A Multi-UAV Logistics Scheduling Method Based on Improved Fractional-Order Particle Swarm Optimization Algorithm

Abstract

The present invention proposes a multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm. First, for the multi-unmanned vehicle scheduling requirements in the logistics transportation scenario, a comprehensive optimization model is constructed. Secondly, an improved fractional-order particle swarm optimization algorithm is innovatively used to solve the above-mentioned combinatorial optimization problem. By introducing a fractional-order Levy step size adjustment mechanism, the limitation of the standard particle swarm optimization algorithm that only uses a uniform step size for optimization is broken through. And a dual adaptive adjustment mechanism is designed: one is the adaptive adjustment of the parameters of the particle swarm optimization algorithm, and the other is the adaptive adjustment of the Levy order. Finally, on the premise of ensuring that various constraint conditions are met, the multi-unmanned vehicle logistics scheduling combinatorial optimization model is solved based on the above objective function to obtain the optimal scheduling scheme. Compared with the prior art, the present invention uses the improved fractional-order particle swarm optimization algorithm solution, and this method has significant advantages in terms of solution accuracy and convergence efficiency.

Description

Technical Field

[0001] The invention relates to a multi-unmanned vehicle logistics scheduling method based on an improved fractional order particle swarm optimization (IFOPSO) algorithm, and belongs to the field of logistics scheduling. Background Art

[0002] With the rapid development of unmanned system technology, the advantages of drones, unmanned vehicles and unmanned boats in practical applications have become more and more significant, especially in logistics and transportation scenarios. Automated transportation based on unmanned systems has become an effective way to improve efficiency, reduce human interference and reduce costs. However, with the increasing complexity of transportation tasks, especially in the face of multi-point, multi-batch and multi-constrained tasks, the limitations of traditional single unmanned vehicle systems in resource scheduling, path planning and task execution have become increasingly prominent.

[0003] In contrast, multi-unmanned vehicle systems can demonstrate higher efficiency and reliability in larger-scale and more complex transportation scenarios through reasonable task allocation and resource integration. However, this also makes the task allocation and scheduling issues more complicated. Especially in a multi-constraint environment, how to reasonably allocate tasks to ensure transportation timeliness, improve the overall performance of the system, and achieve multi-vehicle collaboration has become a research problem that needs to be solved urgently.

[0004] In logistics and transportation tasks, factors such as time constraints, load capacity, and endurance are particularly critical. Therefore, how to reasonably consider these practical needs in multi-vehicle collaborative task allocation remains a challenging topic. Although existing research has made significant progress in path optimization and load balancing, the handling of time constraints in task allocation has not received sufficient attention, especially in dynamic scenarios involving multiple vehicles performing multiple tasks simultaneously.

[0005] The task allocation problem can usually be summarized as a mixed integer programming problem, and intelligent optimization algorithms have become an effective tool for solving this problem due to their high efficiency and flexibility. The particle swarm optimization (PSO) algorithm has been widely used in the task allocation of multi-unmanned systems due to its strong global search capability and low computational complexity. However, when faced with complex scenarios, the traditional PSO algorithm may fall into a local optimal solution, resulting in a decrease in search efficiency. To this end, some improved PSO algorithms have attempted to introduce more efficient global search strategies, but there are still challenges such as insufficient particle diversity and prominent local optimal solution problems in complex scenarios.

[0006] Therefore, it is of great significance to develop an improved fractional-order particle swarm optimization algorithm to achieve fast and effective multi-unmanned vehicle logistics scheduling tasks. Summary of the invention

[0007] The objective of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm.

[0008] The objective of the present invention can be achieved through the following technical solutions:

[0009] A multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm, comprising the following steps:

[0010] S1. Construct a multi-unmanned vehicle logistics scheduling combinatorial optimization model, set an objective function for the logistics transportation scenario, and the objective function is the minimum value of the sum of the travel cost, time violation cost, load violation cost, and unmanned vehicle startup cost; and construct the constraint conditions of the multi-unmanned vehicle logistics scheduling combinatorial optimization model, including decision variable constraints, maximum load constraints, maximum travel constraints, and time window constraints;

[0011] S2. Design an improved fractional-order particle swarm optimization algorithm, and the improved fractional-order particle swarm optimization algorithm improves the uniform step size optimization mechanism of the standard particle swarm optimization algorithm by constructing a fractional-order Levy step size adjustment mechanism;

[0012] S3. On the basis of the fractional-order Levy step size adjustment mechanism designed in step S2, further construct a dual adaptive adjustment mechanism, including a particle swarm optimization algorithm parameter adaptive adjustment mechanism and a Levy order adaptive adjustment mechanism, and the dual adaptive adjustment mechanism is used to enhance the diversity of particles in the optimization process and overcome the inherent defect that the particle swarm optimization algorithm is prone to falling into local optimum;

[0013] S4. On the premise of satisfying the constraint conditions of the multi-unmanned vehicle logistics scheduling combinatorial optimization model constructed in step S1, use the improved fractional-order particle swarm optimization algorithm designed in step S2 to solve the objective function in step S1 for the multi-unmanned vehicle logistics scheduling combinatorial optimization model to obtain the optimal scheduling plan.

[0014] As a preferred technical solution, the multi-unmanned vehicle logistics scheduling combinatorial optimization model described in step S1 is specifically expressed as:

[0015] ,

[0016] In the formula, is to minimize the total cost considering the sum of the travel cost, time violation cost, load violation cost, and unmanned vehicle startup cost; is the total travel cost; is the total cost of violating the pick-up and delivery time; is the total cost of violating the maximum load; is the total unmanned vehicle startup cost, where the total travel cost The expression of is:

[0017] ,

[0018] wherein, represents the driving distance of the driverless vehicle from task point to task point ; represents a decision variable, indicating whether the driverless vehicle has completed the section driving from task point to task point ; represents the total number of task points, represents the total number of driverless vehicles used;

[0019] The expression of the total cost of violating the pick-up and delivery time is:

[0020] ,

[0021] wherein, represents the penalty coefficient for the driverless vehicle arriving at the task point earlier than the earliest pick-up time, represents the penalty coefficient for the driverless vehicle arriving at the task point later than the latest pick-up time; represents the early arrival time of the driverless vehicle at task point , represents the late arrival time of the driverless vehicle at task point ; represents the pick-up time at the th task point;

[0022] The model of the early arrival time and the late arrival time is:

[0023] ,

[0024] wherein, represents the arrival time of the driverless vehicle at task point , represents the earliest service time of task point , represents the latest service time of task point ;

[0025] The expression of the total cost of violating the maximum load is:

[0026] ,

[0027] wherein, represents the penalty coefficient for violating the maximum load of the driverless vehicle, represents the driverless vehicle The weight of goods exceeding the maximum load in the entire path served

[0028] Total startup cost of the driverless vehicle The expression is as follows:

[0029] ,

[0030] In the formula, represents the startup cost of each driverless vehicle, represents the number of driverless vehicles used during the actual task execution.

[0031] As an optimal technical solution, the constraint conditions described in step S1 include decision variable constraints, maximum load constraints, maximum travel constraints, and time window constraints, where:

[0032] The decision variable constraint is:

[0033] ,

[0034] ,

[0035] In the formula, represents the pick-up and delivery relationship between task point and driverless vehicle ;

[0036] ,

[0037] ,

[0038] In the formula, represents the decision variable, indicating whether driverless vehicle has completed the section driving from task point to task point ;

[0039] The maximum load constraint is:

[0040] ,

[0041] In the formula, represents the pick-up quantity of each task point, represents the maximum capacity of driverless vehicle ;

[0042] The maximum travel constraint is:

[0043] ,

[0044] Wherein, represents the maximum travel distance limited for each driverless vehicle;

[0045] The time window constraint is:

[0046] ,

[0047] ,

[0048] Wherein, represents the early arrival time of the driverless vehicle at the task point , represents the late arrival time of the driverless vehicle at the task point .

[0049] As an optimized technical solution, the improved update formula of the improved fractional-order particle swarm optimization algorithm described in step S2 is:

[0050] ,

[0051] ,

[0052] ,

[0053] ,

[0054] ,

[0055] Wherein, represents the velocity of the particle in the th dimension, represents the inertia weight, represents the individual historical best position of the particle in the th dimension, represents the current position of the particle y in the th dimension, represents the historical best position of the entire population in the th dimension, represents the individual learning factor, represents the global learning factor, and represent random numbers subject to the Lévy distribution; represents the maximum value of the inertia weight, represents the minimum value of the inertia weight, represents the current iteration number, represents the maximum iteration number; represents the maximum value of the individual learning factor, Represents the minimum value of the individual learning factor, Represents the maximum value of the global learning factor, Represents the minimum value of the global learning factor;

[0056] The fractional-order Lévy distribution described in step S2 is:

[0057] A random variable Satisfies The Lévy stable distribution whose characteristic function satisfies the following form

[0058] ,

[0059] In the formula, Represents the location parameter, that is, the mean value of the Lévy stable distribution; Represents the symmetry parameter, that is, the skewness of the Lévy distribution, usually ; Represents the characteristic exponent, that is, the Lévy order in the Lévy distribution, The smaller it is, the stronger the impulsiveness and the easier it is to deviate from the central position, Corresponds to the Gaussian distribution when Represents the scale parameter, which affects the "width" of the distribution, denoted by Represents a Lévy stable distribution, that is, the Lévy distribution.

[0060] As a preferred technical solution, the Lévy order adaptive adjustment mechanism described in step S3:

[0061] ,

[0062] In the formula, Represents the minimum value of the Lévy order, Represents the maximum value of the Lévy order.

[0063] As a preferred technical solution, the specific method in step S4 is:

[0064] S41. Data preparation and initialization: Read the logistics scenario data, including the location of the logistics center, the coordinates of the pick-up points, the task volume of the pick-up points, and the service time; Set the basic parameters of the unmanned vehicle, including the number of unmanned vehicles and the maximum loading capacity of each unmanned vehicle; Initialize the particle swarm optimization algorithm parameters, set the population size , the initial number of iterations , the maximum number of iterations , the minimum value of the inertia weight , the maximum value , the minimum value of the individual learning factor , the maximum value , the minimum value of the global learning factor , the maximum value , Levy order , maximum Levy order , minimum value ;

[0065] S42. Construct a logistics scheduling model: Construct a logistics scheduling model with the objective function of minimizing the sum of travel cost, time violation cost, load violation cost, and unmanned vehicle startup cost, and establish constraint conditions, including maximum load constraint, maximum travel constraint, and time window constraint;

[0066] S43. Initialize the particle swarm: Use a heuristic method to construct an initial solution, randomly generate the positions and velocities of the particles, and calculate the initial objective function value. Record the individual optimal positions and objective values of each particle, as well as the global optimal position and objective value;

[0067] S44. Iterative optimization: Update the particle velocities and positions according to the improved fractional order particle swarm algorithm, decode the particle positions into transportation plans, and perform local search optimization. Calculate the total cost of the current transportation plan, and update the individual optimal and global optimal;

[0068] S45. Local search optimization of the global optimal solution: Decode the global optimal solution and further optimize the global optimal transportation plan;

[0069] S46. Output the results: Calculate and output the final total cost, and visualize the evolution curve.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] A multi-unmanned vehicle logistics scheduling method based on an improved fractional order particle swarm algorithm provided by the present invention first constructs a multi-unmanned vehicle pick-up and delivery task scheduling combination optimization model covering travel cost, time violation cost, load violation cost, and startup cost. Then, an improved fractional order particle swarm algorithm (improved fractional order particle swarm optimization, abbreviated as IFOPSO) is proposed. By introducing a fractional order Levy random step size into the particle swarm algorithm (PSO), the global search ability of PSO is improved, and an adaptive adjustment mechanism for the Levy order is further designed to improve the convergence accuracy and optimization performance of IFOPSO. Finally, the IFOPSO algorithm is applied to solve the multi-unmanned vehicle task allocation problem, and through comparative experiments with the traditional particle swarm algorithm (abbreviated as PSO), the improved particle swarm algorithm (abbreviated as IPSO), and the fractional order particle swarm algorithm (abbreviated as FOPSO), the results show that the algorithm can effectively reduce the scheduling cost and quickly find a reasonable logistics scheduling plan. Description of the Drawings

[0072] Figure 1Schematic diagram of multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm provided by the present invention;

[0073] Figure 2 Comparison schematic diagram of Levy distribution and uniform distribution under 350 random values;

[0074] Figure 3 Schematic diagram of the "long tail" of Levy random step size;

[0075] Figure 4 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviation: PSO), improved particle swarm optimization algorithm (abbreviation: IPSO), fractional-order particle swarm optimization algorithm (abbreviation: FOPSO) and the multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviation: IFOPSO) provided by the present invention at position 1 described in the embodiment;

[0076] Figure 5 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviation: PSO), improved particle swarm optimization algorithm (abbreviation: IPSO), fractional-order particle swarm optimization algorithm (abbreviation: FOPSO) and the multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviation: IFOPSO) provided by the present invention at position 2 described in the embodiment;

[0077] Figure 6 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviation: PSO), improved particle swarm optimization algorithm (abbreviation: IPSO), fractional-order particle swarm optimization algorithm (abbreviation: FOPSO) and the multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviation: IFOPSO) provided by the present invention at position 3 described in the embodiment;

[0078] Figure 7 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviation: PSO), improved particle swarm optimization algorithm (abbreviation: IPSO), fractional-order particle swarm optimization algorithm (abbreviation: FOPSO) and the multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviation: IFOPSO) provided by the present invention at position 4 described in the embodiment;

[0079] Figure 8 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviation: PSO), improved particle swarm optimization algorithm (abbreviation: IPSO), fractional-order particle swarm optimization algorithm (abbreviation: FOPSO) and the multi-unmanned vehicle logistics scheduling in the logistics transportation scenario of the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviation: IFOPSO) provided by the present invention at position 5 described in the embodiment;

[0080] Figure 9 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviated as PSO), improved particle swarm optimization algorithm (abbreviated as IPSO), and fractional-order particle swarm optimization algorithm (abbreviated as FOPSO) with the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviated as IFOPSO) provided by the present invention under the logistics transportation scenario with 20 pick-up points for multi-unmanned vehicle logistics scheduling;

[0081] Figure 10 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviated as PSO), improved particle swarm optimization algorithm (abbreviated as IPSO), and fractional-order particle swarm optimization algorithm (abbreviated as FOPSO) with the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviated as IFOPSO) provided by the present invention under the logistics transportation scenario with 30 pick-up points for multi-unmanned vehicle logistics scheduling;

[0082] Figure 11 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviated as PSO), improved particle swarm optimization algorithm (abbreviated as IPSO), and fractional-order particle swarm optimization algorithm (abbreviated as FOPSO) with the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviated as IFOPSO) provided by the present invention under the logistics transportation scenario with 50 pick-up points for multi-unmanned vehicle logistics scheduling;

[0083] Figure 12 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviated as PSO), improved particle swarm optimization algorithm (abbreviated as IPSO), and fractional-order particle swarm optimization algorithm (abbreviated as FOPSO) with the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviated as IFOPSO) provided by the present invention under the logistics transportation scenario with 80 pick-up points for multi-unmanned vehicle logistics scheduling;

[0084] Figure 13 Convergence curve comparison of the traditional particle swarm optimization algorithm (abbreviated as PSO), improved particle swarm optimization algorithm (abbreviated as IPSO), and fractional-order particle swarm optimization algorithm (abbreviated as FOPSO) with the multi-unmanned vehicle logistics scheduling method based on the improved fractional-order particle swarm optimization algorithm (abbreviated as IFOPSO) provided by the present invention under the logistics transportation scenario with 100 pick-up points for multi-unmanned vehicle logistics scheduling;

[0085] Figure 14 It is the method flow chart of the present invention. Detailed implementation manners

[0086] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0087] As Figure 14 shown, a multi-AGV logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm in this embodiment includes the following steps:

[0088] S1. Construct a multi-AGV logistics scheduling combinatorial optimization model, set an objective function for the logistics transportation scenario, and the objective function is the minimum value of the sum of the travel cost, time violation cost, load violation cost, and AGV startup cost; and construct the constraint conditions of the multi-AGV logistics scheduling combinatorial optimization model, including decision variable constraints, maximum load constraints, maximum travel constraints, and time window constraints;

[0089] S2. Design an improved fractional-order particle swarm optimization algorithm, and the improved fractional-order particle swarm optimization algorithm improves the uniform step size optimization mechanism of the standard particle swarm optimization algorithm by constructing a fractional-order Levy step size adjustment mechanism;

[0090] S3. On the basis of the fractional-order Levy step size adjustment mechanism designed in step S2, further construct a dual adaptive adjustment mechanism, including the particle swarm optimization algorithm parameter adaptive adjustment mechanism and the Levy order adaptive adjustment mechanism, and the dual adaptive adjustment mechanism is used to enhance the diversity of particles in the optimization process and overcome the inherent defect that the particle swarm optimization algorithm is prone to falling into local optimum;

[0091] S4. On the premise of satisfying the constraint conditions of the multi-AGV logistics scheduling combinatorial optimization model constructed in step S1, use the improved fractional-order particle swarm optimization algorithm designed in step S2 to solve the objective function described in step S1 for the multi-AGV logistics scheduling combinatorial optimization model to obtain the optimal scheduling plan.

[0092] The multi-AGV logistics scheduling combinatorial optimization model described in step S1 of this embodiment is specifically expressed as:

[0093] ,

[0094] In the formula, is to consider the minimum total cost of the sum of the travel cost, time violation cost, load violation cost, and AGV startup cost; is the total travel cost; is the total cost of violating the pick-up and delivery time; is the total cost of violating the maximum load; is the total AGV startup cost, where the total travel cost The expression of is:

[0095] ,

[0096] In the formula, represents AGV from task point to task point The driving distance represents a decision variable, indicating the driverless vehicle whether it has completed the section driving from the task point to the task point is denotes the total number of task points represents the total number of driverless vehicles used;

[0097] The total cost of violating the pick-up and delivery time The expression is:

[0098] ,

[0099] In the formula, represents the penalty coefficient for the driverless vehicle arriving at the task point earlier than the earliest pick-up time represents the penalty coefficient for the driverless vehicle arriving at the task point later than the latest pick-up time; represents the early arrival time of the driverless vehicle at the task point is represents the late arrival time of the driverless vehicle at the task point is represents at the th task point's pick-up time;

[0100] The early arrival time and the late arrival time The model is:

[0101] ,

[0102] In the formula, represents the time when the driverless vehicle arrives at the task point is represents the earliest service time of the task point is represents the latest service time of the task point is

[0103] The total cost of violating the maximum load The expression is:

[0104] ,

[0105] In the formula, represents the penalty coefficient for violating the maximum load of the driverless vehicle represents the driverless vehicle the weight of the goods exceeding the maximum load in the entire path served;

[0106] The total start-up cost of the driverless vehicle The expression is:

[0107] ,

[0108] In the formula, represents the start-up cost of each driverless vehicle, represents the number of driverless vehicles used during the actual task execution.

[0109] The constraint conditions described in step S1 of this embodiment include decision variable constraint, maximum load constraint, maximum travel constraint, and time window constraint, where:

[0110] The decision variable constraint is:

[0111] ,

[0112] ,

[0113] In the formula, represents the pick-up and delivery relationship between task point and driverless vehicle .

[0114]

[0115] ,

[0116] In the formula, represents a decision variable, indicating whether driverless vehicle has completed the road section driving from task point to task point .

[0117] The maximum load constraint is:

[0118] ,

[0119] In the formula, represents the pick-up quantity of each task point, represents the maximum capacity of driverless vehicle .

[0120] The maximum travel constraint is:

[0121] ,

[0122] In the formula, represents the maximum travel limit of each driverless vehicle;

[0123] The time window constraint is:

[0124] ,

[0125] ,

[0126] In the formula, represents the early arrival time of the driverless vehicle at the task point of. represents the late arrival time of the driverless vehicle at the task point of.

[0127] The improved update formula of the improved fractional-order particle swarm algorithm described in step S2 of this embodiment is:

[0128] ,

[0129] ,

[0130] ,

[0131] ,

[0132] ,

[0133] In the formula, represents the velocity of particle in the th dimension, represents the inertia weight, represents particle in the th dimension of the individual historical best position, represents particle y in the th dimension of the current position, represents the entire population in the th dimension of the historical best position, represents the individual learning factor, represents the global learning factor, and represent random numbers subject to the Levy distribution; represents the maximum value of the inertia weight, represents the minimum value of the inertia weight, represents the current iteration number, represents the maximum number of iterations; represents the maximum value of the individual learning factor, represents the minimum value of the individual learning factor, represents the maximum value of the global learning factor, represents the minimum value of the global learning factor;

[0134] The fractional-order Levy distribution described in step S2 is:

[0135] A random variable satisfies The Lévy stable distribution is defined as its characteristic function satisfying the following form

[0136] ,

[0137] wherein represents the location parameter, i.e., the mean value of the Lévy stable distribution; represents the symmetry parameter, i.e., the skewness of the Lévy distribution, usually ; represents the characteristic exponent, i.e., the Lévy order in the Lévy distribution, the smaller it is, the stronger the impulsiveness and the easier it is to deviate from the central position, corresponds to the Gaussian distribution when represents the scale parameter, which affects the "width" of the distribution, and denotes a Lévy stable distribution, i.e., the Lévy distribution. As Figure 2 shown, it shows the comparison between the Lévy distribution and the uniform distribution under 350 random values.

[0138] The Lévy distribution is a long-tailed distribution with frequent short jumps and occasional long jumps. As Figure 3 shown, it enables particles to make relatively large jumps in space. Lévy flight can capture unusual or rare events and enhance the global search ability. The advantage of the fractional Lévy random step size lies in its multiple large-step perturbations, which helps to improve the global convergence performance.

[0139] The Lévy order adaptive adjustment mechanism described in step S3 of this embodiment:

[0140] ,

[0141] wherein represents the minimum value of the Lévy order, represents the maximum value of the Lévy order.

[0142] The specific method in step S4 of this embodiment is as follows:

[0143] S41. Data preparation and initialization: Read the logistics scenario data, including the location of the logistics center, the coordinates of the pick-up points, the task volume of the pick-up points, and the service time; Set the basic parameters of the unmanned vehicle, including the number of unmanned vehicles and the maximum loading capacity of each unmanned vehicle; Initialize the parameters of the particle swarm algorithm, set the population size , the initial number of iterations , the maximum number of iterations , the minimum value of the inertia weight , the maximum value , the minimum value of the individual learning factor , maximum value , minimum value of global learning factor , maximum value , Levy order , maximum value of Levy order , minimum value ;

[0144] S42. Construct a logistics scheduling model: Construct a logistics scheduling model with the objective function of minimizing the sum of travel cost, time violation cost, load violation cost, and AGV startup cost, and establish constraint conditions, including maximum load constraint, maximum travel constraint, and time window constraint;

[0145] S43. Initialize the particle swarm: Use a heuristic method to construct an initial solution, randomly generate the positions and velocities of particles, calculate the initial objective function value, and record the individual optimal positions and objective values of each particle, as well as the global optimal position and objective value;

[0146] S44. Iterative optimization: Update the particle velocities and positions according to the improved fractional-order particle swarm algorithm, decode the particle positions into transportation plans, and perform local search optimization. Calculate the total cost of the current transportation plan, and update the individual optimal and global optimal;

[0147] S45. Local search optimization of the global optimal solution: Decode the global optimal solution and further optimize the global optimal transportation plan;

[0148] S46. Output the results: Calculate and output the final total cost, and visualize the evolutionary curve.

[0149] Implementation verification example:

[0150] As Figure 1 shown, select the logistics scheduling system of a certain logistics center as the research object, which includes a logistics center, pick-up locations, AGVs, goods (compatible in nature and can be transported together), etc. The simulation experiment parameters are shown in Table 1. The startup cost of each AGV is 100 yuan, the maximum load is 200 kg, the maximum travel is 50 km, and the goods transportation occurs within a certain range. The location information of the logistics center, pick-up locations, goods weights, and time windows for positions 1, 2, 3, 4, 5, as well as 20 pick-up points, 30 pick-up points, 50 pick-up points, 80 pick-up points, and 100 pick-up points, are randomly selected within the allowed map and time range as the initial input of the experiment. Read the document containing the above information at the beginning of the program for simulation experiments.

[0151] Table 1. Simulation experiment parameters

[0152]

[0153] To verify the rationality of the model proposed in this invention, the following conducts a comparative analysis on two types of scenarios: the simulation experiment results under different relative positions and the simulation experiment results under different numbers of pick-up points. Each algorithm runs independently 20 times for each group of experiments and takes the average value:

[0154] Scenario 1: Consider the simulation experiment under different relative positions. The comparative analysis of the experimental results is shown in Table 2. The convergence curves of positions 1, 2, 3, 4, and 5 are shown in Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 respectively.

[0155] Table 2. Comparative results of simulation experiments under different relative positions

[0156]

[0157] It can be seen from the experimental results of the five groups with different relative positions that although in the first, third, fourth, and fifth groups of experiments, the timeliness rate and overloading rate of the IFOPSO algorithm are slightly lower than those of the PSO, IPSO, and FOPSO algorithms, and it does not achieve the optimal performance in all indicators. This also reflects the essential characteristics of the combinatorial optimization problem, that is, when solving the combinatorial optimization problem, it usually involves multiple conflicting objectives or constraints, and it is impossible to optimize all indicators simultaneously by weighing. However, in terms of the total cost obtained by the planning, the IFOPSO algorithm always shows the best results. The total cost differences in each group of experiments are not significant, but the value of the IFOPSO algorithm is always the lowest. The simulation experiment results show that the IFOPSO algorithm can effectively reduce the total cost in the multi-AGV collaborative task allocation problem with different relative positions, find a better pick-up and delivery plan, and demonstrate its advantages in comprehensive performance.

[0158] Scenario 2: Consider the simulation experiment under different numbers of pick-up points. The comparative analysis of the experimental results is shown in Table 3. The convergence curves for the number of pick-up points of 20, 30, 50, 80, and 100 are shown in Figure 9 , Figure 10 , Figure 11 , Figure 12 , Figure 13 respectively.

[0159] Table 3. Comparative results of experiments under different numbers of pick-up points

[0160]

[0161] As can be seen from Table 3, in the 5 experimental scenarios, the average total cost of the IFOPSO algorithm is better than that of the other 3 PSO algorithms. In the scenarios with 20, 30, and 100 pick-up points, the three evaluation indicators of the IFOPSO algorithm are better than those of the other 3 algorithms; in the scenario with 50 pick-up points, although the standard PSO algorithm achieves the optimal value in the overloading rate index of the unmanned vehicle, the result of the IFOPSO algorithm only differs from it by 0.7%, showing good competitiveness; in the scenario with 80 pick-up points, the IPSO algorithm performs optimally in the timeliness index, but the timeliness of the IFOPSO algorithm only differs from it by 1.25%, still maintaining a high level. The simulation experiment results show that as the number of pick-up points increases, the IFOPSO algorithm can still maintain excellent performance, find a better pick-up plan in complex scenarios, and demonstrate its good adaptability and optimization ability.

[0162] In summary, the present invention provides a multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm algorithm. First, analyze the multi-unmanned vehicle logistics scheduling tasks in the logistics transportation scenario, and construct a logistics scheduling model with the minimum sum of travel cost, time violation cost, load violation cost, and unmanned vehicle startup cost as the objective function; then, construct a fractional-order Levy step size adjustment mechanism; construct a Levy order adaptive adjustment mechanism; construct an improved fractional-order particle swarm algorithm based on the constructed fractional-order Levy step size mechanism and Levy order adaptive adjustment mechanism; finally, under the satisfaction of the constraint conditions, perform an optimal solution to the multi-unmanned vehicle logistics scheduling combination optimization model in the logistics transportation scenario based on the MATLAB platform. Compared with the prior art, the present invention can improve the problem that the particle swarm algorithm falls into local optimum in optimization, and the proposed improved fractional-order particle swarm algorithm provides a reference for solving the multi-unmanned vehicle logistics scheduling.

[0163] The above has described in detail the preferred specific embodiments of the present invention. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm, characterized in that The method includes the following steps: S1. Construct a multi-AGV logistics scheduling combinatorial optimization model, set an objective function for the logistics transportation scenario, and the objective function is the minimum value of the sum of the travel cost, time violation cost, load violation cost, and AGV startup cost; and construct the constraint conditions of the multi-AGV logistics scheduling combinatorial optimization model, including decision variable constraints, maximum load constraints, maximum travel constraints, and time window constraints; S2. Design an improved fractional-order particle swarm optimization algorithm, and the improved fractional-order particle swarm optimization algorithm improves the uniform step-size optimization mechanism of the standard particle swarm optimization algorithm by constructing a fractional-order Levy step-size adjustment mechanism; S3. On the basis of the fractional-order Levy step-size adjustment mechanism designed in step S2, further construct a dual adaptive adjustment mechanism, including a particle swarm optimization algorithm parameter adaptive adjustment mechanism and a Levy order adaptive adjustment mechanism, and the dual adaptive adjustment mechanism is used to enhance the diversity of particles in the optimization process and overcome the inherent defect that the particle swarm optimization algorithm is prone to falling into local optimum; S4. On the premise of satisfying the constraint conditions of the multi-AGV logistics scheduling combinatorial optimization model constructed in step S1, use the improved fractional-order particle swarm optimization algorithm designed in step S2 to solve the objective function described in step S1 for the multi-AGV logistics scheduling combinatorial optimization model to obtain the optimal scheduling plan; The improved update formula of the improved fractional-order particle swarm optimization algorithm described in step S2 is: v y,d = ω·ν y,d + c1·levy(β1)·(p y,d - x y,d ) + c2·levy(β2)·(g d - x y,d ) X y (t + 1)= X y (t)+ V y (t + 1) where, v y,d represents the velocity of particle y in the d-th dimension, ω represents the inertia weight, p y,d represents the individual historical best position of particle y in the d-th dimension, x y,d represents the current position of particle y in the d-th dimension, g d represents the historical best position of the entire population in the d-th dimension, c1 represents the individual learning factor, c2 represents the global learning factor, levy(β1) and levy(β2) represent random numbers obeying the Levy distribution; ω max represents the maximum value of the inertia weight, ω min represents the minimum value of the inertia weight, gen represents the current iteration number, gen max represents the maximum iteration number; c 1max represents the maximum value of the individual learning factor, c 1min represents the minimum value of the individual learning factor, c 2max represents the maximum value of the global learning factor, c 2min represents the minimum value of the global learning factor; The fractional-order Levy distribution described in step S2 is: A random variable Y satisfying the Levy stable distribution with 0 < α ≤ 2 means that its characteristic function satisfies the following form Wherein, μ represents the location parameter, i.e., the mean value of the Lévy stable distribution; β represents the symmetry parameter, i.e., the skewness of the Lévy distribution, -1 ≤ β ≤ 1; α represents the characteristic exponent, i.e., the Lévy order in the Lévy distribution. The smaller α is, the stronger the impulsiveness is, and the easier it is to deviate from the central position. When α = 2, it corresponds to the Gaussian distribution; σ represents the scale parameter, which affects the "width" of the distribution, denoted by S α (μ, β, σ) represents a Lévy stable distribution, i.e., the Lévy distribution; The Levy order adaptive adjustment mechanism described in step S3: where α min represents the minimum value of the Lévy order, and α max represents the maximum value of the Lévy order.

2. The multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm according to claim 1, wherein The multi-AGV logistics scheduling combinatorial optimization model described in step S1 is specifically expressed as: min F = f1 + f2 + f3 + f4 In the formula, min F is the lowest total cost considering the sum of the travel cost, time violation cost, load violation cost, and AGV startup cost; f1 is the total travel cost; f2 is the total cost of violating the pick-up and delivery time; f3 is the total cost of violating the maximum load; f4 is the total AGV startup cost, where the expression of the total travel cost f1 is: Where d ij represents the driving distance of the driverless vehicle U k from the task point T i to the task point T j , x ijk represents a decision variable, indicating whether the driverless vehicle U k has completed the section driving from the task point T i to the task point T j . n represents the total number of task points, and K represents the total number of driverless vehicles used; The expression of the total cost f2 of violating the pick-up and delivery time is: Wherein, c z represents the penalty coefficient for the unmanned vehicle arriving at the task point earlier than the earliest pick-up time, and c w represents the penalty coefficient for the unmanned vehicle arriving at the task point later than the latest pick-up time; represents the early arrival time of the unmanned vehicle at task point T i , represents the late arrival time of the unmanned vehicle at task point T i , represents the pick-up time at the i-th task point; Early arrival time and late arrival time The model is as follows: Wherein, S i represents the time when the driverless vehicle arrives at the task point T i , ET i represents the earliest service time of the task point T i , WT i represents the latest service time of the task point T i ; The expression of the total cost f3 of violating the maximum load is: where c3 represents the penalty coefficient for violating the maximum load of the driverless vehicle, and q kv represents the weight of the goods exceeding the maximum load in the entire path served by the driverless vehicle U k ​ The expression of the total AGV startup cost f4 is: f4 = A × K k Where A represents the startup cost of each driverless vehicle, and K k represents the number of driverless vehicles used during the actual task execution.

3. A multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm according to claim 1, characterized in that The constraint conditions described in step S1 include decision variable constraints, maximum load constraints, maximum travel constraints, and time window constraints, where: The decision variable constraint is: where y ik represents the pick-up and delivery relationship i between the task point T k and the driverless vehicle U where x ijk represents a decision variable, indicating whether the unmanned vehicle U k has completed the section driving from task point T i to task point T j ; The maximum load constraint is: where q i represents the pick-up quantity of each task point, and Q k represents the maximum capacity of the driverless vehicle U k . The maximum travel constraint is: where L max represents the maximum travel distance limited for each driverless vehicle; The time window constraint is: In the formula, represents the early arrival time of the driverless vehicle at task point T i , and represents the late arrival time of the driverless vehicle at task point T i .

4. A multi-unmanned vehicle logistics scheduling method based on an improved fractional-order particle swarm optimization algorithm according to claim 1, characterized in that, The specific method in step S4 is: S41. Data Preparation and Initialization: Read logistics scenario data, including the location of the logistics center, the coordinates of the pick-up points, the task volume of the pick-up points, and the service time; Set the basic parameters of the unmanned vehicle, including the number of unmanned vehicles and the maximum load capacity of each unmanned vehicle; Initialize the parameters of the particle swarm optimization algorithm, set the population size N, the initial number of iterations gen, the maximum number of iterations maxgen, the minimum value of the inertia weight ω min , the maximum value of ω max , the minimum value of the individual learning factor c 1mi , the maximum value of c 1max , the minimum value of the global learning factor c 2min , the maximum value of c 2max , the Levy order α, the maximum value of the Levy order α max , the minimum value of α min ; S42. Construct a logistics scheduling model: Construct a logistics scheduling model with the minimization of the sum of the travel cost, time violation cost, load violation cost, and AGV startup cost as the objective function, and establish constraint conditions, including maximum load constraints, maximum travel constraints, and time window constraints; S43. Initialize the particle swarm: Use a heuristic method to construct an initial solution, randomly generate the positions and velocities of the particles, and calculate the initial objective function value, record the individual optimal positions and objective values of each particle, as well as the global optimal position and objective value; S44. Iterative optimization: Update the particle velocity and position according to the improved fractional-order particle swarm optimization algorithm, decode the particle position into a transportation plan, perform local search optimization, calculate the total cost of the current transportation plan, and update the individual optimal and global optimal solutions; S45. Local search optimization of the global optimal solution: Decode the global optimal solution and further optimize the global optimal transportation plan; S46. Output results: Calculate and output the final total cost and visualize the evolutionary curve.

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