A multi-objective optimization method for earthwork transportation considering traffic congestion

Abstract

The present invention relates to the field of earthwork and rock transport methods and systems, and provides a multi-objective optimization method for earthwork and rock transport considering traffic congestion, comprising: step 1: constructing an objective function that considers distance, construction period, and environment as optimization objectives, and obtaining a multi-objective optimization model for earthwork and rock transport considering traffic congestion; step 2: determining model constraints, wherein the constraints include earthwork excavation requirements, storage yard capacity restrictions, dump truck quantity constraints, dump truck circulation constraints, road transport intensity restrictions, section flow calculation, section transport time calculation, path transport time calculation, and decision variable constraints; and step 3: solving the multi-objective optimization model for earthwork and rock transport considering traffic congestion based on a Pareto-based multi-objective optimization intelligent algorithm, and obtaining a multi-objective optimized transportation plan for earthwork and rock transport.

Description

Technical Field

[0001] The present invention relates to the field of earthwork transportation methods and systems, and in particular to a multi-objective optimization method for earthwork transportation taking traffic congestion into consideration. Background Art

[0002] The quality of earthwork transportation solutions significantly impacts the overall construction progress, quality, and economic benefits of a project, and has long been a pressing issue in the engineering field. Large-scale earthwork transportation projects are characterized by large volumes, high density, and high dynamics. Traditional transportation algorithms can only handle static or relatively simple transportation scenarios and are unable to meet the requirements of complex transportation projects.

[0003] Large-scale earthwork transportation projects inevitably involve intensive dump truck traffic. Optimizing and managing traffic flow and the frequency of dump trucks along transportation routes is crucial to the overall efficiency of the project. However, existing transportation models fail to account for the impact of traffic congestion on transportation outcomes, resulting in long earthwork transportation distances and extended construction periods.

[0004] In response to the above problems, a multi-objective optimization method for earthwork transportation that takes traffic congestion into consideration is urgently needed to meet the goals of green, economical and efficient development of earthwork transportation projects. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective optimization method for earthwork transportation taking into account traffic congestion, which is intended to be used for formulating earthwork transportation plans, to provide scientific guidance for real-time adjustment of earthwork transportation projects and decision-making on optimization plans, and to achieve the optimized transportation goals of reducing costs and increasing efficiency.

[0006] To achieve the above objectives, the present invention provides the following technical solutions:

[0007] The present invention provides a multi-objective optimization method for earthwork transportation taking traffic congestion into consideration, the multi-objective optimization method for earthwork transportation comprising:

[0008] Step 1: Construct an objective function that takes distance, construction period, and environment into consideration as optimization targets, and obtain a multi-objective optimization model for earthwork transportation considering traffic congestion;

[0009] Step 2: Determine model constraints, including earthwork excavation requirements, storage yard capacity restrictions, dump truck quantity constraints, dump truck circulation constraints, road transport intensity restrictions, section flow calculations, section transport time calculations, route transport time calculations, and decision variable constraints.

[0010] Step 3: Based on the Pareto multi-objective optimization intelligent algorithm, the multi-objective optimization model of earthwork transportation considering traffic congestion is solved to obtain the multi-objective optimization transportation plan for earthwork.

[0011] Furthermore, the specific steps of step 1 are:

[0012] Define all excavation sites to form a set I, any excavation site ; All the storage yards constitute a set J, any storage yard ; All intermediate nodes constitute a set M, any intermediate node ; The daily excavation volume of excavation site i is The remaining capacity of storage yard j per day is The set of all possible paths from the excavation site to the storage site is L, where any path l L, where the path includes starting from the excavation site to the storage site and returning to the excavation site; when the excavation site and storage yards When there is a path between represents the set of paths starting from excavation site i and ending at storage site j, where the path includes starting from the excavation site, reaching the storage site and returning to the excavation site; For road segment collection, represents the road section that path l passes through; the number of dump trucks owned by excavation site i is ; During the period Time Path The flow rate of dump trucks (i.e. the number of trucks dispatched) is , is the decision variable;

[0013] Minimize total haul distance for:

[0014] (Formula 1);

[0015] Minimize total shipping time for:

[0016] (Formula 2);

[0017] Minimize environmental impact for:

[0018] (Formula 3);

[0019] in, For path Total transport distance; is the carbon emission coefficient of the fuel; is the fuel consumption rate when unladen and traveling at optimal speed; Indicates the time period Dump truck passing by The average speed, It is the most fuel-efficient speed; is the load influence coefficient, is the driving speed influence coefficient; Indicates the path that the dump truck passes through The required transportation time; T represents the set of transportation time periods.

[0020] Furthermore, the model constraints in step 2 are specifically as follows:

[0021] Dump truck from the excavation site The earth and stone transported needs to meet the excavation demand, so the earth and stone excavation demand is:

[0022] (Formula 4);

[0023] Among them, Cap represents the loading capacity of the dump truck;

[0024] Transported to storage yard The earthwork cannot exceed the remaining capacity of the stockpile, so the stockpile capacity limit is:

[0025] (Formula 5);

[0026] From the excavation site The number of dump trucks sent cannot exceed the maximum number, so the number of dump trucks is constrained as follows:

[0027] (Formula 6);

[0028] To ensure the dump truck circulation, the dump truck on each path needs to go from the excavation site to the storage site and then return to the excavation site within each time period. The dump truck circulation constraint is:

[0029] (Formula 7);

[0030] in, is the time period length;

[0031] Passing through the road section at any time The transport intensity of all paths cannot exceed the maximum transport intensity of the road, so the road transport intensity limit is:

[0032] (Equation 8);

[0033] in, for The maximum daily road transport intensity of the road section, Indicates the path Whether it passes through the road section , if passed, it is 1, otherwise it is 0;

[0034] Any time period, road section The flow rate of is equal to the sum of the flow rates of all paths passing through the road section in the current period, so the road section flow rate is:

[0035] (Formula 9);

[0036] in, For the period road section Traffic volume;

[0037] The transport time of a road section is affected by the traffic flow of the road section. When the traffic flow increases, the transport time increases accordingly. The transport time required for a dump truck to pass through road section r is for:

[0038] (Equation 10);

[0039] in, represents the capacity of road section r; Indicates the time period The capacity of road section r; express The transport time corresponding to the free flow speed of the road section; and These are the parameters of the BPR function (Bureau of Public Roads function, Federal Highway Administration of the United States);

[0040] The path transportation time is the sum of the transportation time of each section it passes through, so the path transportation time for:

[0041] (Equation 11);

[0042] The decision variable constraints are:

[0043] (Equation 12);

[0044] in, is a set of non-negative integers.

[0045] Furthermore, the specific process of step 3 is:

[0046] Step 31, initialize the population: The Pareto-based multi-objective optimization intelligent algorithm randomly generates a solution number of The initial solution set , each solution contains A one-dimensional vector of elements (all elements are integers), representing an earthwork transportation plan;

[0047] Step 32, objective function calculation: First, based on (Equation 9)-(Equation 11), calculate the section flow, section transportation time and path transportation time; secondly, based on (Equation 1)-(Equation 3), calculate the minimized total transportation time corresponding to the solution and minimize environmental impact Finally, the degree to which the solution violates the constraint is calculated based on (Equation 4)-(Equation 8), and the sum of all constraint violation values is used as the constraint violation value of the solution.

[0048] Step 33, fast non-dominated sort: traverse the current solution set All solutions in , according to the objective function value and constraint violation value obtained in step 32, judge the dominance relationship between the solutions based on the Pareto dominance relationship and determine any solution Two parameters of and ,in Represents the dominant solution The number of other solutions of To be solved The set of dominated solutions is hierarchically sorted using the fast non-dominated sorting algorithm;

[0049] Step 34, determine the crowding distance: take the sum of the distance differences between two adjacent solutions on each target to calculate the crowding distance, and estimate the density of solutions around the solution;

[0050] Step 35: Generate updated solution set :First, each time from the current solution set Randomly select two solutions from and Compare and select a better solution based on the Pareto dominance relationship, and repeat the operation once to obtain two better and different current solutions obtained by comparison. and ; Then, the two current solutions are selected and Perform parameter reorganization and random perturbation operations to obtain two updated solutions and , and place it into the updated solution set The above selection operation is repeated times, ensuring that the updated solution set The number of solutions is still ;

[0051] Step 36: Use the elite strategy to retain the best solutions: and update solution set All merged into a large collection and will Sort and grade according to the fast non-dominated sorting rule and calculate the congestion distance. Select solutions with non-dominated levels less than the preset level or solutions with congestion distance greater than the preset threshold as the new round of solution sets, where the preset level and preset threshold are pre-set according to the specific application scenario and optimization goal;

[0052] Step 37, evolution termination condition judgment: repeat steps 32 to 36 until the maximum number of iterations is reached or a solution that meets the accuracy requirements is found.

[0053] Furthermore, in step 34, it is assumed that is the objective function, and the solution set size is , when there is When the target is The crowding distance Expressed as:

[0054] (Equation 13)

[0055] in, Indicates the +1 solution objective function values; Indicates the -1 solution The objective function value.

[0056] Further, in step 35, the two current solutions selected are and Reorganize the parameters and get the new solution after reorganization and , where X i Represents the solution No. elements, the specific process is:

[0057] Randomly generate one Random integer in range , and make the new solution Before elements and the current solution Before The elements are equal, To The elements are No. To elements are equal; let the new solution Before elements and the current solution Before The elements are equal, To The elements are No. To elements are equal; that is:

[0058] .

[0059] Furthermore, the random perturbation operation in step 35 is performed on the reorganized new solution and Processing is performed by recombining the new solution with a preset probability and Perturb at certain locations, new solution and After perturbation, we get and , whose expression is:

[0060]

[0061] in, express Uniform distribution within the range, is the upper limit of the random perturbation value, is the probability of random disturbance; is the probability value of random generation.

[0062] The present invention has the following beneficial effects:

[0063] (1) This paper constructs a multi-objective optimization model that takes into account distance, construction period, and the environment. Based on the earthwork excavation requirements and storage yard capacity constraints, it also takes into account multiple influencing factors such as road transport intensity, vehicle numbers, vehicle circulation, and the road network flow-speed-density relationship. The multi-objective optimization transportation plan for earthwork obtained through this model can effectively balance the relationship between transportation distance, transportation time, and environmental impact, avoiding other problems caused by single-objective optimization, thereby achieving cost reduction and efficiency improvement, and improving the overall benefits of the entire project.

[0064] (2) The present invention is based on a Pareto-based multi-objective optimization intelligent algorithm that integrates multiple effective strategies. The objective function of the solution and the constraint violation value are considered together to compare the quality of the solution, enabling the algorithm to better balance various factors during the solution process; fast non-dominated sorting stratifies the solutions according to their quality, which helps to clearly judge the quality level of the solution; parameter reorganization and random perturbation operations increase the algorithm's search capability, enabling it to explore the solution space more widely and find better solutions; the elite strategy retains the better solutions, ensuring that the algorithm does not lose high-quality solutions during the iteration process, and continuously improves the quality of the solution.

[0065] (3) The Pareto frontier obtained by the algorithm of this invention shows the set of multi-objective optimal solutions for earthwork transportation. In actual projects, the makers of transportation plans can flexibly select the most appropriate optimization scheme from the Pareto frontier according to the specific project requirements and actual conditions. For example, when the construction period is high, the scheme with a shorter total transportation time can be selected; in projects that focus on environmental protection, the scheme with lower carbon emissions can be given priority. This flexibility provides a scientific and comprehensive basis for engineering decision-making, which can better meet the diverse needs of green, economical and efficient development of earthwork transportation projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a multi-objective optimization flow chart of earthwork transportation in the present invention.

[0067] Figure 2 It is a schematic diagram of road sections and paths.

[0068] Figure 3 It is a multi-objective optimization intelligent algorithm solution process based on Pareto.

[0069] Figure 4 It is a schematic diagram of calculating the congestion distance in the present invention.

[0070] Figure 5 , which is a Pareto front diagram from a two-dimensional perspective in the embodiment.

[0071] Figure 6 3D Pareto front diagram in the embodiment.

[0072] Figure 7 It is a transportation flow diagram corresponding to the three optimal solutions included in the Pareto front in the embodiment. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described in detail below in conjunction with specific embodiments, but this embodiment is not intended to limit the present invention. All similar structures and similar variations of the present invention should be included in the scope of protection of the present invention. The semicolons in the present invention represent the relationship of and, and the English letters in the present invention are case-sensitive.

[0074] like Figure 1 As shown, the present invention provides a multi-objective optimization method for earthwork transportation considering traffic congestion, the multi-objective optimization method for earthwork transportation comprising:

[0075] S1, construct an objective function that takes distance, construction period, and environment into consideration as optimization targets, and obtain a multi-objective optimization model for earthwork transportation considering traffic congestion; the specific steps are:

[0076] Define all excavation sites to form a set I, any excavation site ; All the storage yards constitute a set J, any storage yard ; All intermediate nodes constitute a set M, any intermediate node ; The daily excavation volume of excavation site i is The remaining capacity of storage yard j per day is The set of all possible paths from the excavation site to the storage site is L, where any path l L, where the path includes starting from the excavation site to the storage site and returning to the excavation site; when the excavation site and storage yards When there is a path between represents a set of paths starting from the excavation site i and ending at the storage site j, where the path includes starting from the excavation site, reaching the storage site and returning to the excavation site, such as Figure 2 As shown, there are two paths from the excavation site I1 to the storage site J1, namely paths L1 and L2. Among them, in path L1, the excavation site I1 to the intermediate node M1 is section R1, the intermediate node M1 to the intermediate node M2 is section R2, and the intermediate node M2 to the storage site J1 is section R4; in path L2, the excavation site I1 to the intermediate node M1 is section R1, the intermediate node M1 to the intermediate node M3 is section R3, and the intermediate node M3 to the storage site J1 is section R5. For road segment collection, represents the road section that path l passes through; the number of dump trucks owned by excavation site i is ; During the period Time Path The flow rate of dump trucks (i.e. the number of trucks dispatched) is , is the decision variable;

[0077] Minimize total haul distance for:

[0078] (Formula 1);

[0079] Minimize total shipping time for:

[0080] (Formula 2);

[0081] Minimize environmental impact for:

[0082] (Formula 3);

[0083] in, For path Total transport distance; is the carbon emission coefficient of the fuel (unit: kg CO2 / liter fuel); is the fuel consumption rate when unladen and traveling at optimal speed (in liters per kilometer); Indicates the time period Dump truck passing by The average speed, It is the most fuel-efficient speed; is the load influence coefficient, is the driving speed influence coefficient, which is usually determined through experimental data;

[0084] Indicates the path that the dump truck passes through The required transportation time; T represents the set of transportation time periods.

[0085] S2, determining model constraints, including earthwork excavation requirements, storage yard capacity restrictions, dump truck quantity constraints, dump truck circulation constraints, road transport intensity restrictions, section flow calculation, section transport time calculation, route transport time calculation, and decision variable constraints;

[0086] Dump truck from the excavation site The earth and stone transported needs to meet the excavation demand, so the earth and stone excavation demand is:

[0087] (Formula 4);

[0088] Among them, Cap represents the loading capacity of the dump truck;

[0089] Transported to storage yard The earthwork cannot exceed the remaining capacity of the stockpile, so the stockpile capacity limit is:

[0090] (Formula 5);

[0091] From the excavation site The number of dump trucks sent cannot exceed the maximum number, so the number of dump trucks is constrained as follows:

[0092] (Formula 6);

[0093] To ensure the dump truck circulation, the dump truck on each path needs to go from the excavation site to the storage site and then return to the excavation site within each time period. The dump truck circulation constraint is:

[0094] (Formula 7);

[0095] in, is the time period length;

[0096] Passing through the road section at any time The transport intensity of all paths cannot exceed the maximum transport intensity of the road, so the road transport intensity limit is:

[0097] (Equation 8);

[0098] in, for The maximum daily road transport intensity of the road section, Indicates the path Whether it passes through the road section , if passed, it is 1, otherwise it is 0;

[0099] Any time period, road section The flow rate of is equal to the sum of the flow rates of all paths passing through the road section in the current period, so the road section flow rate is:

[0100] (Formula 9);

[0101] in, For the period road section Traffic volume;

[0102] The transport time of a road section is affected by the traffic flow of the road section. When the traffic flow increases, the transport time increases accordingly. The transport time required for a dump truck to pass through road section r is for:

[0103] (Equation 10);

[0104] in, represents the capacity of road section r; Indicates the time period The capacity of road section r; express The transport time corresponding to the free flow speed of the road section; and These are parameters of the BPR function (Bureau of Public Roads function, Federal Highway Administration of the United States), with recommended values of 0.15 and 4 respectively.

[0105] The path transportation time is the sum of the transportation time of each section it passes through, so the path transportation time for:

[0106] (Equation 11);

[0107] The decision variable constraints are:

[0108] (Equation 12);

[0109] in, is a set of non-negative integers.

[0110] S3, a Pareto-based multi-objective optimization intelligent algorithm, solves the multi-objective optimization model of earthwork transportation considering traffic congestion and obtains a multi-objective optimization transportation plan for earthwork;

[0111] like Figure 3 As shown, the specific process is:

[0112] S31, initialize the population: The Pareto-based multi-objective optimization intelligent algorithm randomly generates a solution number of The initial solution set , each solution contains A one-dimensional vector of elements (all elements are integers), representing an earthwork transportation plan;

[0113] S32, objective function calculation: First, based on (Equation 9)-(Equation 11), calculate the section flow, section transportation time and path transportation time; secondly, based on (Equation 1)-(Equation 3), calculate the minimized total transportation time corresponding to the solution and minimize environmental impact Finally, the degree to which the solution violates the constraint is calculated based on (Equation 4)-(Equation 8), and the sum of all constraint violation values is used as the constraint violation value of the solution.

[0114] S33, Fast Non-Dominated Sort: Traverse the Current Solution Set All solutions in , according to the objective function value and constraint violation value obtained in step 32, judge the dominance relationship between the solutions based on the Pareto dominance relationship and determine any solution Two parameters of and ,in Represents the dominant solution The number of other solutions of To be solved The set of solutions dominated by the Pareto dominance relation is defined as follows: ,and , called solution Dominant solution , that is, in the objective function, there is at least one objective function component, the solution The value is less than the solution , and other objective function components will not be better than the solution The Pareto optimal solution is defined as: if for a feasible solution , there is no other feasible solution Dominate ,but is the Pareto optimal solution.

[0115] The fast non-dominated sorting algorithm is as follows:

[0116] Set the current solution Initialized to an empty set; for each solution in the current solution set Two parameters of and Initialize, Initialized to 0, Initialized to an empty set; for the current solution , traverse each solution in the solution set except itself, if Dominate , then Add to collection In, if Dominate , then The value of is increased by 1; if The value is 0, indicating that there is no other solution dominating , then Add to the 0th layer P[0] of the layered solution set and initialize the current layer level to 0; when the current layer P[level] is not empty, initialize the next layer P[level+1] to an empty set; for each solution in the current layer P[level] :For Dominated solution set Each solution in ,Will The value of is reduced by 1; if The value of becomes 0, indicating that there is no other solution dominating , then The level is marked as level+2, and Add it to the next layer P[level+1] and increase the level by 1. Through the fast non-dominated sorting algorithm, any solution can be determined Three parameters , and ,in represent The number of all solutions in excluding the current solution, To be solved The set of solutions dominated by , all solutions are hierarchically sorted by the fast non-dominated sorting algorithm, For solution The level it is in (the lowest level is the first level), To be solved The set of solutions dominated by the solution set. This achieves a hierarchical ranking of all solutions, where lower-level solutions dominate higher-level solutions, and solutions at the same level do not dominate each other. This hierarchical structure can help better understand the relationship between the advantages and disadvantages of solutions in the solution set.

[0117] S34, determine the crowding distance: take the sum of the distance differences between two adjacent solutions on each target to calculate the crowding distance, and estimate the density of solutions around the solution; the crowding distance of a solution refers to the measurement of the search space around a solution that is not occupied by any other solution in the population. The significance of calculating the crowding distance is that solutions with a larger crowding distance are farther away from other solutions and are more representative. Figure 4 As shown, there are two sub-goals and , then the solution The sum of the congestion distances is the sum of the length and width of the dotted line in the figure. is the objective function, and the solution set size is , when there is When the target is The crowding distance Expressed as:

[0118] (Equation 13)

[0119] in, Indicates the +1 solution objective function values; Indicates the -1 solution The objective function value.

[0120] S35, generate updated solution set :First, each time from the current solution set Randomly select two solutions from and Compare and select a better solution based on the Pareto dominance relationship, and repeat the operation once to obtain two better and different current solutions obtained by comparison. and ; Among them, X i Represents the solution No. elements, specifically: from the current solution set Randomly select two solutions from and Compare them. If there is a dominance relationship between the two, choose the solution with a lower level. Otherwise, choose the solution with a larger congestion distance. Let the selected solution be ,Right now:

[0121]

[0122] in, is the crowding distance function, Then, repeat the operation and select another solution. and ensure , as the basis for parameter reorganization and random perturbation. , then continue to repeat the operation until the two are different; the above selection operation is repeated N / 2 times to ensure that the updated solution set The number of solutions is still N; then, the two current solutions are selected and Perform parameter reorganization and random perturbation operations to obtain two updated solutions and ;

[0123] For the two current solutions selected and Reorganize the parameters and get the new solution after reorganization and The specific process is:

[0124] Randomly generate one Random integer in range , and make the new solution Before elements and the current solution Before The elements are equal, To The elements are No. To elements are equal; let the new solution Before elements and the current solution Before The elements are equal, To The elements are No. To elements are equal; that is:

[0125] .

[0126] Random perturbation operation targets the new solution after reorganization and Processing is performed by recombining the new solution with a preset probability and Perturbations are performed at certain locations to enhance the global search capability of the algorithm; new solution and After perturbation, we get and , whose expression is:

[0127]

[0128] in, express Uniform distribution within the range, is the upper limit of the random perturbation value, is the probability of random disturbance; is the probability value of random generation.

[0129] S36, using elite strategy to retain high-quality solutions: the current solution set and update solution set All merged into a large collection and will Sort and grade according to the fast non-dominated sorting rule and calculate the congestion distance. The solutions with non-dominated levels less than the preset level or the solutions with congestion distance greater than the preset threshold are selected as the new round of solution sets; the preset level and preset threshold are pre-set according to the specific application scenario and optimization goal;

[0130] S37, determine the evolution termination condition: Repeat steps 32-36 until the maximum number of iterations is reached or a solution that meets the accuracy requirements is found. The set of solutions in the layer with the lowest non-dominated level in the current solution set at termination is considered the Pareto optimal set (Pareto front). The Pareto front is the set of non-dominated solutions in which there is no domination relationship between the solutions. That is, for any solution in the set, there is no solution that is better than all other objectives.

[0131] This invention is based on a Pareto-based multi-objective optimization intelligent algorithm that integrates multiple effective strategies. It compares the quality of solutions by considering both the objective function and the constraint violation value, enabling the algorithm to better balance various factors during the solution process. Fast non-dominated sorting stratifies solutions based on their quality, helping to clearly determine the quality level of the solutions. Parameter reorganization and random perturbation operations enhance the algorithm's search capabilities, enabling it to more extensively explore the solution space and find more optimal solutions. An elitist strategy retains the best solutions, ensuring that high-quality solutions are not lost during the algorithm's iterations, continuously improving the quality of the solutions.

[0132] This paper constructs a multi-objective optimization model that considers distance, construction period, and the environment. Based on earthwork excavation requirements and storage site capacity constraints, it also takes into account multiple influencing factors, including road transport intensity, vehicle numbers, vehicle circulation, and the road network flow-speed-density relationship. The multi-objective optimized earthwork transportation plan derived from this model effectively balances transportation distance, transportation time, and environmental impact, avoiding the problems associated with single-objective optimization, thereby reducing costs and increasing efficiency, and improving the overall benefits of the entire project.

[0133] Example

[0134] In order to verify the adaptability of this scheme and the effectiveness of the algorithm, numerical experiments are carried out through the generated simulation examples to conduct a multi-objective optimization decision analysis of earthwork transportation in a canal considering traffic congestion.

[0135] The engineering information of the simulation example is as follows:

[0136] (1) There are 3 excavation sites, 4 storage sites, and 4 intermediate nodes;

[0137] (2) The information settings of each transportation location are shown in Table 1;

[0138] (3) The road section and path information are shown in Table 2 and Table 3 respectively;

[0139] (4) The maximum cargo capacity of a dump truck is 25 cubic meters, and the speed at which a dump truck has the highest fuel efficiency is The fuel consumption rate of a dump truck traveling at an optimal speed of 48 km / h when empty is 0.25L / km;

[0140] (5) Load influence coefficient The driving speed influence coefficient is 0.3. The carbon emission coefficient of the fuel is 0.2. 2.68 kg CO2 / L fuel;

[0141] (6) The full-day transportation plan is divided into four periods, each of which is 6 hours long, namely: Period 1 (0:00-6:00), Period 2 (6:00-12:00), Period 3 (12:00-18:00), Period 4 (18:00-24:00);

[0142] Table 1

[0143]

[0144] Table 2

[0145]

[0146] Table 3

[0147]

[0148] After calculation, the Pareto frontier and multi-objective earthwork transportation plan are obtained as follows: Figure 5-Figure 7 shown. Figure 5 Show the Pareto front in two dimensions, Figure 6 The three-dimensional Pareto front shows that it's difficult to simultaneously optimize distance, time, and carbon emissions. Focusing on one objective inevitably sacrifices the optimization of the others. Therefore, planners for earthwork transportation need to choose the most appropriate optimization solution based on the actual situation, rather than focusing solely on a specific objective. Figure 7 The Pareto front shows the corresponding solutions when the three goals of distance, time and carbon emissions are optimized. The first row is the solution with the best distance, the second row is the solution with the best time, and the third row is the solution with the best carbon emissions. The road conditions are divided into three levels: slow, good and smooth according to the speed of the dump truck passing through the road section. Slow is represented by a dotted line, good is represented by a dotted line, and smooth is represented by a solid line. Figure 7 It can be seen that compared with the other two options, the option with the best distance has more serious traffic congestion, and some sections of time period four have slow traffic; compared with the other two options, the option with the best time has smoother traffic overall, and there are no sections or time periods with slow traffic; compared with the other two options, the option with the best carbon emissions has a speed in each time period and section that is closer to the optimal speed of dump trucks, thereby reducing overall carbon emissions.

[0149] In summary, the present invention takes traffic congestion into consideration and optimizes the earthwork transportation plan for each time period. First, the earthwork transportation problem is introduced, the reason for combining path optimization is explained, and the problem is abstracted. Then, an effective multi-objective optimization model for earthwork transportation is established, which comprehensively considers the three objectives of distance, construction period and environment. On the basis of considering the earthwork excavation demand and the storage yard capacity limit, it also considers traffic characteristics such as road transportation intensity, number of vehicles, vehicle circulation and road network flow-speed-density relationship, and constructs a multi-objective optimization model for earthwork transportation considering traffic congestion. According to the characteristics of the established multi-objective optimization model, a Pareto-based multi-objective optimization intelligent solution algorithm is designed, and an optimization process is given.

[0150] It should be noted that the above are only preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

[0151] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

Claims

1. A multi-objective optimization method for earthwork transportation considering traffic congestion, characterized in that: The multi-objective optimization method for earthwork transportation includes: Step 1: Construct an objective function that takes distance, construction period, and environment into consideration, and obtain a multi-objective optimization model for earthwork transportation considering traffic congestion; define all excavation sites as a set I, where any excavation site i∈I; all storage sites as a set J, where any storage site j∈J; all intermediate nodes as a set M, where any intermediate node m∈M; the daily excavation volume of excavation site i is O i ; The remaining capacity of storage yard j per day is P j The set of all possible paths from the excavation site to the storage site is L, where any path l∈L includes the path from the excavation site to the storage site and back to the excavation site. When there is a path between excavation site i and storage site j, L(i,j) represents the set of paths starting from excavation site i and ending at storage site j, where the path includes the path from excavation site to storage site and back to the excavation site. R is the set of road segments, and R(l) represents the road segments passed by path l. The number of dump trucks owned by excavation site i is H. i ; The flow of dump trucks on path l at time period t is x lt , x lt is the decision variable; Minimize the total transport distance F1: Minimize the total transportation time F2 as: Minimizing environmental impact F3 is: Among them, EE l is the total transport distance of path l; K f is the carbon emission coefficient of the fuel; FC0 is the fuel consumption rate when the vehicle is unloaded and traveling at the optimal speed; represents the average speed of the dump truck passing through path l during time period t, v opt is the speed with the highest fuel efficiency; k1 is the load influence coefficient, k2 is the driving speed influence coefficient; Tim lt represents the transportation time required for the dump truck to pass through path l; T represents the set of transportation time periods; Step 2: Determine model constraints, including earthwork excavation requirements, storage yard capacity restrictions, dump truck quantity constraints, dump truck circulation constraints, road transport intensity restrictions, section flow calculations, section transport time calculations, route transport time calculations, and decision variable constraints. Step 3: Based on the Pareto multi-objective optimization intelligent algorithm, the multi-objective optimization model of earthwork transportation considering traffic congestion is solved to obtain the multi-objective optimization transportation plan for earthwork; The specific process is: Step 31, initializing the population: The Pareto-based multi-objective optimization intelligent algorithm randomly generates an initial solution set P0 with N solutions at the beginning. Each solution is a one-dimensional vector containing L×T elements, representing an earthwork transportation plan; Step 32, objective function calculation: First, based on (Equation 9)-(Equation 11), calculate the segment flow rate, segment transport time, and path transport time; second, based on (Equation 1)-(Equation 3), calculate the minimized total transport distance F1, minimized total transport time F2, and minimized environmental impact F3 corresponding to the solution; finally, based on (Equation 4)-(Equation 8), calculate the degree of constraint violation of the solution, and sum all constraint violation values as the constraint violation value of the solution; Step 33, fast non-dominated sorting: traverse all solutions in the current solution set P, and judge the dominance relationship between solutions based on the Pareto dominance relationship according to the objective function value and constraint violation value obtained in step 32, and determine any solution X n The two parameters m n and S n , where m n Stands for S n The number of all solutions except the current solution, S n To be solved n The set of dominated solutions is hierarchically sorted using the fast non-dominated sorting algorithm; Step 34, determine the crowding distance: take the sum of the distance differences between two adjacent solutions on each target to calculate the crowding distance, and estimate the density of solutions around the solution; Step 35, generate updated solution set Q: First, randomly select two solutions X1 and X1′ from the current solution set P for comparison, and select the better solution according to the Pareto dominance relationship, and repeat this operation once to obtain two better and different current solutions obtained by comparison. and Then, the two current solutions are selected. and Perform parameter reorganization and random perturbation operations to obtain two updated solutions X3′ and X4′, and place them in the updated solution set Q; repeat step 35 N / 2 times to ensure that the number of solutions in the updated solution set Q remains N; Step 36: Use the elite strategy to retain high-quality solutions: merge the current solution set P and the updated solution set Q into the large set R t and R t Sort and grade according to the fast non-dominated sorting rule and calculate the crowding distance from R t Select the solutions whose non-dominated level is less than the preset level or whose congestion distance is greater than the preset threshold as the new round of solution set; Step 37, evolution termination condition judgment: repeat steps 32 to 36 until the maximum number of iterations is reached or a solution that meets the accuracy requirements is found.

2. The multi-objective optimization method for earthwork transportation considering traffic congestion according to claim 1 is characterized in that: The model constraints in step 2 are as follows: The earth and stone transported by the dump truck from the excavation site i needs to meet the excavation demand, so the earth and stone excavation demand is: Among them, Cap represents the cargo capacity of the dump truck; The earth and stone transported to storage yard j cannot exceed the remaining capacity of the storage yard, so the storage yard capacity limit is: The number of dump trucks sent from excavation site i cannot exceed its maximum number, so the number of dump trucks is constrained as follows: To ensure the dump truck circulation, the dump truck on each path needs to go from the excavation site to the storage site and then return to the excavation site within each time period. The dump truck circulation constraint is: Where DT is the time period length; The transport intensity of all paths passing through road section r at any time cannot exceed the maximum transport intensity of the road. The road transport intensity limit is: Among them, B r is the maximum daily road transport intensity of section r, δ rl Indicates whether the path l passes through the road segment r, if so, it is 1, otherwise it is 0; At any time period, the flow rate of section r is equal to the sum of the flow rates of all paths passing through the section in the current period, so the section flow rate is: Among them, q rt is the flow rate of road section r in time period t; The transport time of a road section is affected by the traffic flow of the road section. When the traffic flow increases, the transport time increases accordingly. The transport time Tim required for a dump truck to pass through road section r is rt for: in, represents the capacity of road section r; q rt represents the capacity of road section r in time period t; represents the transport time corresponding to the free flow speed of section r; α and β are the unknown parameters of the BPR function; The path transportation time is the sum of the transportation time of each section it passes through, so the path transportation time Tim lt for: The decision variable constraints are: Where N0 is a set of non-negative integers.

3. The multi-objective optimization method for earthwork transportation considering traffic congestion according to claim 1 is characterized in that: In step 34, let f k is the objective function, the solution set size is N, when there are K objectives, the solution X n The crowding distance τ n Expressed as: in, represents the kth objective function value of the n+1th solution; Represents the kth objective function value of the n-1th solution.

4. The multi-objective optimization method for earthwork transportation considering traffic congestion according to claim 1, characterized in that: In step 35, the two current solutions are selected. and Perform parameter reorganization to obtain the reorganized new solutions X3 and X4. The specific process is as follows: Randomly generate a random integer γ in the range [1, L·T] and let the first γ elements of the new solution X3 be the same as the current solution The first γ elements are equal to , and the γ+1th to L·Tth elements are equal to The first γ+1 to L·T elements of the new solution X4 are equal; let the first γ elements of the new solution X4 be equal to the current solution The first γ elements are equal to , and the γ+1th to L·Tth elements are equal to The γ+1th to L·Tth elements of are equal; that is:

5. The multi-objective optimization method for earthwork transportation considering traffic congestion according to claim 4 is characterized in that: In step 35, the random perturbation operation is performed on the reorganized new solutions X3 and X4. By perturbing the reorganized new solutions X3 and X4 at certain positions with a preset probability, the new solutions X3 and X4 are perturbed to obtain X3′ and X4′, which are expressed as follows: Among them, U(-ε,ε) represents the uniform distribution within the range of (-ε,ε), ε is the upper limit of the random disturbance value, is the probability of random disturbance; p i is the probability value of random generation.

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