A multimodal transport route optimization method and system under uncertain conditions

Abstract

The present invention belongs to the technical field of intermodal transport path optimization, and discloses a multimodal transport path optimization method and system under uncertainty conditions. The method analyzes and processes the uncertain transportation time, establishes a dual-objective uncertainty stochastic programming model, and then converts the dual-objective uncertainty stochastic programming model through the sample average approximation method to obtain a dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function will estimate the expected cost value with the sample average function; obtain a non-dominated solution set by multiple independent runs of the dual-objective deterministic optimization model, and then summarize the non-dominated solution set obtained based on all samples into a total non-dominated solution set, and approximate the optimal solution through the ideal point method; obtain the optimal path plan; and perform sensitivity analysis on the carbon tax rate and time window. The present invention is based on the improved NSGA-II algorithm to solve to obtain an accurate and reliable optimal path plan decision.

Description

Technical Field

[0001] The present invention belongs to the technical field of multimodal transport path optimization, and in particular, relates to a multimodal transport path optimization method and system under uncertain conditions. Background Art

[0002] In the field of multimodal transport route optimization, the transportation process faces many uncertain factors. Most existing technologies use fuzzification methods to deal with uncertain factors, and then solve them based on the concept of confidence level to obtain a deterministic model. By introducing a fuzzy time window to characterize the uncertainty of transportation time, a multi-objective optimization model is constructed on this basis. Then, by introducing a theoretical framework containing fuzzy parameters to ensure that the decision meets the fuzzy opportunity constraints and reaches or exceeds the preset confidence level, the original uncertainty model is converted into a fuzzy opportunity constraint programming model, and a linear weighted processing is performed on the multi-objective model to obtain a single-objective determination model. Finally, the model is solved using a heuristic algorithm to obtain the optimal path solution.

[0003] Through the above analysis, the problems and defects of the existing technology are as follows: Although the existing technology can quantitatively convert uncertainty into a certain value, the determination of the fuzzy function depends largely on human subjective judgment, and when the slight differences in the original data are blurred, some important features or changing trends may be obscured, and a more accurate path decision cannot be obtained. Secondly, although the conversion of the multi-objective model to a single-objective model for solution can simplify the calculation process, the linear weighted method assumes that the targets can be fully compensated, that is, the loss of one target can be fully compensated by the gain of other targets. However, in many practical problems, there may be non-compensatory relationships between targets. Summary of the invention

[0004] In order to overcome the problems existing in the related art, the embodiments disclosed in the present invention provide a method and system for optimizing multimodal transport paths under uncertainty conditions, and specifically relate to a method and system for optimizing multimodal transport paths under uncertainty conditions based on data-driven.

[0005] The technical solution is as follows: A multimodal transport path optimization method under uncertainty conditions, comprising the following steps:

[0006] S1, analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, transform the dual-objective uncertainty stochastic programming model through the sample average approximation method, and obtain a dual-objective deterministic optimization model;

[0007] S2, establish an independent test sample, test the optimal number of samples, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and the non-dominated solution set is obtained by multiple independent runs of the dual-objective deterministic optimization model; the non-dominated solution set obtained based on all samples is summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path plan;

[0008] S3, conduct sensitivity analysis on carbon tax rates and time windows. By setting different carbon tax rates and time windows, analyze the impact of carbon tax rate and time window fluctuations on the constructed optimal path plan.

[0009] In step S1, the uncertain transportation time is analyzed and processed, including:

[0010] For a multimodal route with origin O and destination D, the departure time is , the arrival time at the destination is ; This route first uses road transport to transport the goods from location A to location B, and then transfers them at location B; then it uses rail transport from location B to location C, and the transportation time is ; Transship at location C and finally arrive at location D by rail transport;

[0011] The transportation time of this route is subject to the following conditions:

[0012] (1);

[0013] In the formula, is the transportation time from location A to location B, is the transit time at location B, is the transit time at location C, is the transportation time from location C to location D;

[0014] The rail transport between location B and location C has a fixed departure time , the truck transportation between location C and location D has a departure time window, that is, the goods must arrive at location B in time for rail transportation, and the departure time of section CD is generated based on the arrival time at location C; then there are the following path feasibility constraints;

[0015] (2);

[0016] (3);

[0017] By using the sample average approximation SAA to consider the uncertainty of the transportation time, multiple samples are generated and optimized on these samples. As the number of samples increases, the sample average approximation SAA provides a result close to the true optimal solution, expressed as:

[0018] (4);

[0019] In the formula, is the transportation time interval, For road sections, is the set of OD centering sections, For OD alignment Segments on the path The distance The transport methods are Maximum and minimum speeds; is a 0-1 variable, in the OD pair From the road segment Transfer to road section When the mode of transport is Transformed into , then it is 1, otherwise it is 0; For transportation and mode of transport The transit time between is the actual transport volume of the OD pair.

[0020] In step S1, a dual-objective uncertainty stochastic programming model is established, including: on the basis of quantifying the uncertainty of transportation time, considering the transportation volume, time window, and carbon emission constraints, taking the preference functions of operating cost, customer satisfaction, and environmental friendliness as the objectives, a dual-objective uncertainty stochastic programming model is constructed.

[0021] In step S1, the dual-objective uncertainty stochastic programming model is transformed by the sample average approximation method to obtain a dual-objective deterministic optimization model, including:

[0022] Monte Carlo simulation generates an independent sample set of size G based on the probability distribution of random variables to simulate the real random variable distribution, and the probability of each generated sample is equal, which is 1 / G; at this time, the superscript of the original model Replaced by , represents the generated random samples; each scenario The probability of It is also replaced by 1 / G; the above model is converted into a dual-objective deterministic optimization model.

[0023] Furthermore, the dual-objective deterministic optimization model includes: constraint formula (37)-constraint formula (46);

[0024] (37);

[0025] (38);

[0026] In the formula, is the generated sample, for A collection of;

[0027]

[0028] Constraining formula (10) - formula (31), we have:

[0029] (39);

[0030] Constraint formula (39) indicates that in each scenario in the generated random sample, each path plan has an associated departure time, transportation time, and arrival time; For the sample scenario The next section s Departure time, For the sample scenario The next section s The transportation time, For the sample scenario The next section s Arrival time;

[0031] ;

[0032] Constraint formula (40) represents the previous road segment in the generated random sample The time of transportation completion plus the transit time must be on the next route Completed before the transportation departure time; For road section Departure time, For the sample scenario The next section and The time delay between

[0033] (41);

[0034] (42);

[0035] (43);

[0036] Constraint formula (41)-constraint formula (43) means that in the generated random samples, when the path plan is not feasible, ensure ;

[0037] (44);

[0038] (45);

[0039] Constraint formulas (44)-(45) represent the time frame of each path plan in the generated random sample. The earliest pickup time of the lower limit is fixed, while the expiration date of the upper limit is variable. For sample scenario Lower section s Delay time in each transportation stage, For path Earliest arrival time;

[0040] (46);

[0041] Constraint (46) represents the road segment in the generated random sample departure time window.

[0042] In step S2, the optimal path solution is obtained, including:

[0043] S201, using the sample average approximation method to generate non-dominated solutions, and testing the optimal number of samples through optimality difference estimation;

[0044] S202, for each sample , the transport time parameter is substituted into the dual-objective uncertainty stochastic programming model, and G dual-objective deterministic optimization models are obtained; Monte Carlo simulation generates a sample set according to the probability distribution of random variables to simulate the real distribution. The sample contains B elements, and the weight of each element is 1 / B; after the sample is generated, The objective function in the samples will use the sample average function to estimate the expected cost value;

[0045] S203, for each dual-objective deterministic optimization model, use the NSGA-Ⅱ algorithm to solve and obtain the corresponding non-dominated solution set and the objective function value and ;

[0046] S204, the non-dominated solution sets obtained based on all samples are summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path solution.

[0047] In step S201, a non-dominated solution is generated by using the sample average approximation method, and the optimal number of samples is checked by optimality difference estimation, including:

[0048] S2011, Monte Carlo simulation method based on the probability distribution of transportation time Generate G independent samples , each sample , Indicates The first Transit time parameters ; Generate a size of Independent test samples are used to evaluate each candidate solution and check whether all constraints are met. If so, it is a feasible solution; the candidate feasible solution with the minimum cost is selected as the optimal solution. ; For any feasible solution, the objective function value under any independent sample is the upper bound of the true objective value; therefore The corresponding upper bound is calculated as formula (40); sort the G optimal values ​​corresponding to different samples to obtain The order statistics of , No. Order Statistics Corresponding to the confidence level The lower bound ;

[0049] (40);

[0050] In the formula, is the upper bound of the true target value, is the objective function value, For standard normal distribution Quantile, is the standard deviation of the target value in the test sample;

[0051] (41);

[0052] (42);

[0053] In the formula, is the confidence level, is an infinite number, For G In independent trials, at most The probability of success, is the number of trials, is the sample set, is a set of time parameters;

[0054] S2022, using optimality difference estimation To evaluate the solution The quality of the sample size was chosen to ensure a reasonable optimality gap;

[0055] In step S202, the objective function is and The expected cost value is and , then:

[0056] (43);

[0057] (44);

[0058] In the formula, is the objective function The expected cost value, is the objective function The expected cost value, is the first r Customer satisfaction of each path, For each sample path Delays at various stages of transportation;

[0059] The specific steps of step S203 are as follows:

[0060] S2031, encode the paths in the alternative solution set to obtain the initial population, i.e., the initial solution alternative set; the road section is coded in 0-1, i.e., 0 means not passing through the road section, and 1 means passing through the road section; the transportation mode used by the road section is coded in 1-2-3, where 1 means railway transportation, 2 means road transportation, and 3 means water transportation; assuming that the shipper has m OD pairs of transportation demands, the code of each path selection on each OD pair is ;

[0061] S2032, calculate the operating costs and preference function values ​​of all individuals in the initial population, perform non-dominated sorting, divide into different Pareto front levels, then calculate the crowding degree between individuals in each Pareto front level, and finally use the tournament selection strategy to select the next generation of individuals from the population;

[0062] S2033, using a non-uniform arithmetic crossover operator and a non-uniform mutation operator, performing crossover and mutation operations on the selected individuals to generate new individuals;

[0063] S2034, combining the newly generated solution set with the previous generation solution set to obtain a new population, and repeating steps S2032 and S2033;

[0064] S2035, judging the termination condition, judging whether to terminate the algorithm according to the set termination condition, such as reaching the maximum number of iterations; if the termination condition is met, outputting the Pareto front solution set; otherwise, returning to step S2022 to continue iteration;

[0065] Step S204 includes: normalizing and standardizing the solution set; denoting the matrix after normalization and standardization as A, see formula (45), and determining the positive ideal point and negative ideal point , calculate each Pareto solution according to formula (46) and formula (47) Distance from optimal solution and the worst solution distance ; Finally, according to formula (48), calculate the Rating of Pareto solutions And sort, select The largest one is the approximate optimal solution:

[0066] (45);

[0067] Where A is the matrix after normalization and standardization, is the matrix value;

[0068] (46);

[0069] (47);

[0070] (48);

[0071] In the formula, For each Pareto solution The distance from the optimal solution, For each Pareto solution The distance from the worst solution, For the The score of a Pareto solution, For the target The ideal point value under For the target The negative ideal point value under is the Pareto solution On Target The value below, Represents two evaluation indexes: operating cost and preference function value.

[0072] In step S3, the carbon tax rate sensitivity analysis includes: setting four carbon tax rate interval levels as Ⅰ[0.00, 0.00, 0.00, 0.00], Ⅱ[0.01, 0.02, 0.03, 0.04], Ⅲ[0.05, 0.10, 0.15, 0.20] and Ⅳ[0.10, 0.20, 0.30, 0.40], and the corresponding carbon emissions are set as And based on the calculation of the optimal path plan, the results of the proportion of transportation modes, operating costs and carbon emissions in the Pareto optimal solution;

[0073] Time window sensitivity analysis includes: obtaining the proportion of transportation modes, operating costs and changes in preference function values ​​of the optimal path through different time window constraint settings.

[0074] Another object of the present invention is to provide a multimodal transport path optimization system under uncertainty conditions, the system implements the multimodal transport path optimization method under uncertainty conditions, and the system comprises:

[0075] The module for obtaining the dual-objective deterministic optimization model is used to analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, and convert the dual-objective uncertainty stochastic programming model through the sample average approximation method to obtain the dual-objective deterministic optimization model;

[0076] The optimal path solution acquisition module is used to establish an independent test sample, test the optimal sample quantity, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and the non-dominated solution set is obtained by multiple independent runs of the dual-objective deterministic optimization model; the non-dominated solution sets obtained based on all samples are summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path solution;

[0077] The sensitivity analysis module is used to perform sensitivity analysis on carbon tax rates and time windows. By setting different carbon tax rates and time windows, the impact of carbon tax rate and time window fluctuations on the constructed optimal path plan is analyzed.

[0078] In combination with all the above-mentioned technical solutions, the beneficial effects of the present invention are as follows: the present invention is based on a data-driven approach and adopts the Sample Average Approximation algorithm (SAA) to deal with uncertain transportation time. First, based on the probability distribution of random variables, a large number of samples are extracted, and then the objective function value is calculated for each sample. Finally, the average value of these values ​​is taken to approximately represent the true expected value, thereby converting the random problem into a deterministic problem for solution. At the same time, the time reliability of the transportation path is used as a quantitative indicator of customer satisfaction, and customer satisfaction and environmental friendliness are weighted to analyze the impact of changes in the emphasis of the two on the decision-making of the transportation plan. A multimodal transport path optimization model is constructed with the preference functions of operating cost and customer satisfaction and environmental friendliness as dual objectives. The present invention also designs an algorithm based on the improved NSGA-II to solve the problem in order to obtain accurate and reliable optimal path plan decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0080] Figure 1 is a flow chart of a multimodal transport path optimization method under uncertainty conditions provided by an embodiment of the present invention;

[0081] Figure 2 is a schematic diagram of a multimodal transport path optimization method under uncertainty conditions provided by an embodiment of the present invention;

[0082] Figure 3 is a multimodal transport route map provided by an embodiment of the present invention;

[0083] Figure 4 is a schematic diagram of a multimodal transport path optimization system under uncertainty conditions provided by an embodiment of the present invention;

[0084] Figure 5 It is a curve diagram of the calculation time and the optimal difference between the upper and lower bounds as the number of sample scenarios increases provided by the present invention;

[0085] Figure 6 The Pareto front solution diagram at the sensitivity level (5, 5) provided by the present invention is obtained;

[0086] Figure 7 is the Pareto front solution diagram at the sensitivity level (1, 9) provided by the present invention;

[0087] Figure 8 is the Pareto front solution diagram obtained at the sensitivity level (9, 1) provided by the present invention;

[0088] Fig. 9 It is a trend chart of the proportion of transportation modes and carbon emissions of the present invention;

[0089] Fig.10 It is an optimization result diagram of the OD pair of a certain place 1-a certain place 2 under different delivery time windows of the present invention;

[0090] In the figure: 1. Dual-objective deterministic optimization model acquisition module; 2. Optimal path solution acquisition module; 3. Sensitivity analysis module. DETAILED DESCRIPTION

[0091] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0092] In order to reduce operating costs, improve customer satisfaction and reduce pollutant emissions, a multimodal transport path optimization model under data-driven uncertainty conditions is proposed based on the uncertainty of transportation time in the multimodal transport process. The model first uses the sample average approximation method to quantify the uncertainty of transportation time; secondly, based on the constraints of transportation capacity, time window, carbon emissions and taking into account the carrier's preferences, a multi-objective optimization model is constructed with the goal of minimizing operating costs, maximizing customer satisfaction and environmental friendliness, and a model solution method based on NSGA-II combined with the ideal point method is designed. Finally, numerical experiments are used to verify the effectiveness of the proposed model and solution method. The experimental results show that the multi-objective optimization scheme obtained by the design model can more effectively reduce operating costs, improve customer satisfaction and reduce the impact of environmental pollution than the single-objective optimization scheme, and is more sensitive to changes in carbon tax rate ranges and time windows.

[0093] Example 1: The multimodal transport path optimization method under uncertainty provided by the present invention first analyzes the uncertainty of transportation time, and then establishes a data-driven random programming model under uncertainty. And proposes:

[0094] The uncertain transportation time is processed based on data-driven approach. Based on data analysis, the probability characteristics of real data are used to quantitatively evaluate the impact of transportation time uncertainty on the optimal path decision.

[0095] Based on data-driven construction, a dual-objective optimization model is established under uncertain conditions. The time reliability of the transportation route is used as a quantitative indicator of customer satisfaction, customer satisfaction and environmental friendliness are weighted, and a multimodal transport route optimization model is constructed with operating costs and preference functions of customer satisfaction and environmental friendliness as dual objectives. Then, the model is converted into a deterministic optimization model using the sample average approximation method for subsequent solution.

[0096] An algorithm based on the improved NSGA-II is designed to solve the model. The sample average approximation method is used to generate a set of sample scenarios for the transportation time of the model. After these samples are generated, the objective function will estimate the expected cost value using the sample average function. The non-dominated solution set is obtained by multiple independent runs of the deterministic optimization model, and then the non-dominated solution set obtained based on all samples is summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method.

[0097] For example, Figure 1 As shown, the multimodal transport path optimization method under uncertainty conditions provided by the embodiment of the present invention includes:

[0098] S1, analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, transform the dual-objective uncertainty stochastic programming model through the sample average approximation method, and obtain a dual-objective deterministic optimization model;

[0099] S2, establish an independent test sample, test the optimal number of samples, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and the non-dominated solution set is obtained by multiple independent runs of the dual-objective deterministic optimization model; the non-dominated solution set obtained based on all samples is summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path plan;

[0100] S3, conduct sensitivity analysis on carbon tax rates and time windows. By setting different carbon tax rates and time windows, analyze the impact of carbon tax rate and time window fluctuations on the constructed optimal path plan.

[0101] For example, Figure 2 This is the principle of the multimodal transport path optimization method under uncertainty conditions provided by an embodiment of the present invention.

[0102] Exemplarily, in step S1 , transportation time uncertainty analysis is performed based on a sample average approximation method.

[0103] In order to quantify the uncertainty of total transportation time caused by external factors such as severe weather conditions and traffic accidents, the total transportation time interval of goods is estimated based on different transportation modes and different transportation routes. See formula (7), where the transportation time interval is determined by the transportation distance and speed, and the transit time is determined by the unit transit time and transportation volume corresponding to the transit transportation type. Based on the sample average approximation method, the uncertainty of transportation time is processed and analyzed to analyze its impact on the multimodal transport route decision. For details, see the model solution.

[0104] In intermodal transport, goods can be transported between cities using different modes of transport. While most road transport does not have a fixed schedule, rail and water transport in an intermodal network usually follow a fixed schedule. Therefore, it is impossible to wait for late goods due to unexpected delays in the transport process. Figure 3 The multimodal route diagram shows a multimodal route with origin O and destination D, so the departure time is , and the arrival time at the destination is This route first uses road transport to transport the goods from point A to point B, and then transfers them at point B. Then it uses rail transport from point B to point C, and the transportation time is . It is transferred at point C and finally transported by rail to point D.

[0105] The present invention innovatively proposes that, assuming that the route is feasible, the transportation time is subject to the following conditions:

[0106] (1);

[0107] In the formula, is the transportation time from location A to location B, is the transit time at location B, is the transit time at location C, is the transportation time from location C to location D;

[0108] To represent a scenario with a fixed schedule combination, in this example, the rail transport between B and C has a fixed departure time , while the truck transportation between C and D has a relatively loose departure time window, that is, the goods must arrive at point B in time for rail transportation, and the departure time of section CD is generated according to the time to arrive at point C. Therefore, the following path feasibility constraints innovatively proposed by the present invention will appear.

[0109] (2);

[0110] (3);

[0111] Therefore, when dealing with uncertainty, transportation route planning should be reliable and accurate. The present invention considers the uncertainty of transportation time by using SAA. This method generates multiple samples and optimizes on these samples. As the number of samples increases, the solution of SAA will gradually approach the true optimal solution. This asymptotic consistency means that when there are enough samples, SAA can provide results close to the true optimal solution. For example, the innovative formula (4) proposed by the present invention.

[0112] (4);

[0113] In the formula, is the transportation time interval, For road sections, is the set of OD centering sections, For OD alignment Segments on the path The distance The transport methods are Maximum and minimum speeds; is a 0-1 variable, in the OD pair From the road segment Transfer to road section When the mode of transport is Transformed into , then it is 1, otherwise it is 0; For transportation and mode of transport The transit time between is the actual transport volume of the OD pair.

[0114] Exemplarily, in step S1, model building includes:

[0115] S101, Problem Description and Hypothesis.

[0116] The shipper has multiple OD pairs of transportation needs, and there are multiple paths between O and D. Connect, every path Contains multiple sections , each road segment At least one mode of transportation exists among rail, road and water There are different transportation modes to choose from, and the transportation speed, unit freight and carbon emission levels of different transportation modes are different. Goods can be converted between two sections of transportation, and the transportation task needs to be completed within the time window allowed by the customer. The uncertainty of transportation time is reflected by running the deterministic optimization model multiple times, in which the model obtains different samples through the distribution function obeyed by the transportation time. During the transportation process, the goal is to minimize operating costs and maximize the preference function of customer satisfaction and environmental friendliness. The equilibrium relationship between the carrier's operating costs, shipper's satisfaction and environmental friendliness is comprehensively considered. At the same time, the impact of the changes in the emphasis of the latter two on the decision-making is paid attention to. Considering the transportation time constraints and carbon emissions, a multi-objective multimodal transport path optimization model is constructed to determine the best transportation path and mode of transportation, including:

[0117] (1) All modes of transport are assumed to be uniform motion.

[0118] (2) Only one mode of transportation can be selected on each road section or one mode of transfer between road sections.

[0119] (3) Each mode of transportation has a dedicated transportation route to avoid congestion.

[0120] (4) A batch of goods cannot be split during transportation.

[0121] (5) During transportation, the amount of goods will neither increase nor decrease, and there will be no replenishment or reduction of goods at the transshipment nodes.

[0122] (6) If the goods arrive at the transit section, transit will begin immediately.

[0123] (7) Due to the high cost of air transportation, air transportation is not considered as a mode of transportation for large quantities of goods.

[0124] S102, model construction.

[0125] On the basis of quantifying the uncertainty of transportation time, considering the constraints such as transportation volume, time window, carbon emissions, and taking the preference function of operating cost, customer satisfaction and environmental friendliness as the target, the present invention innovatively proposes to construct a dual-objective uncertainty stochastic programming model (dual-objective multimodal transport stochastic programming model) as shown in formula (5)-formula (36).

[0126] (5);

[0127] (6);

[0128] In the formula, is the total operating cost of the optimal path for all OD pairs, is the preference function of all ODs for customer satisfaction and environmental friendliness of the optimal path, For the scene The unit penalty cost under As a starting point, for is the transport path, For the mode of transportation, A sample scenario set is a set of paths starting from O and ending at D; Assemble for transport modes;

[0129] For the scene The OD of the next Path segments Transportation method transportation costs, For the scene The OD of the next From the road segment Transfer to road section When the mode of transport is Transformed into The transit cost; For the scene The probability corresponding to the transportation time is For the scene The OD of the next Customer satisfaction of each path, is a 0-1 decision variable. If the OD pair is selected If there are multiple paths, then the value is 1, otherwise it is 0; For path In the scene The delay time of For a certain OD pair The environmental friendliness of each path, the less pollutant emissions, the higher the environmental friendliness; For the Customer satisfaction sensitivity level, For the Environmental friendliness sensitivity level;

[0130]

[0131] (7);

[0132] Constraint formula (7) is the equation for the path operation cost, For transportation fixed costs, For transportation The freight rate, is a 0-1 variable, the OD pair r Path segments s Transportation method k If yes, it is 1, otherwise it is 0;

[0133] (8);

[0134] Constraint formula (8) is the equation for the transit cost, For transportation mode Switch to transport mode fixed costs, For transportation mode Switch to transport mode The freight rate, For the mode of transport;

[0135] (9);

[0136] Constraint (9) is the first The environmental pollution cost of each path is For OD alignment r The environmental pollution cost of each path is For OD alignment Segments on the path Use transportation method the costs of air pollution during transport; For OD alignment Segments on the path Use transportation method the cost of noise pollution during transportation; For a certain OD pair The carbon emission costs of each pathway;

[0137] (10);

[0138] Constraint formula (10) is the normalized treatment of environmental pollution cost. For OD alignment r The environmental friendliness of each path;

[0139] (11);

[0140] Constraint formula (11) is customer satisfaction, and its value range is ; For the Customer satisfaction of each path, For the The transport time and interval in the experiment When it is within the interval, , otherwise it is 0; is the number of simulation tests;

[0141] (12);

[0142] In the formula, For the Unit of unit freight volume per unit distance of the transport mode Emissions of various air pollutants; For the The unit price of the emission of various air pollutants; is the noise pollution cost per unit distance and per unit freight volume;

[0143] (13);

[0144] Constraint formula (12) and constraint formula (13) are respectively Segments on the path Use transportation method The costs of air pollution and noise pollution during transportation;

[0145] (14);

[0146] Constraint formula (14) is the first Segments on the path Use transportation method Carbon emissions during transportation; For OD alignment r Segments on the path s Use transportation method k Carbon emissions during transportation, is the carbon emission per unit distance and per unit freight volume;

[0147] (15);

[0148] Constraint formula (18) is the OD alignment From the road segment Transfer to road section When the mode of transport is Transit carbon emissions converted into l; For OD alignment From the road segment Transfer to road section When the mode of transport is Transformed into l transit carbon emissions, For transportation mode Switch to transport mode The carbon emission factor of transshipment;

[0149] (16);

[0150] Constraint formula (16) indicates that the OD pair Carbon emissions along each path; For OD alignment Carbon emissions along each path;

[0151] (17);

[0152] Constraint formula (17) is the formula for calculating carbon emission costs under the segmented progressive carbon tax mechanism; For OD alignment The carbon emission cost on each path, For the Tiered carbon taxes, For the The range of permissible carbon emissions corresponding to the different levels of carbon tax;

[0153] (18);

[0154] Constraint formula (18) indicates that only one path is selected for each OD pair;

[0155] (19);

[0156] Constraint formula (19) indicates that there is only one mode of transportation for each section of the path;

[0157] (20);

[0158] Constraint formula (20) indicates that there is only one type of transfer between every two road sections;

[0159] (twenty one);

[0160] Constraint formula (21) is a 0-1 variable constraint;

[0161] (twenty two);

[0162] Constraint formula (22) indicates that the sum of the sensitivity coefficients is 1. is the sensitivity coefficient;

[0163] (twenty three);

[0164] (twenty four);

[0165] (25);

[0166] Constraint formula (23)-constraint formula (25) are linear constraints on decision variables;

[0167] (26);

[0168] Constraint formula (26) indicates that the probability that the arrival time is between the maximum time and the minimum time that the customer can tolerate is not less than ;

[0169] (27);

[0170] Constraint formula (27) represents the road segment The freight volume allocated to each mode of transport shall not exceed the maximum capacity of that mode of transport on that section of the route;

[0171] (28);

[0172] Constraint formula (28) represents the constraints on transportation demand;

[0173] (29);

[0174] Constraint formula (29) indicates that each path plan has an associated departure time, transportation time, and arrival time in each scenario; is the departure time of each route segment, is the transportation time of each road segment, is the arrival time of each road segment;

[0175] ;

[0176] Constraint formula (30) represents the previous segment The time of transportation completion plus the transit time must be on the next route Completed before the transportation departure time; For road section Next section The transit time, For the sample scenario The next section s +1 for the shipping time, For road section and The time delay between is the number used for binary constraints;

[0177] (31);

[0178] (32);

[0179] (33);

[0180] Constraint formula (31)-constraint formula (33) means that when the path plan is not feasible, ensure ;

[0181] (34);

[0182] In the formula, For path Earliest departure time;

[0183] (35);

[0184] Constraint formulas (34)-(35) represent the time frame of each routing solution. The earliest pickup time of the lower limit is fixed, while the due date of the upper limit is variable. For sample scenario Lower section s Delays at various stages of transportation;

[0185] (36);

[0186] Constraint (36) represents the road segment The departure time window, is the first r Customer service time window for each path, is a 0-1 variable. If the OD pair is selected If there are two paths, it takes 1, otherwise it takes 0.

[0187] S103, model conversion.

[0188] Monte Carlo simulation generates an independent sample set of size G based on the probability distribution of random variables to simulate the real random variable distribution, and the probability of each generated sample is equal, which is 1 / G; at this time, the superscript of the original model Replaced by , represents the generated random samples; each scenario The probability of At the same time, it is also replaced by 1 / G; therefore, the above model can be converted into a dual-objective deterministic optimization model (deterministic equivalent model II). The present invention innovatively proposes constraint formula (37)-constraint formula (46).

[0189] (37);

[0190] (38);

[0191] In the formula, is the generated sample, for A collection of;

[0192]

[0193] Constraining formula (10) - formula (31), we have:

[0194] (39);

[0195] Constraint formula (39) indicates that in each scenario in the generated random sample, each path plan has an associated departure time, transportation time, and arrival time; For the sample scenario The next section s Departure time, For the sample scenario The next section s The transportation time, For the sample scenario The next section s Arrival time;

[0196] ;

[0197] Constraint formula (40) represents the previous road segment in the generated random sample The time of transportation completion plus the transit time must be on the next route Completed before the transportation departure time; For road section Departure time, For the sample scenario The next section and The time delay between

[0198] (41);

[0199] (42);

[0200] (43);

[0201] Constraint formula (41)-constraint formula (43) means that in the generated random samples, when the path plan is not feasible, ensure ; (44);

[0202] (45);

[0203] Constraint formulas (44)-(45) represent the time frame of each path plan in the generated random sample. The earliest pickup time of the lower limit is fixed, while the expiration date of the upper limit is variable. For sample scenario Lower section s Delays at various stages of transportation, For path Earliest arrival time;

[0204] (46);

[0205] Constraint (46) represents the road segment in the generated random sample departure time window.

[0206] Exemplarily, in step S2, it specifically includes:

[0207] The constructed model is a multi-objective optimization model, whose variable class and constraint type cover 0-1 variables, linear and nonlinear constraints, and belongs to the NP-Hard type of optimization problem. This type of problem generally cannot obtain a unique optimal solution, and usually only a non-inferior solution set can be obtained. For multi-objective decision-making, the NSGA-Ⅱ algorithm is often used to solve it. Given that the non-dominated solution set returned by NSGA-II usually contains multiple solutions, and in practical applications, a clear optimal solution is often required to provide specific guidance for decision-making. Moreover, different non-dominated solutions have their own advantages and disadvantages in terms of each objective, and it is difficult to directly determine which solution is most in line with actual needs. Therefore, the present invention introduces the ideal point method to select the best reconciled solution as the final optimal solution. The specific solution steps are as follows:

[0208] S201, using the sample average approximation method to generate non-dominated solutions, and verifying the optimal number of samples through optimality difference estimation; the steps are as follows:

[0209] S2011, Monte Carlo simulation method based on the probability distribution of transportation time Generate G independent samples , each sample , Indicates The first Transit time parameters ; Generate a size of Independent test samples are used to evaluate each candidate solution and check whether all constraints are met. If so, it is a feasible solution; the candidate feasible solution with the minimum cost is selected as the optimal solution. ; For any feasible solution, the objective function value under any independent sample is the upper bound of the true objective value; therefore The corresponding upper bound is calculated as formula (40); sort the G optimal values ​​corresponding to different samples to obtain The order statistics of , No. Order Statistics Corresponding to the confidence level The lower bound ; (40);

[0210] In the formula, is the upper bound of the true target value, is the objective function value, For standard normal distribution Quantile, is the standard deviation of the target value in the test sample;

[0211] (41);

[0212] (42);

[0213] In the formula, is the confidence level, is an infinite number, is the maximum number of independent trials in G times The probability of success, is the number of trials, is the sample set, is a set of time parameters;

[0214] S202, for each sample , the transport time parameter is substituted into the dual-objective uncertainty stochastic programming model, and G dual-objective deterministic optimization models are obtained; Monte Carlo simulation generates a sample set according to the probability distribution of random variables to simulate the real distribution. The sample contains B elements, and the weight of each element is 1 / B; after the sample is generated, The objective function in the samples will use the sample average function to estimate the expected cost value;

[0215] S2022, using optimality difference estimation To evaluate the solution The quality of the sample size was chosen to ensure a reasonable optimality gap;

[0216] S202, for each sample , substituting the transportation time parameter into the dual-objective uncertainty stochastic programming model, we get G Monte Carlo simulation generates a sample set based on the probability distribution of random variables to simulate the real distribution. B elements, and the weight of each element is 1 / B After the sample is generated, The objective function in the samples will use the sample average function to estimate the expected cost value. The present invention innovatively proposes that the objective function F 1 and F The expected cost of 2 is and , then:

[0217] (43);

[0218] (44);

[0219] In the formula, is the objective function The expected cost value, is the objective function The expected cost value, is the first r Customer satisfaction of each path, For each sample path Delays at various stages of transportation;

[0220] S203, for each dual-objective deterministic optimization model, use the NSGA-Ⅱ algorithm to solve and obtain the corresponding non-dominated solution set and the objective function value and ; The specific steps are as follows:

[0221] S2031, encode the paths in the alternative solution set to obtain the initial population, i.e., the initial solution alternative set; the road section is coded in 0-1, i.e., 0 means not passing through the road section, and 1 means passing through the road section; the transportation mode used by the road section is coded in 1-2-3, where 1 means railway transportation, 2 means road transportation, and 3 means water transportation; assuming that the shipper has m OD pairs of transportation demands, the code of each path selection on each OD pair is ;

[0222] S2032, calculate the operating costs and preference function values ​​of all individuals in the initial population, perform non-dominated sorting, divide into different Pareto front levels, then calculate the crowding degree between individuals in each Pareto front level, and finally use the tournament selection strategy to select the next generation of individuals from the population;

[0223] S2033, using a non-uniform arithmetic crossover operator and a non-uniform mutation operator, performing crossover and mutation operations on the selected individuals to generate new individuals;

[0224] S2034, combining the newly generated solution set with the previous generation solution set to obtain a new population, and repeating steps S2032 and S2033;

[0225] S2035, judging the termination condition, judging whether to terminate the algorithm according to the set termination condition, such as reaching the maximum number of iterations; if the termination condition is met, outputting the Pareto front solution set; otherwise, returning to step S2022 to continue iteration;

[0226] Step S204 includes: normalizing and standardizing the solution set; denoting the matrix after normalization and standardization as A, see formula (45), and determining the positive ideal point and negative ideal point , calculate each Pareto solution according to formula (46) and formula (47) Distance from optimal solution and the worst solution distance ; Finally, according to formula (48), calculate the Rating of Pareto solutions And sort, select The largest one is the approximate optimal solution:

[0227] (45);

[0228] Where A is the matrix after normalization and standardization, is the matrix value;

[0229] (46);

[0230] (47);

[0231] (48);

[0232] In the formula, For each Pareto solution The distance from the optimal solution, For each Pareto solution The distance from the worst solution, For the The score of a Pareto solution, For the target The ideal point value under For the target The negative ideal point value under is the Pareto solution On Target The value below, Represents two evaluation indexes: operating cost and preference function value.

[0233] In step S3, the carbon tax rate sensitivity analysis includes: setting four carbon tax rate interval levels as Ⅰ[0.00, 0.00, 0.00, 0.00], Ⅱ[0.01, 0.02, 0.03, 0.04], Ⅲ[0.05, 0.10, 0.15, 0.20] and Ⅳ[0.10, 0.20, 0.30, 0.40], and the corresponding carbon emissions are set as And based on the calculation of the optimal path plan, the results of the proportion of transportation modes, operating costs and carbon emissions in the Pareto optimal solution;

[0234] Time window sensitivity analysis includes: obtaining the proportion of transportation modes, operating costs and changes in preference function values ​​of the optimal path through different time window constraint settings.

[0235] Embodiment 2, as Figure 4 As shown, the multimodal transport path optimization system under uncertainty conditions provided by the embodiment of the present invention includes:

[0236] The dual-objective deterministic optimization model obtains module 1, which is used to analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, and transform the dual-objective uncertainty stochastic programming model through the sample average approximation method to obtain a dual-objective deterministic optimization model;

[0237] The optimal path solution acquisition module 2 is used to establish an independent test sample, test the optimal sample quantity, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and the non-dominated solution set is obtained by multiple independent runs of the dual-objective deterministic optimization model; the non-dominated solution sets obtained based on all samples are summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path solution;

[0238] Sensitivity analysis module 3 is used to perform sensitivity analysis on carbon tax rates and time windows. By setting different carbon tax rates and time windows, the impact of carbon tax rate and time window fluctuations on the constructed optimal path solution is analyzed.

[0239] The algorithm designed by the present invention based on improved NSGA-II can quickly and efficiently explore the solution space of multi-objective problems, approach the Pareto frontier, and provide decision makers with a series of non-dominated solutions under different objective trade-offs. On this basis, the optimal feasible solution is obtained by introducing the ideal point method.

[0240] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0241] To further illustrate the effects of the embodiments of the present invention, the following experiment was conducted.

[0242] (1) Assume that the shipper has a transportation demand of 7 OD pairs such as place 1-place 2, and each OD pair has multiple transportation modes and transportation routes, forming a multimodal transport network. The transportation route parameter data, transportation costs of different transportation tools, transit route parameter data, and pollutant emissions and emission unit prices of different transportation modes in the example are shown in Tables 1-3. The transportation time-related data are shown in Table 4. At the same time, the following assumptions are made about the sensitivity level: Customer satisfaction sensitivity level = (extremely strong; average; extremely weak) = (9, 5, 1); environmental friendliness sensitivity level =(extremely strong; average; extremely weak)=(9, 5, 1).

[0243] Table 1 Transport route parameter data:

[0244]

[0245] Table 2 Transit path parameter data:

[0246]

[0247] Table 3 Pollutant emissions and unit prices of different modes of transportation:

[0248]

[0249] Table 4 Transportation time related data:

[0250]

[0251] (2) Test of optimal sample size.

[0252] In order to determine the optimal number of samples, the designed solution algorithm is used to solve the constructed optimization model using Matlab. In the algorithm analysis, based on the data in Table 5, for different sample numbers G, the number of cycles 𝑆=5, and the number of iterations are set to 𝑀=20. For example, when 𝑀=20 and G=5, only 5 sample scenarios are generated based on the probability distribution function of random demand, and 50 iterations are performed. At the same time, the confidence level is set to Set to 90%, the number of test samples is G = 120. Only the number of sample scenarios G is changed to observe its impact on the results. The optimal difference between the upper and lower bounds of the objective function value and the calculation time of the sample average approximation algorithm to solve the model under the gradually increasing number of samples are shown in the figure. Figure 5 The calculation time and the optimal difference between the upper and lower bounds change with the increase in the number of sample scenarios.

[0253] It can be seen that, for this example, on the one hand, when the number of samples is greater than 90, a more appropriate solution quality can be obtained, that is, the relative difference between the upper and lower bounds is less than 1.5%; on the other hand, since the solution calculation time increases significantly with the increase in the number of samples, the number of samples should not be too large. Therefore, it is recommended to take the number of samples equal to 110, at which time the relative difference between the upper and lower bounds is less than 1%, and the calculation time is also within an acceptable range, so that a more accurate model decision solution and objective function value can be obtained.

[0254] (3) Optimization result analysis.

[0255] In order to facilitate comparative analysis, the optimal solutions of each single objective value and the multi-objective Pareto optimal solution were selected for comprehensive evaluation. The calculation results under (5, 5), (1, 9), and (9, 1) are shown in Tables 5 to 7, respectively, and the Pareto front solution under the sensitivity level (5, 5) is obtained. Figure 6 , Pareto front solution at sensitivity level (1, 9) Figure 7 , Pareto front solution at sensitivity level (9, 1) Figure 8 As shown in Figure 2, the corresponding multimodal transport network diagrams are obtained based on the multi-objective Pareto optimal solution.

[0256] Table 5 shows the sensitivity levels From the calculation results of Table 5, we can see that the single target The target value is 1.1512 million yuan, and the optimal solution corresponds to Target value: 5.53; Single target The target value of is 6.78, and the optimal solution corresponds to The target value is 1.4237 million yuan; multi-objective Pareto optimal The target value is 1.3018 million yuan. The target value is 6.17. Although the multi-target solution is better than the single-target solution, The operating cost of the scheme is 11.57% higher, but the effect of considering customer satisfaction and environmental friendliness is improved by 10.37%. At the same time, the multi-objective scheme is better than the single-objective scheme. The effect of considering customer satisfaction and environmental friendliness in the plan is 9.87% lower, but the operating cost is improved by 9.36%. It can be seen that the multi-objective plan better balances the relationship between the two target values ​​and is the carrier's first choice.

[0257] Table 5 Sensitivity levels The following operation results:

[0258]

[0259] Table 6 shows the sensitivity levels The calculation results under the single target The target value is 1.1018 million yuan, and the optimal solution corresponds to Target value: 5.45; single target The target value of is 6.88, and the optimal solution corresponds to The target value is 1.4041 million yuan; the multi-objective Pareto optimal transportation solution The target value is 1.286 million yuan. The target value is 6.41. Although the operating cost of the multi-objective Pareto optimal solution is lower than that of the single-objective solution, The operating cost of the solution is 14.32% higher, but the effect of considering customer satisfaction and environmental friendliness is improved by 14.98%. Compared with the other solutions, the effects of considering customer satisfaction and environmental friendliness are relatively similar, with a difference of only 7.33%, while the operating cost has improved by 9.18%. Therefore, considering the operating cost, shipper satisfaction and environmental friendliness, the multi-objective Pareto optimal solution is the preferred solution. The multimodal transport network diagram under the multi-objective optimal solution is as follows: Figure 6 shown.

[0260] Table 6 Sensitivity levels The following operation results:

[0261]

[0262] Table 7 shows the sensitivity levels The calculation results under the single target The target value is 1.0855 million yuan, and the optimal solution corresponds to Target value: 5.78; Single target The target value of is 6.71, and the optimal solution corresponds to The target value is 1.3814 million yuan; the multi-objective Pareto optimal transportation solution The target value is 1.2125 million yuan. The target value is 6.32. At this time, the operating cost of the multi-objective optimal solution is lower than that of the single-objective optimal solution. The operating cost of the solution is 10.47% higher, but customer satisfaction and environmental friendliness are improved by 8.54%. The effect of considering customer satisfaction and environmental friendliness in the solution is 6.71% lower, but the operating cost is improved by 13.93%. The optimization result can still take into account the operating cost, shipper satisfaction and environmental friendliness. Figure 8 When the sensitivity is biased towards customer satisfaction, carriers will choose road and rail transportation, which have fast transportation speeds.

[0263] Table 7 Sensitivity levels The following operation results:

[0264]

[0265] In summary, in a single target Among the transportation options, water transportation is more often chosen, as it has low transportation costs and slow transportation speed, so the corresponding operating cost is the lowest, while the effect of considering customer satisfaction and environmental friendliness is the worst; in the single-target Among the transportation schemes, road and rail transportation are more often selected, which have little impact on environmental pollution or fast transportation speed, and the effect of considering customer satisfaction and environmental friendliness is the best, but its operating cost is the highest. At the same time, at each sensitivity level, the multi-objective optimization scheme can better comprehensively consider operating costs, customer satisfaction and environmental friendliness, so that all three are taken into account, so the effectiveness of its scheme is significantly better than that of the single-objective scheme. From the perspective of the selected multi-objective scheme, when the carrier pays more attention to environmental friendliness, the transportation scheme tends to choose water transportation and rail transportation, while when the carrier pays more attention to customer satisfaction, the transportation scheme chooses road transportation and rail transportation more. Therefore, multimodal transport carriers can obtain different multimodal transport reference schemes based on the proposed model.

[0266] (4) Sensitivity analysis example.

[0267] The present invention adopts numerical experiments to analyze the impact of carbon tax rate and time window fluctuations on the constructed optimal path solution by setting different carbon tax rates and time windows, including:

[0268] (4.1) Carbon tax rate sensitivity analysis.

[0269] In order to analyze the impact of carbon tax rate on the optimal path scheme, the carbon tax rate range is adjusted while ensuring that other parameters remain unchanged. Referring to the existing technology, the carbon tax rate range is 0.01~0.40 yuan / kg, and four carbon tax rate intervals are set as Ⅰ[0.00,0.00,0.00,0.00], Ⅱ[0.01,0.02,0.03,0.04], Ⅲ[0.05,0.10,0.15,0.20] and Ⅳ[0.10,0.20,0.30,0.40], and the corresponding carbon emissions are set as ( , , , ) = (10000, 15000, 20000, 25000) and the results of calculating the proportion of transportation modes, operating costs and carbon emissions in the Pareto optimal solution based on the optimal path plan are shown in Table 8. The trend of transportation mode proportion and carbon emissions is shown in Table 8. Fig. 9 The proportion of transportation modes and the changing trends of carbon emissions are shown.

[0270] Table 8 Sensitivity analysis results for different carbon tax rate ranges:

[0271]

[0272] Depend on Fig. 9 From Table 8, we can see that the proportion of various modes of transport in the multi-objective path schemes between the carbon tax rate intervals of Level II [0.01, 0.02, 0.03, 0.04] and Level I [0.00, 0.00, 0.00, 0.00] is relatively small, mainly highway and railway transportation, and carbon emissions have increased slightly. At this time, the constraint of carbon tax is not strong, and carriers will be more inclined to save operating costs. However, starting from the carbon tax rate interval [0.05, 0.10, 0.15, 0.20], the choice of transportation mode has obviously shifted from highway to railway and waterway, and carbon emissions have also shown a significant downward trend, indicating that the increase in carbon tax value can effectively promote multimodal transport carriers to choose transportation schemes with less environmental pollution and give full play to the advantages of railway and waterway transportation.

[0273] (4.2) Time window sensitivity analysis.

[0274] In order to further explore the impact of the transportation time window constraint on the model, the proportion of transportation modes, operating costs and preference function values ​​of the optimal path are obtained by setting different time window constraints. The results of each OD pair under different delivery time windows are different. It can be seen that the change of the transportation time window has a certain impact on the multimodal transport path optimization results. Fig.10Taking the optimization results of the OD pair of a certain place 1-a certain place 2 under different delivery time windows as an example, when the time window interval is [180,480], road transportation is more often chosen. The use of road transportation can save transfer time, thereby shortening the transportation time overall, but the transportation cost is relatively high at this time, the impact on the environment is also high, and the preference function value is low. When the time window interval increases to [480,680], the sea-rail transport mode begins to play a price advantage, the operating cost drops significantly, and it is more environmentally friendly, and the preference function value increases. Therefore, when the time window constraint requirements are high, the constructed model will choose road and rail transportation more. As the time window constraint weakens, the overall proportion of water transportation in the optimal path increases, while the proportion of road transportation decreases, the operating cost decreases, and the environmental friendliness increases, which in turn prompts the carrier to choose water and rail transportation with relatively slow transportation speed and low cost, so as to achieve the purpose of reducing operating costs.

[0275] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A multimodal transport route optimization method under uncertainty, characterized in that: The method comprises the following steps: S1, analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, transform the dual-objective uncertainty stochastic programming model through the sample average approximation method, and obtain a dual-objective deterministic optimization model; S2, establish an independent test sample, test the optimal number of samples, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and the non-dominated solution set is obtained by multiple independent runs of the dual-objective deterministic optimization model; the non-dominated solution set obtained based on all samples is summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path plan; S3, conduct sensitivity analysis on carbon tax rate and time window, and analyze the impact of carbon tax rate and time window fluctuations on the constructed optimal path plan by setting different carbon tax rates and time windows; In step S1, a dual-objective uncertainty stochastic programming model is established, including: on the basis of quantifying the uncertainty of transportation time, considering the transportation volume, time window, and carbon emission constraints, taking the preference functions of operating cost, customer satisfaction, and environmental friendliness as the objectives, a dual-objective uncertainty stochastic programming model is constructed; The expression of the dual-objective uncertainty stochastic programming model is formula (5)-formula (36); Where F1 is the total operating cost of all ODs for the optimal path, F2 is the preference function of all ODs for customer satisfaction and environmental friendliness for the optimal path, is the unit penalty cost under scenario ρ, O is the starting point, D is the end point, r is the transportation path, k is the transportation method, Ω is the sample scenario set; R od is the set of paths starting from O and ending at D; M is the set of transportation modes; is the transportation cost of transport mode k on the segment s of the rth path in the OD pair under scenario ρ, is the transit cost of changing the mode of transport from k to l when transferring from section s to section s+1 on the rth path of the OD pair under scenario ρ; π ρ is the probability corresponding to the transportation time under scenario ρ, is the customer satisfaction of the rth path in the OD pair under scenario ρ, x od,r is a 0-1 decision variable. If the rth path of the OD pair is selected, it takes 1, otherwise it takes 0; is the delay time of path r in scenario ρ; is the environmental friendliness of the rth path in a certain OD pair. The less pollutant emissions, the higher the environmental friendliness. i is the sensitivity level of customer satisfaction of the ith customer, β i is the i-th environmental friendliness sensitivity level.

2. The multimodal transport path optimization method under uncertainty conditions according to claim 1, characterized in that: In step S1, the uncertain transportation time is analyzed and processed, including: For a multimodal transport route with origin O and destination D, the departure time is T dep , the arrival time at the destination is T due ; This route first uses road transport to transport the goods from location A to location B, and then transfers them at location B; then it uses rail transport from location B to location C, and the transportation time is t BC ; Transship at location C and finally arrive at location D by rail transport; The transportation time of this route is subject to the following conditions: T dep +t AB +t B +t BC +t C +t CD ≤T due (1) Where, t AB is the transportation time from location A to location B, t B is the transit time at location B, t C is the transit time at location C, t CD is the transportation time from location C to location D; The rail transport between location B and location C has a fixed departure time t BC , the truck transportation between location C and location D has a departure time window, that is, the goods must arrive at location B in time for rail transportation, and the departure time of section CD is generated based on the arrival time at location C; then there are the following path feasibility constraints; T dep +t AB +t B ≤T BC (2) T BC +t BC +t C +t CD ≤T due (3) By using the sample average approximation SAA to consider the uncertainty of the transportation time, multiple samples are generated and optimized on these samples. As the number of samples increases, the sample average approximation SAA provides a result close to the true optimal solution, expressed as: Where [T1, T2] is the transportation time interval, s is the road section, is the set of OD centering sections, d od，r，s is the distance of the segment s on the rth path in the OD pair, are the maximum speed and minimum speed of transport mode k respectively; x od，r，s，s+1，k，l is a 0-1 variable. When the transport mode changes from k to l on the rth path in the OD pair from section s to section s+1, it takes 1, otherwise it takes 0; t k，l is the transit time between transport mode k and transport mode l, q od is the actual transport volume of the OD pair.

3. The multimodal transport path optimization method under uncertainty conditions according to claim 1, characterized in that: In step S1, the dual-objective uncertainty stochastic programming model is transformed by the sample average approximation method to obtain a dual-objective deterministic optimization model, including: Monte Carlo simulation generates an independent sample set of size G based on the probability distribution of random variables to simulate the real random variable distribution, and the probability of each generated sample is equal, which is 1 / G; at this time, the superscript ρ of the original model is replaced by g, representing the generated random sample; the probability π under each scenario ρ ρ It is also replaced by 1 / G; the above model is converted into a dual-objective deterministic optimization model.

4. The multimodal transport path optimization method under uncertainty conditions according to claim 3 is characterized in that: The dual-objective deterministic optimization model includes: constraint formula (37)-constraint formula (46); In the formula, g is the generated sample, and G is the set of g; st Constraining formula (10) - formula (31), we have: Constraint formula (39) indicates that in the generated random sample, each path plan has an associated departure time, transportation time, and arrival time in each scenario; is the departure time of road segment s under the sample scenario ρ, is the transportation time of road section s under the sample scenario ρ, is the arrival time of road segment s under the sample scenario ρ; Constraint formula (40) indicates that the transportation end time of the previous segment s plus the transfer time in the generated random sample must be completed before the transportation departure time of the next segment s+1; D s+1 is the departure time of segment s+1, is the time delay between road segments s and s+1 under the sample scenario ρ; Constraint formula (41)-constraint formula (43) means that in the generated random samples, when the path plan is not feasible, ensure that x od，r，s，k =0; Constraint formula (44)-constraint (45) represent the time frame of each path plan in the generated random sample. The earliest pickup time of the lower limit is fixed, while the expiration date of the upper limit is variable. is the delay time of each transportation stage of road section s under sample scenario g, is the earliest arrival time of path r; Constraint (46) represents the departure time window of the segment s in the generated random sample.

5. The multimodal transport path optimization method under uncertainty conditions according to claim 1, characterized in that: In step S2, the optimal path solution is obtained, including: S201, using the sample average approximation method to generate non-dominated solutions, and testing the optimal number of samples through optimality difference estimation; S202, for each sample g, the transportation time parameter is substituted into the dual-objective uncertainty stochastic programming model to obtain G dual-objective deterministic optimization models; Monte Carlo simulation generates a sample set according to the probability distribution of the random variable to simulate the real distribution, the sample contains B elements, and the weight of each element is 1 / B; after the sample is generated, the objective function in the g-th sample will use the sample average function to estimate the expected cost value; S203, for each dual-objective deterministic optimization model, use the NSGA-Ⅱ algorithm to solve and obtain the corresponding non-dominated solution set {x1, x2…x B } and the objective function value and S204, the non-dominated solution sets obtained based on all samples are summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path solution.

6. The multimodal transport path optimization method under uncertainty conditions according to claim 5, characterized in that: In step S201, a non-dominated solution is generated by using the sample average approximation method, and the optimal number of samples is checked by optimality difference estimation, including: S2011, using the Monte Carlo simulation method to calculate the probability distribution of transport time π ρ Generate G independent samples {T1, T2…T G }, each sample T g ={t1, t2…t B }, t b represents the bth transport time parameter (b = 1, 2 ... B) in the gth (g = 1, 2 ... G)th ​​sample; generates an independent test sample of size G to evaluate each candidate solution and check whether it satisfies all constraints. If so, it is a feasible solution; selects the candidate feasible solution with the minimum cost as the optimal solution x * ; For any feasible solution, the objective function value under any independent sample is the upper bound of the true objective value; therefore x * The corresponding upper bound is calculated as formula (40); sort the G optimal values ​​corresponding to different samples to obtain the order statistic F with g = 1, 2...G [G] , the Lth-order statistic F [L] The lower bound LB corresponding to the confidence level λ; Where UB is the upper bound of the true target value, F G is the objective function value, For standard normal distribution Quantile, σ U is the standard deviation of the target value in the test sample; In the formula, λ is the confidence level, L is an infinite number, is the maximum number of independent trials in G times The probability of success, i is the number of trials, G is the sample set, and B is the time parameter set; S2022, using optimality difference estimation To evaluate the solution x * The quality of the sample size was chosen to ensure a reasonable optimality gap; In step S202, the expected cost values ​​of objective functions F1 and F2 are assumed to be and Then we have: In the formula, is the expected cost value of the objective function F1, is the expected cost value of the objective function F2, is the customer satisfaction of the rth path in sample b, is the delay time of path r in each transport stage in each sample; The specific steps of step S203 are as follows: S2031, encode the paths in the alternative solution set to obtain the initial population, i.e., the initial solution alternative set; the road section is coded in 0-1, i.e., 0 means not passing through the road section, and 1 means passing through the road section; the transportation mode used by the road section is coded in 1-2-3, where 1 means railway transportation, 2 means road transportation, and 3 means water transportation; assuming that the shipper has m OD pairs of transportation demands, the code of each path selection on each OD pair is M od ; S2032, calculate the operating costs and preference function values ​​of all individuals in the initial population, perform non-dominated sorting, divide into different Pareto front levels, then calculate the crowding degree between individuals in each Pareto front level, and finally use the tournament selection strategy to select the next generation of individuals from the population; S2033, using a non-uniform arithmetic crossover operator and a non-uniform mutation operator, performing crossover and mutation operations on the selected individuals to generate new individuals; S2034, combining the newly generated solution set with the previous generation solution set to obtain a new population, and repeating steps S2032 and S2033; S2035, judging the termination condition, judging whether to terminate the algorithm according to the set termination condition, such as reaching the maximum number of iterations; if the termination condition is met, outputting the Pareto front solution set; otherwise, returning to step S2022 to continue iteration; Step S204 includes: normalizing and standardizing the solution set; denoting the normalized and standardized matrix as A, see formula (45), and determining the positive ideal point A + and negative ideal point A - , calculate the distance between each Pareto solution i and the optimal solution according to formula (46) and formula (47) and the worst solution distance Finally, the score S of the i-th Pareto solution is calculated according to formula (48): i And sort, select S i The largest one is the approximate optimal solution: Where A is the matrix after normalization and standardization, a ij is the matrix value; In the formula, For each Pareto solution i, the distance from the optimal solution is: For each Pareto solution i, S is the distance between it and the worst solution. i is the score of the ith Pareto solution, For the target F j The ideal point value under For the target F j The negative ideal point value under ij is the value of Pareto solution i under target j, and j represents the two evaluation indexes of operating cost and preference function value.

7. The multimodal transport path optimization method under uncertainty conditions according to claim 1, characterized in that: In step S3, the carbon tax rate sensitivity analysis includes: setting 4 carbon tax rate interval levels as Ⅰ[0.00, 0.00, 0.00, 0.00], Ⅱ[0.01, 0.02, 0.03, 0.04], Ⅲ[0.05, 0.10, 0.15, 0.20] and Ⅳ[0.10, 0.20, 0.30, 0.40], and the corresponding carbon emissions are set as (Z1, Z2, Z3, Z4) = (10000, 15000, 20000, 25000) and calculating the proportion of transportation modes, operating costs and carbon emissions in the Pareto optimal solution according to the optimal path plan; Time window sensitivity analysis includes: obtaining the proportion of transportation modes, operating costs and changes in preference function values ​​of the optimal path through different time window constraint settings.

8. A multimodal transport route optimization system under uncertainty, characterized in that: The system implements the multimodal transport path optimization method under uncertainty conditions as described in any one of claims 1 to 7, and the system comprises: The module (1) of the dual-objective deterministic optimization model is used to analyze and process the uncertain transportation time, establish a dual-objective uncertainty stochastic programming model, and transform the dual-objective uncertainty stochastic programming model through the sample average approximation method to obtain a dual-objective deterministic optimization model; The optimal path solution acquisition module (2) is used to establish an independent test sample, test the optimal sample quantity, and use the sample average approximation method to generate a sample scenario set for the transportation time of the dual-objective deterministic optimization model; after the sample scenario set is generated, the objective function uses the sample average function to estimate the expected cost value, and obtains a non-dominated solution set by independently running the dual-objective deterministic optimization model multiple times; the non-dominated solution sets obtained based on all samples are summarized into a total non-dominated solution set, and the optimal solution is approximated by the ideal point method to obtain the optimal path solution; The sensitivity analysis module (3) is used to perform sensitivity analysis on the carbon tax rate and time window. By setting different carbon tax rates and time windows, the impact of carbon tax rate and time window fluctuations on the constructed optimal path solution is analyzed.

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