Multi-objective optimization design modeling method based on freight carbon emission and profit

Abstract

The invention relates to the technical field of multi-objective optimization function modeling, in particular to a freight carbon emission and profit-based multi-objective optimization design modeling method, which comprises the following steps of: 1, defining objective functions according to optimal design, the objective functions being respectively the minimum freight carbon emission and the maximum freight profit; 2, designing decision variables; 3, verifying constraint conditions to ensure feasibility and reasonability of the model; 4, performing multi-objective function operation on the six decision variables of the experimental data, and calculating how each decision variable independently meets the minimum freight carbon emission and the maximum freight profit; and step 5, according to a particle swarm optimization algorithm, calculating an overall condition meeting the optimal design of all objective functions. Through the innovative modeling and optimization scheme, the freight carbon emission can be effectively reduced, the freight profit is improved, and the optimization model has reasonability and effectiveness.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-objective optimization function modeling, and in particular to a multi-objective optimization design modeling method based on freight carbon emissions and profits. Background Art

[0002] The freight structure has long been dominated by road transportation, which has led to high energy consumption and serious environmental pollution. It also faces problems such as traffic congestion and high transportation costs.

[0003] Existing research on freight carbon emissions forecasting and structural optimization has significant shortcomings. Data limitations hinder refined forecasting due to provincial macroeconomic data. Existing optimization models often focus on a single carbon emissions metric, neglecting economic objectives such as transport profits, making sustainable development difficult. Furthermore, forecasting and optimization models are independent and lack effective integration, preventing a closed-loop approach to fully support decision-making. Furthermore, existing optimization models are inadequate when considering multi-objective collaborative optimization, making it difficult to balance carbon emissions reductions with economic benefits. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology and propose a multi-objective optimization design modeling method based on freight carbon emissions and profits. Through innovative modeling and optimization schemes, it can effectively reduce freight carbon emissions, increase freight profits, and make the optimization model reasonable and effective.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-objective optimization design modeling method based on freight carbon emissions and profits includes the following steps:

[0007] Step 1: Define objective functions based on the optimization design, wherein the objective functions are minimizing freight carbon emissions and maximizing freight profits;

[0008] Step 2: Design decision variables. In this modeling method, the decision variables mainly include six: railway freight volume, highway freight volume, water freight volume, railway freight mileage, highway freight mileage, and water freight mileage;

[0009] Step 3: Verify the constraints to ensure the feasibility and rationality of the model and effectively improve the practicality and accuracy of the optimization model. This mainly includes: fitting verification of freight volume forecasts and actual values, sensitivity analysis of the obtained values, and the degree of fit between data changes and relevant national policies;

[0010] Step 4: Perform multi-objective function calculations on the six decision variables of the experimental data to determine how each decision variable can individually meet the requirements of minimum freight carbon emissions and maximum freight profits.

[0011] Step 5: Calculate the overall conditions for the optimal design that meets all objective functions based on the particle swarm optimization algorithm.

[0012] Preferably, in step 1, the primary optimization objective of the multi-objective optimization model is freight carbon emissions, that is, minimizing freight carbon emissions within a reasonable range to reduce the pressure on society to deal with carbon emissions. Minimizing freight carbon emissions is used as the first objective function, and the objective function for solving the minimum carbon emissions is:

[0013] minf(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=11.33M 铁 ·X 铁 +97.6M 公 ·X 公 +8.65M 水 ·X 水 (1)

[0014] Among them, M 铁 、M 公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X 铁 、X

[0015] 公 、X 水 They represent railway mileage, highway mileage and waterway mileage respectively.

[0016] In reality, minimizing freight carbon emissions is not the only goal; profitability must also be considered. This means minimizing freight carbon emissions while maximizing profits. To this end, maximizing freight profit is used as the second objective function. Freight profit is calculated by subtracting the unit turnover cost from the previously published unit turnover rate for each freight mode to obtain the profit per unit turnover k (yuan / t·km). This is then multiplied by the corresponding freight turnover volume, and the sum is calculated to obtain the freight profit value.

[0017] Taking the maximum freight profit as the second objective function, the objective function of the maximum freight profit is:

[0018] maxg(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=0.075M 铁·X 铁 +0.072M 公 ·X 公 +0.022M 水 ·X 水 (2)

[0019] Among them, M 铁 、M 公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X

[0020] 铁 、X 公 、X 水 They represent railway mileage, highway mileage and waterway mileage respectively.

[0021] Preferably, in step three, setting and verifying the constraint conditions specifically includes: taking weighted regression prediction of the decision variables based on public data, obtaining the predicted value data of the decision variables corresponding to the three freight modes in the next ten years, reasonably floating up and down according to the above data, and setting the value range of the decision variables to avoid extreme optimization solutions.

[0022] Preferably, in step 4, the optimization model code is written in Python to calculate how each decision variable can individually meet the minimum freight carbon emissions and maximum freight profit.

[0023] Preferably, in step 5, the optimization model code is written in Python, and the particle swarm optimization algorithm is used to solve the optimal solution and perform sensitivity analysis to obtain the values ​​of each parameter under the optimal condition. The steps of the particle swarm optimization algorithm are as follows:

[0024] Step 5.1. At each iteration, calculate the fitness function value of each particle in the population to evaluate the current state of the population particles. Its mathematical expression is:

[0025]

[0026] Among them, x i Represents the data point corresponding to the i-th particle, correspondingly, x i+1 Represents the data point corresponding to the i+1th particle.

[0027] Step 5.2: Evaluate the fitness function value of the particle. If the current value is better than the individual extreme value, replace the individual extreme value and complete its update.

[0028] Step 5.3: If the individual extreme value of the particle is better than the group extreme value, the group extreme value is replaced to achieve the update of the group extreme value;

[0029] Step 5.4: Perform obstacle collision detection on the particle, loop through the obstacles in the map, calculate the distance and contact degree between each point on the path and the obstacle, and take the average to obtain the path violation degree;

[0030] Step 5.5: Update the velocity of each particle according to formula (4);

[0031]

[0032] Where X=(X1,X2,…,X n ) represents a particle group consisting of particles, V i =(V i1 ,V i2 ,…,V iD ) T represents the speed of the i-th particle, c1 and c2 represent the individual acceleration factors, respectively, which represent the ability of individual particles to share and communicate information; r1 and r2 are the core random factors of the PSO algorithm.

[0033] Step 5.6: Update the particle position according to formula (5), and also limit the position to the range of the given independent variable;

[0034]

[0035] Step 5.7: Check whether the maximum number of iterations has been reached or whether the change in the global optimal solution is less than a certain threshold; if the conditions are met, stop the iteration and output the global optimal position and the corresponding function minimum; otherwise, return to step 5.2 to continue the iteration.

[0036] By adopting the above technical solution: it mainly realizes the optimization of freight structure with minimum carbon emissions and maximum profits in the Yangtze River Delta region, which takes into account the freight volume and freight mileage of the three freight modes respectively, with minimum freight carbon emissions as the first objective function and maximum freight profits as the second objective function. The variables in the two objective functions are assigned corresponding weights based on the fitting of existing data, and constraints are established based on existing data and regression prediction data. Finally, the particle swarm algorithm is used to obtain parameter conditions that meet the above goals.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. This paper uses simulated annealing algorithm and particle swarm optimization algorithm to compare the optimal algorithms and select the algorithm that best fits the model, and implements the multi-objective optimization problem of minimum freight carbon emissions and maximum freight profits through Python.

[0039] 2. The present invention achieves minimum freight carbon emissions and maximum freight profits by optimizing the freight structure. Under the decision variables such as freight volume and freight mileage of the three freight modes, the optimal variable parameters that meet the conditions are obtained, providing solid theoretical and technical support for the optimization design of freight structures that are low-carbon, efficient, and guarantee economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the present invention;

[0041] Figure 2 This is the flow chart of the PSO algorithm in the present invention;

[0042] Figure 3 This is the particle swarm diagram obtained during the freight structure optimization process in the Yangtze River Delta region in this embodiment. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings so that those skilled in the art can better understand the advantages and features of the present invention and thus more clearly define the scope of protection of the present invention. The embodiments described in the present invention are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative work shall fall within the scope of protection of the present invention.

[0044] A multi-objective optimization design modeling method based on freight carbon emissions and profits includes the following steps:

[0045] Step 1: Define objective functions based on the optimization design, wherein the objective functions are minimizing freight carbon emissions and maximizing freight profits;

[0046] Step 2: Design decision variables. In this modeling method, the decision variables mainly include six: railway freight volume, highway freight volume, water freight volume, railway freight mileage, highway freight mileage, and water freight mileage;

[0047] Step 3: Verify the constraints to ensure the feasibility and rationality of the model and effectively improve the practicality and accuracy of the optimization model. This mainly includes: fitting verification of freight volume forecasts and actual values, sensitivity analysis of the obtained values, and the degree of fit between data changes and relevant national policies;

[0048] Step 4: Perform multi-objective function calculations on the six decision variables of the experimental data to determine how each decision variable can individually meet the requirements of minimum freight carbon emissions and maximum freight profits.

[0049] Step 5: Calculate the overall conditions for the optimal design that meets all objective functions based on the particle swarm optimization algorithm.

[0050] Example:

[0051] The present invention first performs a weighted linear regression forecast on the freight volume of the three modes of transport in the next ten years. Based on the forecast results, the freight volume of the three modes of transport is adjusted up and down within a reasonable range to avoid the situation where one mode of transport is zero in the final optimization result. The present invention sets the constraint range of highway freight volume as:

[0052] 650000×10 4 ≤M 公 <750000×10 4 (1)

[0053] Among them, the lower limit of the constraint range is the value obtained by floating downward the average road freight volume in the next ten years, and the upper limit of the constraint range is the value obtained by floating upward.

[0054] Similarly, the freight volume constraints for other modes of transportation can be obtained as follows:

[0055] Railway freight volume constraints:

[0056] 20000×10 4 ≤M 铁 <30000×10 4 (2)

[0057] Restrictions on waterborne freight volume:

[0058] 450000×10 4 ≤M 水 <550000×10 4 (3)

[0059] Since the above weighted linear regression model predicts the highway mileage for the next ten years, the principle of the mileage constraint is similar to the above. The lower limit is the average value of the predicted data, floating downward, and the upper limit is the average value, floating upward. The specific constraint ranges are as follows:

[0060] Constraints on highway mileage:

[0061] X 公 ∈[400000,600000) (4)

[0062] Railway mileage constraints:

[0063] X 铁 ∈[12000,16000) (5)

[0064] Constraints on water transport mileage:

[0065] X水 ∈[30000,50000) (6)

[0066] In order to ensure that all variables do not take the minimum value when calculating the optimization model, the present invention also sets three reasonable ranges of freight structures for constraints. The constraint range of road transportation here is based on the proportion of road transportation structure in the Yangtze River Delta region in 2023, and takes into account the proportion of road transportation structure in the Yangtze River Delta in recent years. It is based on the proportion of road transportation freight structure in 2023 of 0.5828, and is floated up by 10% and down by 30%, so as to conform to the actual social development law and will not be divorced from reality. Similarly, the proportion of railway freight volume fluctuates within a reasonable range based on 0.0191 in 2023, and the proportion of water freight volume fluctuates within a reasonable range based on 0.3981 in 2023. The following are three constraints on freight structure:

[0067] The proportion of road transport in the three freight modes is as follows:

[0068]

[0069] The proportion of rail transport in the three freight modes is as follows:

[0070]

[0071] The proportion of water transport in the three freight modes is as follows:

[0072]

[0073] When establishing the optimization model, it must be satisfied that the total freight volume after optimization is greater than the social freight demand to avoid the situation where supply exceeds demand. Therefore, the present invention sets a lower limit for the total freight volume of the three freight modes:

[0074] M 铁 +M 公 +M 水 >1231344×10 4 (10)

[0075] The primary optimization objective of this multi-objective optimization model is freight carbon emissions, aiming to minimize freight carbon emissions within a reasonable range to alleviate the burden on society to address carbon emissions. In the optimization model, the present invention multiplies the carbon emission factor generated by each unit of freight turnover by the turnover of the three freight modes, and the resulting sum is used to ultimately derive the freight carbon emissions value. Therefore, the first objective function of the optimization model, used to minimize carbon emissions, is:

[0076] minf(M 铁 ,M 公 ,M 水 ,X铁 ,X 公 ,X 水 )=11.33M 铁 ·X 铁 +97.6M 公 ·X 公 +8.65M 水 ·X 水 (11)

[0077] Among them, M 铁 、M 公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X 铁 、X

[0078] 公 、X 水 They represent railway mileage, highway mileage and waterway mileage respectively.

[0079] In actual situations, it is not only necessary to meet the minimum carbon emissions of freight, but also to consider the issue of freight profits on this basis, that is, to meet the highest possible profits while keeping freight carbon emissions as small as possible. To this end, the present invention takes the maximum freight profit as the second objective function. The method for calculating freight profit is: subtract the unit turnover cost from the unit turnover freight rate of each freight mode announced in previous years to obtain the profit k (yuan / t·km) per unit turnover, and then multiply it by the corresponding freight turnover, and finally sum them up to obtain the freight profit value. Through the above calculation method, the unit turnover profits corresponding to the three freight modes can be obtained as shown in Table 1:

[0080] Table 1 Unit turnover profit data corresponding to three freight modes

[0081]

[0082]

[0083] Therefore, the objective function for maximizing freight profit involved in the present invention is:

[0084] maxg(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=0.075M 铁 ·X 铁 +0.072M 公 ·X 公 +0.022M 水 ·X 水 (12) Among them, M 铁 、M公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X 铁 、X 公 、X 水 They represent railway mileage, highway mileage and waterway mileage respectively.

[0085] In summary, the mathematical expression of the multi-objective optimization design model based on minimizing freight carbon emissions and maximizing freight profits is:

[0086] minf(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=11.33M 铁 ·X 铁 +97.6M 公 ·X 公 +8.65M 水 ·X 水

[0087] maxg(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=0.075M 铁 ·X 铁 +0.072M 公 ·X 公 +0.022M 水 ·X 水

[0088]

[0089] There are many methods for solving multi-objective optimization, which need to be determined based on factors such as data and the established model. The present invention adopts the particle swarm optimization algorithm (PSO) to solve the multi-objective optimization model.

[0090] The PSO algorithm's origins can be traced back to 1995, when it was proposed by Kennedy and Eberhart. This algorithm aims to efficiently solve multi-objective optimization problems by simulating the learning behavior of animal groups and natural phenomena. It falls into the category of intelligent algorithms. Its core concept is inspired by the foraging behavior of birds—in a flock, birds are randomly distributed in locations and flight directions. Through social information sharing within the flock, the entire flock gradually converges on food.

[0091] In this algorithmic model, potential optimal solutions to the problem are abstracted as individuals, or "particles," in the target search space. During the search process, each particle records its own optimal solution as an individual extremum and shares this information with the swarm. The optimal individual extremum constitutes the global optimal solution for the swarm. Based on this, particles within the swarm dynamically adjust their search strategy based on the global optimal solution, continuously converging toward the region containing the optimal particle. After multiple iterations, the particle swarm gradually approaches the region containing the global optimal solution.

[0092] The steps of the particle swarm optimization algorithm are as follows:

[0093] Step 5.1. At each iteration, calculate the fitness function value of each particle in the population to evaluate the current state of the population particles. Its mathematical expression is:

[0094]

[0095] Among them, x i Represents the data point corresponding to the i-th particle, correspondingly, x i+1 Represents the data point corresponding to the i+1th particle.

[0096] Step 5.2: Evaluate the fitness function value of the particle. If the current value is better than the individual extreme value, replace the individual extreme value and complete its update.

[0097] Step 5.3: If the individual extreme value of the particle is better than the group extreme value, the group extreme value is replaced to achieve the update of the group extreme value;

[0098] Step 5.4: Perform obstacle collision detection on the particle, loop through the obstacles in the map, calculate the distance and contact degree between each point on the path and the obstacle, and take the average to obtain the path violation degree;

[0099] Step 5.5: Update the velocity of each particle according to formula (15);

[0100]

[0101] Where X=(X1,X2,…,X n ) represents a particle group consisting of particles, V i =(V i1 ,V i2 ,…,V iD ) T represents the speed of the i-th particle; c1 and c2 represent individual acceleration factors, which represent the ability of individual particles to share and communicate information; r1 and r2 are the core random factors of the PSO algorithm.

[0102] Step 5.6: Update the particle position according to formula (16), and also limit the position to the range of the given independent variable;

[0103]

[0104] Step 5.7: Check whether the maximum number of iterations has been reached or whether the change in the global optimal solution is less than a certain threshold; if the conditions are met, stop the iteration and output the global optimal position and the corresponding function minimum; otherwise, return to step 5.2 to continue the iteration.

[0105] For the multi-objective optimization model of freight structure optimization in the Yangtze River Delta region, the present invention adopts the particle swarm optimization algorithm (PSO) to solve it in order to balance the goals of minimizing freight carbon emissions and maximizing freight profits.

[0106] The algorithm initializes a particle swarm, sets a range of decision variables encompassing freight volume and mileage for the three modes of transportation, and constructs a feasible solution space based on constraints. Using a linear weighted method, the dual objectives are converted into a fitness function, and particle velocities and positions are iteratively updated, gradually approaching the Pareto optimal solution set. Through algorithmic optimization, an optimal structural solution is derived, with a moderate reduction in the proportion of road transport and an increase in the proportion of rail and water transport. This achieves a synergistic effect of lowering carbon emissions compared to predicted values ​​while simultaneously increasing profits. The specific data for the optimized variables is shown in Table 2:

[0107] Table 2 Optimized data of variables involved in the optimization model

[0108]

[0109] The data obtained also confirms the feasibility of the "road to rail" and "road to water" strategic policies in the adjustment of regional freight structure.

[0110] In order to further verify the rationality of the model, the present invention compares the optimized carbon emission data and its independent variable data with the predicted data for the next ten years of the above-mentioned weighted linear regression model. It is found that the freight carbon emission data processed by the multi-objective optimization model has significantly improved compared with the original predicted data, and the proportions of road transport, rail transport, and water transport have been adjusted, and the proportions of water transport and rail transport have increased, which is in line with the strategic policies of "road to rail" and "road to water". The present invention shows a comparison of freight carbon emission values ​​before and after optimization, as shown in Table 3:

[0111] Table 3 Comparison of freight carbon emissions before and after optimization

[0112]

[0113]

[0114] This shows that the optimization capability of this model is strong and its credibility is high. It has achieved the optimization of freight structure and provided effective ideas and improvement suggestions for improving freight carbon emissions.

[0115] In addition, the basic symbols of the design formula and algorithm of the present invention are explained as follows:

[0116]

[0117] In summary, the present invention can improve the existing freight structure through innovative modeling and optimization solutions, ensuring that freight carbon emissions are minimized while maximizing freight profits.

[0118] The descriptions and practices disclosed in this invention are easy to understand and comprehend for those skilled in the art, and modifications and refinements may be made without departing from the principles of the invention. Therefore, modifications and improvements made without departing from the spirit of the invention should also be considered within the scope of protection of this invention.

Claims

1. A multi-objective optimization design modeling method based on freight carbon emissions and profits, characterized by: The steps include: Step 1: Define the objective function according to the optimization design, which is to minimize the freight carbon emissions and maximizing freight profits; Step 2: Design decision variables. The decision variables in this modeling method include six: railway freight volume, road freight volume, water freight volume, railway freight mileage, road freight mileage, water freight mileage Number of trips; Step 3: Verify the constraints to ensure the feasibility and rationality of the model and effectively improve the effectiveness of the optimization model. Applicability and accuracy, including: fitting verification of freight volume forecasts and actual values, sensitivity analysis of the obtained values Analysis, the degree of alignment of data changes with relevant national policies; Step 4: Perform multi-objective function calculations on the six decision variables of the experimental data to calculate the How can the policy variables alone satisfy the minimum freight carbon emissions and maximum freight profits? Step 5: Calculate the optimal design that satisfies all objective functions based on the particle swarm optimization algorithm condition.

2. A multi-objective optimization design based on freight carbon emissions and profits according to claim 1 The module method is characterized in that In step 1, minimizing freight carbon emissions is used as the first objective function, using The objective function for solving the minimum carbon emission is: minf(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=11.33M 铁 ·X 铁 +97.6M 公 ·X 公 +8.65M 水 ·X 水 (1) Among them, M 铁 、M 公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X 铁 、X 公 、X 水 They represent the railway mileage, highway mileage and waterway mileage respectively; Taking the maximum freight profit as the second objective function, the objective function of the maximum freight profit is: maxg(M 铁 ,M 公 ,M 水 ,X 铁 ,X 公 ,X 水 )=0.075M 铁 ·X 铁 +0.072M 公 ·X 公 +0.022M 水 ·X 水 (2) Among them, M 铁 、M 公 、M 水 represent the railway freight volume, highway freight volume and waterway freight volume respectively; X 铁 、X 公 、X 水 They represent railway mileage, highway mileage and waterway mileage respectively.

3. A multi-objective optimization design based on freight carbon emissions and profits according to claim 1 The module method is characterized in that In step 3, setting and verifying the constraints specifically include: According to the weighted regression prediction of decision variables, the corresponding decision variables of the three freight modes in the next ten years are obtained. The measured data fluctuates up and down according to the above data to set the value range of the decision variable.

4. The multi-objective optimization design modeling method based on freight carbon emissions and profits according to claim 1 is characterized in that: In step 4, the optimization model code is written in Python to calculate how each decision variable can individually meet the requirements of minimum freight carbon emissions and maximum freight profits.

5. The multi-objective optimization design modeling method based on freight carbon emissions and profits according to claim 1 is characterized in that: In step five, the steps of the particle swarm optimization algorithm are as follows: Step 5.

1. At each iteration, calculate the fitness function value of each particle in the population to evaluate the current state of the population particles. Its mathematical expression is: Among them, x i Represents the data point corresponding to the i-th particle, correspondingly, x i+1 represents the data point corresponding to the i+1th particle; Step 5.2: Evaluate the fitness function value of the particle. If the current value is better than the individual extreme value, replace the individual extreme value and complete its update. Step 5.3: If the individual extreme value of the particle is better than the group extreme value, the group extreme value is replaced to achieve the update of the group extreme value; Step 5.4: Perform obstacle collision detection on the particle, loop through the obstacles in the map, calculate the distance and contact degree between each point on the path and the obstacle, and take the average to obtain the path violation degree; Step 5.5: Update the velocity of each particle according to formula (4); Where X=(X1,X2,…,X n ) represents a particle group consisting of particles, V i =(V i1 ,V i2 ,…,V iD ) T represents the speed of the i-th particle, c1 and c2 represent the individual acceleration factors, which represent the ability of individual particles to share and communicate information; r1 and r2 are the core random factors of the PSO algorithm; Step 5.6: Update the particle position according to formula (5), and also limit the position to the range of the given independent variable; Step 5.7: Check whether the maximum number of iterations has been reached or whether the change in the global optimal solution is less than a certain threshold; if the conditions are met, stop the iteration and output the global optimal position and the corresponding function minimum; otherwise, return to step 5.2 to continue the iteration.

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