Aerospace Cable Layout Optimization Method Based on Genetic Algorithm

Abstract

The present invention relates to an aviation cable layout optimization method based on a genetic algorithm. The objective function of cable layout optimization is defined, including minimizing cable length, reducing cable intersections, optimizing cable weight distribution and reducing cable costs, and the bending radius limit, fixed point position and interference limit constraint conditions of the cable are clearly defined for the target; a graph-based encoding scheme is designed to encode the starting point, end point, path and necessary intermediate nodes of each cable as a gene sequence in a genetic algorithm; then the population is initialized, and a certain number of cable layout schemes are randomly generated as the initial population, in which each individual represents a single solution; the population is optimized through selection, crossover and mutation genetic operations, in which the selection operation selects a better scheme for reproduction according to a fitness function, the crossover operation generates offspring from two cable layout schemes, and the mutation operation randomly modifies some genes in the offspring cable layout to increase population diversity.

Description

Technical Field

[0001] The invention relates to an aviation cable layout optimization method, in particular to an aviation cable layout optimization method based on a genetic algorithm. Background Art

[0002] Current methods for optimizing aviation cable layouts often face a series of challenges and limitations that may affect the efficiency, cost, reliability of the design, and the performance of the final product. First, traditional cable layout optimization methods usually rely on manual experience and simplified mathematical models. This method that relies on manual experience is not only time-consuming and labor-intensive, but is often inefficient when dealing with complex or non-standard aircraft designs. Designers must conduct a large number of trial and error within a limited time, which lacks systematicity and predictability, resulting in long design cycles and high costs. In addition, simplified mathematical models often fail to accurately reflect the various constraints and physical phenomena in actual operations, such as interference between cables and the influence of environmental factors, which may lead to poor performance of the optimization results in actual applications. Second, existing optimization methods often ignore the dynamic variability in cable layout design. Aviation cable systems must adapt to changes in multiple conditions such as ambient temperature and vibration, but many traditional optimization methods assume that these conditions are static or constant. The result of this assumption is that although the theoretical layout may look optimal, it may cause premature failure or performance degradation of the cable system under actual flight conditions. For example, temperature changes may cause cable materials to expand or contract, and the influence of these factors is often not considered in traditional methods. Existing methods also often ignore multi-objective conflicts in the optimization process. In cable layout optimization, designers need to consider not only cost and efficiency, but also safety, maintainability, and reliability. There is often a natural conflict between these goals. For example, reducing material usage can reduce costs, but it may sacrifice the overall strength and reliability of the system. Traditional optimization methods often find it difficult to find a true balance between these diverse goals.

[0003] In summary, although the current aviation cable layout optimization methods have made progress in some aspects, they still have shortcomings and disadvantages in many aspects such as efficiency, cost, reliability, flexibility and technical adaptability. Summary of the invention

[0004] The purpose of the present invention is to provide an aviation cable layout optimization method based on a genetic algorithm, thereby solving some of the drawbacks and shortcomings pointed out in the background technology.

[0005] The present invention solves the above-mentioned technical problems by adopting the following technical solutions: including:

[0006] S1. First, define the objective function of cable layout optimization, including minimizing cable length, reducing cable crossing points, optimizing cable weight distribution and reducing cable cost, and define the cable bending radius limit, fixed point position and interference limit constraints between cables according to the objectives;

[0007] S2. Then design a graph-based encoding scheme to encode the starting point, end point, path and necessary intermediate nodes of each cable into a gene sequence in the genetic algorithm;

[0008] S3, then initialize the population, randomly generate a certain number of cable layout solutions as the initial population, where each individual represents a single solution;

[0009] S4, then design a fitness function to comprehensively consider the total length of the cable, the number of cross points, the weight distribution and the cost factors to evaluate the pros and cons of each layout scheme;

[0010] S5. Optimize the population through selection, crossover and mutation genetic operations, where the selection operation selects the better solution for reproduction according to the fitness function, the crossover operation generates offspring from two cable layout solutions, and the mutation operation randomly modifies some genes in the offspring cable layout to increase population diversity;

[0011] S6. Finally, the genetic operations of S1-S5 are iteratively executed until the preset number of iterations is reached or the fitness is not significantly improved. After each iteration, the individual with the highest fitness is retained as the optimal solution.

[0012] Furthermore, the objective function of the cable layout optimization comprehensively considers minimizing the cable length L, reducing the cable intersections C, optimizing the cable weight distribution W and reducing the cable cost K, and the formula is expressed as:

[0013] F(x)=a1·e -α·L +a2·log(1+c)+a3·sin(β·W)+a4·cos(γ·K)

[0014] Among them, a1, a2, a3, a4 are weight coefficients, α, β, γ are adjustment coefficients;

[0015] Then, based on the cable layout objectives, the cable bending radius limit R is determined and formulated as:

[0016]

[0017] Among them, δ, θ, x0 are specific constants, representing the dynamic adjustment factors of the bending radius;

[0018] Then the optimization of the fixed point position is expressed as:

[0019] P(x)=λ·tan-1 (ω·x)

[0020] Among them, λ and ω adjust the slope and position of the fixed point position response curve;

[0021] Finally, the cable-to-cable interference limit is adopted:

[0022]

[0023] where κ,v adjusts the sensitivity and scale of the interference between cables.

[0024] Furthermore, the coding scheme adopts a multi-level graph, each layer corresponds to the specific characteristics of the cable including the voltage layer and the signal type, and the position and connection status of each node are encoded as (n i ,l j ), where n i =f i (j) is the node number dynamically calculated according to level j, using the function:

[0025] f i (j) = k·j 2 +m·j+c

[0026] Among them, k, m, c are adjustment coefficients;

[0027] Next, dynamic path interpolation coding is applied, which allows the cable path to be dynamically adjusted according to the optimization goal during the algorithm iteration process. The path is defined by key control points, and the position of each point is calculated by:

[0028] p i (t) = a·sin(b·t+c i )

[0029] Calculate, where t represents the parameters on the path, a, b and c i is the adjustment coefficient, which allows the path to be optimized in iterations based on the fitness evaluation;

[0030] Finally, the function-based path generation uses a polynomial path generation function to dynamically generate the actual layout path of the cable using control points. The formula is:

[0031]

[0032] where p i (t) is the dynamic position of each control point under parameter t, allowing the overall performance of the path to be optimized while maintaining layout rationality.

[0033] Furthermore, the cable layout scheme is optimized as an initial population for different aircraft models, cable types and layout complexity; during the initialization process, the probability of selecting a template is determined by a probability density function, which is the difference between the template and the current optimization target, and the formula is:

[0034]

[0035] Where T i (t) describes the configuration state of template i at time t, while O(t) is the description of the optimization goal;

[0036] Then, a noise perturbation model is introduced to randomly generate the start and end positions of each cable, using the formula:

[0037] (x,y)=(Rcos(θ+∈1(t)),Rsin(θ+∈2(t)))

[0038] Implementation, where R and θ are random parameters based on cable length and direction, while ∈1(t) and ∈2(t) are disturbance terms that increase the randomness of the design, reflecting the random effects at different times t;

[0039] Finally, a method based on constraint satisfaction problem is adopted. When initializing the population, the physical and environmental constraints of the cable layout are used as part of the optimization algorithm. By solving the optimization problem involving all nodes, the layout solution that minimizes the degree of constraint violation is found; the relevant formula is:

[0040]

[0041] Where N(c) represents the number of nodes that satisfy constraint c, ξ i is the weight of node i, and v i is the position vector of the node.

[0042] Furthermore, the fitness function is specifically implemented as follows:

[0043] S1. First, define the contribution to the total length as:

[0044]

[0045] where γ i (t) represents the position of the i-th cable at time t;

[0046] S2. Then the contribution of the number of intersections is evaluated by the high-level model:

[0047]

[0048] where θ ij is the angle between cable i and cable j at the intersection, αij is to adjust the parameters to emphasize the influence of intersections close to right angles;

[0049] S3, then the evaluation of the weight distribution is given by the dynamic model:

[0050]

[0051] where ρ i (t) is the line density of cable i at position t, * denotes the convolution operation, and σ is the kernel function used to smooth the line density distribution;

[0052] S4. The final cost contribution is:

[0053]

[0054] where p i (t) is the unit cost of cable i, which varies with time, λ i is the installation cost factor, μ i is the maintenance cost factor of cable i, ds i / dt represents the maintenance cost that changes over time.

[0055] Furthermore, the selection, crossover and mutation genetic operation methods include:

[0056] S1. First, define the composite fitness evaluation function:

[0057] S(x)=w1·L(x)+w2·C(x)+w3·E(x)+w4·M(x)

[0058] Where L(x) represents the total length of the layout, C(x) is the number of intersections, E(x) represents the electromagnetic compatibility score, M(x) represents the maintainability score, and w1, w2, w3, w4 are weight factors adjusted to suit different design requirements;

[0059] S2, then the crossover operation is performed through the path-dependent crossover algorithm, the model is:

[0060] γ child =(1-μ)γ parent1 +μγ parent2 +ηsin(β·(γ parent1 -γ parent2 ))

[0061] Where μ is a weight randomly selected from a distribution adjusted based on the parent's fitness, and η and β are parameters that adjust for cross-effects;

[0062] S3. Finally, the directed mutation operation is implemented, and the model is:

[0063]

[0064] where ξ is the strength of the variation, τ indicates the specific problem area, and σ controls the scope of the variation’s impact.

[0065] Furthermore, the iteratively executed genetic operation implements genetic operations including dynamic fitness threshold adjustment, diversity elite retention strategy and iterative termination mechanism optimization:

[0066] S1. First, define the dynamic fitness threshold adjustment mechanism. The minimum threshold for fitness improvement is based on the formula:

[0067]

[0068] Dynamic adjustment, where ΔS i is the fitness improvement of the i-th iteration, n is the reference iteration window, and ρ is the dynamic adjustment coefficient;

[0069] S2, then implement the diversity elite retention strategy, in addition to retaining the individuals with the highest fitness, also based on the genetic distance between individuals:

[0070]

[0071] Select individuals with unique genetic characteristics, where d(x,y) represents the genetic distance between individual x and any individual y in the elite individual set Elite;

[0072] S3. Finally, decide whether to continue iterating based on the changing trend of the fitness improvement curve. If the fitness change rate If it is less than a preset minimum value ∈, the iteration stops.

[0073] Beneficial effects of the present invention:

[0074] 1. Improved cost efficiency: By optimizing the overall length and layout of the cable, the amount of material required is reduced, which directly reduces the material cost. The dynamic fitness threshold and iteration termination mechanism reduce unnecessary design iterations, saving time and computing resources, and further reducing design costs.

[0075] 2. Enhanced system reliability: By reducing the number of cable crossovers, the physical and electromagnetic interference of the cable system is reduced, and the overall reliability of the system is improved. Directed variation and elite retention strategies ensure the diversity and innovation of design solutions, which helps to explore more reliable layout solutions.

[0076] 3. Improved design flexibility and accuracy: The application of genetic algorithms makes it possible to handle complex constraints and multi-objective optimization problems, enhancing the flexibility and adaptability of the design. The composite fitness evaluation function integrates multiple key performance indicators to make design decisions more scientific and accurate.

[0077] 4. Improved maintenance convenience: The optimized cable layout takes into account the ease of maintenance, simplifies the maintenance process, and reduces long-term operation and maintenance costs. By implementing a diversity elite retention strategy and selecting cable layouts with unique genetic characteristics, the design scheme is more fault-tolerant and capable of adapting to possible future changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is a flow chart of the aviation cable layout optimization method based on genetic algorithm. DETAILED DESCRIPTION

[0079] The specific implementation modes of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0080] The aviation cable layout optimization method based on genetic algorithm involves defining the objective function of cable layout optimization. The objective of this function is to minimize cable length, reduce cable intersections, optimize cable weight distribution and reduce cable cost. At the same time, the method also sets constraints for specific goals, such as cable bending radius restrictions, fixed point locations and interference restrictions between cables. These constraints ensure that the cable layout meets functional and safety standards while also taking into account cost efficiency and physical layout feasibility. The objective function and constraints jointly guide the genetic algorithm to search for the optimal cable layout solution. Through a continuous iterative evolutionary process - selecting the cable layout with the best fitness, crossing and mutating to generate new layout solutions - the optimal design solution is finally achieved. This method effectively solves the complexity and multi-objective optimization problems of aviation cable layout, and provides an efficient and economical cable layout design strategy.

[0081] The key to designing a graph-based encoding scheme is to effectively encode the starting point, end point, path, and necessary intermediate nodes of each cable into a gene sequence in the genetic algorithm. In this scheme, a graph representation is used to describe the physical layout of the cable, where nodes represent the connection points of the cable (including the starting point, end point, and any transition points), and edges represent cable segments. Graph encoding treats the cable layout problem in the form of a mathematical model, and each cable layout scheme is converted into a series of gene sequences that can be operated by the genetic algorithm. In the operation of the genetic algorithm, these gene sequences are optimized through selection, crossover, and mutation processes to generate new cable layout schemes. Each gene in the genetic algorithm corresponds to a part of the cable layout, so that the design and optimization of the entire cable system can be carried out within the genetic algorithm framework. This encoding method can accurately capture the complexity of the cable layout and can also be efficiently optimized through the genetic algorithm, thereby minimizing design errors and costs while ensuring functionality and efficiency.

[0082] In the population initialization phase, a certain number of cable layout solutions are first randomly generated as the initial population. This step is a critical part of the algorithm's start, because the diversity of the initial population directly affects whether the genetic algorithm can explore different areas of the solution space. In this process, each cable layout solution is considered as an individual, representing a potential solution. These individuals are constructed by randomly selecting the starting point, end point, and intermediate path points of the cable. In this way, each individual has a unique cable path configuration that will be evaluated and optimized in subsequent genetic operations. The size of the initial population and the randomness of the individuals are adjustable parameters, and the settings of these parameters depend on the complexity of the specific problem and the computing resources required for the optimization process. By effectively initializing the population, the genetic algorithm can search the solution space more comprehensively, thereby increasing the probability of finding the optimal solution. The purpose of this stage is to ensure that there is sufficient population diversity when the algorithm starts, laying the foundation for achieving the final optimization goal.

[0083] The fitness function is a multi-objective evaluation tool that comprehensively considers multiple key performance indicators in the cable layout scheme, including the total length of the cable, the number of crossovers, weight distribution and cost factors, so as to evaluate the pros and cons of each layout scheme. The purpose of the fitness function is to provide a quantitative score for each cable layout scheme, which reflects the performance of the scheme on various evaluation indicators. In this function, the total length of the cable is the key factor, because shorter cable length usually means lower material costs and easier installation. The number of crossovers is considered to reduce interference between cables and potential maintenance difficulties. Each additional crossover increases the number of failure points and maintenance costs. Weight distribution is a factor of particular concern in the aviation field. Uneven weight distribution affects the balance and safety of the aircraft. Finally, the cost factor includes not only the cost of the cable itself, but also the cost of installation, maintenance and potential replacement. By combining these factors, the fitness function provides a way for the genetic algorithm to select and optimize those cable layout schemes that perform best in terms of cost efficiency, ease of maintenance, performance and safety. During the operation of the algorithm, solutions with high fitness scores will be considered as better solutions and have a greater probability of being selected for further genetic operations, such as crossover and mutation, to continuously improve the design of the cable layout.

[0084] Selection, crossover, and mutation are the three core genetic operations used to optimize the population of cable layout. The selection operation selects the better cable layout scheme for reproduction based on the results of the fitness function evaluation to ensure that the high-quality genetic characteristics can be passed on to the next generation. This process is similar to natural selection, where individuals with better performance have a greater chance of being selected. The crossover operation generates offspring from two selected cable layout schemes, usually by exchanging some genes in the two schemes, similar to the mating process of organisms, which can produce a new layout scheme that contains the advantages of both parents. The mutation operation also plays a key role in the genetic algorithm, increasing the diversity of the population by randomly modifying some genes in the gene sequence of the offspring cable layout. This step can introduce new genetic mutations, which helps the algorithm explore a wider solution space and prevent the algorithm from falling into the local optimal solution too early. Through the cyclic iteration of these three operations, the genetic algorithm can gradually improve the cable layout scheme and find a more efficient, cost-effective cable layout that meets the design requirements.

[0085] Genetic operations S1-S5 include population initialization, fitness function calculation, selection, crossover and mutation operations, which are iteratively executed during the algorithm operation. The iteration process continues until the preset number of iterations is reached or the fitness is observed to be not significantly improved. This means that the algorithm will evaluate the fitness of each individual in the current population after each iteration and select the individual with the highest fitness as the optimal solution. This strategy ensures that the best solution in each generation of the population can be identified and retained, so that the optimal cable layout solution is gradually approached during the iteration process. The individual with the highest fitness is retained as the optimal solution to ensure that excellent genetic characteristics are not lost due to random mutation or crossover operations. It also provides a standard for monitoring the progress of the algorithm and judging whether to continue the iteration. When the improvement in fitness is no longer significant or the predetermined number of iterations is reached, the algorithm stops, and it is considered that a feasible solution or optimal solution to the problem has been found. This method effectively utilizes the exploration and utilization capabilities of genetic algorithms to optimize complex cable layout problems and find reasonable and efficient solutions.

[0086] Embodiment 1:

[0087] Suppose an airline company's goal is to redesign the cable system of an aircraft to improve efficiency and safety and reduce maintenance costs.

[0088] The objective function is defined as:

[0089] F(x)=a1·e -α·L +a2·log(1+C)+a3·sin(β·W)+a4·cos(γ·K)

[0090] Among them, L represents the total length of the cable (unit: meter), C represents the number of cable intersections, W represents the cable weight distribution (unit: kilogram), and K represents the cable cost (unit: yuan).

[0091] Assuming a specific scenario, the initial cable layout of the aircraft is as follows: total cable length L = 1200 meters; number of cable intersections C = 30; total cable weight W = 450 kilograms; total cost K = 75,000 yuan.

[0092] Selection of weights and adjustment coefficients: To reflect the importance of different factors, the weight coefficients are set as follows:

[0093] a1=500,a2=150,a3=300,a4=50 (weight coefficient unit is yuan)

[0094] The adjustment coefficients are set to: α = 0.001, β = 0.01, γ = 0.0001 to ensure that the function value is moderate and each part can significantly affect the overall result.

[0095] Calculation of objective function: Substitute specific data to calculate the objective function:

[0096] F(x)=500·e -0.001·1200 +150·log(1+30)+300·sin(0.01·450)+50·cos(0.0001·75000)

[0097] The calculation results are:

[0098] F(x)=500·0.3012+150·3.434+300·0.4258+50·0.9965

[0099] F(x)=150.6+515.1+127.74+49.825

[0100] F(x)=843.265

[0101] This value represents the "cost" of the current cable layout, including both the actual monetary cost and the abstract cost of lost design efficiency.

[0102] Iteration process: In each generation of the genetic algorithm, we will use this function to evaluate the fitness of the cable layout schemes and perform selection, crossover, and mutation operations based on the schemes with high fitness. For example, if the new layout scheme reduces the total length to 1150 meters and the number of crossovers to 25, while keeping the weight and cost unchanged, we can expect its fitness to improve, thus guiding further iterations. Through continuous iterative optimization, the algorithm will gradually find a better cable layout scheme until the fitness improvement is no longer significant or the preset number of iterations is reached.

[0103] In order to ensure that the bending radius of the cable will not cause cable damage or performance degradation due to excessive bending, a new objective function R(x) is introduced to clarify the bending radius limit of the cable to ensure the physical feasibility and long-term reliability of the cable in the design.

[0104] Definition and calculation of bending radius objective function:

[0105]

[0106] Where δ is the maximum bend radius adjustment factor, θ is the bend sensitivity adjustment factor, and x0 is the bend radius baseline or equilibrium point in the cable design. This function form is a variation of the logistic function that is used to model the bend radius variation of cables at different lengths and configurations.

[0107] The design parameters of the cable are set as follows:

[0108] δ = 150 meters, representing the maximum bending radius limit of the cable;

[0109] θ = 0.05, indicating the sensitivity of the bending radius to the length change;

[0110] x0 = 600 meters, representing the ideal or balanced bending radius of the cable design.

[0111] This function ensures that the actual bending radius of the cable at any length x does not exceed its physical limit. For example, when the cable length x = 1000 meters, its bending radius is calculated as:

[0112]

[0113]

[0114] R(1000)=150·(1-0.000000002)

[0115] R(1000)≈150 meters

[0116] This result shows that at a length of 1000 meters, the bending radius of the cable is close to the maximum allowable value, suggesting that designers need to consider adjusting the cable layout or selecting cable materials with higher bending tolerance.

[0117] With this approach, we can ensure that appropriate physical and engineering constraints are implemented in the cable design, and use genetic algorithms to iteratively optimize the cable layout to achieve optimal design efficiency and cost-effectiveness, ensuring the long-term reliability and safety of the aircraft cable system. In addition, the values ​​of δ, θ, and x0 can be adjusted to suit different aircraft models and design requirements, making this model more flexible and practical.

[0118] The next step is to optimize the location of the cable fixing points to ensure that the installation of the cable in the entire aircraft structure meets safety regulations and optimizes the maintenance and repair path. To this end, a mathematical model is introduced to describe and optimize the location of the cable fixing points. This model is represented by the following function:

[0119] P(x)=λ·tan -1 (ω·x)

[0120] Where λ and ω are coefficients that adjust the slope and position of the fixed point position response curve. This function uses the inverse tangent function to provide a smooth and gradual response curve that can dynamically adjust the position of the fixed point based on the length of the cable or other relevant parameters.

[0121] Set the selected parameters to:

[0122] λ = 30 meters, which represents the maximum distance that the fixed point position can be adjusted;

[0123] ω=0.01, which is the sensitivity parameter of position adjustment.

[0124] When optimizing the cable system of a large commercial aircraft, it is necessary to determine the location of a key cable fixing point inside the wing, and the cable length is x = 500 meters. Apply the above formula to calculate the optimal location of the fixing point:

[0125] P(500)=30·tan -1 (0.01 500)

[0126] P(500)=30·tan -1 (5)

[0127] P(500) = 30 1.3734 (inverse tangent value obtained using a standard calculator or mathematical software)

[0128] P(500) = 41.202 m

[0129] This means that in order to achieve the best cable layout and maintenance convenience, the cable's fixing point inside the wing should be located about 41 meters from the starting point. In this way, the cable's free swing inside the wing can be effectively reduced, reducing potential damage caused by vibration or external forces, and facilitating future maintenance work.

[0130] To minimize the interference between cables in the aircraft's critical communication and power transmission systems, a mathematical model is introduced to quantify and limit the electromagnetic interference between cables. The model is defined as follows:

[0131]

[0132] This formula is used to evaluate the degree of interference between cables, where x represents the relative position between cables or other parameters that affect interference, such as the current strength or signal frequency between cables. The coefficients κ and v adjust the sensitivity and scale of interference respectively, and their selection critically affects the accuracy of interference assessment and the breadth of application.

[0133] Setting parameters:

[0134] κ = 100 decibels (dB), representing the maximum interference level, used to quantify the most severe interference situation;

[0135] v = 0.02 m -1 , represents the sensitivity of position or other parameter changes to interference.

[0136] Consider a practical application scenario to evaluate the layout of two cables in an aircraft, whose relative position difference is x = 50 meters. Use the above formula to calculate the interference level:

[0137]

[0138] I(50)=100·(1-0.707)

[0139] I(50)=29.3dB

[0140] This calculation result shows that at a relative position of 50 meters, the expected interference between cables is about 29.3 dB. This level of interference is acceptable for most avionics systems, and the genetic algorithm is used to explore whether there is a better cable layout to further reduce the interference to a lower level. The genetic algorithm will iteratively search for multiple cable layout solutions, each of which is evaluated according to the defined interference model, and the solution with the least interference is selected for reproduction, crossover and mutation operations.

[0141] Embodiment 2:

[0142] In this embodiment, how to efficiently encode and process the multi-level complex information of the cable to achieve a highly optimized design result. To this end, a multi-level graph encoding scheme is introduced, which can represent the specific characteristics of each cable at different functional levels (such as voltage layer, signal type, etc.) in detail. Each layer of the cable is assigned a code, which includes not only the location of the node, but also the connection status between the nodes, forming a complete multi-dimensional data structure.

[0143] In this encoding scheme, the position and connection status of each node is represented as (n i ,l j ), where n iis the node number dynamically calculated based on the cable level j. This number is calculated by a mathematical function, namely:

[0144] f i (j) = k·j 2 +m·j+c

[0145] Here, k, m, and c are adjustment factors used to adjust the way node numbers are generated based on the specific needs and design rules of the cable.

[0146] The adjustment coefficients are set within the following ranges to ensure sufficient flexibility and accuracy:

[0147] k ranges from 0.1 to 0.5. This coefficient determines the degree of quadratic effect of level changes on node numbering. Higher values ​​mean that the level has a greater impact on the numbering.

[0148] m ranges from 1 to 10. This factor adjusts the linear effect of the layer on the numbering, allowing the designer to adjust the numbering rate according to different cable characteristics;

[0149] c ranges from 0 to 100, and this constant term allows a baseline to be set in the numbering system so that adjustments can be made based on the starting numbering of the cable.

[0150] In a real application, for the communication system of a commercial aircraft, the system needs three layers of coding: power line (low voltage), data line (high frequency signal), control line (medium frequency signal). Set the coefficients k = 0.3, m = 5, and c = 50. If you are processing the data line layer (set j = 2), the node number will be calculated as follows:

[0151] f i (2) = 0.3 2 2 +5·2+50

[0152] f i (2) = 0.3·4 + 10 + 50

[0153] f i (2) = 1.2 + 10 + 50

[0154] f i (2) = 61.2

[0155] This numbering helps to identify the exact location of each node in the cable system, and through the structuring and systematic processing of the coding scheme, it greatly enhances the efficiency and reliability of cable layout design.

[0156] In order to control the cable path more flexibly and accurately, a dynamic path interpolation coding strategy is adopted. During the iteration of the algorithm, the layout path of the cable is dynamically adjusted according to the optimization goal. Especially in the case of complex fuselage structure and multi-electronic equipment interference, the cable path can be optimized to reduce interference and improve safety. In this process, the cable path is defined by a series of key control points, and the position of each point is calculated by mathematical formulas to achieve dynamic adjustment of the path.

[0157] The calculation formula for the location of critical control points is:

[0158] p i (t) = a·sin(b·t+c i )

[0159] Where: t represents the parameter on the path, usually the distance from the starting point or other measurement that can represent the location of the cable layout; a, b, and c i are adjustment factors, which allow the shape of the path to be adjusted according to the actual laying needs of the cable and the expected cable performance.

[0160] The specific value range of the adjustment coefficient is set as follows to ensure sufficient adjustment flexibility and adaptability:

[0161] The value of a ranges from 10 to 50 meters, which represents the maximum deviation of the amplitude of the cable path;

[0162] The value of b ranges from 0.01 to 0.1 radian / m, which represents the rate of change of the frequency of the cable path;

[0163] c i The value range of is 0 to 2π, which represents the phase offset of each control point relative to the starting point of the path.

[0164] When designing a cable system for a large passenger aircraft, you need to set a control point to adjust the cable path to avoid the high electromagnetic interference in the main fuel tank area. If the target location of the control point is 200 meters from the starting point, select the following parameter settings:

[0165] a = 30 meters, to ensure that the cable path is far enough away from high interference areas;

[0166] b = 0.05 rad / m, providing moderate path curvature to meet fuselage structural constraints;

[0167] c i =π / 4, providing an initial phase for the control point to ensure a smooth transition of the path.

[0168] Apply the formula to calculate the specific position of the control point:

[0169] p i(200)=30·sin(0.05·200+π / 4)

[0170] p i (200) = 30 sin(10 + π / 4)

[0171] p i (200) = 30 sin(10.785)

[0172] p i (200) = 30 0.979 (sine value obtained using a calculator)

[0173] p i (200) = 29.37 m

[0174] This calculation result shows that through dynamic path interpolation coding, the vertical offset of the cable at 200 meters will be close to 30 meters, which is enough to bypass the high interference area. Through the continuous iteration of the parameters of these control points by genetic algorithm, the entire cable path can be continuously optimized, and finally a safe and efficient cable layout solution can be achieved.

[0175] A function-based path generation method is used to dynamically generate the actual layout path of the cable based on the control points using a polynomial path generation function. This method increases the flexibility of cable layout design and improves the accuracy of the design, and is suitable for the cable layout requirements of complex spaces inside aircraft.

[0176] The polynomial path generating function is defined as:

[0177]

[0178] In this formula, is the binomial coefficient, which represents the number of combinations of i elements from n elements; t is a parameter ranging from 0 to 1, representing the relative position from the starting point to the end point of the cable; p i (t) is the dynamic position of each control point under parameter t.

[0179] The cable needs to pass through four main control points, ie n=3 (control points from p0 to p3).

[0180] The position function p of each control point i (t) is set to be based on the previously defined dynamic path interpolation encoding, such as p i (t) = a i ·sin(b i ·t+c i ).

[0181] a i Range is 10 to 50 meters, with controlled amplitude;

[0182] b i Range 0.01 to 0.1 rad / m, control frequency;

[0183] c i The range is 0 to 2π and controls the phase.

[0184] Set the path parameter t to be uniformly distributed in the design, from 0 to 1.

[0185] Calculating the path position B(t) for each value of t actually combines the position contributions of all control points to form a continuous and smooth path.

[0186] Suppose you are designing a cable system that needs to bypass sensitive equipment. The parameters of the control point are set as follows:

[0187] p0(t)=10·sin(0.05·t)

[0188] p1(t)=20·sin(0.05·t+π / 3)

[0189] p2(t)=30·sin(0.05·t+π / 2)

[0190] p3(t)=40·sin(0.05·t+2π / 3)

[0191] When t = 0.5 (midpoint of the path), the path position B(0.5) is calculated as follows:

[0192]

[0193] B(0.5)≈3(0.125)·10·0.0025+3(0.25)(0.5)·20·0.8532+3(0.5)(0.25)·30·1+1(0.125)·40·0.8532

[0194] B(0.5)≈0.075+12.798+11.25+4.2656

[0195] B(0.5)≈28.3886 m

[0196] This calculation shows how to optimize the cable path by dynamically adjusting the position function of each control point. This approach is very flexible to adapt to various space constraints and design requirements, ensuring the best performance and minimum interference of the cable system.

[0197] Embodiment 3:

[0198] In this embodiment, a genetic algorithm-based approach is used, involving the use of multiple different cable layout solutions as the initial population. Templates are pre-designed for different aircraft models, cable types, and layout complexities, each of which has been optimized based on specific design specifications and previous successful cases. In order to more effectively select which of these templates will constitute the initial population of the genetic algorithm, a selection mechanism based on a probability density function is introduced, which takes into account the difference between each template and the current optimization target.

[0199] Definition and application of probability density function:

[0200]

[0201] In this formula:

[0202] T i (t) describes the configuration state of template i at time t, which includes complex parameters such as cable length, location, and type;

[0203] O(t) is the description of the current optimization goal, which includes the design specifications, safety requirements, and detailed requirements for efficiency maximization;

[0204] λ is the tuning parameter that determines the weight of the difference in the selection probability.

[0205] Adjustment parameter value range:

[0206] The value range of λ is usually set to 0.1 to 1 to adjust the sensitivity of the difference. A higher value means more sensitivity to the difference, thus more likely to select templates with smaller differences from the current target.

[0207] There are three templates T1, T2, and T3, which correspond to different types of aircraft cable layouts. In a specific design task, the optimization goal O(t) requires maximizing space utilization and minimizing electromagnetic interference. The difference between the three templates and the optimization goal is preliminarily calculated, and the integral result is:

[0208] For T1, the integral value is 0.5

[0209] For T2, the integral value is 0.2

[0210] For T3, the integral value is 0.8

[0211] Assume λ = 0.5 and apply the formula to calculate the selection probability of each template:

[0212]

[0213] After calculation, it is found that the value of P(T2) is the highest, indicating that the configuration of T2 is closest to the current optimization goal. Therefore, T2 will be selected as part of the initial population and enter the iterative process of the genetic algorithm.

[0214] In this embodiment, in order to simulate random events and uncertain factors that occur in the real world, such as installation errors, different material bendability, or slight changes in the body structure, a noise perturbation model is introduced to randomly generate the start and end positions of each cable.

[0215] Model formula and parameter description:

[0216] (x,y)=(Rcos(θ+∈1(t)),Rsin(θ+∈2(t)))

[0217] in:

[0218] R and θ are random parameters at the starting and ending positions of the cable, representing the cable length and initial angle, respectively. These parameters are randomly selected based on the actual requirements of cable installation and the spatial layout of the fuselage;

[0219] ∈1(t) and ∈2(t) are noise disturbance terms at time t, which are used to simulate the uncertainty and random changes in the design process.

[0220] Parameter value range:

[0221] The value of R is usually based on the aircraft model and cable type. For example, for a medium-sized commercial aircraft, R varies between 10 meters and 100 meters.

[0222] The value of θ can range from 0 to 2π (0 to 360 degrees), ensuring full coverage of the cable layout;

[0223] ∈1(t) and ∈2(t) can be set according to the cable layout complexity and design accuracy requirements. Typically, the values ​​of these noise terms are in the range of -0.05 to 0.05 radians, which is sufficient to cause significant layout changes but not to cause design failure.

[0224] Suppose you are designing a cable system for a large commercial aircraft. The cable needs to extend from the wing root to the tail. Select R = 80 meters and As basic parameters, at a certain design stage (time t), it is decided to introduce noise disturbances, setting ∈1(t) = 0.03 and ∈2(t) = -0.03.

[0225] Apply the formula to calculate the start and end positions:

[0226]

[0227] (x,y)=(80cos(0.785+0.03),80sin(0.785-0.03))

[0228] Using appropriate calculation tools or software, specific (x,y) values ​​can be obtained, reflecting small deviations in actual installation due to material properties or installation techniques.

[0229] To ensure that the cable system meets strict aviation standards and adapts to complex airframe structures, a constraint satisfaction problem (CSP)-based approach is used to initialize the population. The physical and environmental constraints of the cable layout are considered early in the design phase to ensure that all generated layout solutions do not violate these constraints. In this way, the reliability and compliance of the design can be significantly improved while avoiding costly design modifications at a later stage.

[0230] Implementation steps and calculation formula explanation:

[0231]

[0232] In this formula:

[0233] N(c) represents the number of nodes that satisfy the constraint conditions under a given constraint c;

[0234] ξ i are the weights of node i, which indicate the relative importance of different nodes in satisfying the constraints;

[0235] v i is the position vector of node i, representing the specific position of the node within the aircraft structure;

[0236] V is the set of all nodes.

[0237] Specific value range of the parameter:

[0238] Weight ξ i The value of is usually between 0 and 1 to ensure that the sum of the squares of all node weights is 1, which is a common constraint in optimization problems and is used to normalize the weights.

[0239] Suppose the design is dealing with the cable system of a large passenger aircraft. The cables need to be arranged in the fuselage to avoid critical systems (such as fuel system, electronic equipment, etc.). The location of these systems defines the constraints c of the cable layout. Each cable node v i It is set at specific positions of the fuselage, such as wings, tail, bottom of the fuselage, etc.

[0240] There are three key nodes that need to be configured, located at: v1 at the root of the wing; v2 in the middle of the fuselage; v3 at the tail.

[0241] If constraint c specifies that the cable must not pass through the central fuel tank area, it is necessary to find the optimal layout by adjusting the weights ξ1, ξ2, ξ3 and positions v1, v2, v3 of these three nodes so that the cable avoids the fuel tank as much as possible.

[0242] Applying the CSP method, it is decided to increase the weight of ξ2, because v2 is located closest to the fuel tank, and increasing its weight can more effectively avoid this area. Through the optimization process, a set of weights, such as ξ1=0.2, ξ2=0.6, ξ3=0.2, are obtained to ensure that the influence of v2 is maximized, thereby optimizing the layout while satisfying the constraints.

[0243] Embodiment 4:

[0244] In this embodiment, it is critical to accurately measure and evaluate the impact of the total length of the cables on the overall layout quality. The contribution to the total length in the fitness function is a core part that helps ensure that the cable layout is as economical and effective as possible, while avoiding unnecessary extra length, which can lead to increased costs and reduced efficiency. To this end, an integration-based method is used to calculate the total length of each cable, which not only calculates the straight section, but also accurately calculates any curved sections in the cable path.

[0245] Implementation steps and calculation formula explanation:

[0246]

[0247] In this formula:

[0248] γ i (t) represents the position of the i-th cable at time t, where “time t” is actually a parameter along the cable path, from 0 to N, where N is the end point of the path;

[0249] is the derivative of the cable path and reflects the rate of change of the shape of the cable path, that is, the slope of the cable path.

[0250] Specific value range:

[0251] N, the parameter of the path end point, depends on the actual layout length of the cable. Usually this value ranges from tens of meters to hundreds of meters, depending on the aircraft model and the functional requirements of the cable.

[0252] Suppose you are designing a cable system that needs to span across the main cabin of an aircraft. The cable path is set to pass through multiple important system components in a complex curved manner to avoid electromagnetic interference and physical contact. The path of this cable γ i (t) is defined as a cubic polynomial curve, such as:

[0253] γ i (t) = at 3+bt 2 +ct+d

[0254] The parameter values ​​are set to a=0.1, b=0.5, c=2, d=5, and t ranges from 0 to 100 meters.

[0255] Apply the total length contribution formula in the fitness function:

[0256]

[0257] Here, γ i The derivative of (t) is 0.3t 2 Substitute +1+2 into the formula.

[0258] Through numerical integration methods (such as Simpson's rule or numerical integration software tools), the specific value of L(x) can be calculated, which will be directly reflected in the fitness score and guide the genetic algorithm to further iterate and optimize the cable layout.

[0259] Cable crossovers cause physical and electromagnetic interference, degrading system reliability and performance. To assess and minimize this effect, a specialized model is used to quantify the contribution of crossovers to the overall cable layout quality. This model focuses specifically on the angles of the cables at the crossovers, with particular emphasis on crossovers that are close to right angles, as these are typically the most likely to cause interference.

[0260] The formula and steps of the advanced evaluation model are explained:

[0261]

[0262] In this formula:

[0263] θ ij is the angle between cable i and cable j at the intersection, with right-angle intersection being considered the most interference-inducing case;

[0264] α ij It is a tuning parameter used to emphasize the influence of intersections close to right angles. It determines the intensity of the penalty when the intersection angle deviates from a right angle.

[0265] Specific value range: α ij Typically set in the range of 0.1 to 1.0, this range is enough to adjust the model's sensitivity to angles that deviate from perpendicular angles, with larger values ​​meaning a stronger penalty for angles that deviate from perpendicular angles.

[0266] Suppose a new passenger aircraft cable system is being designed. The system includes multiple cables interlaced in a narrow space. In order to evaluate the impact of the intersection, it is assumed that two cables cross in a narrow channel with a crossing angle θ 12 =100°(approximately equal to radian).

[0267] Select α 12 = 0.5 to evaluate this intersection:

[0268]

[0269] C(x)=e -0.5·0.055 (Convert radians to approximate values)

[0270] C(x)=e -0.0275

[0271] C(x)=0.9728

[0272] This result shows that although the angle of the crossover point is close to a right angle, because it deviates slightly, the impact on the overall layout is considered small. This advanced evaluation allows for accurate quantitative analysis of the impact of different cable crossing configurations and optimization of these crossover points in an iterative process of the genetic algorithm to reduce potential interference and improve the overall reliability of the system.

[0273] Accurately evaluating and optimizing the weight distribution of cables is critical because uneven weight distribution affects the balance, efficiency, and even safety of the aircraft. To this end, an advanced dynamic model is used to evaluate the weight distribution of cables. This model uses mathematical convolution operations to smooth the distribution of cable line density, thereby more accurately simulating the weight distribution in the actual cable layout.

[0274] Model formula and step explanation:

[0275]

[0276] In this formula:

[0277] ρ i (t) is the linear density of cable i at position t, which usually depends on the material composition of the cable and the cable diameter;

[0278] It represents the slope or rate of change of the cable path, which affects the change of line density in space;

[0279] σ is the kernel function used to smooth the line density distribution. Generally, a Gaussian kernel or similar function is selected to provide a good smoothing effect.

[0280] * denotes a convolution operation, a mathematical tool used to combine two functions (such as a kernel function and a line density function) to produce a new smoothed function.

[0281] Specific value range: The shape and width of σ are crucial. Usually the width can be set in the range of 0.1 to 1.0 m, depending on the actual diameter of the cable and the expected smoothness level.

[0282] Suppose you are designing a cable system that passes through the main wing of an aircraft and the tail wing. You need to ensure that the weight of the cable is evenly distributed to avoid affecting the balance of the aircraft. Set the initial linear density of the cable to i (t) varies in different sections due to the thickness of the cable protective layer, such as from 0.5kg / m to 0.8kg / m.

[0283] The Gaussian kernel function is selected as σ and the width is set to 0.5 m to smooth the linear density distribution of the cable. i (t) is a simple straight line, so It can be approximated as a constant. The evaluation model for calculating weight distribution is as follows:

[0284]

[0285] Among them, 0.65kg / m is the average value of cable line density.

[0286] Through numerical methods (such as numerical integration), the overall WQ(x) can be calculated to obtain a total evaluation of the cable weight distribution. This evaluation not only helps to verify the rationality of the cable layout, but also ensures that weight distribution problems can be identified in the design stage and solved through iterative optimization of genetic algorithms.

[0287] To evaluate the cost-effectiveness of the cable system in detail, a dynamic cost model that includes unit cost, installation cost factor and maintenance cost factor is used. This model can help quantify the cost impact of different design options and select the most cost-optimized cable layout.

[0288] Cost model formula and parameter explanation:

[0289]

[0290] In this formula:

[0291] p i (t) is the unit cost of cable i, which represents the cost per unit length of the cable and varies with time or cable type;

[0292] λ i is the installation cost factor of cable i, which takes into account the difficulty, time and cost of materials used in the cable installation process;

[0293] μ i is the maintenance cost factor of cable i, reflecting the difficulty and frequency of cable maintenance;

[0294] is the rate of change of cable maintenance cost over time, which depends on the cable's fragility and the frequency of failures.

[0295] Specific value range:

[0296] p i (t) can vary from 5 to 50 yuan / m, depending on the material and specifications of the cable;

[0297] λ i The price ranges from 100 to 1,000 yuan / m, depending on the complexity of the installation environment and the difficulty of the project;

[0298] μ i The range is from 0.01 to 0.1 yuan / m / year, which reflects the quality and expected service life of the cable.

[0299] Suppose the design is dealing with a cable system for a large passenger aircraft, where a specific cable i has an initial length of 200 meters and is expected to be installed in a difficult-to-access area, requiring special materials and technology. Select parameter p i (t) = 20 yuan / m, λ i =500 yuan / m, μ i = 0.05 yuan / m / year. The rate of increase in maintenance costs over time is assumed to be very low because the cable quality is high.

[0300] Apply the cost model to calculate the total cost contribution of the cable:

[0301]

[0302] S(x)=2000000.4 yuan

[0303] This calculation provides a comprehensive assessment of the initial installation and long-term maintenance costs of the cable, helping to evaluate different design options from a cost-effectiveness perspective.

[0304] Embodiment 5:

[0305] In this embodiment, the efficiency and effect of cable layout are optimized by using a genetic algorithm-based method for selection, crossover and mutation genetic operations. The key is to define a composite fitness evaluation function that can comprehensively consider multiple key factors to ensure that the selected solution meets the strict standards and actual operational requirements of the aviation industry.

[0306] Steps for constructing and applying the composite fitness evaluation function:

[0307] S(x)=w1·L(x)+w2·C(x)+w3·E(x)+w4·M(x)

[0308] In this formula:

[0309] L(x) represents the total length of the cable layout and is a key factor affecting cost and material usage;

[0310] C(x) is the number of crossover points in the cable layout. More crossover points will increase the risk of failure and reduce system reliability.

[0311] E(x) represents the electromagnetic compatibility score, the key is to prevent the cable from interfering with the normal operation of other electronic equipment;

[0312] M(x) is the maintainability score, which reflects the maintenance cost and operation difficulty of the cable system;

[0313] w1, w2, w3, and w4 are the weights of each factor, which are adjusted according to different design requirements and goals.

[0314] The specific value range of the weight factors: w1, w2, w3, and w4 are usually between 0 and 1. The specific values ​​are adjusted according to the requirements and design goals to balance the importance of each factor.

[0315] Assume that a cable system for a new commercial aircraft is being designed. Assume that a preliminary assessment indicates that the total length of the system L(x) is 1200 meters, the number of crossovers C(x) is 25, the electromagnetic compatibility score E(x) is 85 points, and the maintainability score M(x) is 95 points. The weighting factors are set to w1=0.25, w2=0.25, w3=0.25, and w4=0.25 according to the emphasis.

[0316] Calculate the fitness evaluation function:

[0317] S(x)=0.25·1200+0.25·25+0.25·85+0.25·95

[0318] S(x)=300+6.25+21.25+23.75

[0319] S(x)=351.25

[0320] This evaluation result provides a quantitative and comprehensive perspective to judge the current design scheme. Through the iterative process based on genetic algorithms, the design can be continuously adjusted, different cable layout configurations can be tried, new layout features can be introduced through crossover and mutation operations, and finally the optimal cable layout scheme can be found.

[0321] The core step of the genetic algorithm is the crossover operation, and the path-dependent crossover algorithm is used here. The design aims to produce offspring with potential advantages by combining the characteristics of two parents, while introducing a certain degree of variability to explore new solution spaces. This method can not only speed up the process of finding the optimal solution, but also increase the diversity of solutions, thereby preventing the algorithm from falling into a local optimal solution.

[0322] Specific implementation steps and examples of the path-dependent crossover algorithm:

[0323] The crossover model is:

[0324] γ child =(1-μ)γ parent1 +μγ parent2 +ηsin(β·(γ parent1 -γ parent2 ))

[0325] in:

[0326] μ is a weight randomly selected from a distribution adjusted based on the parent's fitness, affecting which parent's characteristics the offspring tends to have more of;

[0327] η and β are parameters that adjust for crossover effects, and they control the magnitude and frequency of oscillatory effects caused by parent-generation differences.

[0328] Specific value range of the parameter:

[0329] μ is usually taken between 0 and 1 to ensure a reasonable fusion of the characteristics of the two parents;

[0330] The value range of η can be set from 0.1 to 0.5, controlling the intensity of the oscillation;

[0331] The recommended range of β is between π and 2π to generate effective periodic oscillations.

[0332] Assume that during the optimization process, there are two parent layouts γ parent1 and γ parent2 ,in:

[0333] γ parent1 =150m cable layout path length.

[0334] γ parent2 =130m cable layout path length.

[0335] Set the parameters μ=0.7, η=0.3, and β=3.14 (ie, π).

[0336] Apply the crossover model to calculate the offspring paths:

[0337] γ child=(1-0.7)·150+0.7·130+0.3·sin(3.14·(150-130))

[0338] γ child =45+91+0.3·sin(62.8)

[0339] γ child ≈136.3

[0340] This newly generated offspring γ child It combines the layout characteristics of the two parent generations and increases the design diversity by introducing perturbations in the form of sinusoidal functions. This design can make the cable layout have better fault tolerance and maintenance convenience while meeting space constraints and functional requirements.

[0341] Perform directed mutation operations to make precise adjustments to specific problem areas while keeping the majority of the layout stable. This approach is particularly useful in responding to specific design challenges, such as the need to improve cable layout to avoid sensitive areas or optimize cable routing to reduce material usage and cost.

[0342] Explanation of the specific implementation steps of the directed mutation model:

[0343]

[0344] In this formula:

[0345] γ original It is the original cable layout;

[0346] γ new It is a proposed new layout based on considerations of design optimization or avoiding conflicting areas;

[0347] ξ is the mutation intensity, which determines the influence of the new feature in the original layout;

[0348] τ indicates the specific problem area where the variation should be focused, such as the portion of the cable path causing interference or increased costs;

[0349] σ controls the range of the variation effect, that is, the length of the cable affected by the variation effect.

[0350] Specific value range:

[0351] The value range of ξ is usually set between 0.1 and 1.0, which is sufficient to produce significant but not excessive variation effects;

[0352] The specific value of τ depends on the specific location of the identified problem area in the cable layout;

[0353] The value of σ ranges from 5 meters to 50 meters, and the extent of the variation is determined by the local or distributed nature of the problem.

[0354] Assume that during the design process, a problem area in a cable layout is identified at 100 meters because the cable is too close to a hot component. Original cable layout original The length is 150 meters. A new design was proposed. new , where the routing of this portion of the cable is adjusted to move away from heat sources.

[0355] Set the parameters ξ=0.5, τ=100 meters, σ=20 meters. Apply the directed mutation model to calculate the layout after mutation:

[0356]

[0357] At t = 100 meters, the impact factor The maximum is close to 1 and decreases rapidly in other areas, so the new layout is mainly adjusted around the problem area without affecting the cable layout far away from the problem area.

[0358] This directed variation allows precise modification of specific problem areas in the cable layout without destroying the advantages of the overall layout. In this way, the cable layout can be effectively optimized to improve the overall performance and safety of the system.

[0359] Embodiment 6:

[0360] In this embodiment, a method based on a genetic algorithm is used, which includes complex genetic operations such as dynamic fitness threshold adjustment, diversity elite retention strategy, and optimization of the iteration termination mechanism. These strategies ensure that the algorithm can effectively find the optimal solution while maintaining the diversity of the population and preventing premature convergence.

[0361] Define dynamic fitness threshold:

[0362]

[0363] in:

[0364] ΔS i is the fitness improvement of the i-th iteration;

[0365] n is the number of iterations considered, usually selected as the most recent iterations, such as 5 to 10;

[0366] ρ is a dynamic adjustment coefficient used to adjust the sensitivity of the fitness threshold.

[0367] The fitness improvements recorded in 10 consecutive iterations are set to 0.1, 0.2, 0.1, 0.3, 0.1, 0.2, 0.4, 0.1, 0.2, 0.3. The dynamic adjustment coefficient ρ is set to 0.5.

[0368] First, calculate the average value of the fitness improvement for 10 iterations:

[0369]

[0370] Then the dynamic adjustment coefficient is applied to calculate the dynamic fitness threshold:

[0371] ΔS min =0.2×0.5=0.1

[0372] This means that in subsequent iterations, the algorithm is considered to be making effective progress only when the fitness improvement is greater than or equal to 0.1.

[0373] This mechanism of dynamically adjusting the fitness threshold allows the genetic algorithm to dynamically adjust its desired amount of progress based on recent progress, which helps the algorithm refine the search when approaching the optimal solution rather than stopping iterations prematurely.

[0374] Implement a diversity elite retention strategy, the core of which is to retain not only the individuals with the highest fitness, but also those with unique genetic characteristics. The purpose of this is to maintain the diversity of the population, prevent the algorithm from converging to the local optimal solution too early, and improve the overall quality and innovation of the solution.

[0375] Define the genetic distance formula:

[0376]

[0377] Where d(x,y) represents the genetic distance between individual x and any individual y in the elite individual set Elite.

[0378] First, the fitness of each individual in the population is evaluated, and the individuals with the highest fitness are determined as the elite set.

[0379] Next, for each individual x in the population, calculate its genetic distance d(x,y) with all individuals y in the elite set, and find the minimum distance to each elite individual.

[0380] Then, find the largest one among these minimum distances, which is D unique , which represents the individuals in the population that are least similar to the elite individuals.

[0381] Parameter range: The calculation method and range of the genetic distance d(x,y) depend on the encoding and quantification method of the cable layout characteristics. Usually, these distances are calculated based on factors such as the physical properties of the cable and the layout location.

[0382] Assume that a population in an aviation cable layout optimization contains 100 individuals, each of which represents a cable layout solution. The elite set Elite contains the top 10% of individuals with the highest fitness, that is, 10 individuals.

[0383] Calculate the genetic distance between each individual in the population and the 10 elite individuals. Set these distances based on factors such as cable length, path complexity, etc.

[0384] For each individual in the population, find its minimum distance to each individual in the elite set, and select the maximum value D from these minimum distances unique .

[0385] If we find that D unique The value is the largest, that is, this individual is most different from the elite individual in genetic characteristics, then this individual will be retained in the new population, even if its fitness is not the highest. This strategy ensures the genetic diversity of the population and increases the probability of finding the global optimal solution through iteration.

[0386] When using genetic algorithm-based methods, a key decision point is to determine when to stop iterating. This is usually done by monitoring the trend of the fitness improvement curve. This approach helps ensure efficient use of resources and avoids unnecessary iterations after sufficient optimization has been achieved, thus saving time and computing resources, while also preventing overfitting.

[0387] 1. Calculate the fitness change rate: fitness change rate It represents the speed of change of fitness during continuous iterations, where S is the fitness value and t is the number of iterations.

[0388] 2. Set the stop condition: When the fitness change rate is less than a preset minimum value ∈, stop the iteration. This preset value ∈ is set according to specific needs and historical data experience to determine whether the fitness improvement has stabilized, that is, further iterations are unlikely to bring significant improvements.

[0389] 3. Parameter value range: The specific value of ∈ is usually very small, such as 0.001 to 0.01. The exact value should be selected based on the complexity of the cable layout, the accuracy required by the design, and the availability of computing resources.

[0390] In the genetic algorithm for cable layout optimization, the fitness values ​​of the past 50 iterations are recorded. By analyzing these data, the fitness improvement ΔS of each iteration is calculated. Then, the average value and change rate of the fitness improvement are calculated:

[0391] Assume that in the last 10 iterations, the fitness improvements are:

[0392] 0.02,0.018,0.015,0.012,0.01,0.008,0.006,0.004,0.002,0.001

[0393] First, calculate the average rate of change of these changing values:

[0394]

[0395] Then, compare this average rate of change with the preset minimum value ∈=0.01:

[0396] Because the average rate of change 0.0096 is already less than ∈=0.01, the iteration can be stopped according to the stopping condition.

[0397] This approach ensures that the algorithm will not continue to consume additional resources after achieving a certain optimization effect, while ensuring the efficiency and practicality of the design results.

[0398] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. The aviation cable layout optimization method based on genetic algorithm is characterized by The following steps are involved: S1. First, define the objective function of cable layout optimization, including minimizing cable length, reducing cable crossing points, optimizing cable weight distribution and reducing cable cost, and define the cable bending radius limit, fixed point position and interference limit constraints between cables according to the objectives; S2. Then design a graph-based encoding scheme to encode the starting point, end point, path and necessary intermediate nodes of each cable into a gene sequence in the genetic algorithm; S3, then initialize the population, randomly generate a certain number of cable layout solutions as the initial population, where each individual represents a single solution; S4, then design a fitness function to comprehensively consider the total length of the cable, the number of cross points, the weight distribution and the cost factors to evaluate the pros and cons of each layout scheme; S5. Optimize the population through selection, crossover and mutation genetic operations, where the selection operation selects the better solution for reproduction according to the fitness function, the crossover operation generates offspring from two cable layout solutions, and the mutation operation randomly modifies some genes in the offspring cable layout to increase population diversity; S6. Finally, the genetic operations of S1-S5 are iteratively executed until the preset number of iterations is reached or the fitness is not significantly improved. After each iteration, the individual with the highest fitness is retained as the optimal solution. The objective function of the cable layout optimization comprehensively considers minimizing the cable length L, reducing the cable intersections C, optimizing the cable weight distribution W and reducing the cable cost K, and the formula is expressed as: F(x)=a1·e -α·L +a2·log(1+C)+a3·sin(β·W)+a4·cos(γ·K) Among them, a1, a2, a3, a4 are weight coefficients, α, β, γ are adjustment coefficients; Then, based on the cable layout objectives, the cable bending radius limit R(x) is determined and formulated as: Among them, δ, θ, x0 are specific constants, representing the dynamic adjustment factors of the bending radius; Then the optimization of the fixed point position is expressed as: P(x)=λ tan -1 (ω x) Among them, λ and ω adjust the slope and position of the fixed point position response curve; Finally, the cable-to-cable interference limit is adopted: where κ,v adjusts the sensitivity and scale of the interference between cables; A multi-level graph encoding scheme is adopted, and dynamic path interpolation encoding is applied, which allows the cable path to be dynamically adjusted according to the optimization goal during the algorithm iteration process. The path is defined by key control points, and the position of each point is determined by: p i (t)=a·sin(b·t+c i ) Calculate, where t represents the parameters on the path, a, b and c i is the adjustment coefficient, which allows the path to be optimized in iterations based on the fitness evaluation; Function-based path generation uses a polynomial path generation function to dynamically generate the actual layout path of the cable using control points. The formula is: where p i (t) is the dynamic position of each control point under parameter t, allowing the overall performance of the path to be optimized while maintaining layout rationality.

2. The method for optimizing aviation cable layout based on genetic algorithm according to claim 1, characterized in that The cable layout scheme is optimized as an initial population for different aircraft models, cable types and layout complexity; during the initialization process, the probability of selecting a template is determined by a probability density function, which is the difference between the template and the current optimization target, and the formula is: Where T i (t) describes the configuration state of template i at time t, while O(t) is the description of the optimization goal; Then, a noise perturbation model is introduced to randomly generate the start and end positions of each cable, using the formula: (x,y)=(Rcos(θ+∈1(t)),Rsin(θ+∈2(t))) Implementation, where R and θ are random parameters based on cable length and direction, while ∈1(t) and ∈2(t) are disturbance terms that increase the randomness of the design, reflecting the random effects at different times t; Finally, a method based on constraint satisfaction problem is adopted. When initializing the population, the physical and environmental constraints of the cable layout are used as part of the optimization algorithm. By solving the optimization problem involving all nodes, the layout solution that minimizes the degree of constraint violation is found; the relevant formula is: Where N(c) represents the number of nodes that satisfy constraint c, ξ i is the weight of node i, and v i is the position vector of node i.

3. The method for optimizing aviation cable layout based on genetic algorithm according to claim 1, characterized in that The fitness function is specifically implemented as follows: S1. First, define the contribution to the total length as: where γ i (t) represents the position of the i-th cable at time t; S2. Then the contribution of the number of intersections is evaluated by the high-level model: where θ ij is the angle between cable i and cable j at the intersection, α ij is to adjust the parameters to emphasize the influence of intersections close to right angles; S3, then the evaluation of the weight distribution is given by the dynamic model: where ρ i (t) is the line density of cable i at position t, * denotes the convolution operation, and σ is the kernel function used to smooth the line density distribution; S4. The final cost contribution is: where p i (t) is the unit cost of cable i, which varies with time, λ i is the installation cost factor, μ i is the maintenance cost factor of cable i, ds i / dt represents the maintenance cost that changes over time.

4. The method for optimizing aviation cable layout based on genetic algorithm according to claim 1, characterized in that The selection, crossover and mutation genetic manipulation methods include: S1. First, define the composite fitness evaluation function: S(x)=w1·L(x)+w2·C(x)+w3·E(x)+w4·M(x) Where L(x) represents the total length of the layout, C(x) is the number of intersections, E(x) represents the electromagnetic compatibility score, M(x) represents the maintainability score, and w1, w2, w3, w4 are weight factors adjusted to suit different design requirements; S2, then the crossover operation is performed through the path-dependent crossover algorithm, the model is: c child =(1-μ)γ parent1 +μγ parent2 +ηsin(β·(γ parent1 -c parent2 )) Where μ is a weight randomly selected from a distribution adjusted based on the parent's fitness, and η and β are parameters that adjust for cross-effects; S3. Finally, the directed mutation operation is implemented, and the model is: where ξ is the strength of the variation, τ indicates the specific problem area, and σ controls the scope of the variation’s impact.

5. The method for optimizing aviation cable layout based on genetic algorithm according to claim 1, characterized in that The iterative genetic operation implementation includes dynamic fitness threshold adjustment, diversity elite retention strategy and iterative termination mechanism optimization genetic operation: S1. First, define the dynamic fitness threshold adjustment mechanism. The minimum threshold for fitness improvement is based on the formula: Dynamic adjustment, where ΔS i is the fitness improvement of the i-th iteration, n is the reference iteration window, and ρ is the dynamic adjustment coefficient; S2, then implement the diversity elite retention strategy, in addition to retaining the individuals with the highest fitness, also based on the genetic distance between individuals: Select individuals with unique genetic characteristics, where d(x,y) represents the genetic distance between individual x and any individual y in the elite individual set Elite; S3. Finally, decide whether to continue iterating based on the changing trend of the fitness improvement curve. If the fitness change rate If it is less than a preset minimum value ∈, the iteration stops.

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