Shared electric bicycle battery distribution path planning method based on improved hybrid genetic algorithm

Abstract

The invention relates to the field of logistics distribution, and particularly provides a shared electric bicycle battery distribution path planning method based on an improved hybrid genetic algorithm. In order to solve the problems of low distribution efficiency, high operation cost, unreasonable resource scheduling and the like of the existing shared electric bicycle system (EBSS) battery management, the invention constructs a battery distribution optimization model considering the demand urgency degree. According to the method, firstly, through data analysis and literature research, an evaluation index system of the battery demand urgency degree is established, and the evaluation index system comprises the number of power-shortage electric bicycles, the human traffic, the regional population density and the number of available vehicles at a station; and quantifying the demand urgency degree of each station by adopting an entropy weight TOPSIS method, and determining the battery distribution priority according to the demand urgency degree. In the aspect of optimization scheduling, the invention provides an improved hybrid genetic algorithm (SVGA), and by combining a simulated annealing criterion and a variable neighborhood search strategy, the global search capability of the algorithm is improved, and local optimum is avoided. Experimental results show that compared with a traditional genetic algorithm (GA) and a simulated annealing improved genetic algorithm (SAGA), the SVGA has remarkable advantages in the aspects of solution cost, calculation time and solution stability. According to the invention, intelligent optimization of shared electric bicycle battery distribution is realized, the resource utilization rate is improved, the operation cost is reduced, and an innovative solution is provided for efficient management of EBSS.

Description

Technical Field

[0001] The present invention relates to the field of logistics distribution, and particularly to a method for planning the distribution path of shared e-bike batteries based on an improved hybrid genetic algorithm. Background Art

[0002] The shared electric bicycle system (EBSS) has been rapidly popularized globally due to its advantages such as environmental protection, high efficiency, economy, and intelligence. First of all, as a green travel mode, EBSS helps to reduce carbon emissions and air pollution, and promotes the sustainable development of cities. Secondly, it greatly improves the convenience of short-distance travel. Users can pick up and return vehicles at any time without worrying about parking problems, especially suitable for daily needs such as commuting, shopping, and tourism. Compared with shared bicycles, electric bicycles are more labor-saving, faster, and have a wider coverage area, meeting more travel scenarios. In addition, the use cost of EBSS is much lower than that of taking a taxi or maintaining a private car. Many platforms also offer membership discounts and promotional activities, making it a cost-effective choice. In today's fast-paced urban life, EBSS not only improves travel efficiency but also promotes the construction of intelligent transportation, becoming an indispensable short-distance travel mode for modern urbanites.

[0003] However, the challenges of battery management faced by the shared e-bike system during operation are becoming increasingly prominent, mainly reflected in aspects such as low distribution efficiency, high operation cost, and unreasonable resource scheduling, seriously affecting the operation quality and user experience of the system. The existing battery distribution methods mainly rely on fixed scheduling rules or path planning based on simple optimization algorithms. These methods usually ignore the dynamic changes in battery demand, resulting in shortages of batteries in high-demand areas and waste of resources in low-demand areas. In addition, most studies do not fully consider the urgency of battery demand, making it difficult for resource scheduling to match real-time demand and affecting the service level. Summary of the Invention

[0004] The present invention proposes a method for planning the distribution path of shared e-bike batteries based on an improved hybrid genetic algorithm. This method obtains the factors affecting the use of shared e-bikes through data analysis and literature research methods, establishes an index for evaluating the urgency of battery demand on this basis, then combines the entropy weight TOPSIS method for quantitative demand assessment, and finally uses the improved hybrid genetic algorithm to optimize the distribution path. Specifically, it includes the following:

[0005] First of all, in order to scientifically quantify the urgency of battery demand, the present invention constructs a complete evaluation index system based on data analysis and literature research. Through in-depth analysis of the public data of shared bicycles in Shenzhen, combined with key factors such as historical orders, population flow density, and site power consumption patterns, the present invention determines four core indicators affecting the urgency of battery demand:

[0006] 1) Number of e - bikes with low power: The more e - bikes with insufficient power in the station, the higher the urgency of demand.

[0007] 2) Pedestrian flow: The greater the density of the pedestrian flow around the station, the higher the potential demand for e - bikes.

[0008] 3) Regional population density: For stations with a relatively large permanent population in the surrounding area, the battery consumption rate is relatively fast.

[0009] 4) Number of available vehicles at the station (negative indicator): If there are still sufficient available vehicles at the station, the urgency of demand is relatively low.

[0010] Based on the above indicators, the present invention uses the entropy - weight TOPSIS method for quantitative analysis. The entropy - weight method is used to calculate the weights of each indicator to ensure the objectivity of the evaluation system and avoid human intervention. At the same time, the TOPSIS method calculates the relative closeness of each station to the ideal state to obtain the demand urgency coefficient, and determines the priority of battery distribution accordingly, so that stations with high demand can be replenished with batteries first, improving the overall operation efficiency.

[0011] The entropy - weight method is an objective weighting method based on the degree of difference between indicators and is widely used in priority ranking problems due to its high decision - making credibility. For the battery demand distribution problem of shared electric bicycles, this paper uses the entropy - weight method to calculate the weights of the battery demand indicators affecting the stations. The specific operation steps are as follows:

[0012] Step 1: Establish an evaluation index matrix:

[0013] Let the set of n stations be X = {x1, x2,..., x n}, and each station in the set has m evaluation indicators. Let the data of the j - th (j = 1, 2,..., m) influencing factor indicator of the i - th station xi i be xi ij , and construct the initial demand urgency evaluation index matrix of each station.

[0014] X=(xi ij ) n×m (i = 1, 2,..., n; j = 1, 2,..., m)

[0015] Step 2: Standardize the data:

[0016] In order to eliminate the inconsistency in the order of magnitude and dimension of different evaluation indicators, first use the range method to standardize each indicator xi ij for evaluating the demand urgency. The standardized value is The calculation formula is as follows:

[0017]

[0018] Step 3: Normalization of the index matrix

[0019] By normalizing the index matrix X, the matrix P is obtained:

[0020]

[0021] P = (p ij ) n×m

[0022] Step 4: Calculate the entropy value e of the j-th index j

[0023]

[0024] Step 5: Calculate the weights w of each index j

[0025]

[0026] The TOPSIS method is used to evaluate the urgency of the EBSS site's demand for batteries to obtain the demand urgency coefficient of each site. This method mainly uses the Euclidean distance between the site and the positive and negative ideal solutions to obtain the battery demand urgency coefficient of the site. The steps are as follows:

[0027] Step 6: Construct the weighted standardized matrix:

[0028] The standardized matrix p ij Multiply each column by the corresponding weight w j to obtain the weighted matrix R.

[0029] R ij = p ij × w j , i = 1, 2, …, n; j = 1, 2, …, m, R = (R ij ) n×m

[0030] Step 7: Determine the positive ideal solution R + and the negative ideal solution R - :

[0031] The positive ideal solution consists of the maximum value of each column element in the weighted standardized matrix, and the negative ideal solution consists of the minimum value of each column element.

[0032]

[0033] Step 8: Use the Euclidean distance to calculate the distances between the object and the positive and negative ideal solutions:

[0034]

[0035]

[0036] Step 9: Calculate the relative affinity of site i:

[0037]

[0038] Step 10: Determine the battery demand coefficient for each site:

[0039]

[0040] Where: i is the demand urgency of demand point i. The greater the demand urgency coefficient of the station, the higher the demand urgency of the station and the higher the priority. Therefore, it should be given priority in the actual shared electric bicycle battery distribution process.

[0041] Secondly, in terms of optimization and scheduling, the present invention proposes an improved hybrid genetic algorithm (SVGA) for efficiently solving battery distribution path problems. Traditional genetic algorithms are prone to fall into local optimality and converge slowly when solving complex path optimization problems. Therefore, the present invention introduces the simulated annealing criterion, and accepts a certain probability of poor solutions through the Metropolis criterion in the selection stage of the genetic algorithm to enhance the global search capability and avoid premature convergence. In addition, in order to further improve the optimization effect, the SVGA algorithm is also combined with a variable neighborhood search strategy, which continuously adjusts the search space to improve the algorithm's exploration ability and the quality of the solution, thereby finding a better distribution path in a short time.

[0042] Improvement 1: Improve the selection mechanism based on the Metropolis criterion

[0043] Interested in the distribution of shared electric bicycle batteries, optimizing the distribution route is a complex task. Although the traditional genetic algorithm has a strong solution ability, its roulette selection mechanism easily leads to the loss of excellent individuals, causing the algorithm to fall into the local optimum too early, affecting the distribution efficiency. However, the simulated annealing algorithm has excellent global search capabilities and can always accept a better solution during the search process, which just makes up for the shortcomings of the roulette selection mechanism. The specific improvement operations are as follows:

[0044] Step 1: Randomly select two individuals P1 and P2 from the population and calculate their objective function values Z(P1) and Z(P2).

[0045] Step 2: Based on the simulated annealing Metropolis criterion, if Z(P1) <Z(P2),依据准者第一条,选择个体P1进入子代;否则,依据准则第二条,以概率P s Receive individual P1 into the offspring.

[0046]

[0047] In the above formula, the temperature T gradually cools with the iteration of the algorithm, and the calculation formula is:

[0048] T = T0 × k

[0049] where T0 is the initial temperature and k is the cooling rate.

[0050] Step 3: Repeat Step 1 and Step 2 until the offspring population reaches the established scale.

[0051] Algorithm.1

[0052]

[0053]

[0054] Improvement 2: Improving the optimal individual by variable neighborhood search

[0055] Add the variable neighborhood search operation after the mutation operation and before the next loop. This can not only improve the local search ability of the genetic algorithm, but also effectively reduce the calculation time, so as to find a high-quality distribution plan within a limited time. Therefore, the variable neighborhood search operation is performed on the current optimal individual.

[0056] (1) Two-point transposition. In a distribution path, randomly select two different stations and exchange them. When a distribution path is encoded as "3475281", if the randomly selected positions are 1 and 6, the new path encoding generated after the exchange operation will become "8475231".

[0057] (2) Random shuffling. Randomly select multiple stations and shuffle the order of the selected stations. The distribution path is encoded as "3475281". Suppose positions 1, 3, 4, and 6 are randomly selected, and the extracted station sequence is "3758". After random shuffling, assuming the new order is "7385", the final generated new path encoding will be "7438251".

[0058] (3) Insertion operation. Randomly select two stations and insert the station at the higher index position before the lower index position, while shifting the stations after the lower position one position to the right in turn. The distribution path is encoded as "3475281". If the two randomly selected positions are 1 and 7, the new path encoding after the insertion operation will become "1347528".

[0059] (4) Reversal operation. Randomly select two positions and reverse the station segment between these two positions. For the distribution path encoded as "3475281", if the randomly selected positions are 3 and 7, after reversing the station segment in this interval, the new path encoding obtained will be "3418257".

[0060] In summary, by combining the entropy weight TOPSIS method and the improved hybrid genetic algorithm, the present invention realizes the intelligent optimization of the battery distribution of the shared electric bicycle system, improves the resource utilization rate, reduces the operating cost, and provides an innovative solution for the efficient management of the EBSS. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a schematic diagram of the model process of the present invention;

[0062] Figure 2 is a framework diagram of the hybrid genetic algorithm of the present invention;

[0063] Figure 3 is a schematic diagram of the variable neighborhood search operator of the present invention;

[0064] Figure 4 is the comparison of R101 / 102 / 103 / 104 / 105, RC101 / 102 / 103 / 104 / 105 of the present invention with other methods under 10 data sets;

[0065] Figure 5 is the comparison of the present invention with other methods under the data set R101; DETAILED DESCRIPTION OF THE INVENTION

[0066] In order to make the objectives, technical solutions and advantages of the present invention clearer, the following will, with reference to the accompanying drawings, elaborate on the method for planning the battery distribution path of shared electric bicycles based on an improved hybrid genetic algorithm proposed by the present invention. It should be understood that the specific implementation methods described herein are only for explaining the present invention and not for limiting the present invention. Improvements, changes or substitutions made by those skilled in the art within the scope of the present invention shall all be covered by the scope of the claims of the present invention.

[0067] Figure 1 shows a schematic diagram of the model process of the present invention. First, based on the real-time data of the shared electric bicycle stations, the system evaluates the urgency of the battery demand at each station. Through the analysis of historical order data, key indicators such as the number of power-deficient electric bicycles at the station, the surrounding pedestrian flow density, the regional population density, and the number of available electric bicycles are extracted, and the entropy weight TOPSIS method is used to calculate the demand priority of each station, and it is introduced into the objective function to form a comprehensive distribution plan that balances the priority and the operating cost.

[0068] Without loss of generality, the following assumptions need to be made first to construct the model of the present invention: (1) Immediately return to the distribution center after the delivery task is completed; (2) Each site is served by only one vehicle; (3) When a user arrives at a certain site, if there is an available shared electric bicycle, start riding, otherwise leave; (4) The distances between each site (including the distribution center), the number of shared electric bicycles at each site, and the number of batteries to be replaced are known, and the time window can be predicted.

[0069] This paper introduces the concept of demand urgency, that is, prioritize the delivery of sites with high demand urgency. If the delivery is delayed, economic penalties will be imposed according to the delay time, and the economic penalty cost is positively correlated with the total delivery cost; conversely, combined with the demand urgency of the shared electric bicycle battery, appropriate additional economic compensation will be given to the delivery driver, and the economic compensation is negatively correlated with the total delivery cost. Therefore, this objective function includes vehicle travel cost, delay penalty cost, and on-time delivery subsidy, and their cost functions are respectively:

[0070]

[0071] p i =α2(T i -E i )λ i ,T i ≥E i

[0072] b i =|α2(T i -E i )λ i |,T i <E i

[0073] Where C ig is the operating cost of the delivery vehicle from site i directly to point g (g ∈ N); p i is the penalty cost for the delivery vehicle's delay in delivering to site i; b i is the subsidy cost for the delivery vehicle when there is no delay in delivering to the electric bicycle site i, and the longer the delay time, the greater the penalty cost. Similarly, the longer the time of early delivery without delay, the higher the subsidy cost. Therefore, the objective function is:

[0074]

[0075] Figure 2Shows the framework diagram of the hybrid genetic algorithm of the present invention. This framework consists of multiple steps such as initializing the population, selection, crossover, mutation, local search, and termination determination. First, when initializing the population, an initial solution generation strategy based on the urgency of demand is adopted to improve the quality of the initial solution. Subsequently, in the selection stage, the simulated annealing criterion (Metropolis criterion) is introduced to accept sub-optimal solutions with a certain probability, thereby enhancing the global search ability and avoiding premature convergence of the algorithm. In the crossover stage, the partially mapped crossover (PMX) strategy is used for gene exchange to retain excellent sub-structures and improve the diversity of solutions. The mutation stage uses the inversion mutation operator to randomly select chromosome segments for inversion to enhance the local search ability. In addition, for the current optimal solution, a local search operation is further performed to optimize the final path. Finally, when the algorithm reaches the preset termination condition (such as the maximum number of iterations or the convergence criterion), the optimal delivery plan is output.

[0076] Figure 3 Shows the schematic diagram of the variable neighborhood search operator of the present invention. This algorithm improves the quality of solutions by dynamically adjusting the search neighborhood. The variable neighborhood search adopts four operators: two-point transposition, random shuffle, insertion operation, and inversion operation. Two-point transposition randomly exchanges two stations in the path to enhance the local perturbation ability; random shuffle rearranges the selected path segment to increase the diversity of solutions; the insertion operation inserts the selected station into a new position to optimize the local path; the inversion operation reverses the order of the path segment to reduce the driving cost. These operators act on the current solution in turn to find a better solution in multiple neighborhood structures and improve the overall solution quality of the algorithm.

[0077] Figure 4 Shows the comparison of the present invention with other methods under 10 data sets (R101 / 102 / 103 / 104 / 105, RC101 / 102 / 103 / 104 / 105).

[0078] Comparison between the improved algorithm and Gurobi:

[0079] Gap = (Cost SVGA - Cost gurobi ) / Cost gurobi × 100%

[0080] The average Gap between the optimal solutions obtained by SVGA and Gurobi is 3.79%, and its solution time is less than that of Gurobi while the solution obtained is less different from the exact solution, with an obvious time advantage. Therefore, it can be considered that the SVGA algorithm has good solution ability.

[0081] Figure 5Shows the comparison of the improved algorithm with the traditional genetic algorithm and the simulated annealing improved genetic algorithm under 10 different data sizes of the dataset R101 of the present invention:

[0082] Gap = (Cost cur - Cost SVGA ) / Cost SVGA × 100%

[0083] The experimental results show that compared with the traditional genetic algorithm (GA) and the simulated annealing improved genetic algorithm (SAGA), the solution cost of the SVGA algorithm is reduced by 33%, the calculation time is reduced by 19.5 seconds, and the stability of the solution is improved by 67%.

[0084] The present invention realizes the intelligent optimization of the battery distribution of shared electric bicycles by constructing a demand urgency evaluation method based on entropy weight TOPSIS and combining an improved hybrid genetic algorithm to optimize the distribution path, improves the resource utilization rate, reduces the operating cost, and provides an innovative solution for the efficient management of EBSS.

Claims

1. A method for planning the battery distribution path of shared e-bikes based on an improved hybrid genetic algorithm, which is used to optimize battery scheduling, improve distribution efficiency, and reduce operating costs, including the following: (1) Quantitatively evaluate the urgency of battery demand at each station using the entropy weight TOPSIS method. Calculate the demand urgency coefficient based on the four core indicators of the number of power - short e - bikes at the station, the surrounding pedestrian flow density, the regional population density, and the number of available vehicles at the station, and add the demand urgency coefficient to the objective function to obtain the economic compensation p for timely delivery i The penalty b for delivery delay i And the delivery driving cost C ig Together to form the total cost. The higher the demand urgency of a certain station, the greater the corresponding compensation for timely delivery and the penalty for untimely delivery; (2) Optimize the battery distribution path by combining the improved hybrid genetic algorithm (SVGA). The algorithm includes a simulated annealing criterion optimization selection mechanism and uses a variable neighborhood search strategy to enhance the global search ability, and finally obtains the optimal battery distribution plan.

2. The method for planning the battery distribution path of shared electric bicycles based on the improved hybrid genetic algorithm according to claim 1, wherein Evaluate the urgency index of the battery replacement demand of shared e-bikes. Through 200,000 riding orders in the public data of shared bikes in Shenzhen, explore the spatio-temporal usage characteristics of shared bikes. Based on the cleaned data, the analysis results show that the high-frequency usage areas of shared bikes are mainly concentrated in areas with high population density and frequent travel activities, showing significant spatial aggregation characteristics. Specifically, Nanshan District, Luohu District, and Longhua District are the main aggregation areas of riding orders, indicating that the usage frequency of shared bikes in these areas is relatively high. In addition, places such as Longjing Subway Station, University Town, and Fangdacheng in Nanshan District have become the core areas of shared bike usage, reflecting the strong travel demand of residents in these areas and the high utilization rate of shared bikes. This spatial distribution pattern not only reveals the close relationship between the usage of shared bikes and population density and travel activities, but also further shows that other urban characteristics, such as employment density and commercial functional areas, may play an important role in promoting the demand for shared bikes. To scientifically evaluate the urgency of battery demand, an evaluation index system based on the above factors can be established. (1) The more the number of e-bikes lacking electricity at the station, the greater the demand gap at this demand point, so the higher the urgency. (2) The more the pedestrian flow near the station, the greater the probability of using an e-bike, and the higher the urgency. (3) The greater the population density within 1 km of the station, the higher the urgency. (4) The more the number of non-electricity-lacking e-bikes parked at the station, the lower the urgency. Among them, (1)-(3) are positive indicators, that is, the larger the index value, the better the result under the set evaluation system, and (4) is a negative indicator, that is, the smaller the index value, the better the result.

3. The method for planning the battery distribution path of shared electric bicycles based on the improved hybrid genetic algorithm according to claim 1, wherein Combine the entropy weight method to calculate the weight of the demand urgency index, and then calculate the demand urgency according to the TOPSIS method. The entropy weight method is an objective weighting method based on the degree of difference between indicators, and is widely used in priority ranking problems due to its high decision-making credibility. For the battery demand distribution problem of shared electric bikes, this paper uses the entropy weight method to calculate the weights of the battery demand indicators affecting the stations. The specific operation steps are as follows: Step 1: Establish an evaluation index matrix: Let the set of n sites be X = {x1, x2,..., x n}, and each site in the set has m evaluation indicators. Let the j-th (j = 1, 2,..., m) influencing factor index data of the i-th site x i be x ij , and construct the evaluation index matrix of the initial demand urgency of each site. X = (x ij ) n×m (i = 1, 2, … n; j = 1, 2, …, m) Step 2: Standardize the data: In order to eliminate the inconsistencies in the order of magnitude and dimension of different evaluation indicators, the range method is first used to standardize each indicator x of the evaluation requirement urgency ij The standardized value is The calculation formula is as follows: Step 3: Normalize the index matrix By normalizing the index matrix X, the matrix p is obtained: Step 4: Calculate the entropy value e of the j-th indicator j Step 5: Calculate the weight w of each indicator j Use the TOPSIS method to evaluate the urgency of the battery demand of EBSS stations to obtain the demand urgency coefficients of each station. This method mainly uses the Euclidean distance between the station and the positive and negative ideal solutions to obtain the battery demand urgency coefficients of the station. The steps are as follows: Step 6: Construct a weighted standardized matrix: Normalized matrix p ij Each column is multiplied by the corresponding weight w j to obtain the weighted matrix R. R ij = p ij × w j , i = 1, 2, …, n; j = 1, 2, …, m, R = (R ij ) n×m Step 7: Determine the positive ideal solution R + and the negative ideal solution R - : The positive ideal solution consists of the maximum values of each column element in the weighted standardized matrix, and the negative ideal solution consists of the minimum values of each column element. Step 8: Calculate the distances between the object and the positive ideal solution and the negative ideal solution using the Euclidean distance: Step 9: Calculate the relative closeness degree of site i: Step 10: Determine the demand tightness coefficient of each site for the battery: where: λ i is the demand urgency of demand point i. The greater the demand urgency coefficient of the station, the higher the demand urgency of the station and the higher the priority. Therefore, it should be preferentially satisfied during the actual distribution process of shared electric bicycle batteries.

4. The method for planning the battery distribution path of shared electric bicycles based on the improved hybrid genetic algorithm according to claim 1, characterized in that During the optimization process of the battery distribution path, a target function based on the battery demand urgency and transportation cost is established. The specific steps are as follows: Without loss of generality, the following assumptions need to be made first to construct the model of the present invention: (1) Immediately return to the distribution center after the distribution task is completed; (2) Each site is served by only one vehicle; (3) When a user arrives at a certain site, if there is an available shared electric bicycle, start riding, otherwise leave; (4) The distances between each site (including the distribution center), the number of shared electric bicycles at each site, and the number of batteries to be replaced are known, and the time window can be predicted; This paper introduces the concept of demand urgency, that is, priority is given to distributing to sites with high demand urgency. If the distribution is delayed, economic penalties will be imposed according to the delay time, and the economic penalty cost is positively correlated with the total distribution cost; conversely, combined with the demand urgency of the shared electric bicycle battery, appropriate additional economic compensation is given to the distribution driver, and the economic compensation is negatively correlated with the total distribution cost. Therefore, this target function includes vehicle driving cost, delay penalty cost, and timely distribution subsidy, and their cost functions are respectively: p i = α2(T i - E i )λ i , T i ≥ E i b i = |α2(T i - E i )λ i |, T i <E i Among which C ig is the operating cost for the delivery vehicle to directly travel from station i to point g (g ∈ N); p i is the penalty cost for the delivery delay of the delivery vehicle to station i; b i is the subsidy cost for the delivery vehicle when there is no delivery delay at the electric bicycle station i. And the longer the delay time, the greater the penalty cost. Similarly, the longer the time of early delivery (i.e., no delay), the higher the subsidy cost. The objective function formula is obtained:

5. The method for planning the battery distribution path of shared electric bicycles based on the improved hybrid genetic algorithm according to claim 1, wherein The improved hybrid genetic algorithm (SVGA) is used to efficiently solve the battery distribution path problem. When the traditional genetic algorithm solves complex path optimization problems, it is easy to fall into local optima and has a slow convergence speed. Therefore, the present invention introduces a simulated annealing criterion, and accepts worse solutions with a certain probability through the Metropolis criterion in the selection stage of the genetic algorithm to enhance the global search ability and avoid premature convergence. In addition, to further improve the optimization effect, the SVGA algorithm also combines a variable neighborhood search strategy, continuously adjusts the search space, improves the exploration ability of the algorithm and the quality of the solution, so as to find a better distribution path in a short time. The specific steps include: Improvement 1: Improve the selection mechanism based on the Metropolis criterion Interest In the distribution of shared electric bicycle batteries, optimizing the distribution path is a complex task. Although the traditional genetic algorithm has a powerful solving ability, its roulette wheel selection mechanism is prone to the loss of excellent individuals, resulting in the algorithm falling into local optima prematurely and affecting the distribution efficiency. However, the simulated annealing algorithm has excellent global search ability and can always accept better solutions during the search process, just making up for the deficiency of the roulette wheel selection mechanism. The specific improvement operations are as follows: Step 1: Randomly select two individuals P1 and P2 in the population and calculate their objective function values Z(P1) and Z(P2). Step 2: Based on the Metropolis criterion of simulated annealing, if Z(P1) < Z(P2), according to the first criterion of the better one, select individual P1 to enter the offspring; otherwise, according to the second criterion, with probability P s Receive individual P1 to enter the offspring. In the above formula, the temperature T gradually cools with the iteration of the algorithm, and the calculation formula is: T = T0 × k where T0 is the initial temperature and k is the cooling rate. Step 3: Repeat Steps 1 and 2 until the size of the offspring population reaches the established scale. Algorithm.1 Improvement 2: Improve the optimal individual with variable neighborhood search Add a variable neighborhood search operation after the mutation operation and before the next loop. This can not only improve the local search ability of the genetic algorithm, but also effectively reduce the calculation time, enabling a high-quality delivery plan to be found within a limited time. Therefore, perform the variable neighborhood search operation on the current optimal individual. (1) Two-point transposition. In a delivery route, randomly select two different stations and exchange them. When a delivery route is encoded as "3475281", if the randomly selected positions are 1 and 6, the new route encoding generated after the exchange operation will become "8475231". (2) Random shuffle. Randomly select multiple stations and shuffle the order of the selected stations. The delivery route encoding is "3475281". Suppose positions 1, 3, 4, and 6 are randomly selected, and the extracted station sequence is "3758". After random shuffling, assuming the new order is "7385", the final generated new route encoding is "7438251". (3) Insertion operation. Randomly select two stations and insert the station at the higher index position before the lower index position, while shifting the stations after the lower position one position to the right in sequence. The delivery route encoding is "3475281". If the two randomly selected positions are 1 and 7, the new route encoding after the insertion operation will become "1347528". (4) Inversion operation. Randomly select two positions and reverse the station segment between these two positions. For the delivery route encoding "3475281", if the randomly selected positions are 3 and 7, after reversing the station segment in this interval, the new route encoding obtained will be "3418257".

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