Dynamic information entropy-based PSO method for optimization design of size parameters of combined load unit

Abstract

The application discloses a kind of based on dynamic information entropy PSO's combined unit load size parameter optimization design method, belongs to "railway and water" container freight field.The application first models the packing process of combined unit load and clearly defines its constraint condition;Then minimum value and constraint condition of integrated space loss rate are used to build optimization model;Next, in PSO optimization algorithm, respectively, construct dynamic search space solution strategy and dynamic weight parameter adjustment strategy based on information entropy;Finally, the entire optimization process is realized by software programming, i.e. only need to provide the internal dimension parameter of common container unit can automatically solve the optimal size parameter of unit load.The application effectively solves the problem of low efficiency and experience limitation caused by artificial determination of unit load size parameter on the one hand, and the proposed dynamic information entropy PSO also improves the iteration solving speed and solving accuracy of traditional PSO optimization algorithm on the other hand.

Description

Technical Field

[0001] This invention belongs to the field of "road-rail-water" containerized freight technology, specifically involving a method for optimizing the size parameters of modular transport units based on dynamic information entropy (PSO). Background Technology

[0002] In the context of economic globalization and ever-increasing logistics demands, developing containerized freight technology and equipment for road-rail-water transport is a crucial way to reduce logistics costs and improve efficiency. Traditional wooden or iron pallets, as a type of transport unit, primarily play the role of loading goods in road-rail-water containerized freight transport. However, the size and modularity of these transport units directly affect the space utilization rate of standardized containers. Therefore, improving and innovating the size and structure of traditional pallets to develop a modular transport unit with higher space utilization is a significant undertaking. Pallets are merely planar loading devices, with their main dimensions being length and width; they lack vertical load-bearing capacity. Conversely, modular transport units are loading devices with vertical load-bearing capacity, involving more dimensional optimization variables and related constraints. Currently, optimization algorithms, such as PSO (Particle Swarm Optimization), still use fixed search spaces and fixed weights to find the optimal solution, which negatively impacts their convergence speed and solution accuracy. Therefore, developing an optimization design method with faster iteration speed and higher solution accuracy for combined transport units is of great significance for promoting the transformation and upgrading of road-rail intermodal transport equipment. Summary of the Invention

[0003] To address the problems existing in the prior art, the purpose of this invention is to provide a method for optimizing the size parameters of modular transport units based on dynamic information entropy (PSO). First, the packing process of the transport units is parametrically modeled. Then, an optimization model containing constraints and minimizing space loss is constructed. Finally, a dynamic search space solution strategy based on information entropy and a dynamic weight parameter adjustment strategy are introduced into the traditional PSO algorithm, providing a more accurate and faster solution method for optimizing the size of transport units.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A dynamic information entropy PSO optimization algorithm for the design of combined transport unit size parameters is presented, and the specific steps of the algorithm are as follows:

[0006] Step 1: Perform parametric modeling based on the packing process of the modular transport unit and define the constraints;

[0007] Step 2: Construct an optimization model using the minimum comprehensive spatial loss rate and constraints;

[0008] Step 3: In the PSO optimization algorithm, a dynamic search space solution strategy based on information entropy is constructed, and the information entropy formula is used to obtain the change scale of the solution space before each round of iteration optimization of the carrier unit size parameter;

[0009] Step 4: In the PSO optimization algorithm, construct a dynamic weight parameter adjustment strategy; so that before each iteration of optimizing the carrier unit size parameters, the weight parameters can be adjusted in real time according to the exponential decay characteristic.

[0010] The specific method for parametrically modeling and defining constraints based on the packing process of the modular transport unit is as follows:

[0011] (1) The internal storage space of the standardized container numbered i is modeled as a regular cuboid, the volume of which can be mathematically described as

[0012] V i =L i ×W i ×H i ,i=1,2,…,M (1)

[0013] Where M represents the total number of common container types that need to be considered; L i W i H i These represent the dimensional parameters of the container's interior in the length, width, and height directions, respectively.

[0014] (2) The effective volume occupied by the transport unit to be optimized after being loaded into the i-th type of container can be expressed in the following form:

[0015] v i =N i ×l×w×h (2)

[0016] Where, N i Let represent the total number of transport units loaded in the i-th type of container, and l, w, and h represent the length, width, and height of the transport unit, respectively. Then, the constraints of the loading process can be expressed as follows:

[0017] v i ≤V i ,i=1,2,…M (3)

[0018]

[0019] in, V represents the total mass of the transport unit and its cargo. i g This indicates the rated load capacity of the i-th type of container.

[0020] The specific method for constructing an optimization model using the minimum comprehensive space loss rate and constraints is as follows:

[0021] (1) The ratio of the remaining space volume after the transport unit is loaded into the container to the total volume of the container can be expressed as:

[0022] S i =V i -v i / V i (4)

[0023] (2) Averaging these ratios yields the overall space loss rate. According to formula (4), the overall space loss rate of the transport unit to be optimized after loading into different types of containers is expressed in the following form:

[0024]

[0025] Based on formulas (3) and (5), the following optimization model can be constructed:

[0026]

[0027] Here, f(h) represents the objective function to be optimized.

[0028] The specific method for constructing the dynamic search space solution strategy based on information entropy is as follows:

[0029] (1) Based on the upper bound U of the solution space corresponding to the j-th optimization variable B,j and the lower bound U L,j Solve for the length of the interval

[0030] (2) Equal intervals to split into Q j Sub-intervals.

[0031] (3) For each subspace, calculate the ratio of the number of particles falling in this subspace to the total number of particles K set in the initialization phase, denoted as p. j,l ,l=1,2,…,Q j .

[0032] (4) According to the definition of information entropy formula, the change scale of the solution space corresponding to the j-th optimization variable in the t-th iteration can be calculated:

[0033]

[0034] Where, p t,j,l It represents the ratio of the number of particles related to the j-th optimization variable distributed in the l-th sub-interval to the total number of particles K during the t-th iteration.

[0035] (5) During the t-th iteration, calculate the average value of the feasible solutions related to the j-th optimization variable, denoted as . Find the optimal solution related to the j-th optimization variable, denoted as .

[0036] (6) In the (t+1)th iteration, the upper bound of the solution space related to the j-th optimization variable is expressed as:

[0037]

[0038] Where β represents the scaling factor.

[0039] (7) If Then, in the (t+1)th iteration, the upper bound of the solution space related to the j-th optimization variable should be expressed as:

[0040]

[0041] (8)If U B,t+1,j >U B,0,j In the (t+1)th iteration, the upper bound of the solution space related to the j-th optimization variable is expressed as:

[0042] U B,t+1,j =U B,0,j (10)

[0043] Among them, U B,0,j This represents the maximum boundary value set for the j-th optimization variable during the initialization phase.

[0044] (9) In the (t+1)th iteration, the lower bound of the solution space related to the j-th optimization variable is expressed as:

[0045]

[0046] (10) If Then, in the (t+1)th iteration, the lower bound of the solution space related to the j-th optimization variable should be expressed as:

[0047]

[0048] (11)If U L,t+1,j <U L,0,j In the (t+1)th iteration, the lower bound of the solution space related to the j-th optimization variable is expressed as:

[0049] U L,t+1,j =U L,0,j (13)

[0050] Among them, U L,0,j This represents the minimum boundary value set for the j-th optimization variable during the initialization phase.

[0051] The specific method for constructing the dynamic weight parameter adjustment strategy is as follows:

[0052] (1) Set the initial value W for the weight change. I and termination value W E Then, the ratio of the current remaining iterations to the total number of iterations is used as a smooth transition variable, and finally, an exponential decay strategy is adopted to achieve a smooth transition from the initial weight value to the final weight value.

[0053] (2) The smooth transition variable is represented as (tt) m ) / t, where t m This indicates the total number of iterations.

[0054] (3) The specific values ​​of the weight parameters in the t-th iteration can be expressed by the following formula using the exponential decay strategy:

[0055]

[0056] Compared with the prior art, the present invention has the following advantages:

[0057] ①The method for optimizing the size of the transport unit of the present invention can find a structural design scheme for the transport unit with a smaller space loss rate, promote the transformation and upgrading of traditional palletized transport methods and improve the loading and unloading efficiency in multimodal transport.

[0058] ② This invention employs a solution space search strategy based on dynamic information entropy, which can adjust the solution space region to be searched in the next iteration in real time according to changes in the concentrated distribution region of feasible solutions. Compared with the fixed solution space search method used by the traditional PSO algorithm, the dynamic space search strategy proposed in this invention can effectively avoid searching some regions in the solution space that are far from the optimal solution, which can significantly improve the convergence speed of the iteration.

[0059] ③ The present invention is based on a dynamic weight parameter adjustment strategy with exponential transition. On the one hand, it can set a larger weight value in the early stage of iteration to improve the search speed; on the other hand, in the late stage of iteration, the weight parameter has become a very small parameter value. This can not only improve the solution accuracy, but also avoid the solution oscillation problem caused by excessive search speed. Attached Figure Description

[0060] Figure 1 The flowchart for solving the dynamic information entropy PSO optimization algorithm is shown.

[0061] Figure 2 This is a graph showing the change in space loss rate under different iteration numbers.

[0062] Figure 3 This is a 3D rendering of a modular transport unit. Detailed Implementation

[0063] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0064] like Figure 1 As shown, a dynamic information entropy (PSO) optimization algorithm for the design of dimensional parameters of combined transport units includes the following steps:

[0065] (1) Perform initialization settings, including setting the upper and lower bounds of the search interval, population size, learning factor, speed limit, total number of iterations and other traditional PSO parameters; setting the scale adjustment coefficient in the dynamic space search strategy; setting the initial and final values ​​of the weights in the dynamic weight adjustment strategy.

[0066] (2) Randomly generate the initial particle swarm and calculate the initial optimization objective function value.

[0067] (3) Enter the iterative optimization process, which mainly includes important steps such as calculating the proportion of effective particles in each subspace, calculating the change scale of the solution space, updating the search area of ​​the solution space, updating the velocity of the particle swarm and limiting its amplitude, and updating the position of the particle swarm.

[0068] (4) Determine whether the calculation result meets the pre-set iteration termination condition (reaching the maximum number of iterations or the change amplitude of the optimal solution is less than a given threshold). If the termination condition is met, output the optimal solution; otherwise, continue to the next round of iteration to solve and optimize.

[0069] Example

[0070] 1. Packing process modeling

[0071] (1) This embodiment assumes that the transport unit will be loaded into three common types of containers: 20-foot, 40-foot, and 45-foot containers. The internal dimensions of a 20-foot container are 5.895m long, 2.350m wide, and 2.390m high. The internal dimensions of a 40-foot container are 12.032m long, 2.350m wide, and 2.390m high. The internal dimensions of a 45-foot container are 13.556m long, 2.350m wide, and 2.698m high. Therefore, the internal volume of the three types of containers can be expressed as follows:

[0072] V1 = 33.1093m 3 V2 = 67.5777m 3 V3 = 86.0223m 3 (15) Therefore, the total number of packing types is M = 3.

[0073] (2) The effective volume occupied by the transport unit to be optimized after being loaded into the i-th type of container can be expressed in the following form:

[0074] v i =N i ×l×w×h (16) Since the rationality of the length parameter has been effectively verified in numerous loading and unloading scenarios, it is assumed that the length of the transport unit, l = 1.2m, remains constant. Next, the proposed Dynamic Information Entropy (PSO) algorithm is mainly used to optimize the two important parameters of the transport unit: width and height. Once the width and height are determined, the total number N of transport units accommodated in each container will be... i It can also be solved.

[0075] (3) Assuming that the transport unit is loaded with lightweight goods such as digital products and electronic components, the load constraint can be temporarily ignored.

[0076] 2. Initialize parameter settings

[0077] The upper and lower bounds of the search interval for both width and height optimization variables are set to U. B,0 =0.9, U L,0 =0.5. Population size is set to 95, learning factor is set to 1.3, maximum particle swarm speed is limited to ±0.2, and total number of iterations is set to 200; scale adjustment coefficient in dynamic space search strategy is set to 0.006; initial weight value in dynamic weight adjustment strategy is set to 0.9, and termination value is set to 0.4.

[0078] 3. Iterative optimization process

[0079] The iteration terminates when the maximum number of iterations is used as the criterion, and the iterative optimization process begins. Figure 2This paper demonstrates the variation of the combined space loss rate with the number of iterations when using the traditional PSO algorithm and the proposed dynamic entropy PSO algorithm for carrier cell size optimization design. It can be observed that the proposed dynamic entropy PSO algorithm, due to its dynamic space search strategy, significantly improves the iteration convergence speed. The traditional PSO algorithm requires 10⁹ iterations before its space loss rate stabilizes, indicating a stable solution. However, the proposed dynamic entropy PSO algorithm reaches a stable state after only 59 iterations, resulting in an iteration speed improvement of approximately 10⁹ - 5⁹ / 10⁹ ≈ 45.9%. Furthermore, the use of a dynamic weight parameter setting strategy ensures a relatively slow particle swarm speed at the end of the iteration, which improves solution accuracy. The proposed dynamic entropy PSO algorithm finds a space loss rate of 10.18% for the size parameters, while the traditional PSO algorithm finds a space loss rate of 10.89%. Therefore, the solution accuracy is improved by approximately 0.1089 - 0.1018 / 0.1089 ≈ 6.52%.

[0080] 4. Output the optimal solution

[0081] Knowing the 59th iteration, the program only needs to read the 59th row of stored data from the optimal solution storage matrix to obtain the optimal design parameters for the width and height of the transport unit: 0.5703m and 0.7588m, respectively. Based on this optimized dimensional information, a 3D model of the transport unit was created in SolidWorks software, as shown below. Figure 3 As shown.

Claims

1. A dynamic information entropy PSO-based combined unit load size parameter optimization design method, characterized in that: Comprise the following specific steps: Step one: parameterized modeling according to the containerization process of the combined carrier unit and clear constraint conditions; Step two: build an optimization model using the minimum value of the comprehensive space loss rate and the constraint conditions; The specific method is: first, the combined carrier unit to be optimized in size is respectively loaded into different types of containers, then the ratio of the remaining space volume in each container to its total volume is calculated, next the average of these ratios is obtained to obtain the comprehensive space loss rate, and finally the optimization model is composed of the minimum value of the comprehensive space loss rate and the inequality constraint conditions; Step three: in the PSO optimization algorithm, a dynamic search space solving strategy based on information entropy is constructed, and the information entropy formula is used to obtain the change scale of the solution space before optimizing the carrier unit size parameters in each iteration; The construction is based on the dynamic search space solving strategy of information entropy, and the specific method is as follows: firstly, the size range of the carrier unit is estimated, and the range is taken as the initial solving space; then, the first round of iteration optimization process is entered, and the distribution of the particle swarm in the solution space is updated; next, the key information entropy formula Describes the degree of aggregation of the feasible solution particle swarm in some areas of the solution space; then, the change scale of the initial solving space is determined according to the information entropy value; finally, the range of the initial solving space is updated by using the change scale, so as to provide a new search space closer to the optimal solution for the next round of iteration; before each round of iteration optimization solving of the size parameters of the carrier unit, the solution space used in the last round of solving is updated by using the information entropy, so it is called dynamic search space solving; in the key information entropy formula, p t,j,l The ratio of the number of particles related to the jth optimization variable distributed in the lth subinterval to the total number of particles K in the tth iteration process, and Q represents the total number of subintervals; Step four: in the PSO optimization algorithm, a dynamic weight parameter adjustment strategy is constructed; so that before each iteration to optimize the carrier unit size parameters, the weight parameter can be adjusted in real time according to the exponential decay characteristic; The construction dynamic weight parameter adjustment strategy, its specific method is: first set the initial value W of weight change I And the final value W E , then the ratio of the current remaining iteration number (t-t m ) and total iteration number t is used as a smooth transition variable, next, the weight parameter W t Used in this round of iteration is calculated before each round of iteration optimization solution of the size parameter of the carrying unit; During the whole iteration optimization process, the weight parameter presents exponential decay trend.

2. The method of claim 1, wherein the method is based on dynamic information entropy PSO for combined unit load size parameter optimization design. The parameterized modeling according to the containerization process of the combined carrier unit and the clear constraint conditions, the specific method is: the internal space of the standardized container is modeled as a regular cuboid, and the load and temperature constraint conditions are considered.

Images