An amphibious delivery multi-agent cooperative scheduling method based on improved genetic algorithm

Abstract

The application discloses an amphibious delivery method based on multi-agent efficiency cooperation, and belongs to the technical field of amphibious operation command control and intelligent scheduling. In view of the problem that a traditional amphibious delivery model ignores the transportation cooperation and tactical cooperation between hovercraft and personnel equipment, a multi-agent efficiency optimization model including transportation efficiency cooperation and tactical efficiency cooperation is constructed. The method firstly establishes a delivery agent cooperation mechanism, describes the mutual influence relationship between the hovercraft and the personnel equipment to calculate the delivery time, and describes the mutual influence relationship between the personnel and the equipment to calculate the cumulative combat efficiency; secondly, an improved genetic algorithm based on double-layer integer coding is designed, and a hybrid initialization strategy, an adaptive crossover and mutation operator and a dynamic penalty function are used for solving. The method can realize the cooperative optimization of the delivery time and the combat efficiency, significantly shorten the total delivery time and improve the cumulative combat efficiency, and provides decision support for the generation of the amphibious delivery scheme.

Description

Technical Field

[0001] This invention belongs to the field of intelligent scheduling technology, specifically relating to an amphibious delivery scheduling optimization method that considers the coordination of transportation efficiency and tactical efficiency. Background Technology

[0002] Amphibious landing operations are a key operational style for seizing coastal targets in modern joint operations. During the assault and landing phase, hovercraft, with their high speed and amphibious capabilities, become the core vehicle connecting sea voyages and land operations, responsible for rapidly deploying landing forces from the mother ship to the beachhead.

[0003] In recent years, achievements in optimizing the deployment and scheduling of amphibious forces can be mainly divided into two core directions: the construction and solution of amphibious deployment mission planning models. Existing technologies have the following shortcomings:

[0004] The delivery models mostly adopt idealized and simplified assumptions, and do not take into account the multi-entity transportation coordination law of hovercraft and personnel equipment. They are significantly different from complex delivery scenarios, making it difficult for the scheduling scheme to meet the needs of engineering applications.

[0005] The tactical coordination relationship between combat personnel and combat equipment is not systematically depicted, making it impossible to achieve synergistic optimization of delivery time and combat effectiveness.

[0006] Existing solution algorithms are ill-suited to the multi-dimensional and strongly constrained decision-making characteristics of amphibious delivery. They have shortcomings in feasible region convergence, global optimization, and stability, and cannot generate delivery schemes that meet engineering deployment requirements.

[0007] Therefore, there is an urgent need for an amphibious delivery scheduling method that can simultaneously take into account both the physical characteristics of transportation and the requirements of tactical coordination. Summary of the Invention

[0008] This invention addresses the shortcomings of existing amphibious delivery scheduling models, such as insufficient adaptability to delivery scenarios, lack of tactical coordination characterization, and weak algorithmic solution capabilities. This method constructs a multi-agent optimization model that integrates transportation efficiency coordination and tactical efficiency coordination, and combines it with a customized improved genetic algorithm solution framework to achieve dual-objective collaborative optimization that minimizes the total amphibious delivery time and maximizes cumulative combat effectiveness. This significantly improves the adaptability of the scheduling scheme to delivery scenarios, combat effectiveness, and solution stability.

[0009] This invention discloses an amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm, which includes the following steps:

[0010] Step 1: Construct a multi-agent effectiveness coordination model, which includes a transportation effectiveness coordination sub-model and a tactical effectiveness coordination sub-model. This model describes the mutual influence between the hovercraft and personnel / equipment, and establishes a multi-objective, strongly constrained optimization framework.

[0011] Step 2: Employ a two-layer integer encoding strategy and a hybrid initial population strategy. The two-layer integer encoding strategy includes a wave allocation string and a vehicle allocation string.

[0012] Step 3: The initial population is iteratively evolved using an improved genetic algorithm. Individuals in the population are updated through adaptive crossover and mutation operators to balance global search and local exploitation capabilities. The hybrid initial population strategy includes greedy feasible solutions, repaired random solutions, completely random solutions, and mutated excellent solutions.

[0013] Step 4: Introduce a dynamic penalty function to handle the strong constraints of the model, complete the fitness assessment of individuals in the population and the selection of high-quality individuals, and generate the offspring population through an adaptive crossover and mutation operator;

[0014] Step 5: Determine if the iteration termination condition is met. If it is, output the multi-wave delivery scheduling scheme corresponding to the individual with the best fitness. Otherwise, return to step 3 to continue iterative evolution.

[0015] Furthermore, step 1 also includes the following steps:

[0016] Step 11: Construct a multi-agent effectiveness synergy model. The decision variables of the multi-agent effectiveness synergy model include:

[0017] Combat squad allocation variables are If the first The class of The combat squad was assigned to the first wave after wave One hovercraft, ,otherwise ;

[0018] Equipment allocation variables are If the first The class of The equipment was allocated to the first Waves One hovercraft, ,otherwise ;

[0019] Hovercraft scheduling variables are If the first 10 hovercraft participated in the wave, then ,otherwise ;

[0020] Step 12: Based on the delivery and transportation process and vehicle attributes, integrate all operational links of the entire wave, clarify the temporal recursion relationship between waves, and construct a transportation efficiency collaboration model:

[0021] ;

[0022] in, , , , , , , They represent the first The time allotted for each wave of attack includes: preparation time for sortie, time to leave the mothership, time to form a wave, time to land on shore, time to unload on the beach, time to return to port, and time to rejoin the mothership. For the first The start time of the wave, For the first End time of the wave;

[0023] Step 13: Establish a static basic tactical combat capability model and determine the inherent capability benchmarks of personnel and equipment;

[0024] Step 14: Set constraints, including area load capacity constraints, number of hovercraft constraints, delivery timing constraints, hovercraft delivery process constraints, uniqueness constraints, and non-negativity constraints.

[0025] S15: Establish a dual-objective optimization function:

[0026] ;

[0027] ;

[0028] To minimize system delivery time, To maximize cumulative combat effectiveness.

[0029] Furthermore, in step 12, multiple hovercraft within the same wave will exhibit a significant queuing effect during the departure from the mothership, wave formation, and entry into the mothership phases:

[0030] ;

[0031] ;

[0032] ;

[0033] in, For the ship deployment coefficient, For the wave coding coefficient, This refers to the coefficient for entering the ship; 0-1 decision variables; , , These are the baseline fixed times for the processes of leaving the mothership, forming a wave, and entering the mothership when operating as a single vessel; This represents the total number of hovercraft.

[0034] Considering the load-speed coupling characteristics of hovercraft, the time required for a single hovercraft to land is... Nonlinear decay with load factor:

[0035] ;

[0036] In the formula: This is the baseline time for an unloaded hovercraft to make an emergency landing. The load attenuation coefficient characterizes the extent to which the load factor affects the speed. The nonlinear exponent characterizes the nonlinear characteristics of speed decay; the landing time for a single wave of assault is taken as the maximum value of all participating hovercraft, i.e. .

[0037] Furthermore, in step 13, the first basic combat strength of the wave The sum of the inherent tactical values ​​of all combat teams and equipment deployed in this wave:

[0038] ;

[0039] in, , Each represents a single first Class of combat squads and individual The basic tactical values ​​of this type of equipment The total number of combat squad categories, Let i be the total number of combat squads of type i. This represents the total number of categories of combat equipment. Let i be the total number of equipment of type i;

[0040] When combat teams with complementary tactics and supporting equipment are deployed to land in the same wave, they can form a system-of-systems combat capability and generate synergy gains; synergy gains are calculated based on the principle of minimum matching. :

[0041] ;

[0042] in, Let be the element of the cooperative gain matrix, representing the th Type of combat squad and the first The coordination coefficient of this type of equipment and The first middle of wave Type of combat squad and the first The number of equipment types The function represents taking the smaller of the two values ​​as the number of effective cooperative units;

[0043] The battlefield value of subsequent waves of troops decreases exponentially with delivery delay, and the time-effectiveness decay coefficient... for:

[0044] ;

[0045] The battlefield agility factor reflects the rate at which combat effectiveness decays with delivery time; a larger value indicates that the battlefield environment is more sensitive to the timing of delivery.

[0046] No. Integrated combat effectiveness of waves for:

[0047] ;

[0048] These are the coupling weight coefficients.

[0049] Furthermore, in step 14, area load constraints: each hovercraft participating in this wave must individually meet the load and area constraints and must not be overloaded.

[0050] ;

[0051] ;

[0052] In the formula: , Each of the single first Weight and area occupied by a combat squad; , Each of the single first The weight and area occupied by this type of combat equipment; , These are the maximum load capacity and maximum carrying area limit for a single hovercraft, respectively.

[0053] Hovercraft quantity constraint: The number of hovercraft used in each wave cannot exceed the total number of available hovercraft.

[0054] ;

[0055] In the formula: For the set of all delivery waves;

[0056] Delivery timing constraints: The next wave can only begin delivery after the previous wave is completed.

[0057] ;

[0058] In the formula: To the maximum number of wavelets delivered, For the first +1 wave start time;

[0059] Uniqueness constraint: Each combat squad and each piece of combat equipment can be deployed exactly once, and cannot be deployed repeatedly or omitted.

[0060] ;

[0061] ;

[0062] Non-negativity constraint: All variables such as duration, combat power, gain, and coefficients must be non-negative.

[0063] Furthermore, in step 2, the first layer is a wave allocation string with a length equal to the total number of delivery units, and the gene value represents the delivery wave of the corresponding unit; the second layer is a vehicle allocation string with a length equal to the total number of delivery units, and the gene value represents the hovercraft number loaded by the corresponding unit.

[0064] Furthermore, in step 4, the adaptive crossover probability and mutation probability The adjustment is based on the dynamic adjustment of the population fitness distribution, and the adjustment strategy is as follows:

[0065] When an individual's fitness is greater than the population's average fitness, the crossover probability and mutation probability decrease linearly with the difference between the individual's fitness and the maximum fitness.

[0066] When the fitness of an individual is less than the average fitness of the population, the crossover probability and mutation probability remain at preset constants.

[0067] The calculation formula is as follows:

[0068] ;

[0069] ;

[0070] in, For the maximum fitness of the population, For average fitness, The larger fitness value among the two individuals to be crossovered. The fitness value of the individual to be mutated. This is an adjustment coefficient, with a range of values. ;

[0071] Dynamic penalty function The construction method is as follows:

[0072] ;

[0073] in, The penalty value is for the individual. For individuals, the constraints violate the measurement value. For iterative algebra The dynamic penalty coefficient changes. It monotonically increases with the iteration process, and its calculation formula is:

[0074] ;

[0075] in, Basic penalty factor, For iterative algebra.

[0076] Furthermore, in step 4, the fitness function After standardizing the two objectives, a weighted sum is taken, and a penalty term is added to obtain the individual fitness. The smaller the fitness value, the better the individual.

[0077] ;

[0078] In the formula: This is a standardized value for the total delivery time; Standardized values ​​for accumulated combat effectiveness; , The weighting coefficients for the two objectives satisfy... .

[0079] Furthermore, in step 5, the algorithm terminates the iteration under the following conditions:

[0080] 1. Reach the preset maximum number of iterations. ;

[0081] 2. Continuous The optimal fitness value of the next generation population did not improve significantly, indicating that the algorithm has converged.

[0082] Furthermore, in step 5, after the iteration terminates, the individual with the lowest fitness in the output population is output, and the corresponding multi-wave delivery scheduling scheme is decoded, including: the delivery wave of each combat squad and equipment, the number of the loaded hovercraft, the delivery sequence of each wave, the combat force composition, and core indicators such as total delivery time and cumulative combat effectiveness.

[0083] The beneficial effects achieved by this invention are:

[0084] This invention has strong adaptability to delivery scenarios: it incorporates real combat patterns such as dock queuing, load and speed coupling, avoids idealized assumptions, and the delivery time calculation fits the complex working conditions of the delivery scenario. The solution can be directly used for command and decision-making.

[0085] This invention has superior collaborative optimization capabilities: it quantifies the tactical coordination relationship between personnel and equipment, and optimizes delivery timeliness and combat effectiveness, resulting in a significant improvement in combat effectiveness compared to traditional methods.

[0086] This invention offers high solution stability: customized encoding and evolutionary strategies are adapted to the characteristics of strong-constrained high-dimensional decision-making, significantly improving global optimization capabilities. Attached Figure Description

[0087] Figure 1 Flowchart of a multi-agent cooperative scheduling method for amphibious delivery based on an improved genetic algorithm;

[0088] Figure 2 To improve the execution flowchart of the Genetic Algorithm (EGA);

[0089] Figure 3 Gantt chart for multi-wave hovercraft deployment. Detailed Implementation

[0090] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as a result. However, these embodiments are merely exemplary and do not constitute any limitation on the scope of the present invention. Those skilled in the art should understand that modifications or substitutions can be made to the details and form of the technical solutions of the present invention without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0091] like Figure 1 As shown, this invention provides a multi-agent cooperative scheduling method for amphibious delivery based on an improved genetic algorithm. This method includes the following steps:

[0092] Step 1: Construct a multi-agent effectiveness coordination model, which includes a transportation effectiveness coordination sub-model and a tactical effectiveness coordination sub-model. This model describes the mutual influence between the hovercraft and personnel / equipment, and establishes a multi-objective, strongly constrained optimization framework.

[0093] Specifically, step 1 also includes the following steps:

[0094] Step 11: Construct a multi-agent effectiveness synergy model, wherein the model decision variables include:

[0095] Combat Squad Allocation Variables If the first The class of The combat squad was assigned to the first Waves One hovercraft, ,otherwise .

[0096] Equipment allocation variables If the first The class of The equipment was allocated to the first Waves One hovercraft, ,otherwise .

[0097] Hovercraft scheduling variables If the first 10 hovercraft participated in the wave, then ,otherwise ;

[0098] Step 12: Based on the delivery and transportation process and vehicle attributes, integrate all operational stages of each wave, clarify the temporal recursive relationship between waves, construct a transportation efficiency collaboration model, and ultimately achieve accurate calculation of the total system delivery time. The model can be represented as:

[0099]

[0100] in, , , , , , , They represent the first The time allotted for each wave of attack includes: preparation time for sortie, time to leave the mothership, time to form a wave, time to land on shore, time to unload on the beach, time to return to port, and time to rejoin the mothership. For the first The start time of the wave, For the first The end time of the wave.

[0101] Because only one hovercraft can enter and exit the mothership's dock hatch at a time, a significant queuing effect will occur when multiple hovercraft in the same wave are leaving the mothership, forming a wave, and entering the mothership: for each additional hovercraft deployed in a single wave, the operation time of the corresponding stage will increase linearly. The quantitative relationship of the time of each stage is as follows: - As shown:

[0102]

[0103]

[0104]

[0105] in, For the ship deployment coefficient, For the wave coding coefficient, This refers to the coefficient for entering the ship; 0-1 decision variables; , , These are the baseline fixed times for the processes of leaving the mothership, forming a wave, and entering the mothership when operating as a single vessel; This represents the total number of hovercraft.

[0106] Considering the load-speed coupling characteristics of hovercraft, the time for a single hovercraft to land on shore decreases non-linearly with load factor:

[0107]

[0108] In the formula: This is the baseline time for an unloaded hovercraft to make an emergency landing. The load attenuation coefficient characterizes the extent to which the load factor affects the speed. This is a nonlinear exponent, characterizing the nonlinear properties of speed decay. The landing time for a single wave of attacks is taken as the maximum value among all participating hovercraft, i.e. .

[0109] Step 13: Establish a static basic tactical combat capability model and determine the inherent capability benchmarks of personnel and equipment; then the... The basic combat power of a wave is the sum of the inherent tactical values ​​of all combat squads and equipment deployed in that wave, calculated using the following formula:

[0110]

[0111] , Each represents a single first Class of combat squads and individual first Basic tactical values ​​for this type of equipment.

[0112] When combat teams with complementary tactics and supporting equipment are deployed and landed in the same wave, they can form a system-of-systems combat capability and generate synergy gains. This invention calculates synergy gains based on the minimum matching principle, and the calculation formula is as follows:

[0113]

[0114] in, Let be the element of the cooperative gain matrix, representing the th Type of combat squad and the first The coordination coefficient of this type of equipment and The first middle of wave Type of combat squad and the first The number of equipment types The function represents taking the smaller of the two values ​​as the number of effective cooperative units.

[0115] Amphibious operations are highly time-sensitive; the battlefield value of subsequent waves of troops deployed decreases exponentially with deployment delays. The formula for calculating the time-effectiveness attenuation coefficient is as follows:

[0116]

[0117] In the formula: The battlefield agility factor reflects the rate at which combat effectiveness decays with delivery time; a larger value indicates that the battlefield environment is more sensitive to the timing of delivery.

[0118] No. The comprehensive combat effectiveness of a wave is the weighted sum of basic combat power and synergistic gains, multiplied by a time-effect decay coefficient. The calculation formula is as follows: The model described above can be expressed as:

[0119]

[0120] Step 14: Set constraints, including area load capacity constraints, hovercraft quantity constraints, deployment timing constraints, hovercraft deployment process constraints, uniqueness constraints, and non-negativity constraints; among which,

[0121] Area and load constraints: Each hovercraft participating in this wave must individually meet the load and area constraints and must not be overloaded. The calculation formula is as follows:

[0122]

[0123]

[0124] In the formula: , Each of the single first Weight and area occupied by a combat squad; , Each of the single first The weight and area occupied by this type of combat equipment; , These represent the maximum load capacity and maximum carrying area of ​​a single hovercraft, respectively.

[0125] Hovercraft Number Constraint: The number of hovercraft used in each wave cannot exceed the total number of available hovercraft. The calculation formula is as follows:

[0126]

[0127] In the formula: This is the set of all delivery waves.

[0128] Delivery timing constraint: The next wave can only begin delivery after the previous wave is completed. The calculation formula is as follows:

[0129]

[0130] In the formula: This represents the maximum number of wave drops.

[0131] Uniqueness constraint: Each combat squad and each piece of combat equipment can be delivered exactly once, and cannot be delivered repeatedly or omitted. The calculation formula is as follows:

[0132]

[0133]

[0134] Non-negativity constraint: All variables such as duration, combat power, gain, and coefficients must be non-negative.

[0135] S15: Establish a dual-objective optimization function. The objective function of the multi-agent efficiency collaborative optimization model is:

[0136]

[0137]

[0138] Step 2: Employ a two-layer integer encoding strategy and a hybrid initial population strategy. The two-layer integer encoding strategy includes a wave allocation string and a vehicle allocation string.

[0139] The length of the wave allocation string is equal to the total number of delivery units, and the gene value represents the delivery wave of the corresponding unit;

[0140] The length of the vehicle allocation string is equal to the total number of delivery units, and the gene value represents the hovercraft number loaded in the corresponding unit.

[0141] Step 3: The initial population is iteratively evolved using an improved genetic algorithm. Individuals in the population are updated through adaptive crossover and mutation operators to balance global search and local exploitation capabilities. The mixed initial population strategy includes greedy feasible solutions, repaired random solutions, completely random solutions, and mutated excellent solutions. The mixed initial population strategy includes: 70% greedy feasible solutions, 10% repaired random solutions, 10% completely random solutions, and 10% mutated excellent solutions.

[0142] Step 4: Introduce a dynamic penalty function to handle the strong constraints of the model, complete the fitness assessment of individuals in the population and the selection of high-quality individuals, and generate the offspring population through an adaptive crossover and mutation operator;

[0143] Specifically, step 4 also includes the following steps:

[0144] Decode the individual population data to obtain total delivery time, cumulative combat effectiveness, and constraint violation data, and then process the strong constraints using a dynamic penalty function:

[0145] Dynamic penalty function The construction method is as follows:

[0146]

[0147] in, This represents the numerical value of the individual's penalty item. For individuals, the constraints violate the measurement value. For iterative algebra The dynamic penalty coefficient changes. It monotonically increases with the iteration process, and its calculation formula is:

[0148]

[0149] in, It is the basic penalty factor.

[0150] fitness function After standardizing the two objectives, a weighted sum is taken, and a penalty term is added to obtain the individual fitness. A lower fitness value indicates a better individual. The calculation formula is as follows:

[0151]

[0152] In the formula: This is a standardized value for the total delivery time; Standardized values ​​for accumulated combat effectiveness; , The weighting coefficients for the two objectives satisfy... .

[0153] Based on the calculated fitness values, high-quality individuals are selected for evolution, and excellent individuals are retained for subsequent evolutionary stages.

[0154] Adaptive crossover probability and mutation probability The adjustment is based on the dynamic adjustment of the population fitness distribution, and the adjustment strategy is as follows:

[0155] When an individual's fitness is greater than the population's average fitness, the crossover probability and mutation probability decrease linearly with the difference between the individual's fitness and the maximum fitness.

[0156] When the fitness of an individual is less than the average fitness of the population, the crossover probability and mutation probability remain at preset constants.

[0157] The calculation formula is as follows:

[0158]

[0159]

[0160] in, For the maximum fitness of the population, This represents the average fitness. The larger fitness value among the two individuals to be crossovered. This represents the fitness value of the individual to be mutated. This is an adjustment coefficient, with a range of values. .

[0161] Step 5: Determine if the iteration termination condition is met. If it is, output the multi-wave delivery scheduling scheme corresponding to the individual with the best fitness. Otherwise, return to step 3 to continue iterative evolution.

[0162] The algorithm terminates its iterations under the following conditions:

[0163] 1. Reach the preset maximum number of iterations. ;

[0164] 2. Continuous The optimal fitness value of the next generation population did not improve significantly, indicating that the algorithm has converged.

[0165] The present invention will be further described in detail below with reference to specific embodiments. This embodiment takes the carrier-based hovercraft performing a multi-wave sea-skimming delivery mission as a typical scenario, and fully describes the specific implementation process of the method of the present invention. Those skilled in the art can reproduce the present invention and obtain the corresponding technical effects without creative effort based on the content disclosed in this embodiment. The specific parameters described in this embodiment are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0166] This embodiment sets the scenario as follows: An amphibious dock landing ship carrying six identical hovercraft is carrying out a troop deployment mission, requiring the deployment of combat teams and heavy equipment to the designated beachhead in multiple waves. Specific parameter settings are as follows:

[0167] The maximum load-bearing capacity and maximum load-bearing area of ​​each hovercraft are as follows: , The time parameters for each of the seven stages in a single-wave deployment of the hovercraft are shown in Table 1.

[0168] Table 1. Time Setting Table for Each Stage of the Hovercraft

[0169]

[0170] Among them, the ship dispatch coefficient Waveform Coefficient , ship entry coefficient Both are 5; the time to reach the shore during a rapid landing is affected by the nonlinear load attenuation coefficient. Influence.

[0171] The combat squads are divided into 6 categories, totaling 122 combat squad groups. The parameter settings for each type of combat squad are shown in Table 2.

[0172] Table 2 Combat Squad Parameter Setting Table

[0173]

[0174] In addition to the equipment carried by the combat squads themselves, the combined arms brigade also needs to deploy a certain number of equipment systems during landing operations. These systems are usually large and heavy, do not belong to any single combat squad, and have a significant impact on the hovercraft loading scheme.

[0175] Based on the actual needs of combined arms brigade amphibious landing operations, this paper classifies combat equipment into 17 categories, including equipment for different purposes such as assault, protection, firepower, support, and engineering, totaling 141 pieces of equipment. The quantity, weight, and area parameters of each type of combat equipment are set as shown in Table 3.

[0176] Table 3 Equipment Parameter Setting Table

[0177]

[0178] According to the tactical principles of combined arms battalions, the organic combination of different military branches can produce emergent effects. The synergistic gain matrix is ​​set in Table 4 below.

[0179] Table 4 Synergistic Gain Matrix

[0180]

[0181] Population size Maximum number of evolutions Crossover probability Probability of mutation Elite retention rate Bi-objective weighting coefficients .

[0182] According to the process shown in Figure 1, the specific implementation steps of this embodiment are as follows:

[0183] Step 1: Construct a multi-agent efficiency collaborative optimization model

[0184] S11: Define decision variables: According to the definition of this invention, three types of 0-1 decision variables are defined for 122 combat squads, 141 pieces of equipment, 6 hovercraft, and a maximum of 10 waves. , , .

[0185] S12: Construct a transportation efficiency coordination sub-model: Substitute the operational process parameters of this embodiment, and follow the formula in the invention content. - Construct a collaborative model for transportation efficiency.

[0186] S13: Constructing a tactical effectiveness coordination sub-model: Substituting the troop parameters and coordination gain coefficients of this embodiment, and following the formula in the invention... - Establish the calculation logic of basic combat power, synergistic gain, and time-effect decay to obtain the calculation method of single-wave comprehensive combat effectiveness.

[0187] S14: Set constraints: In accordance with the requirements of this invention, set area load constraints, hovercraft quantity constraints, delivery timing constraints, uniqueness constraints, and non-negativity constraints to clarify the feasible domain boundaries of all scheduling schemes.

[0188] S15: Establish a dual-objective optimization function: Based on the objective function formula in the invention, establish a dual-objective optimization framework that "minimizes the total delivery time and maximizes the cumulative combat effectiveness".

[0189] The core of this invention lies in using an improved genetic algorithm specifically designed for amphibious delivery scenarios to solve the model. The execution flow of this algorithm is as follows, and its overall flow is as follows: Figure 2 As shown.

[0190] Step S2: Double-layer integer coding. The 263 delivery units (122 combat squads + 141 pieces of equipment) are uniformly numbered, with a range of 1 to 263; a double-layer coded chromosome of length 263 is generated.

[0191] First layer (wave allocation string): The value of each gene position is an integer from 1 to 10, corresponding to the delivery wave of the numbered delivery unit;

[0192] The second layer (vehicle allocation string): each gene position has an integer value from 1 to 6, corresponding to the hovercraft number loaded by the numbered delivery unit.

[0193] The strategy example diagram is as follows Figure 3 As shown.

[0194] S3: Initial Population Generation

[0195] Initial population generation: Generate 600 initial individuals in a 7:1:1:1 ratio.

[0196] ①70% (420) Greedy feasible solution: Sort the 263 delivery units in descending order of weight and load them into the hovercraft in sequence. After each unit is loaded, check whether the load and area of ​​the hovercraft exceed the limits. If the limits are exceeded, switch to the next hovercraft until all units are loaded, ensuring that all individuals meet the load and area constraints.

[0197] ②10% (60) Repair random solutions: Randomly generate wave allocation and vehicle allocation results, count the load and area of ​​each hovercraft, and for overloaded hovercraft, adjust the unit with the largest weight to other hovercraft that are not overloaded, until all hovercraft meet the constraints and generate feasible solutions.

[0198] ③ 10% (60) completely random solutions: The wave and vehicle allocation results are generated completely randomly without constraint repair, thus preserving the genetic diversity of the population;

[0199] ④10% (60) of the best mutated solutions: Randomly select 10 gene loci from the greedy feasible solution to mutate and adjust their wave or vehicle allocation, retain the core structure of the greedy solution, and introduce gene diversity.

[0200] Step 4: Iterative Evolution Solution

[0201] S41: Population Decoding: Decode the chromosome of each individual, performing two calculations per wave:

[0202] ① Decoding Transportation Efficiency: Count the number of hovercraft participating in each wave, calculate the time for mothership deployment, wave formation, and entry into the mothership; calculate the load factor of each hovercraft, calculate the single-craft landing time, and take the maximum value as the landing time for that wave; finally, calculate the total delivery time. ;

[0203] ② Tactical effectiveness decoding: Statistically determine the number of combat squads and equipment in each wave, calculate basic combat strength, synergy gains, and time-based effectiveness decay, and sum them to obtain cumulative combat effectiveness. .

[0204] S42: Fitness Calculation

[0205] ① Total delivery time and cumulative combat effectiveness Perform min-max standardization to obtain the standardized value. , ;

[0206] ② Calculate the overload and overcapacity of each individual unit, and then calculate the constraint violation degree. ;

[0207] ③ Calculate the dynamic penalty coefficient based on the current iteration algebra gen. With penalty items ;

[0208] ④ According to the formula Calculate the fitness of an individual; the lower the fitness, the better the individual.

[0209] S43: Selection Operation: Employing an elite retention + tournament selection strategy:

[0210] ①Elite Preservation: The 10 individuals with the lowest fitness in the current population are directly preserved and enter the next generation of the population;

[0211] ② Tournament selection: Randomly select 3 individuals from the remaining individuals, and select the individual with the lowest fitness to enter the next generation. Repeat the operation until the next generation population size reaches 600.

[0212] S44: Adaptive crossover mutation:

[0213] ① Crossover operation: Pair individuals in the population into two groups and calculate the crossover probability of each pair of individuals according to the formula in the invention. If the random number is less than Then, the wave allocation string and vehicle allocation string of the two individuals are intersected at two points to generate two new individuals;

[0214] ② Mutation operation: For each individual, calculate its mutation probability according to the formula in the invention content. If the random number is small Then, a new individual is generated by randomly selecting a gene locus and modifying its wave number or carrier number.

[0215] Step 5: Termination Condition Determination

[0216] In each iteration, the optimal fitness of the current population is calculated, and the iteration terminates if any of the following conditions are met:

[0217] ① The number of iterations reached 1200 generations;

[0218] ② If the change in optimal fitness is less than 1e-4 over 150 consecutive generations, the algorithm is considered to have converged.

[0219] After the iteration terminates, the individual with the lowest fitness in the output population is output, and the corresponding multi-wave delivery scheduling scheme is decoded, including: the delivery wave of each combat squad and equipment, the number of the loaded hovercraft, the delivery sequence of each wave, the combat force composition, and core indicators such as total delivery time and cumulative combat effectiveness.

[0220] Implementation Results and Verification:

[0221] Example 1

[0222] Three classic algorithms suitable for scheduling optimization problems were selected for comparison: the traditional genetic algorithm (GA), particle swarm optimization (PSO), and simulated annealing (SA). These were solved in the same simulation environment as the improved genetic algorithm (EGA) proposed in this invention. Each experiment was independently repeated 10 times, and the comparison results of the core performance indicators are shown in Table 5.

[0223] Table 5. Detailed Results of Superiority Test

[0224]

[0225] The Gantt chart of the results obtained from the improved genetic algorithm is as follows: Figure 3 As shown, the nine waves were delivered in a strictly sequential manner, with the total delivery time of the system converging at 2760 minutes. The duration of each wave generally showed a pattern of longer duration at the beginning and shorter duration at the end.

[0226] The experimental results show that:

[0227] ① Solution Quality: The EGA algorithm of this invention performs optimally in core optimization metrics. The total system time is 2786.12 minutes, which is 25.8% shorter than GA, 25.7% shorter than PSO, and 19.6% shorter than SA. The cumulative combat effectiveness reaches 3274.04, which is 156.1% higher than GA, 96.7% higher than PSO, and 6.7% higher than SA. The fitness value is -0.006736 (the smaller the better), which is far superior to GA's 1000.85, PSO's 0.773742, and SA's 0.279239, indicating that the method of this invention has significant advantages in bi-objective optimization.

[0228] ② Convergence Performance: The average convergence number of the EGA algorithm in this invention is 1026.6 generations. GA and PSO both reached the maximum number of iterations of 1200 generations without complete convergence. Although SA converged the fastest (225 generations), the solution quality was poor. EGA achieved a good balance between convergence number and convergence quality, indicating that the improved adaptive crossover mutation operator and elite preservation strategy effectively improved the search efficiency.

[0229] ③ Stability: The fitness variance of the EGA algorithm in this invention is 0.000861, which is slightly higher than PSO (0.000759) and SA (0.000594), but far better than GA (0.174505), with a variance reduction of 99.5%. Considering the significant advantage of EGA in solution quality, this variance level is within an acceptable range, indicating that the algorithm has good robustness.

[0230] ④ Dual Objective Trade-off: The EGA algorithm of this invention outperforms the comparative algorithms in both total system time and cumulative combat effectiveness, achieving true dual-objective collaborative optimization. GA and PSO overemphasize one objective, leading to poor performance of the other, while SA gets trapped in local optima due to insufficient search capabilities. EGA achieves the optimal balance between the two objectives through a dynamic penalty function and a hybrid population initialization strategy.

[0231] In conclusion, the dual-objective optimization method for multi-wave scheduling of amphibious delivery based on particle swarm optimization outperforms traditional optimization algorithms in terms of solution quality, convergence performance, stability, and feasibility. It is particularly suitable for large-scale, multi-constraint amphibious operations delivery scheduling problems and has significant application value.

[0232] Example 2

[0233] Generality testing

[0234] This embodiment is used to verify the universality of the method of the present invention in combat scenarios of different scales.

[0235] Three simulated combat scenarios—small-scale, medium-scale, and large-scale—were designed, and the proposed method was used to optimize the multi-wave scheduling of amphibious delivery. The environmental parameters for each scenario are shown in Table 6.

[0236] Table 6 General Test Scenario Parameter Settings

[0237]

[0238] Each experiment was independently repeated 10 times. The solution results for the three scale scenarios are shown in Table 7.

[0239] Table 7. Details of Generality Test Results

[0240]

[0241] Results Analysis

[0242] ① Scalability: As the problem size increased from 128 dimensions to 1200 dimensions (an increase of about 9.4 times), the total system time increased from 3100.90 minutes to 5106.75 minutes (an increase of about 1.65 times), and the cumulative combat effectiveness increased from 1450.16 to 4045.52 (an increase of about 2.79 times), indicating that the algorithm has good scalability and can adapt to the needs of combat missions of different scales.

[0243] ② Solution quality: The cumulative combat effectiveness under the three scale scenarios increases significantly with the increase of scale. The effectiveness value of the large-scale scenario reaches 4045.52, indicating that the algorithm can effectively optimize the delivery scheme under different scales and give full play to the collaborative advantages of multiple ships and multiple waves.

[0244] ③ Convergence performance: The number of convergence generations remains stable as the problem size increases, without any sharp increase, indicating that the improved genetic algorithm designed in this invention has good convergence characteristics, and the two-layer encoding strategy and dynamic penalty function mechanism effectively control the expansion of the search space.

[0245] ④ Economies of scale: A comparison of the efficiency increase (2.79 times) and the time increase (1.65 times) shows that the method of the present invention has better economies of scale in large-scale scenarios. That is, the increase in combat efficiency brought about by the increase in the number of delivery units is greater than the increase in time cost. This is due to the effective mining of synergistic gains and the optimized allocation of wave resources by the algorithm.

[0246] in conclusion

[0247] Based on the above experimental results, it can be concluded that the amphibious delivery multi-wave scheduling dual-objective optimization method proposed in this invention can effectively solve amphibious delivery scheduling problems of three different scales: small-scale, medium-scale, and large-scale. It shows stability in key indicators such as total system time, cumulative combat effectiveness, and convergence speed, and has good versatility and application value.

[0248] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformations or equivalent substitutions fall within the scope of protection of the present invention; the parts of the present invention not described in detail are well-known technologies to those skilled in the art.

Claims

1. A multi-agent cooperative scheduling method for amphibious delivery based on an improved genetic algorithm, characterized in that, The amphibious delivery multi-agent cooperative scheduling method based on the improved genetic algorithm includes the following steps: Step 1: Construct a multi-agent effectiveness coordination model, which includes a transportation effectiveness coordination sub-model and a tactical effectiveness coordination sub-model. This model describes the mutual influence between the hovercraft and personnel / equipment, and establishes a multi-objective, strongly constrained optimization framework. Step 2: Employ a two-layer integer encoding strategy and a hybrid initial population strategy. The two-layer integer encoding strategy includes a wave allocation string and a vehicle allocation string. Step 3: The initial population is iteratively evolved using an improved genetic algorithm. Individuals in the population are updated through adaptive crossover and mutation operators to balance global search and local exploitation capabilities. The hybrid initial population strategy includes greedy feasible solutions, repaired random solutions, completely random solutions, and mutated excellent solutions. Step 4: Introduce a dynamic penalty function to handle the strong constraints of the model, complete the fitness assessment of individuals in the population and the selection of high-quality individuals, and generate the offspring population through an adaptive crossover and mutation operator; Step 5: Determine if the iteration termination condition is met. If it is, output the multi-wave delivery scheduling scheme corresponding to the individual with the best fitness. Otherwise, return to step 3 to continue iterative evolution.

2. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, Step 1 also includes the following steps: Step 11: Construct a multi-agent effectiveness synergy model. The decision variables of the multi-agent effectiveness synergy model include: Combat squad allocation variables are If the first The class of The combat squad was assigned to the first Waves One hovercraft, ,otherwise ; Equipment allocation variables are If the first The class of The equipment was allocated to the first Waves One hovercraft, ,otherwise ; Hovercraft scheduling variables are If the first 10 hovercraft participated in the wave, then ,otherwise ; Step 12: Based on the delivery and transportation process and vehicle attributes, integrate all operational links of the entire wave, clarify the temporal recursion relationship between waves, and construct a transportation efficiency collaboration model: ； in, , , , , , , They represent the first The time allotted for each wave of attack includes: preparation time for sortie, time to leave the mothership, time to form a wave, time to land on shore, time to unload on the beach, time to return to port, and time to rejoin the mothership. For the first The start time of the wave, For the first End time of the wave; Step 13: Establish a static basic tactical combat capability model and determine the inherent capability benchmarks of personnel and equipment; Step 14: Set constraints, including area load capacity constraints, number of hovercraft constraints, delivery timing constraints, hovercraft delivery process constraints, uniqueness constraints, and non-negativity constraints. S15: Establish a dual-objective optimization function: ； ； To minimize system delivery time, To maximize cumulative combat effectiveness.

3. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 2, characterized in that, In step 12, multiple hovercraft within the same wave will exhibit a significant queuing effect during the departure from the mothership, wave formation, and entry into the mothership phases: ； ； ； in, For the ship deployment coefficient, For the wave coding coefficient, This refers to the coefficient for entering the ship; 0-1 decision variables; , , These are the baseline fixed times for the processes of leaving the mothership, forming a wave, and entering the mothership when operating as a single vessel; This represents the total number of hovercraft. Considering the load-speed coupling characteristics of hovercraft, the time required for a single hovercraft to land is... Nonlinear decay with load factor: ； In the formula: This is the baseline time for an unloaded hovercraft to make an emergency landing. The load attenuation coefficient characterizes the extent to which the load factor affects the speed. The nonlinear exponent characterizes the nonlinear characteristics of speed decay; the landing time for a single wave of assault is taken as the maximum value of all participating hovercraft, i.e. .

4. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 2, characterized in that, In step 13, the first basic combat strength of the wave The sum of the inherent tactical values ​​of all combat teams and equipment deployed in this wave: ； in, , Each represents a single first Class of combat squads and individual first The basic tactical values ​​of this type of equipment The total number of combat squad categories, Let i be the total number of combat squads of type i. This represents the total number of categories of combat equipment. Let i be the total number of equipment of type i; When combat teams with complementary tactics and supporting equipment are deployed to land in the same wave, they can form a system-of-systems combat capability and generate synergy gains; synergy gains are calculated based on the principle of minimum matching. : ； in, Let be the element of the cooperative gain matrix, representing the th Type of combat squad and the first The coordination coefficient of this type of equipment and The first middle of wave Type of combat squad and the first The number of equipment types The function represents taking the smaller of the two values ​​as the number of effective cooperative units; The battlefield value of subsequent waves of troops decreases exponentially with delivery delay, and the time-effectiveness decay coefficient... for: ； The battlefield agility factor reflects the rate at which combat effectiveness decays with delivery time; a larger value indicates that the battlefield environment is more sensitive to the timing of delivery. No. Integrated combat effectiveness of waves for: ； These are the coupling weight coefficients.

5. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 2, characterized in that, In step 14, area load constraints: Each hovercraft participating in this wave must individually meet the load and area constraints and must not be overloaded. ； ； In the formula: , Each of the single first Weight and area occupied by a combat squad; , Each of the single first The weight and area occupied by this type of combat equipment; , These are the maximum load capacity and maximum carrying area limit for a single hovercraft, respectively. Hovercraft quantity constraint: The number of hovercraft used in each wave cannot exceed the total number of available hovercraft. ； In the formula: For the set of all delivery waves; Delivery timing constraints: The next wave can only begin delivery after the previous wave is completed. ； In the formula: To the maximum number of wavelets delivered, For the first +1 wave start time; Uniqueness constraint: Each combat squad and each piece of combat equipment can be deployed exactly once, and cannot be deployed repeatedly or omitted. ； ； Non-negativity constraint: All variables such as duration, combat power, gain, and coefficients must be non-negative.

6. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, In step 2, the first layer is the wave allocation string, the length of which is equal to the total number of delivery units, and the gene value represents the delivery wave of the corresponding unit; the second layer is the vehicle allocation string, the length of which is equal to the total number of delivery units, and the gene value represents the hovercraft number loaded by the corresponding unit.

7. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, In step 4, adaptive crossover probability and mutation probability The adjustment is based on the dynamic adjustment of the population fitness distribution, and the adjustment strategy is as follows: When an individual's fitness is greater than the population's average fitness, the crossover probability and mutation probability decrease linearly with the difference between the individual's fitness and the maximum fitness. When the fitness of an individual is less than the average fitness of the population, the crossover probability and mutation probability remain at preset constants. The calculation formula is as follows: ； ； in, For the maximum fitness of the population, For average fitness, The larger fitness value among the two individuals to be crossovered. The fitness value of the individual to be mutated. This is an adjustment coefficient, with a range of values. ; Dynamic penalty function The construction method is as follows: ； in, The penalty value is for the individual. For individuals, the constraints violate the measurement value. For iterative algebra The dynamic penalty coefficient changes. It monotonically increases with the iteration process, and its calculation formula is: ； in, Basic penalty factor, For iterative algebra.

8. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, In step 4, the fitness function After standardizing the two objectives, a weighted sum is taken, and a penalty term is added to obtain the individual fitness. The smaller the fitness value, the better the individual. ； In the formula: This is a standardized value for the total delivery time; Standardized values ​​for accumulated combat effectiveness; , The weighting coefficients for the two objectives satisfy... .

9. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, In step 5, the algorithm terminates the iteration under the following conditions:

1. Reach the preset maximum number of iterations. ; 2. Continuous The optimal fitness value of the next generation population did not improve significantly, indicating that the algorithm has converged.

10. The amphibious delivery multi-agent cooperative scheduling method based on an improved genetic algorithm according to claim 1, characterized in that, In step 5, after the iteration terminates, the individual with the lowest fitness in the output population is output, and the corresponding multi-wave delivery scheduling scheme is decoded, including: the delivery wave of each combat squad and equipment, the number of the loaded hovercraft, the delivery sequence of each wave, the combat force composition, and core indicators such as total delivery time and cumulative combat effectiveness.

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