migrates as a whole under the drive of energy field gradient forces. The coarse-resolution stage allows the path to traverse large-scale terrain features, thus quickly determining the location of macroscopic corridors; the fine-resolution stage, dominated by local energy structures, refines the path morphology, gradually conforming to low-energy valleys while maintaining overall smoothness.

[0159] Ultimately, the path converges to a stable configuration in which the external energy gradient force and the internal constraint force reach equilibrium.

[0160] Unlike the traditional elastic band method applied in fixed physical potential fields, path evolution here occurs in an energy landscape conditioned by policy preferences.

[0161] Cross-domain universality across infrastructure types:

[0162] Figures 12, 13, 14, and 15 verify the universality of the Game-Field-Shape framework in different linear infrastructure types, providing examples of linear shapes generated by GFS in different engineering case studies. Figure 12 is a high-speed railway engineering case, Figure 13 is a highway engineering case, Figure 14 is a power transmission line case, and Figure 15 is an oil and gas pipeline case.

[0163] Under a unified planning paradigm, this framework is applied to engineering scenarios such as high-speed railways, highways, power transmission lines, and oil and gas pipelines. Although different projects differ in specifications and cost models, the underlying generation mechanism remains unchanged, and the framework can be adapted without structural modifications.

[0164] Comparison with benchmarks of domain-specific planning methods:

[0165] Figures 16, 17, 18, and 19 systematically compare this invention with human expert design schemes and improved Hybrid A* methods in the field of railway alignment optimization. All comparison methods employ the best practice configurations recommended in the corresponding literature. The figures demonstrate a comparison of this method with alignments designed by human experts and existing mature railway alignment optimization algorithms in a railway case study. Figure 16 compares the planar alignment results of this method, the human expert-designed alignment, and the Hybrid A* method in the railway case study (the bottom of Figure 16 shows a real-world view of the construction project). Figure 17 shows the longitudinal profile of the human expert-designed alignment, Figure 18 shows the longitudinal profile of the GFS alignment, and Figure 19 shows the longitudinal profile of the Hybrid A* alignment.

[0166] It is worth noting that the circuit scheme generated by this invention, although without any human intervention or the introduction of domain-specific heuristic rules, exhibits a high degree of structural consistency with the scheme designed by human experts.

[0167] This similarity is not an imitation of human decision-making, but rather demonstrates that the generative process proposed in this invention can reveal implicit multi-objective trade-offs that typically require expert judgment to clarify. In contrast, traditional rule-based search methods often require extensive parameter tuning to approximate the above results; while the GFS framework transforms the equivalent route selection logic into emergent characteristics driven by policy-constrained physical mechanisms.

[0168] The above results indicate that the circuit scheme designed by experts can be interpreted as a stable configuration within the generalized generation field, and the method proposed in this invention can directly obtain such configurations.

[0169] The Game-Field-Shape planning paradigm proposed in this invention provides a unified generative perspective for the linear infrastructure routing problem. Unlike traditional methods that view planning as path search or rule combination, this paradigm understands multi-agent decision-making, the formation of continuous physical fields and geometric shapes as a coherent generative process. From this perspective, routes are not "selected," but rather emerge naturally as the steady state of the system under specific strategies and constraints.

[0170] From optimization to generative paradigms:

[0171] Most existing route selection studies focus on "optimization" as their core objective, that is, finding the optimal solution under predefined objective functions and constraints. However, the analysis in the Results section shows that understanding linear infrastructure planning as a simple optimization problem is insufficient to characterize its complexity. The Game-Field-Shape paradigm emphasizes that what truly determines the route shape is not a specific objective function, but rather the generation logic that determines how these objectives enter the space. By compiling policy preferences into a continuous energy field, the planning problem is transformed from "solving the optimal path" to "constructing the physical environment that generates reasonable paths."

[0172] This shift is significant. First, it reduces the reliance on precise weight settings, allowing policy preferences to influence outcomes in an interpretable and traceable manner. Second, it provides a theoretical basis for cross-engineering transfer, since different domains share generative mechanisms rather than specific rules.

[0173] Physics conditioned by strategy as a unified layer:

[0174] Multi-agent strategies do not directly correspond to spatial decision-making, but rather indirectly influence path evolution by reshaping the energy landscape. This finding provides a unified explanation for the long-standing problem of "decision-physics disconnect" in infrastructure planning. Unlike traditional methods that transform preferences into weights or hard constraints, the physical field of strategy conditionalization allows preferences to have a global and consistent impact in continuous space.

[0175] From a broader perspective, this "strategy-conditioned physics" mechanism provides a new path for introducing social and policy factors into engineering systems. Strategies are no longer exogenous perturbations but become part of shaping the physical environment, thus avoiding ex-post corrections or rule overlays.

[0176] The unified planning paradigm proposed in this invention comprises three logical layers: the Game layer models planning as multi-agent strategy interaction under incomplete information; the Field layer transforms equilibrium strategies into continuous parameters with engineering semantics; and the Shape layer evolves the final three-dimensional linear shape in a parameterized energy field through elastic band dynamics. The methods for each layer are described in detail below.

[0177] Bayesian game framework and equilibrium solution:

[0178] The linear infrastructure alignment problem is defined in a three-dimensional continuous space. Find a feasible construction path Connect to the given starting point and the finish line .path Discretized into a set of ordered control points ,in Adjacent points maintain geometric continuity through elastic connections.

[0179] The planning was first modeled as an incomplete information Bayesian game. (Set of participating entities) These represent the investors, the design institute, and the local government, respectively. Each entity... Having private types (such as the geological complexity known to the design institute) Local government subsidy policies The type follows a known prior distribution. Each entity selects its type based on its type selection strategy. They strive to maximize their expected utility.

[0180] Specifically, the set of Bayesian Nash equilibrium states of the game By simultaneously solving for the optimal strategies of each agent, we obtain:

[0181] ;

[0182] ;

[0183] ;

[0184] in These are decision variables for investors, design institutes, and the government, respectively. These are the utility functions for investors, designers, and local governments, respectively. This system of equations is solved using the sequential L-BFGS-B minimization method, where the maximum change in strategy is less than... The iteration terminates when the time is right.

[0185] From game equilibrium to compiling engineering parameters:

[0186] To inject an abstract preference structure into the spatial planning process, this invention defines a compiler function. To achieve game equilibrium Mapped to a continuous set of parameters with explicit engineering semantics. :

[0187] ;

[0188] Among them, each parameter To regulate the intensity of specific cost components in an energy field. For example:

[0189] : Surface ecological disturbance penalty coefficient, reflecting concern about environmental sensitivity.

[0190] The relative cost coefficient for tunnel construction stems from the trade-off between the risks and costs of underground engineering.

[0191] Safety margin coefficient, derived from the risk avoidance strategy of the design institute.

[0192] Curvature penalty coefficient: controls the sensitivity of the energy field to the "degree of path curvature".

[0193] Each adjustment parameter is calculated through a convex combination of normalized equilibrium actions:

[0194] ;

[0195] ;

[0196] ;

[0197] ;

[0198] in This is a truncation function used to apply hard engineering limits. (where b is the minimum tunnel cost weight and b is the maximum tunnel cost weight) This reflects the relative influence of investor and government preferences. Hyperparameters , , Calibrated based on historical project data. The expected value of the local government's equilibrium strategy. The expected value of the equilibrium strategy of the design institute. These represent the theoretical lower and upper bounds for the investor's strategy variables. The range of values ​​for the design institute's strategy variables. The range of values ​​for the government strategy variable. , The normalized weighting coefficient is used to balance the combined effects of "design institute preferences" and "investor preferences" on the curvature of the line. , This represents the normalized strategy value. This modeling method has been validated in regional high-speed rail investment decision-making game.

[0199] Construction of a continuous energy field with strategic conditions:

[0200] In a given parameter set The present invention is in the planning domain. Construct a unified continuous energy field on top. This field is used to describe the comprehensive cost of any spatial point x. It is a linear superposition of multiple physically meaningful components:

[0201] ;

[0202] Terrain adaptation field Calculations based on a digital elevation model (DEM) penalize unfavorable terrain features such as steep slopes and high curvature; economic cost field. It integrates spatial distribution estimations of earthwork volume and permanent land use costs; constraint field Ecological protection zones, cultural relics sites, and other restricted areas are modeled as high repulsion barriers. , , These are the weights for each field.

[0203] Vertical economic gradient field The smoothing penalty function is used to distinguish between embankment, cutting, bridge and tunnel types:

[0204] ;

[0205] in Used to generate a repulsive potential field near the terrain surface, influencing the choice of route alignment between elevation (bridge) and excavation (tunnel). Bias term Positive values ​​are used when policies favor tunnels, and negative values ​​are used when policies favor bridges. For design elevation, Ground elevation, This represents the range of the repulsive force.

[0206] This design avoids pre-defined discrete structure type rules, allowing the engineering structure to emerge naturally as a result of energy balance in the vertical dimension of the path. The concept of energy field construction originates from the potential field method in robot path planning and cost surface analysis in geographic information systems.

[0207] Elastic band dynamics and multi-resolution path evolution:

[0208] path Modeled as an energy field An elastic band within it. Its total energy functional Including the sum of external field energy and internal elastic potential energy:

[0209] ;

[0210] in is the elastic coefficient, controlling the tensile stiffness of the path; N represents the number of control points. This represents the nth control point. The path evolution follows gradient descent dynamics:

[0211] ;

[0212] in For virtual time steps, Let be the energy gradient, representing the energy gradient at point . The slope vector at the point. The first term on the right-hand side of the equation is the energy field gradient force, driving the path to migrate to the lower energy region; the second term is the internal elastic force, ensuring the continuity and smoothness of the path. This invention uses the explicit Euler method for iterative solution until the path energy converges to a stable state. The 'elastic band dynamics' method used here is conceptually related to the 'string methods' used to find the lowest energy path in complex environments, but it differs in that it incorporates an energy field mechanism based on specific policy conditions and employs multi-resolution optimization techniques.

[0213] line Iterative evolution via gradient descent with adaptive reparameterization:

[0214] ;

[0215] in Indicates the first The path position after the next iteration. This is the iteration step size. As a projection operator, it projects the line onto the slope with the maximum gradient. and minimum slope length Defined feasible set Inside. Sliding head and smoothing weights Used to suppress high-frequency oscillations. Each iteration Next, the line is reparameterized by the arc length to avoid the point set from clustering in the high-energy region.

[0216] The multi-resolution strategy consists of two phases:

[0217] Coarse stage: using Pixel Gaussian smoothing and quantization of energy levels (7 levels, mixing coefficient = 0.15) to identify macroscopic corridors; learning rate. Set the settings to be large and disable projection for faster exploration.

[0218] Refinement stage: using Pixels are Gaussian smoothed and combined with corridor masks; the learning rate is reduced by 10x, and projection operations are enabled to meet strict geometric constraints.

[0219] This multi-scale concept is widely used in image processing and computational geometry optimization: Gaussian smoothing generates a series of energy approximations from coarse to fine, making the optimization more stable and less prone to getting trapped in suboptimal solutions.

[0220] Geometric implementation, evaluation, and robustness analysis:

[0221] Path control points after evolution convergence After geometric post-processing, it is transformed into a constructable alignment that meets engineering standards. This includes: smoothing the plane and longitudinal profile using spline curves to ensure continuous changes in curvature and slope; checking constraints such as maximum slope and minimum curve radius according to industry standards (such as railway alignment design specifications); and automatically marking suggested bridge, tunnel, and roadbed sections by comparing continuous elevations with the terrain.

[0222] Evaluation metrics: This invention uses three core metrics for comparison with baseline methods: 1) Comprehensive cost, based on detailed engineering quantity and unit price calculations; 2) Surface disturbance index, which measures the extent to which the line occupies sensitive surface areas; 3) Constraint violation rate, which statistically analyzes the proportion of lengths that violate mandatory engineering specifications.

[0223] Robustness Testing: To verify the stability of the method, this invention conducted three analyses: 1) Data Perturbation: Random elevation noise was applied to the input terrain to observe corridor stability; 2) Initial Path Sensitivity: Different initial conjectured paths were used to test the consistency of convergence results; 3) Policy Scenario Exploration: The game compilation parameters were continuously adjusted. (such as improving) (This involves) observing the smooth, interpretable changes in the shape and structure of the lines to demonstrate their potential as a policy analysis tool.

Claims

1. A method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict, characterized in that, include: S1. Construct a multi-agent strategy decision-making model and solve for a set of strategy parameters describing the preferences and constraints of different stakeholders; S2. Based on the set of strategy parameters, the continuous energy field in the planning space is structurally constructed to form a structurally evolvable energy field; S3. In the structurally evolvable energy field, the planned target path is modeled as a three-dimensional elastic band, and during the path evolution process in the form of the three-dimensional elastic band, external forces generated by the gradient of the structurally evolvable energy field, smoothing constraint forces generated inside the elastic band, and geometric constraint forces generated by engineering geometric constraints are applied simultaneously. S4. By adjusting the resolution and path evolution parameters of the structurally evolving energy field in stages, the path in the form of a three-dimensional elastic band gradually converges during continuous evolution, generating a three-dimensional linear path that satisfies engineering geometric constraints. The planar and vertical evolution of the three-dimensional linear path employs a decoupled mechanical control method. A unified planning paradigm with three logical levels is adopted: a game theory layer, a field layer, and a shape layer. The game theory layer models the planning as multi-agent strategy interaction under incomplete information. The field layer transforms equilibrium strategies into continuous parameters with engineering semantics. The shape layer, within the parameterized energy field, through the elastic band... The dynamics evolve to produce the final three-dimensional linear shape; S1 corresponds to the game layer, and the linear infrastructure route selection problem is defined as finding a constructable path in a three-dimensional continuous space, connecting a given starting point and an ending point; the path is discretized into a set of ordered control points, and adjacent points maintain geometric continuity through elastic connections; the multi-agent strategy decision-making model is an incomplete information Bayesian game, with the participating agents representing investors, design institutes, and local governments; each agent has a private type, which follows a known prior distribution, and each agent chooses a strategy based on its type, pursuing the maximization of its expected utility; the set of Bayesian Nash equilibrium states of the game is obtained by simultaneously solving for the optimal strategies of each agent. The set of strategy parameters is obtained by solving the Bayesian Nash equilibrium of the Bayesian game model; S2 corresponds to the field layer, and through a compilation function, the game equilibrium is mapped into a set of continuous parameters with clear engineering semantics; among them, each parameter regulates the intensity of a specific cost component in the energy field, including: the surface ecological disturbance penalty coefficient, reflecting the concern for environmental sensitivity; the relative cost coefficient of tunnel construction, derived from the trade-off between underground engineering risks and costs; the safety margin coefficient, derived from the design institute's risk avoidance strategy; and the curvature penalty coefficient, controlling the sensitivity of the energy field to the degree of path curvature; each adjustment parameter is calculated through a convex combination of normalized equilibrium actions; given Under a fixed parameter set, a unified continuous energy field is constructed over the planning domain to describe the comprehensive cost of any spatial point. This field is a linear superposition of multiple physically meaningful components, including a terrain adaptation field, an economic cost field, a constraint field, and a vertical economic gradient field. The terrain adaptation field is calculated based on a digital elevation model and penalizes unfavorable terrain. The economic cost field integrates spatial distribution estimates. The constraint field models restricted areas as high repulsion barriers. The vertical economic gradient field distinguishes between embankment, cutting, bridge, and tunnel types through a smoothing penalty function. S3 corresponds to the shape layer, and the path evolution in the form of the three-dimensional elastic band follows the elastic band dynamics, evolving into the final three-dimensional linear shape in the parameterized energy field.

2. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The structure-evolvable energy field is a multi-stage evolvable energy field. Different spatial smoothing scales and constraint strengths are used at different stages of the generation of the three-dimensional linear path to guide the global shaping and local geometric refinement of the three-dimensional linear path, respectively.

3. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The phased adjustment is as follows: in the initial stage, a low-resolution structurally evolvable energy field is constructed to suppress local terrain disturbances and quickly lock in a macroscopically reasonable path corridor; in the subsequent stage, a high-resolution structurally evolvable energy field is switched to accurately introduce local terrain features and engineering constraints and optimize the path details.

4. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The decoupled mechanical control method is as follows: the planar displacement of the three-dimensional linear path is controlled by the terrain-related gradient of the structure's evolvable energy field, and the vertical displacement is jointly controlled by engineering geometric constraints and structural bias energy, thus avoiding path oscillation caused by mutual interference between planar and vertical constraints.

5. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The engineering geometric constraints include at least one or more of the following: maximum slope constraint, minimum slope length constraint, and curvature continuity constraint. All engineering geometric constraints are embedded in the evolution process of the three-dimensional linear path in the form of continuous constraint forces, without the need for post-processing correction after path generation.

6. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The structure-evolvable energy field includes two types of core energy terms: one is the surface repulsion energy term generated by the ground cost weight parameter in the strategy parameter set, and the other is the vertical bias energy term generated by the structure preference parameter in the strategy parameter set. The two types of energy terms work together to guide the three-dimensional linear path to adapt to the terrain and interest preferences.

7. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The strategy parameters in the set of strategy parameters are used to selectively modulate the spatial distribution of the structurally evolving energy field, change the range and shape of the low-energy region in the energy field, so that the three-dimensional linear path avoids local low-energy traps during the evolution process, and improves the stability and convergence efficiency of the generation process.

8. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 3, characterized in that, Low-resolution structurally evolving energy fields highlight the overall trend of the terrain by amplifying the spatial scale and enhancing smoothing; high-resolution structurally evolving energy fields accurately capture local terrain differences and engineering constraint boundaries by reducing the smoothing degree and refining the spatial grid.

9. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 1, characterized in that, The multi-agent strategy decision-making model is a Bayesian game model under incomplete information.

10. The method for generating linear infrastructure paths for structurally evolving energy fields under multi-subject conflict as described in claim 9, characterized in that, The set of strategy parameters is obtained by solving the Nash equilibrium of the Bayesian game model. It includes at least the surface disturbance penalty parameter, tunnel cost parameter, and safety margin parameter. All of these parameters are directly used to regulate the energy distribution of the structurally evolving energy field, thereby directionally influencing the evolution direction and final form of the three-dimensional linear path.

Images