Cigarette distribution path planning method based on improved NSGA-II

Abstract

The invention relates to the technical field of production scheduling, in particular to a cigarette distribution path planning method based on improved NSGA-II, which comprehensively considers the transportation cost and the transportation risk in the cigarette distribution process, constructs a cigarette distribution path optimization model, and improves the NSGA-II on the probability of population initialization and crossover variation at the same time. And then the improved NSGA-II is used for solving the model, so that the quality and diversity of the solution are improved, and the cigarette distribution path with lower cost and lower risk is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and particularly relates to a cigarette distribution path planning method based on improved NSGA-II. Background Art

[0002] Cigarette distribution is an important part of tobacco logistics, which refers to the safe and timely distribution of cigarette products from the warehouse to retail customers. The cigarette distribution mode usually has typical characteristics of "single category + multiple distribution points + regional allocation + path optimization". However, there are still the following problems:

[0003] ① Rigidity of single path adjustment. Path planning mainly relies on manual experience arrangement, and cannot achieve dynamic path optimization, resulting in problems such as inaccurate path planning, path duplication, unbalanced distribution task allocation, and waste of some transportation capacity;

[0004] ② Imbalance of multi-path allocation. Due to the lack of algorithm support, it is difficult to balance the workload among different paths, resulting in significant imbalances in aspects such as distribution workload, working hours, and distribution mileage for different routes. Summary of the Invention

[0005] The purpose of the present invention is to provide a cigarette distribution path planning method based on improved NSGA-II, which comprehensively considers transportation cost and transportation risk, constructs a cigarette distribution path optimization model, and improves NSGA-II to optimize the cigarette distribution path.

[0006] To achieve the above purpose, the present invention provides a cigarette distribution path planning method based on improved NSGA-II, including the following steps:

[0007] Step 1: Define the environment of the tobacco transportation path problem;

[0008] Step 2: Construct a cigarette distribution path optimization model, in which a dual-objective function is established with the minimum transportation cost and the minimum transportation risk;

[0009] Step 3: Use NSGA-II improved by multi-strategy initialization and crossover mutation to solve the cigarette distribution path optimization model and obtain the cigarette distribution route.

[0010] Optionally, when constructing the model in Step 2, the following assumptions are satisfied:

[0011] The vehicle starts from the distribution center, passes through each distribution point in turn, and the vehicle completes the distribution task of this point once it passes through this distribution point. After all distribution points are distributed, the vehicle returns to the distribution center;

[0012] The transportation cost is linearly related to the vehicle driving distance, and the additional cost generated by other accidents during transportation is not considered;

[0013] The vehicle has sufficient capacity to meet the needs of all delivery points.

[0014] Optionally, the objective function of the minimum transportation cost is:

[0015]

[0016] Where λ represents the unit cost per kilometer traveled by the transport vehicle; x ij ∈{0, 1}, which is a decision variable, that is, the route selection from delivery point i to delivery point j. When x ij = 1, it represents the selection of this route, otherwise it represents the non - selection of this route; l ij represents the distance from delivery point i to delivery point j; N = {0, 1, 2…n} represents the set of all points, and 0 represents the distribution center.

[0017] Optionally, the objective function of the minimum transportation risk is:

[0018]

[0019] Where k is the risk scaling factor; r ij represents the risk of the road itself from delivery point i to delivery point j; f ij represents the number of cigarettes loaded on the vehicle when traveling on the road from delivery point i to delivery point j; β ij represents the vehicle load risk, where β ij = f(g), g is the vehicle load rate. According to different transported goods, the vehicle load risk has different functional relationships according to the load rate of the transported goods.

[0020] Optionally, during the execution of the multi - strategy initialization in step 3, first, a population is randomly generated. Each chromosome in the population is encoded as [0, 1, 2,...n], indicating that the vehicle starts from the distribution center 0 and sequentially passes through delivery points 1, 2...n. Then, for each chromosome, the following three strategies are randomly selected: The first strategy is to keep the first point unchanged and randomly arrange the subsequent delivery points; the second strategy is to keep the first point unchanged and reverse the order of the subsequent delivery points; the third strategy is to keep the first point unchanged, randomly slice the subsequent delivery point sequence, and then randomly permute and combine these divided slices.

[0021] Optionally, the improvement directions of the crossover and mutation in step 3 are the improvement of the adaptive crossover and mutation probabilities and the improvement of the crossover and mutation methods. The formulas are as follows:

[0022] D = a / A

[0023] porb m= 0.1 + 0.3 * (1 - D)

[0024] porb c = 0.9 - 0.3 * (1 - D)

[0025] where D is the diversity of the population, a is the number of different chromosomes in the population, A is the total number of chromosomes in the population, and prob m is the mutation probability of the population, which decreases as the diversity of the population increases. prob c is the crossover probability of the population, which increases as the diversity increases, and dynamically adjusts the crossover and mutation probabilities.

[0026] The present invention provides a method for planning a cigarette distribution route based on improved NSGA-II. By comprehensively considering the transportation cost and transportation risk in the cigarette distribution process, an optimization model for the cigarette distribution route is constructed. At the same time, NSGA-II is improved in terms of population initialization and the probabilities of crossover and mutation, and then the improved NSGA-II is used to solve the model, improving the quality and diversity of the solutions, and solving for a cigarette distribution route with lower cost and less risk. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0028] Figure 1 is a schematic flow chart of the steps of a method for planning a cigarette distribution route based on improved NSGA-II of the present invention.

[0029] Figure 2 is a heat map of road risk values in a specific embodiment of the present invention.

[0030] Figure 3 is a schematic diagram of the Pareto front obtained by traditional NSGA-II in a specific embodiment of the present invention.

[0031] Figure 4 is a schematic diagram of the Pareto front obtained by the improved NSGA-II in a specific embodiment of the present invention.

[0032] Figure 5 is a schematic diagram of the route of the improved NSGA-II solution 2 in a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0034] Please refer to Figure 1 , the present invention provides a cigarette distribution route planning method based on improved NSGA-II, including the following steps:

[0035] Step 1: Define the environment of the tobacco transportation route problem;

[0036] Step 2: Build an optimization model for the cigarette distribution route, where a bi-objective function is established with the minimum transportation cost and the minimum transportation risk;

[0037] Step 3: Use NSGA-II improved by multi-strategy initialization and crossover mutation to solve the optimization model for the cigarette distribution route and obtain the cigarette distribution route.

[0038] The following is a further description in combination with the implementation steps:

[0039] In Step 1, in order to effectively meet the cigarette distribution needs of customers and at the same time consider the influence of transportation cost and transportation risk, the following assumptions are made for the tobacco transportation route problem:

[0040] ① The vehicle starts from the distribution center, passes through each distribution point in turn. Once the vehicle passes through this distribution point, the distribution task at this point is completed. After all distribution points are served, the vehicle returns to the distribution center;

[0041] ② The transportation cost is linearly related to the vehicle driving distance, and no additional costs caused by other accidents during transportation are considered;

[0042] ③ The vehicle has sufficient capacity to meet the needs of all distribution points.

[0043] Step 2 is the process of building an optimization model for the cigarette distribution route, including the establishment of the objective function and the definition of the constraint conditions. The establishment process of the bi-objective function is as follows:

[0044] Step 2.1, Objective function 1: Minimum transportation cost

[0045] In the process of cigarette distribution, the transportation cost refers to the consumption cost of the vehicle during driving. And the minimum transportation cost represents optimizing various factors in the transportation process to complete the transfer of cigarettes from one location to another at the lowest cost. Minimizing the transportation cost not only helps to directly reduce the logistics cost, but also indirectly improves the efficiency and service level of the entire supply chain.

[0046] The present invention assumes that N = {0, 1, 2... n} represents the set of all points, where 0 represents the distribution center, and N0 = {1, 2... n} represents the set of all distribution merchant points; E = {(i, j): i, j ∈ N and i ≠ j} represents the set of arcs from distribution point i to distribution point j.

[0047] The objective function of the minimum transportation cost is as follows:

[0048]

[0049] In the formula: λ represents the unit cost per kilometer of the transport vehicle; x ij ∈ {0, 1}, which is a decision variable, that is, the route selection from distribution point i to distribution point j. When x ij = 1, it represents the selection of this route, otherwise it represents the non - selection of this route; l ij represents the distance from distribution point i to distribution point j.

[0050] Step 2.2, Objective function 2: Minimum transportation risk

[0051] The minimum transportation risk refers to reducing various potential threats that the goods may encounter during transportation to the lowest level through a series of measures. These threats include goods damage, loss, delay, and safety issues, etc. During the cigarette distribution process, because the conditions of each road are different, the road risks of different roads are also different. Effectively reducing the transportation risk in tobacco logistics can ensure the safety and integrity of the goods, and at the same time enhance the trust and satisfaction of customers.

[0052] The objective function of the minimum transportation risk is as follows:

[0053]

[0054] In the formula: k is the risk scaling factor (ensuring that the risk value is within a certain specified range); r ij represents the risk of the road itself from distribution point i to distribution point j; f ij represents the number of cigarettes loaded on the vehicle when driving on the road from distribution point i to distribution point j; β ij represents the vehicle load risk, where β ij = f(g), g is the vehicle load rate. According to different transported goods, the vehicle load risk has different functional relationships according to the load rate of the transported goods.

[0055] Step 2.3: The corresponding constraints are as follows:

[0056]

[0057] Among them, constraint conditions (3) and (4) ensure that for each delivery point, the vehicle passes through it exactly once; constraint condition (5) ensures that the vehicle passes through each delivery point in sequence without interruption and finally returns to the warehouse; constraint condition (6) means that the load of the vehicle when departing from the warehouse meets the demand of all delivery points; constraint condition (7) means that when the vehicle passes through a delivery point, the load decreases by the demand of this delivery point; constraint condition (8) ensures the constraint of the vehicle's load during transportation; constraint condition (9) represents the decision variable, x ij = 1 indicates passing through this road, x ij = 0 indicates not passing through this road; constraint condition (10) means that the load of the vehicle is non - negative.

[0058] The specific strategies for improving NSGA - II in step 3 are as follows:

[0059] (1) Multi - strategy initialization

[0060] When initializing the population of the algorithm, a real - value encoding method is adopted for multi - strategy initialization. First, a population is randomly generated. Each chromosome in the population is encoded as [0, 1, 2,...n], indicating that the vehicle departs from distribution center 0 and passes through delivery points 1, 2...n in sequence. Then, for each chromosome, the following three strategies are randomly selected. The first strategy is to keep the first point (0) unchanged and randomly permute the subsequent delivery points, such as becoming [0, 3, 5, 1,...,n]; the second strategy is to keep the first point unchanged and reverse the order of the subsequent delivery points, such as becoming [0, n, n - 1,...,1]; the third strategy is to keep the first point unchanged and randomly slice the subsequent delivery point sequence. Suppose it is divided into [1, 2, 3], [4, 5, 6],…,[n - 2, n - 1, n], and then randomly permute and combine these divided slices, such as becoming [0, 4, 5, 6,...,n - 2, n - 1, n,...,1, 2, 3].

[0061] (2) Improvement of crossover and mutation

[0062] The second improvement direction is mainly the improvement of the adaptive crossover and mutation probability and the improvement of the crossover and mutation methods. See formulas (11) - (13) specifically.

[0063] D = a / A (11)

[0064] porb m = 0.1 + 0.3*(1 - D) (12)

[0065] porb c = 0.9 - 0.3*(1 - D) (13)

[0066] Where D is the diversity of the population, a is the number of different chromosomes in the population, A is the total number of chromosomes in the population, and prob m is the mutation probability of the population, which decreases as the diversity of the population increases. prob c is the crossover probability of the population, which increases as the diversity increases, and the crossover and mutation probabilities are dynamically adjusted. To maintain the diversity of the population during the loop, the crossover and mutation probabilities are dynamically adjusted according to the diversity of the population to promote the exploration process.

[0067] In the crossover operation, for two chromosomes [0, m a1 , m a2 ,....m ak ,...m an and [0, m b1 , m b2 ,....m bk ,...m bn , a number k is randomly generated, and the segments at the k-th position of the two chromosomes are exchanged and recombined, that is, it becomes [0, m a1 , m a2 ,....m bk ,...m bn and [0, m b1 , m b2 ,....m ak ,...m an .

[0068] In the mutation operation, for a chromosome [0, m1, m2,... m a ,... m b ,..., m n , two numbers p1 and p2 are randomly generated, and then the following two methods are randomly selected for mutation: ① Exchange the values at positions a and b, that is, the chromosome becomes [0, m1, m2,... m b ,... m a ,..., m n ; ② Shuffle the order of the segments between m a and m b while keeping the other positions unchanged.

[0069] Finally, the improved NSGA-II is used to solve the model. For the traditional NSGA-II, it can improve the search ability of the solution, improve the quality and diversity of the solution, and solve the cigarette distribution path with lower cost and less risk.

[0070] Furthermore, the present invention is demonstrated by specific embodiments using simulated data.

[0071] The simulated data in the embodiments is composed as follows:

[0072] Set 20 specified points for the scenario, where point 0 is the cigarette logistics distribution center and points 1 - 19 are the distribution demand points.

[0073] 1.1 Distribution points

[0074] In this embodiment, the designated points are represented by coordinate values (x, y), as shown in Table 1 for details.

[0075] Table 1 Coordinate values of distribution points

[0076]

[0077] 1.2 Demand at distribution points

[0078] The cigarette demand at each distribution point (in pieces) is allocated according to customer level classification. For specific values, see Table 2.

[0079] Table 2 Demand at distribution points

[0080]

[0081] 1.3 Road risk value

[0082] Considering the differences in road risks and other factors in the distribution routes between each point, the risk values of each route are determined to form a road risk matrix, which represents the risk situation of each road. The value in the i-th row and j-th column represents the risk value of the road from point i to point j itself. For details, see Figure 2 .

[0083] 1.4 Other parameters

[0084] According to the vehicle model, the fuel consumption is 18 liters per 100 kilometers, and the fuel price is 7.8 yuan per liter. Therefore, the fuel cost is 1.4 yuan per kilometer. According to the actual transportation situation, in the process of tobacco transportation, the relationship between the load factor and the vehicle load risk can be ignored. Therefore, in this experiment, a simplified β ij = 1. The variable f ij represents the number of cigarette pieces loaded on the vehicle from point i to point j, and k is a risk scaling factor used to limit the risk value within the range of 1 - 100. In this experiment, k is set to 0.0001.

[0085] 2. Algorithm solution verification

[0086] The experiment was conducted on a system equipped with an Intel i5-13500HX processor, 16.0GB of memory, and an NVIDIA RTX 4050 GPU, running on Python 3.12. The optimization process first used the traditional NSGA-II with a population size of 500 individuals and 200 generations of iteration. Through systematic parameter tuning, the experiment proved that the configuration with a crossover probability of 0.9 and a mutation probability of 0.1 could obtain the optimal Pareto solution set. Figure 3 Figure 2 shows the Pareto front of NSGA-II, while Table 3 details the vehicle routing schemes corresponding to each solution and the corresponding cost and risk metrics.

[0087] Table 3. Optimized Routes Generated by NSGA-II

[0088]

[0089] Subsequently, the improved NSGA-II was used for optimization, maintaining the same evolutionary parameters: a population size of 500 individuals and 200 generations of iteration. Through multiple experimental verifications, the improved NSGA-II demonstrated better solution diversity compared to the traditional NSGA-II. Figure 4 Figure 3 shows the Pareto front of the improved NSGA-II, while Table 4 details the vehicle routing schemes corresponding to each solution and the corresponding cost and risk metrics.

[0090] The comparison results show that the improved NSGA-II is significantly superior to the traditional NSGA-II in terms of diversity and solution quality. In cigarette distribution operations, considering that the cost of finished cigarettes is much higher than the transportation cost, the solution with the lowest risk was selected in this embodiment. The experimental results show that the improved algorithm performs excellently in multi-objective optimization. The lowest risk value of the benchmark NSGA-II is 35.9, corresponding to a transportation cost of 1,017.51 yuan, while the improved NSGA-II achieved significant optimization in both metrics - the risk value decreased to 34.76 (a decrease of 3.18%), and the operating cost decreased to 904.51 yuan (a decrease of 11.11%), thus improving the quality of the solution. Therefore, as Figure 4 shown, Solution 2 in the improved NSGA-II was finally selected as the cigarette distribution route.

[0091] Table 4. Optimized Routes Generated by the Improved NSGA-II

[0092]

[0093] The above-disclosed is only one or more preferred embodiments of the present invention. Of course, the scope of rights of the present invention cannot be limited thereby. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A cigarette distribution route planning method based on improved NSGA-II, characterized in that, It includes the following steps: Step 1: Conduct the environmental limitation of the tobacco transportation path problem; Step 2: Construct an optimization model for the cigarette distribution path, where a bi-objective function is established with the minimum transportation cost and the minimum transportation risk; Step 3: Solve the optimization model for the cigarette distribution path by using NSGA-II improved with multi-strategy initialization and crossover mutation to obtain the cigarette distribution route.

2. The method for planning the cigarette distribution path based on the improved NSGA-II according to claim 1, wherein when constructing the model in Step 2, the following assumptions are satisfied: The vehicle starts from the distribution center, passes through each distribution point in sequence. Once the vehicle passes through this distribution point, the distribution task at this point is completed. After all distribution points are distributed, the vehicle returns to the distribution center; The transportation cost has a linear relationship with the vehicle driving distance, and the additional costs generated by other accidents during the transportation process are not considered; The vehicle has sufficient capacity to meet the needs of all distribution points.

3. The method for planning the cigarette distribution path based on the improved NSGA-II according to claim 2, wherein The objective function of the minimum transportation cost is: Among them, λ represents the unit cost per kilometer traveled by the transport vehicle; x ij ∈ {0, 1}, which is a decision variable, that is, the route selection from distribution point i to distribution point j. When x ij = 1, it represents the selection of this route, otherwise it represents the non-selection of this route; l ij represents the distance from distribution point i to distribution point j; N = {0, 1, 2…n} represents the set of all points, and 0 represents the distribution center.

4. The method for planning the cigarette distribution path based on the improved NSGA-II according to claim 3, wherein The objective function of the minimum transportation risk is: where k is the risk scaling factor; r ij represents the risk of the road itself from distribution point i to distribution point j; f ij represents the number of cigarettes carried by the vehicle when driving on the road from distribution point i to distribution point j; β ij represents the vehicle load risk, where β ij = f(g), g is the vehicle load rate, and according to different transported goods, the vehicle load risk has different functional relationships according to the load rate of the transported goods.

5. The method for planning the cigarette distribution path based on the improved NSGA-II according to claim 4, wherein During the execution of the multi-strategy initialization in Step 3, first, a population is randomly generated. Each chromosome in the population is encoded as [0, 1, 2,... n], indicating that the vehicle starts from the distribution center 0 and passes through the distribution points 1, 2... n in sequence; then for each chromosome among them, the following three strategies are randomly selected: The first strategy is to keep the first point unchanged and randomly arrange the subsequent distribution points; the second strategy is to keep the first point unchanged and reverse the order of the subsequent distribution points; the third strategy is to keep the first point unchanged, randomly slice the subsequent distribution point sequence, and then randomly permute and combine these sliced areas.

6. The method for planning the cigarette distribution path based on the improved NSGA-II according to claim 5, wherein The improvement direction of the crossover mutation in Step 3 is the improvement of the adaptive crossover mutation probability and the improvement of the crossover mutation method, and the formula is as follows: D = a / A porb m = 0.1 + 0.3*(1 - D) porb c = 0.9 - 0.3*(1 - D) Among them, D is the diversity of the population, a is the number of different chromosomes in the population, A is the total number of chromosomes in the population, and prob m is the mutation probability of the population, which decreases as the diversity of the population increases, and prob c is the crossover probability of the population, which increases as the diversity increases, and the crossover and mutation probabilities are dynamically adjusted.

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