Low-carbon cold-chain logistics path optimization method based on improved marine predator algorithm

Abstract

The invention discloses a low-carbon cold-chain logistics path optimization method based on an improved marine predator algorithm. The low-carbon cold-chain logistics path optimization method comprises the steps of establishing a multi-target distribution path optimization model according to cold-chain logistics distribution task requirements and urban traffic network conditions; minimization of total distribution cost and maximization of customer satisfaction are taken as a comprehensive optimization objective function, and constraint conditions are determined; applying a Tent chaotic mapping mode to randomly generate an initialized population, wherein the population represents a set composed of a plurality of path planning schemes; performing iterative optimization on the initial population, updating each path planning scheme in the population according to global search and local search mechanisms of a marine predator algorithm in each iteration, evaluating the fitness of each path planning scheme according to a comprehensive optimization objective function, and updating the population according to an evaluation result; and when a preset termination condition is reached, outputting the path planning scheme with the highest fitness in the population as an optimization result.

Description

Technical Field

[0001] The present invention relates to the research field of low-carbon cold chain logistics path optimization algorithms considering traffic conditions, and in particular to a multi-objective low-carbon cold chain logistics path optimization method based on a marine predator algorithm considering traffic conditions and customer satisfaction. Background Art

[0002] Most research on logistics routing optimization is static, based on factors such as customer demand and vehicle travel time, which are relatively stable during transportation. However, in real life, many dynamic factors exist, such as unstable traffic conditions due to road congestion or weather conditions, and fluctuating customer demand. These factors all affect the delivery routes of logistics vehicles. Traditional static vehicle routing research is no longer suitable for today's logistics development. Scientific and rational planning of delivery routes, taking into account dynamic factors such as traffic conditions and immediate customer needs, is a practical necessity. Research on dynamic routing for logistics vehicles has become a key focus of vehicle routing research. Because real-life traffic conditions are volatile and can change with weather conditions and morning and evening rush hours, logistics routing optimization research is more difficult. Therefore, the challenge of completing delivery tasks within the customer's required timeframe, while accounting for various dynamic factors such as changes in vehicle speed, is gaining increasing attention in academia.

[0003] Researchers are increasingly concerned about the impact of traffic conditions on carbon emissions during the distribution process of logistics companies. They are trying to use advanced traffic monitoring, data analysis, and model optimization technologies to develop more environmentally friendly and efficient distribution plans, thereby reducing carbon emissions and promoting the green transformation of the logistics industry. [1] Taking intra-city logistics distribution as the research object, considering the time-varying traffic network and the customer's door-to-door pickup needs, taking the carbon emission cost into account in the total distribution cost, an improved Eagle algorithm based on an adaptive large-scale neighborhood search strategy is proposed to study the time-dependent simultaneous pickup and delivery green vehicle routing problem under the intra-city distribution model; Zhang Yujing [2] It is proposed to calculate the traffic congestion index based on the CRITIC-entropy weight-TOPSIS method, take the minimum total distribution cost as the goal, and combine the genetic algorithm to build a low-carbon cold chain logistics distribution path optimization model considering the traffic congestion index; Wang Ning [3] In response to the increasing number of vehicles and the increasingly serious congestion, etc., taking into account factors such as customer value, customer satisfaction and cost, a piecewise function is used to characterize vehicle speed, and constraints such as time window and vehicle load are considered at the same time, and a multi-objective mathematical model is established for solution; Sun Yihang [4] Quantify the urban congestion index, build three cold chain logistics distribution models, consider congestion and low carbon factors respectively, and use improved genetic algorithms to conduct simulation experiments; Huang Zhifeng [5]Aiming at the path planning problem of mobile robots in dynamic environments, et al. proposed a fusion algorithm of the improved Harris Hawk algorithm with an adaptive weight strategy and an improved dynamic window algorithm; Chengming Qi [6] et al., with the goal of minimizing the time required for emergency cold chain logistics resource scheduling, constructed a mathematical model for emergency cold chain logistics scheduling that included changes in vehicle loss, refrigeration consumption, and cargo damage over time. Taking into account the traffic conditions of the actual distribution path, they used a heuristic algorithm based on network optimization ideas and the Baidu Maps application programming interface to solve the emergency cold chain logistics scheduling model; Sun Weifeng [7] To address the randomness and ambiguity in the evaluation process of green cold chain logistics suppliers, researchers

[15] and

[16] proposed a cloud model evaluation method for cold chain logistics suppliers based on a combination weighting method based on the minimum information discriminant principle. Therefore, it is crucial to effectively utilize intelligent algorithm models to solve the dynamic routing problem of logistics vehicles caused by unstable traffic conditions under weather changes, provide logistics companies with high-quality delivery services, and thus achieve low-carbon cold chain logistics.

[0004] The Particle Swarm Optimization (PSO) algorithm begins by initializing a swarm of N particles. The particles in the swarm search in a D-dimensional space at a constant rate, ultimately finding the optimal solution through multiple iterations. PSO is widely used in optimization problems due to its simplicity, easy parameter setting, and ease of implementation.

[0005] The Harris Hawk Optimization (HHO) algorithm, proposed in 2019 by scholars Heidari, Mirjalili, and others, is a new stochastic swarm search optimization algorithm. By observing the unique pursuit style and cooperative hunting behavior of Harris Hawk swarms during hunting, a corresponding mathematical model was established, enabling the hawks to gradually converge to the rabbit's location during the pursuit, which is the optimal solution. The Harris Hawk algorithm has the advantages of few parameters, simple structure, and fast convergence.

[0006] The Marine Predators Algorithm (MPA) is a meta-heuristic optimization algorithm proposed by Faramarzi et al. based on the foraging behavior of marine predators and the optimal encounter probability strategy during predator-prey interactions. This algorithm simulates predation behavior in marine ecosystems and seeks the optimal solution through interactions and information exchange between individuals. It exhibits strong evolutionary capabilities, fast search speed, and robust optimization capabilities.

[0007] Marine predators use a Brownian motion strategy in areas where prey is abundant. Standard Brownian motion is a random process in which their step size is determined by a normal distribution with zero mean (μ = 0) and unit variance (σ 2 =1), the probability function at point w is shown in formula (1):

[0008]

[0009] Where μ is the expected value, σ is the standard deviation, and exp(·) is the exponential function.

[0010] Marine predators use the Lévy flight strategy when their prey is unevenly distributed and scarce. Lévy motion is a random walk in which the probability density function of the step length is heavy-tailed, meaning that particles moving according to the Lévy motion perform occasional large-step movements interspersed with many frequent small-step movements. Its movement pattern generally follows the following rule: the particle first moves locally, performing a small-step displacement, then performs a large-step displacement in global space, and then alternates between the two displacement operations, as shown in Equations (2) to (6):

[0011] P i '=P i ×(1+L(α)) (2)

[0012]

[0013]

[0014] Among them, P i is the displacement of the i-th particle, x and y are two normally distributed variables, and the standard deviation is σ x and σ y ,σ y =1, α=1.5, Γ is the gamma function.

[0015] The initial solution of the marine predator algorithm is evenly distributed in the search space and initialized according to the following formula (7):

[0016] X0=X min +rand(X max -X min ) (7)

[0017] Among them, X0 represents the initial solution position, X max and X min Represent the upper and lower limits of the search space, respectively, and rand is a random variable uniformly distributed in the range [0,1].

[0018] The most important step in finding the optimal solution is updating the Elite matrix, the top predator matrix. This matrix contains the positions of the predators with the highest fitness. After each iteration, if a predator with a higher fitness is discovered, the Elite matrix is ​​updated. The Prey matrix, Prey, contains the positions of the prey. The predator updates its own position based on this information. The Prey matrix has the same dimensions as the Elite matrix, and the predator updates its position based on the Prey matrix. At the end of each iteration, if a predator with a higher fitness value emerges, the Elite matrix is ​​updated accordingly.

[0019] The Elite and Prey matrices are expressed as formula (8):

[0020]

[0021] Where n is the number of initial solutions, d is the dimension, I is the current iteration number, X I Represents the top predator of generation I. Elite consists of n copies of it. X in the Prey matrix i,j represents the jth dimension of the i-th prey, X i represents the i-th prey.

[0022] After the initialization phase, according to the different speed ratios v between the predator and the prey, three different phases of position update formulas are defined to simulate the dynamic interaction between the predator and the prey, as follows:

[0023] Stage 1: High speed ratio (v≥10)

[0024] This stage occurs in the initial iteration of the optimization process, that is, Iter < 1 / 3Max_Iter. At this time, the speed of the predator is much greater than the speed of the prey. The predator remains stationary, and the prey updates its position using Brownian motion, as defined in formula (9):

[0025]

[0026] Among them, Iter represents the current number of iterations, Max_Iter represents the maximum number of iterations, represents the standard Brownian motion, which obeys the standard normal distribution. is a term-by-term multiplication operator, P=0.5 is a constant, It is a random variable that is very uniformly distributed in the interval [0,1], and stepsize represents the step size.

[0027] Stage 2: Same speed ratio (v≈1)

[0028] This stage is in the middle of the iterative process, that is, (1 / 3Max_Iter<Iter<2 / 3Max_Iter). At this time, the speeds of the prey and the predator are basically the same. Half of the prey is responsible for development based on the Levy flight strategy, and the other half is responsible for exploration based on the Brownian walk strategy, as defined in formulas (10) and (11):

[0029] The position update formula of the prey using the Levy flight strategy is as follows:

[0030]

[0031] The position update formula of the prey using the Brownian walk strategy is as follows (11):

[0032]

[0033] in, represents the Lévy flight, which is a random variable that follows the Lévy distribution. Indicates that the prey performs Levi locomotion, It indicates that the predator performs Brownian motion, and CF is the step length control parameter of the predator motion, as shown in formula (12):

[0034]

[0035] Stage 3: Low speed ratio (v=0.1)

[0036] The low speed ratio phase belongs to the development phase of the algorithm. In this phase, regardless of whether the prey adopts the Brownian strategy or the Lévy strategy to move, the predator will use the Lévy strategy to capture the prey. This phase occurs at the end of the iterative process (2 / 3Max_Iter<Iter), and the prey position update formula is shown in formula (13):

[0037]

[0038] Research has found that external environmental disturbances such as artificial fish aggregation devices (FADs) or eddy currents can alter the foraging behavior of marine predators. To address issues such as premature convergence and falling into local optima during the optimization process, the marine predator algorithm introduces the FADs effect, as shown in formula (14):

[0039]

[0040] in, is a binary vector, r is a random number in the interval [0,1], and FADs is a variable with a default value of 0.2. and are random values ​​of the prey matrix, r1 and r2 are random numbers, 1≤r1,r2≤n.

[0041] References:

[0042] [1] Shi Xiaojuan. Research on intra-city delivery route optimization considering time-dependent road network[D]. Yantai: Shandong Technology and Business University, 2023.

[0043] [2] Zhang Yujing. Research on the Optimization of Cold Chain Low-Carbon Logistics Distribution Path of M Company Considering Traffic Congestion Index[D]. Handan: Hebei University of Engineering, 2022.

[0044] [3] Wang Ning, Hu Dawei, Xu Jie, et al. Time-varying routing problem of urban cold chain logistics based on customer value and satisfaction [J]. China Journal of Highway and Transport, 2021, 34(09): 297-308.

[0045] [4] Sun Yihang. Research on vehicle routing problem of cold chain logistics considering congestion and low carbon[D]. Zhengzhou: Henan University of Technology, 2022.

[0046] [5] Huang Zhifeng, Liu Yuanhua, Ren Zhihao, et al. Robot dynamic path planning based on improved Harris Hawk and improved dynamic window[J]. Computer Application Research, 2024, 41(02): 450-458.

[0047] [6]Chengming Qi and Lishuan Hu.Optimization of vehicle routing problem for emergency cold chain logistics based on minimum loss[J].PhysicalCommunication,2020,40(C):101085.

[0048] [7] Sun Weifeng and Gu Xiaoyan and Wu Dengsheng. Research on theSelection of Green Cold Chain Logistics Service Providers Based on CombinedWeighting-Cloud Model[J]. Procedia Computer Science, 2022, (214): 1409-1416. Summary of the Invention

[0049] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a low-carbon cold chain logistics path optimization method based on an improved marine predator algorithm. This method starts from real life and, under the premise of considering traffic conditions, combines low-carbon logistics with vehicle distribution path optimization problems, solves practical application problems, and rationally plans vehicle paths, thereby improving customer satisfaction while reducing the total distribution cost. Reducing logistics transportation costs, energy conservation and emission reduction, and improving customer satisfaction not only play an important role in promoting the development of low-carbon logistics, but also have important significance and value for studying vehicle distribution path optimization problems from the perspective of low-carbon logistics. At the same time, compared with traditional path optimization problems, dynamic vehicle path optimization problems considering traffic conditions are closer to real life. Only by scientifically and efficiently arranging distribution routes can we provide customers with better services, which is also beneficial to the long-term development of logistics companies.

[0050] In addition, multi-objective optimization means that when solving a problem, multiple objective functions must be optimized simultaneously. Generally speaking, when looking for the optimal solution of an objective function, it is often at the expense of other objective functions. The multi-objective distribution path optimization model can solve this problem very well. Based on this, the present invention establishes a multi-objective distribution path optimization model that takes traffic conditions into consideration, and uses an improved ocean predator algorithm to complete the solution. The method is compared with other algorithms such as particle swarm optimization, Harris eagle algorithm, ocean predator algorithm, etc. to verify the effectiveness of this method in low-carbon cold chain logistics path optimization.

[0051] The purpose of the present invention is achieved through the following technical solutions:

[0052] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0053] 1. Reduce delivery costs and improve delivery efficiency. By comprehensively considering multiple objectives, including traffic congestion, carbon emissions, delivery costs, and customer satisfaction, and combining cold chain temperature control costs with operating cost models, the resulting routing solution reduces carbon emissions and controls overall costs during delivery while better meeting customer needs. This effectively reduces delivery costs, improves delivery efficiency, and enhances customer satisfaction.

[0054] 2. Effectively improve the quality and diversity of the initial candidate solution space. Using Tent Chaos Map for swarm initialization makes the initial solution space more uniform and diverse, helping the algorithm escape local optima and obtain more optimal delivery routes, thereby reducing overall delivery distance and carbon emissions.

[0055] 3. Effectively improve the algorithm's convergence speed and accuracy. The introduction of an elite selection strategy allows the optimal path to be retained in each iteration, thereby improving the algorithm's convergence speed and stability and shortening the optimization time. High-quality paths can be obtained within a limited number of iterations, effectively reducing operating costs during the delivery process.

[0056] 4. Effectively improve local search capabilities. Combining greedy algorithms with global and local search processes allows for rapid local optimization of the current solution, improving search efficiency and enhancing path quality, resulting in shorter delivery times and more optimal routes. This strategy further reduces carbon emissions and transportation costs while meeting timeliness requirements and increasing customer satisfaction.

[0057] 5. Combined with multi-dimensional modeling, the practicality and robustness of the algorithm are enhanced. The present invention deeply considers the important impact of traffic conditions and carbon emissions on the total distribution cost and customer satisfaction in low-carbon cold chain logistics, introduces a customer satisfaction function, and constructs a multi-objective distribution path optimization model that comprehensively considers multiple costs. In order to deal with this complex problem, the present invention not only fully utilizes the advantages of the marine predator algorithm's strong global search capability and low time complexity, but also combines its multi-stage optimization strategy, considers environmental factors (vortex formation or fish aggregation device effect), fast search speed, and strong optimization ability to further improve the optimization efficiency, and compares it with the particle swarm algorithm and the Harris Eagle algorithm to further verify the superiority of the marine predator algorithm in this field. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic flow diagram of the method of the present invention

[0059] Figure 2 It is a schematic diagram of time penalty cost.

[0060] Figure 3 This is the MOPSO delivery route map on snowy days.

[0061] Figure 4 This is the MOHHO delivery route map on snowy days.

[0062] Figure 5 This is the MOMPA delivery route map on snowy days.

[0063] Figure 6 This is the IMOMPA delivery route map on snowy days.

[0064] Figure 7 It is the iterative graph of the total cost of delivery under sunny conditions.

[0065] Figure 8 It is the iteration graph of customer satisfaction under sunny conditions.

[0066] Figure 9 It is the iterative graph of the total cost of delivery under rainy day conditions.

[0067] Figure 10 It is the iteration graph of customer satisfaction under rainy day conditions.

[0068] Figure 11 It is the iterative graph of the total cost of delivery under snowy conditions.

[0069] Figure 12 It is the iteration graph of customer satisfaction under snowy conditions.

[0070] Figure 13 It is the iterative graph of the total cost of delivery under foggy conditions.

[0071] Figure 14 It is the iteration graph of customer satisfaction under foggy conditions.

[0072] Among them, MOPSO involved in the accompanying drawings represents multi-objective particle swarm optimization; MOHHO represents multi-objective Harris Hawk algorithm; MOMPA represents multi-objective marine predator algorithm; and IMOMPA represents improved multi-objective marine predator algorithm. DETAILED DESCRIPTION

[0073] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0074] Example 1

[0075] This embodiment provides a low-carbon cold chain logistics route optimization algorithm based on an improved marine predator algorithm. This algorithm considers the dynamic factors of traffic conditions and provides a solution for optimizing low-carbon cold chain logistics vehicle routes under different traffic conditions. This embodiment studies the current dynamic vehicle route optimization problem and establishes a multi-objective optimization model for distribution routes. Based on the route optimization scheme of the improved multi-objective marine predator algorithm, it utilizes its search mechanism that simulates the predation behavior of marine organisms, combines the low-carbon emissions of cold chain logistics, weather changes, and customer satisfaction, and realizes the optimization of low-carbon cold chain logistics routes.

[0076] See Figure 1 , specifically:

[0077] S1. Establish a multi-objective distribution path optimization model based on the cold chain logistics distribution task requirements and the urban transportation network conditions. The multi-objective distribution path optimization model considers factors such as vehicle fixed costs, vehicle transportation costs, cargo damage costs, refrigeration costs, carbon emission costs, time window penalty costs, and customer satisfaction.

[0078] (1) Establish a vehicle speed characteristic model considering traffic conditions.

[0079] In the real world of logistics and transportation, factors such as weather conditions and peak hours directly impact the speed of delivery vehicles, leading to fluctuations in delivery costs and customer satisfaction. Therefore, this example simulates real-world transportation scenarios and investigates the problem of optimizing low-carbon cold chain logistics routes, taking traffic conditions into account. This problem requires scientifically and rationally arranging delivery vehicle routes to minimize total delivery costs while maximizing customer satisfaction.

[0080] Weather conditions have a significant impact on traffic conditions. When weather conditions are good, the traffic network operates well and will not have much impact on the travel of transport vehicles; but under severe weather conditions, due to factors such as slippery roads and low visibility, vehicles travel slowly or even stagnate, which will have a serious impact on the urban road traffic system. Therefore, when severe weather conditions occur on the road, it is a very common phenomenon that the road network operation status changes. This embodiment refers to the actual monitoring data of "Optimization of Fresh Agricultural Product Distribution Routes Based on Road Conditions" and obtains the vehicle speed characteristic model under different weather conditions and different time periods. The impact rate of vehicle speed at different time periods under different weather conditions (sunny, rainy, snowy, foggy) is ζ con , (con=sun,rain,snow,fog). The specific mathematical expressions are shown in (15), (16), (17), and (18):

[0081]

[0082] Among them, the vehicle speed

[0083] (2) Low-carbon cold chain logistics transportation and distribution cost modeling.

[0084] The total delivery cost includes vehicle transportation costs (including vehicle fixed costs and vehicle transportation costs), cargo damage costs, cooling costs, time window penalty costs, and carbon emission costs. Each cost component is modeled as follows:

[0085] 1) Fixed costs of vehicles.

[0086] The fixed cost of a vehicle refers to the expenses incurred by a refrigerated truck to complete a single mission, including driver salaries, training costs, vehicle maintenance and depreciation costs, etc. This expenditure is closely related to the number of vehicles allocated by the distribution center for the mission. It is represented by C1, as shown in formula (19):

[0087]

[0088] Among them, H is the fixed cost of starting the vehicle, G k Is vehicle k enabled? K is the set of transport vehicles, the kth vehicle, k = 1, 2, ..., K

[0089] 2) Transportation cost of vehicles.

[0090] Transportation cost is composed of fuel cost and toll cost, which is proportional to the distance of refrigerated vehicles. The increase of vehicle mileage will lead to the rise of transportation cost. Denote it as C2, which is shown in equation (20):

[0091]

[0092] where N is the set of nodes, 0 represents the distribution center, and the rest of the nodes represent customers, is the unit transportation cost of vehicle k from node i to node j, d ij is the distance from node i to node j, is 1 if vehicle k travels from node i to node j, otherwise 0.

[0093] 3) Loss cost of goods.

[0094] Loss cost of goods mainly considers the transportation process and loading and unloading process. In the transportation process of refrigerated vehicles, although the low-temperature freezing process can maintain the freshness of goods to a certain extent, the freshness of goods will still decrease gradually with the accumulation of time. This part of the loss caused by the time factor is called the loss cost of goods in transportation, denoted as C 3a ; In the loading and unloading process of goods, improper loading and unloading operation will cause damage to goods, and frequent opening and closing of the door will cause convection with the outside air, so that the temperature in the vehicle compartment will be affected by the outside environment, and then will cause the loss of goods related to temperature fluctuations. This part of the loss caused by improper operation and external environmental factors is denoted as C 3b . Denote the loss cost of goods as C3, which is shown in equations (21) to (23):

[0095]

[0096] C3 = C 3a +C 3b (23)

[0097] where p1 is the unit value of cold-chain products, is the demand of node i served by vehicle k, ε1 is the loss rate per unit time when the vehicle is in transportation, ε2 is the loss rate per unit time when the vehicle is unloading, is the departure time of vehicle k from the distribution center, is the arrival time of vehicle k at node i, w i is the service time of node i, is 0 or 1, which is 1 if node i is served by vehicle k, otherwise 0.

[0098] 4) Refrigeration cost.

[0099] The cooling cost of a vehicle mainly consists of two parts. One is the loss of cooling efficiency during transportation due to the airtightness of the vehicle compartment. 4a Second, when loading and unloading goods, the door is inevitably opened, resulting in heat exchange with the outside hot air, which causes additional cooling demand, expressed as C 4b C4 is used to represent the cooling cost, as shown in formulas (24) to (26):

[0100]

[0101] C4=C 4a +C 4b (26)

[0102] Among them, p2 is the unit cooling cost, B1 is the heat load coefficient when the door is closed, is the time it takes for vehicle k to reach delivery point n, is the departure time of vehicle k from the distribution center, B2 is the heat load coefficient when the door is open, t si is the service time of vehicle k at node i.

[0103] 5) Carbon emission costs.

[0104] The carbon emission cost of a vehicle mainly includes the carbon emissions generated by fuel consumption during transportation, expressed as C 5a Indicates the carbon emissions generated by refrigeration equipment during operation, expressed as C 5b Indicates that C5 represents the carbon emission cost.

[0105] Related research has found that there is a linear relationship between the fuel consumption per unit distance η and the vehicle load, as shown in formula (27):

[0106] η(Q)=e(Q O +Q ij )+f (27)

[0107] Among them, the load capacity of the transport vehicle is Q ij , e and f are constants, the vehicle's own weight is Q0, and the vehicle's maximum load is Q m . .

[0108] The carbon emissions generated by the vehicle during transportation and refrigeration at point (i, j) are calculated using formulas (28) and (29):

[0109] C 5a =θ1×η(Q)×d ij (28)

[0110] C 5b =θ2×Q ij×d ij (29)

[0111] The embodiment adopts a carbon tax method to estimate the carbon emission cost generated by the vehicle in the distribution process, which is determined by the carbon tax and the corresponding carbon emission amount, and the calculation formula is: carbon emission cost = carbon tax × carbon emission amount. The carbon emission cost generated by the vehicle is C5, as shown in formula (30):

[0112]

[0113] Wherein, θ0 is the carbon tax, θ1 is the carbon emission generated by the vehicle per unit fuel consumption, and θ2 is the carbon emission generated by the vehicle driving unit distance refrigeration equipment operation.

[0114] 6) Time window penalty cost.

[0115] Fresh products have a high requirement for the time efficiency of distribution due to their natural perishable nature, which is directly related to the time-related penalty cost. Once the distribution is delayed, it will cause the product freshness to decline, and will also trigger a chain reaction such as return, customer complaint, and even brand reputation damage. Customers usually have a specific time range for product distribution and hope to receive the product within this time range, which is called the expected time window. Fresh distribution service must strictly comply with this time window to ensure product freshness and meet customer demand. If the distribution cannot be completed within the scheduled time range, not only the customer's satisfaction will be affected, but also the customer may face a penalty fee. However, during the distribution process, various unexpected situations may occur, such as traffic delays, weather changes, vehicle breakdowns, etc., which may cause the distribution time to exceed the customer's expected time window. In order to deal with such situations, the distribution service provider needs to establish a flexible and efficient distribution path optimization model that can consider time window constraints and adjust as necessary to minimize the risk of delay. The time penalty cost function γ(t i ) is shown in Figure 2 , and γ(t i ) is represented by formula (31):

[0116]

[0117] Wherein, M is the maximum penalty cost, μ1 is the penalty cost coefficient of the vehicle arriving early, μ2 is the penalty cost coefficient of the vehicle arriving late, ET i is the earliest time for the vehicle to arrive at node i, LT i is the latest time for the vehicle to arrive at node i, ET i ' is the earliest time for the vehicle to accept arrival at node i, LT i ' is the latest time for the vehicle to accept arrival at node i, t iis the time when the vehicle arrives at node i.

[0118] C6 is used to represent the time penalty cost, as shown in formula (32):

[0119]

[0120] 7) Customer satisfaction analysis.

[0121] Assume that the customer's expected delivery time is [ET i ,LT i ], if the delivery is carried out within this period, the customer satisfaction function is the largest, and its value is 1. However, in the real delivery environment, the delivery time will be affected by many factors such as traffic congestion, which may cause the actual delivery time to be advanced or delayed, and fail to meet customer expectations, resulting in reduced customer satisfaction. i ', LT i 'represent the earliest and latest delivery time that the customer can accept, so in [ET i ',ET i ] or [LT i ,LT i '] time range, customer satisfaction also changes with the time difference from the scheduled service time window. If the delivery time is within [ET i ',LT i '], the customer satisfaction is 0. The customer satisfaction function is shown in formula (33).

[0122]

[0123] S2. Minimize total delivery cost and maximize customer satisfaction as the comprehensive optimization objective function, and determine the constraints; specifically:

[0124] Under the constraints of traffic conditions, this embodiment takes minimizing total delivery costs and maximizing customer satisfaction as optimization goals. Specifically:

[0125]

[0126] For ease of description, set the decision variables Its value is shown in formula (36)(37).

[0127]

[0128] The constraints are as follows:

[0129] 1) Vehicle size constraint: The number of vehicles used in the distribution process cannot exceed the vehicle size K of the distribution center. The constraint can be expressed by formula (38):

[0130]

[0131] Where N is the node set, 0 represents the distribution center, and the remaining nodes represent customers; Indicates that vehicle k travels from the distribution center to node j;

[0132] 2) Customer access constraint: Each customer point can be visited by one and only one transport vehicle once. The constraint can be expressed by formula (39):

[0133]

[0134] 3) Distribution center round-trip constraint: Each transport vehicle must start from the distribution center and return to the distribution center, and each vehicle cannot have more than one predecessor node and successor node at the distribution center. The constraint can be expressed by formula (40):

[0135] Indicates that vehicle k travels from node j to the distribution center;

[0136] 4) Customer point penalty cost function: The time penalty cost function of the vehicle at customer point i. The constraint can be expressed by formula (41):

[0137]

[0138] 5) Customer point load constraint: The load of vehicle k when it leaves customer point j. The constraint can be expressed by formula (42):

[0139]

[0140] in, represents the vehicle load when vehicle k leaves node i, q j is the demand of customer point j;

[0141] 6) Vehicle load upper limit constraint: The load of vehicle k at any time must not exceed its load upper limit. The constraint can be expressed by formula (43):

[0142]

[0143] 7) Service time constraint: the time t at which the vehicle arrives at customer point j j , c ij is the congestion or delay risk factor, is the time required from customer point i to customer point j. The constraint is expressed as: w i The service duration of node i is expressed by formula (44):

[0144]

[0145] 8) Travel time constraint: The travel time of a vehicle from customer point i to customer point j is expressed by formula (45):

[0146]

[0147] Among them, d ij represents the distance from node i to node j, and the vehicle speed represents the average vehicle speed, ζ con Indicates the impact rate of different weather conditions on vehicle speed at different times.

[0148] 9) Total number of vehicles constraint: The total number of vehicles m used in the entire delivery process is expressed as follows using formula (46):

[0149]

[0150] 10) Initial load constraint: The initial load of vehicle k when it leaves the distribution center It can be expressed as follows using formula (47):

[0151]

[0152] S3. Apply the Tent chaotic mapping method to randomly generate and initialize the candidate solution space, where the candidate solution space represents a set of several path planning schemes; each path planning scheme contains a series of service point sequences and load times;

[0153] The improvement of the multi-objective marine predator algorithm includes the improvement of the initialization of the candidate solution space, that is, the introduction of Tent chaos map in the algorithm initialization.

[0154] By using random generation to initialize the candidate solution space, the improved multi-objective marine predator algorithm may require a different number of iterations and computational resources to find the optimal solution each time it is run. A chaotic mapping method is used to generate initial solutions, improving their quality and algorithm stability. The randomness generated by the tent mapping helps introduce diversity into the candidate solution space at the initial stage, helping the algorithm explore a wider range of solutions and reducing the likelihood of being trapped in local optima.

[0155] The chaotic sequence generated by the Tent chaotic map in the interval [0,1] is more uniform and has a faster number of iterations. The formula of the Tent chaotic map is shown in (46): where Tent(i,j) is the j-th dimension tent random number of the i-th individual, and R is the random coefficient in [0,1].

[0156]

[0157] S4. Iteratively optimize the initial candidate solution space. In each iteration, update each path planning scheme in the group according to the global search and local search mechanism of the marine predator algorithm, evaluate the fitness of each path planning scheme according to the comprehensive optimization objective function, and update the candidate solution space based on the evaluation results. The specific steps are as follows:

[0158] (401) Algorithm parameter setting: setting key parameters in the marine predator algorithm, such as the range of candidate solution space, the number of predators (actively explored path planning schemes), the number of iterations, etc.

[0159] (402) Calculating fitness: Based on the above comprehensive optimization objective function, calculate the fitness of each path planning scheme;

[0160] (403) Fitness evaluation: Use the comprehensive optimization objective function (minimizing total cost, maximizing customer satisfaction) to evaluate the fitness of each path planning scheme, that is, its quality (the higher the fitness, the higher the quality of the path planning scheme); update the optimal path planning scheme based on the fitness evaluation results and directly retain it in the next generation candidate solution space; in the selection process, give priority to path planning schemes with higher comprehensive fitness to balance the conflicts between different optimization objectives.

[0161] (404) Candidate solution space search: The prey (candidate path planning solution) moves in the candidate solution space and explores new solutions by simulating the predation behavior of marine organisms such as sharks and whales. In each iteration, the prey (candidate path planning solution) adjusts its movement direction and step size based on its current position and surrounding environment (traffic conditions, carbon emission costs, etc.); the number of iterations increases by 1. If the maximum number of iterations is not reached, go to (402), otherwise go to (405).

[0162] (405) Result output: Output the final optimal path planning scheme (i.e., the top predator, the current optimal path planning scheme), including data such as the order of service points, estimated delivery time, total cost, cooling cost, and carbon emission cost.

[0163] S5. When the preset termination condition is reached, the path planning solution with the highest fitness in the candidate solution space is output as the optimization result.

[0164] Specifically, the improvement of the multi-objective marine predator algorithm includes not only the introduction of the Tent chaos map in initialization, but also the following:

[0165] Improvements to the global search process involve the introduction of an elite selection strategy. In each generation, the path plan with the best fitness is retained as the elite to ensure convergence. This elite selection strategy enhances the algorithm's global search capabilities by retaining the best individuals (path plans with the best fitness). The marine predator algorithm evaluates the fitness of the current candidate solution space to determine the strengths and weaknesses of each individual. The best individuals are selected as elites and directly passed on to the next generation, ensuring the continuity of excellent solutions. Through iterative evolution, the algorithm maintains the discovered optimal solution while continuously exploring new potential solutions, thereby increasing the probability of finding the global optimal solution. When the algorithm reaches a predetermined number of iterations, the optimal solution is output and iterations cease. During elite selection, the candidate solution space is non-dominated sorted according to each objective function, setting the congestion of the boundary individuals to infinite. The fitness of each individual (prey) is then calculated sequentially, and the more optimal individuals are selected from them to replace the current individual solutions in the elite matrix, reconstructing the elite matrix to avoid falling into local optima.

[0166] In the Ocean Predator algorithm for solving logistics vehicle delivery routing, the elite matrix, a matrix composed of information about the top predator (the current optimal routing solution), is used to monitor the search process and search for prey (candidate routing solutions) based on their location information. The elite matrix is ​​constructed after the algorithm initializes the candidate solution space, calculates the fitness value of the prey matrix, and records the optimal position. In each iteration, if a predator (routing solution) with a higher fitness value emerges, the top predator (the current optimal routing solution) is replaced, and the elite matrix is ​​updated accordingly.

[0167] The fitness value g of the i-th individual (prey) i The calculation formula is shown in formula (49):

[0168]

[0169] where g i The fitness value is calculated by all the objective function values ​​of the i+1th individual and the i-1th individual, f s,i+1 is the sth objective function value of the i+1th individual, f s,i-1 is the sth objective function value of the i-1th individual, f s,max 、f s,min are the maximum and minimum values ​​of the sth objective function respectively.

[0170] It also includes improvements in the global search and local search processes, that is, the introduction of greedy algorithms in this process. Combined with the idea of ​​the greedy algorithm, some path planning schemes are mutated in the hope of finding a better solution. A greedy algorithm is an algorithm that takes the best or optimal (i.e., most favorable) choice in the current state at each step, hoping to lead to the best or optimal result globally. By combining the greedy algorithm with the marine predator algorithm, this embodiment can effectively balance the global search capability and local search capability of the algorithm, improve the convergence speed of the algorithm and the quality of the solution. It helps the algorithm to quickly find high-quality solutions, and can also jump out of the local optimum, thereby increasing the probability of finding the global optimal solution.

[0171] Example 2

[0172] Combining the characteristics of the multi-objective particle swarm algorithm with strong global search capability and low time complexity, the multi-objective Harris Hawk algorithm with few parameters and simplicity, and the multi-objective ocean predator algorithm with strong evolutionary capability, fast search speed and strong optimization capability, the multi-objective particle swarm algorithm, multi-objective Harris Hawk algorithm, multi-objective ocean predator algorithm and improved multi-objective ocean predator algorithm are respectively applied to realize the low-carbon cold chain logistics path optimization scheme considering traffic conditions. The superiority of low-carbon cold chain logistics path optimization based on the improved multi-objective ocean predator algorithm has been verified.

[0173] (1) Path optimization scheme based on multi-objective particle swarm optimization. The multi-objective particle swarm optimization algorithm uses the concepts of non-dominated sorting and crowding to sort and select individuals in the population to maintain the diversity of the population. The specific steps and process are as follows.

[0174] The main steps of the multi-objective particle swarm optimization algorithm are:

[0175] 1) Initialize the particle swarm and set relevant parameters. Calculate the fitness value of each particle based on the objective function, randomly generate a certain number of particles within a corresponding range, and obtain the Pareto dominance relationship between the fitness values ​​of the evaluated particles. In practical applications of this invention, "particle swarm" represents a certain number of potential vehicle routing solutions; "objective function" is the optimization objective function of minimizing total delivery cost minZ1 and maximizing customer satisfaction maxZ2; "particles" represent potential routing solutions; and "corresponding range" refers to the range of constraints corresponding to the objective functions minZ1 and maxZ2.

[0176] 2) Perform a non-dominated sort and calculate the individual crowding. A non-dominated sort is performed based on the objective function values ​​of the particles to find the optimal set of solutions. By calculating the crowding between particles, diversity within the population is maintained. In practical applications of this invention, "individual" represents a potential path solution, and "population" represents the collection of particles that represent a potential path solution.

[0177] 3) External Archive Set: Based on the Pareto dominance principle, the dominance relationship of individuals in the particle swarm is judged, and non-inferior individuals are placed in the pre-set Archive set for archiving.

[0178] 4) Use the grid partitioning method to calculate the density information of the particles in the Archive set, and select the particles as Gbest in the Archive set according to the roulette method.

[0179] 5) The positions and velocities of particles in the swarm are altered, allowing them to be guided by Gbest and Pbest in their search for the optimal solution. Gbest provides the global optimal direction, while Pbest provides each particle's own optimal direction. Particles use this information to guide their movement through the search space, gradually finding better solutions.

[0180] 6) Update the Archive set and delete redundant individuals to prevent the best individuals of the current group from being lost in the next generation.

[0181] 7) Update the Archive set and determine whether the population has converged.

[0182] (2) Path optimization scheme based on multi-objective Harris Hawk algorithm. First, the target space is divided into several grids, and any grid is a candidate object, and the fitness value of the population individuals in the Archive set is calculated; secondly, the number of particles in each grid is calculated and used as the distribution density. The inverse of the distribution density is the probability of the grid being selected, and the grid is selected by roulette. Finally, the prey position is randomly determined in the selected grid. Among them, "prey" represents potential vehicle path solutions; "target space" refers to the search space in the multi-objective optimization problem, including all possible solutions. In the path optimization problem, it represents all possible paths or path combinations, which are determined by the objective function, model parameters, etc.; "population individuals in the Archive set" represent specific vehicle path solutions, and the algorithm finds the optimal path by improving these individuals; "particles in the grid" refer to population individuals located in the same grid.

[0183] The main steps of the multi-objective Harris Hawk algorithm are as follows.

[0184] 1) Randomly initialize the position vector of the population according to the problem dimension, set the parameters of the multi-objective Harris Hawk algorithm, calculate the fitness value of each hawk, and retain the individual position and fitness value.

[0185] 2) Non-dominated sorting and calculating individual crowding degree. Non-dominated sorting is performed according to the objective function value, and an optimal set of solutions is found; by calculating the crowding degree, the diversity in the Harris hawk population is maintained. The objective function is the optimization objective of minimizing the total distribution cost minZ1 and maximizing the customer satisfaction maxZ2.

[0186] 3) External archive set. The individuals in the Harris hawk population are subjected to dominance relationship judgment according to the Pareto dominance principle, and the non-inferior solutions are put into the archive set set in advance.

[0187] 4) The density information of the particles in the archive set is calculated using the grid division method, and the individuals in the Harris hawk population are selected as the population historical optimal solution according to the roulette method in the archive set.

[0188] 5) The selected excellent population individuals are used to update the position information of the Harris hawk population, and the basic Harris hawk algorithm operation is performed.

[0189] 6) The non-inferior solution set of the archive set is updated, and the redundant population individuals are deleted.

[0190] 7) The algorithm is ended according to the set iteration number control condition, and the algorithm is ended when the ending condition is reached; if the ending condition is not reached, go to 2) and continue to execute until the end.

[0191] In this embodiment, the related data provided by M Fresh Cold Chain Logistics Distribution Company is used to sort out the data information between the distribution center and each distribution point. It mainly includes one distribution center 0 and 20 distribution points, and each distribution point is numbered as 1, 2, …, 20. The basic information about the distribution center and the distribution point is shown in Table 1.

[0192] Table 1 Distribution point information table

[0193]

[0194]

[0195] In this embodiment, the actual situation is considered, the normal average speed of the vehicle is set to 60 km / h, the maximum vehicle capacity is 1495 kg, the maximum time penalty cost is 20 yuan, the fixed cost of each vehicle and the unit driving cost are 100 yuan and 2 yuan / km respectively, and the unit refrigeration cost is 1.5 yuan / kCal. The specific parameter expression is shown in Table 2.

[0196] Table 2 Parameter information table

[0197]

[0198]

[0199] The experimental operating environment is an experimental platform of Windows11 Intel (R) Core (TM) i5-10210U CPU @ 1.60GHz2.11GHz, 8GB of memory, and a 64-bit operating system. MATLAB R2023a is used to develop software for programming and experimental simulation to verify the model and algorithm proposed in the present invention. In order to more intuitively express the effectiveness of the improved multi-objective ocean predator algorithm, the total cost and fixed cost, transportation cost, cargo damage cost, refrigeration cost, carbon emission cost, and time penalty cost of the designed multi-objective particle swarm algorithm (MOPSO), multi-objective Harris Hawk algorithm (MOHHO), multi-objective ocean predator algorithm (MOMPA), and improved multi-objective ocean predator algorithm (IMOMPA) under four different weather conditions (sunny, rainy, snowy, and foggy) are summarized. All four algorithms use 4 vehicles for delivery tasks. The algorithm experimental results are compared as follows.

[0200] Taking snowy conditions as an example, the delivery path diagrams of the four algorithms are shown below:

[0201] The vehicle delivery path of MOPSO under snowy conditions is as follows: Figure 3 As shown in the figure. In addition, the delivery path experimental results obtained by the multi-objective particle swarm algorithm show that the total distance traveled by the vehicles is 34.73 km; the time taken by the four vehicles to complete the delivery tasks is 1.46 hours, 1.36 hours, 1.42 hours, and 1.51 hours respectively; the vehicle loads are 1045 kg, 973 kg, 967 kg, and 945 kg respectively; the service paths of the vehicles are as follows: the service order of vehicle 1 is 0→11→16→19→12→1→0; the service order of vehicle 2 is 0→3→4→9→10→13→0; the service order of vehicle 3 is 0→8→2→5→17→6→0; and the service order of vehicle 4 is 0→7→14→15→18→20→0.

[0202] MOHHO's vehicle delivery routes under snowy conditions are as follows: Figure 4 As shown in the figure. Furthermore, the delivery path experimental results obtained by the multi-objective Harris Eagle algorithm show that the total distance traveled by the vehicles is 36.63 km; the time taken for the vehicles to complete the delivery tasks is 1.66 hours, 1.49 hours, 1.66 hours, and 1.15 hours, respectively; the vehicle loads are 976 kg, 1071 kg, 1195 kg, and 688 kg, respectively; and the service paths of the vehicles are as follows: the service order for vehicle 1 is 0→1→4→10→14→11→0; the service order for vehicle 2 is 0→8→16→19→12→7→0; the service order for vehicle 3 is 0→2→5→3→13→20→9→0; and the service order for vehicle 4 is 0→6→15→18→17→0.

[0203] MOMPA's vehicle delivery routes under snowy conditions are as follows: Figure 5 As shown in the figure. Furthermore, the delivery path experimental results obtained by the multi-objective ocean predator algorithm show that the total distance traveled by the vehicles is 31.53 km; the time taken for the vehicles to complete the delivery tasks is 1.43 hours, 1.37 hours, 1.21 hours, and 1.45 hours, respectively; the vehicle loads are 1008 kg, 1029 kg, 1093 kg, and 800 kg, respectively; and the service paths of the vehicles are as follows: the service order of vehicle 1 is 0→1→2→4→5→7→0; the service order of vehicle 2 is 0→8→12→19→16→11→0; the service order of vehicle 3 is 0→6→9→18→13→20→0; and the service order of vehicle 4 is 0→3→17→10→14→15→0.

[0204] The vehicle delivery path of IMOMPA under snowy conditions is as follows: Figure 6 The delivery path experimental results obtained by the improved multi-objective marine predator algorithm show that the total distance traveled by the vehicles is 31.95 km; the time taken for the vehicles to complete the delivery tasks is 1.60 hours, 1.12 hours, 1.32 hours, and 1.37 hours respectively; the vehicle loads are 971 kg, 1029 kg, 1150 kg, and 780 kg respectively; and the service paths of the vehicles are as follows: the service order of vehicle 1 is 0→1→3→4→5→6→0; the service order of vehicle 2 is 0→8→11→12→16→19→0; the service order of vehicle 3 is: 0→2→7→14→10→13→0; and the service order of vehicle 4 is: 0→17→20→18→15→9→0.

[0205] Figures 7 to 14 The relationship between total delivery cost, customer satisfaction and number of iterations under four weather conditions (sunny, rainy, snowy and foggy) is shown respectively.

[0206] Table 3 shows the cost breakdown of the four algorithms under sunny conditions. It can be seen that the improved multi-target marine predator algorithm has the lowest total cost and the shortest total distance to complete the delivery task. The total cost to complete the delivery task is 560.71 yuan, of which the cargo damage cost is 2.37 yuan, the cooling cost is 5.28 yuan, the carbon emission cost is 105.71 yuan, and the time penalty cost is 3.27 yuan.

[0207] Table 3 Cost details under sunny conditions (yuan)

[0208]

[0209] Table 4 shows the cost details of the four algorithms under rainy conditions. It can be seen that the improved multi-objective marine predator algorithm has the lowest total cost and the lowest time penalty cost. The total cost of completing the delivery task is 558.31 yuan, of which the cargo damage cost is 2.58 yuan, the cooling cost is 5.1 yuan, the carbon emission cost is 108.66 yuan, and the time penalty cost is 1.43 yuan.

[0210] Table 4 Cost details under rainy conditions (yuan)

[0211]

[0212]

[0213] Table 5 shows the cost details and total delivery distance of the four algorithms under snowy conditions. The improved multi-objective ocean predator algorithm has the lowest total cost, and the total cost of completing the delivery task is 546.24 yuan, of which the cargo damage cost is 2.62 yuan, the refrigeration cost is 5.81 yuan, the carbon emission cost is 93.79 yuan, and the time penalty cost is 3.93 yuan; the total cost of the multi-objective ocean predator algorithm to complete the delivery task is 569.58 yuan, of which the refrigeration cost is 5.78 yuan, which is the lowest under snowy conditions; the total cost of the multi-objective Harris Eagle algorithm to complete the delivery task is 587.37 yuan, of which the time penalty cost is 3.66 yuan, which is the lowest under snowy conditions.

[0214] Table 5 Cost details under snowy conditions (yuan)

[0215]

[0216] Table 6 shows the cost breakdown of the four algorithms under foggy conditions. It can be seen that the improved multi-objective marine predator algorithm has the lowest total cost, the lowest time penalty cost, and the highest customer satisfaction. The total cost of completing the delivery task is 560.34 yuan, of which the cooling cost is 5.59 yuan, the carbon emission cost is 106.16 yuan, and the time penalty cost is 1.28 yuan.

[0217] Table 6 Cost details under foggy conditions (yuan)

[0218]

[0219]

[0220] Next, the total cost and time penalty cost of the designed multi-objective particle swarm optimization algorithm (MOPSO), multi-objective Harris Hawk algorithm (MOHHO), multi-objective ocean predator algorithm (MOMPA) and improved multi-objective ocean predator algorithm (IMOMPA) under four different weather conditions are summarized, and the algorithm comparison is shown in Table 7.

[0221] Table 7 Summary of total costs of four algorithms under different weather conditions (yuan)

[0222]

[0223] Table 8 Comparison of time penalty costs under different weather conditions (yuan)

[0224]

[0225] Tables 7 and 8 show the total costs of the multi-objective particle swarm algorithm, multi-objective Harris Hawk algorithm, multi-objective ocean predator algorithm, and improved multi-objective ocean predator algorithm designed in this embodiment under four different weather conditions. It can be concluded that the improved multi-objective ocean predator algorithm reduces the total cost of M Company's original distribution by 21.90%, 22.23%, 23.91%, and 23.06%, respectively; compared with the multi-objective particle swarm algorithm, the total cost is reduced by 3.67%, 4.55%, 4.53%, and 6.12%, respectively; compared with the multi-objective Harris Hawk algorithm, the total cost is reduced by 12.68%, 7.40%, 7.00%, and 14.08%, respectively; and compared with the multi-objective ocean predator algorithm, the total cost is reduced by 4.99%, 1.89%, 4.10%, and 4.29%, respectively. The above comparison clearly demonstrates the effectiveness of the improved multi-objective ocean predator algorithm. Properly utilizing the optimization algorithm to plan delivery routes can effectively reduce a company's delivery costs and improve its profitability. Table 5 compares the time penalty cost of the improved multi-objective ocean predator algorithm with the original time penalty cost for Company M. After optimizing the routes, the time penalty cost was significantly reduced by 81.22%, 91.79%, 77.40%, and 90.0%, respectively, and customer satisfaction also increased significantly.

[0226] According to the analysis of the sunny day data in Table 9, compared with the initial distribution plan, when four cold chain logistics vehicles of the same specifications are used to distribute goods, the total cost, transportation cost, refrigeration cost, and vehicle driving distance of the distribution plan simulated by the improved multi-objective ocean predator algorithm are significantly reduced. In terms of the specific costs of each part, the transportation cost optimization is the most significant, reducing by 59.86%. The cargo damage cost, refrigeration cost, and total distribution time are reduced by 43.34%, 43.99%, and 43.45%, respectively.

[0227] Table 9 Comparative Analysis Table (Sunny Day)

[0228]

[0229] The analysis of the rainy day data in Table 10 shows that compared to the initial delivery solution, the improved multi-objective ocean predator algorithm significantly reduced total delivery costs, vehicle travel distance, carbon emissions, and total delivery time. Specifically, transportation costs were reduced by 63%, and cargo damage and refrigeration costs also decreased. The improved multi-objective ocean predator algorithm achieved significant results in optimizing delivery solutions. By optimizing delivery routes, it not only reduced total delivery costs and improved efficiency, but also reduced environmental pollution.

[0230] Table 10 Comparative Analysis Table (Rainy Day)

[0231]

[0232]

[0233] Through the analysis of the snowy day data in Table 11, it can be seen that compared with the initial distribution plan, when four cold chain logistics vehicles of the same specifications are used to distribute goods, the total cost, transportation cost, refrigeration cost, and vehicle driving distance of the distribution plan simulated by the improved multi-objective ocean predator algorithm are significantly reduced. In terms of the specific costs of each part, the transportation cost optimization is the most significant, reducing by 63.49%, and the refrigeration cost, carbon emission cost, and total distribution time are reduced by 38.43%, 47.04%, and 41.05%, respectively.

[0234] Table 11 Comparative Analysis Table (Snowy Day)

[0235]

[0236] According to the foggy data analysis in Table 12 below, compared with the initial delivery plan, the improved multi-objective ocean predator algorithm has a significant reduction in total cost, transportation cost, cargo damage cost, refrigeration cost, and total delivery time when using four cold chain logistics vehicles of the same specifications to deliver goods. In terms of the specific costs of each component, the transportation cost optimization is the most significant, reducing by 59.08%. The cargo damage cost, refrigeration cost, and total delivery time have decreased by 43.26%, 40.67%, and 43.12%, respectively.

[0237] Table 12 Comparative Analysis Table (Fog Day)

[0238]

[0239]

[0240] Table 13 shows the comparison between the improved multi-objective ocean predator algorithm and the multi-objective particle swarm algorithm under sunny conditions. Compared with the optimization results of the multi-objective particle swarm algorithm, the total cost, transportation cost, cargo damage cost, refrigeration cost, carbon emission cost, and total driving distance of the improved multi-objective ocean predator algorithm are reduced to varying degrees. Among them, the carbon emission cost comparison result is the most obvious. The cost of the improved multi-objective ocean predator algorithm is reduced by 14.85% compared with the multi-objective particle swarm algorithm. The transportation cost and total driving distance are reduced by 10.63% and 14.85% respectively.

[0241] Table 13 Comparative analysis of MOPSO and IMOMPA under sunny conditions

[0242]

[0243] Table 14 shows the comparison between the improved multi-objective ocean predator algorithm and the multi-objective Harris Hawk algorithm under snowy conditions. Compared with the optimization results of the multi-objective Harris Hawk algorithm, the improved multi-objective ocean predator algorithm has reduced the total cost, transportation cost, cargo damage cost, refrigeration cost, carbon emission cost, total driving distance, and total delivery time to varying degrees. Among them, the improvement in transportation cost is the most obvious, reducing the cost by 28.94%. The carbon emission cost and total driving distance are reduced by 20.87% and 12.78% respectively compared with MOHHO.

[0244] Table 14 Comparative analysis of MOHHO and IMOMPA under snowy conditions

[0245]

[0246]

[0247] In summary, the application of the Ocean Predator algorithm revealed that its candidate solution space exhibited low initial stability and was prone to falling into local optima. This embodiment innovatively combined improvements such as the Tent Chaos Map, an elite selection strategy, and greedy mutation to enhance the Ocean Predator algorithm's balance between exploration and exploitation, better adapting to the practical needs of cold chain logistics route optimization. These improvements enable the algorithm to rapidly identify high-quality delivery routing solutions in the face of ever-changing traffic conditions and complex low-carbon requirements.

[0248] The embodiment takes M Fresh Cold Chain Logistics Distribution Company as an example to solve the problem, and through actual data simulation test, the experimental results show that, compared with the total cost of the original distribution of M Company, the total cost of the improved multi-objective marine predator algorithm is reduced by 21.90%, 22.23%, 23.91% and 23.06% respectively under four weather conditions (sunny, rainy, snowy and foggy); compared with the total cost of the multi-objective particle swarm algorithm, the total cost is reduced by 3.67%, 4.55%, 4.53% and 6.12% respectively; compared with the total cost of the multi-objective Harris eagle algorithm, the total cost is reduced by 12.68%, 7.40%, 7.00% and 14.08% respectively; compared with the total cost of the multi-objective marine predator algorithm, the total cost is reduced by 4.99%, 1.89%, 4.10% and 4.29% respectively. In addition, the time penalty cost of the improved multi-objective marine predator algorithm is greatly reduced compared with the original time penalty cost of M Company, which is reduced by 81.22%, 91.79%, 77.40% and 90.0% respectively under four weather conditions (sunny, rainy, snowy and foggy). The comparison results of the above experimental results not only verify the significant effect of the model in reducing the total distribution cost and improving customer satisfaction, but also demonstrate the stability and practicality of the algorithm in actual operation. This innovative achievement not only provides strong technical support for the development of low-carbon cold chain logistics, but also provides a new solution for path optimization problems in related industries.

[0249] As can be seen, under the same data premise and constraint conditions, the improved multi-objective marine predator algorithm proposed by the present application can reduce the total distribution cost and improve customer satisfaction in the cold chain logistics path optimization simulation experiment considering traffic conditions, further verifying the effectiveness of the improved multi-objective marine predator algorithm. The improved multi-objective marine predator algorithm optimizes the distribution scheme, not only significantly reduces carbon emissions and energy consumption, promotes the sustainable development of enterprises, but also optimizes the distribution route and time, improves customer satisfaction and ensures the rapid and on-time delivery of goods. Its flexibility enables enterprises to adjust distribution strategies in real time according to market demand and weather changes, enhances the enterprise's response ability, reduces the risk of goods transportation, and provides valuable data support for enterprises, helping scientific decision-making.

[0250] Preferably, the embodiment of the present application provides a specific implementation of a low-carbon cold chain logistics path optimization device capable of realizing a low-carbon cold chain logistics path optimization method, specifically including the following contents:

[0251] A multi-objective optimization model construction module is configured to establish a multi-objective distribution path optimization model according to the cold chain logistics distribution task demand and the urban traffic network condition, wherein the multi-objective distribution path optimization model considers the vehicle fixed cost, the vehicle transportation cost, the goods loss cost, the refrigeration cost, the carbon emission cost, the time window penalty cost and the customer satisfaction influencing factor;

[0252] a target function setting module configured to set a comprehensive optimization target function as minimizing total distribution cost and maximizing customer satisfaction, and determine a constraint condition;

[0253] an initial candidate solution space setting module configured to randomly generate an initial candidate solution space based on a Tent chaotic mapping mode, wherein the candidate solution space represents a set composed of a plurality of path planning schemes;

[0254] an iterative optimization module configured to perform iterative optimization on the candidate solution space, in each iteration, update each path planning scheme in the population according to a global search and a local search mechanism of the marine predator algorithm, evaluate the fitness of each path planning scheme according to the comprehensive optimization target function, and update the candidate solution space according to the evaluation result;

[0255] an output module configured to output a path planning scheme with the highest fitness in the candidate solution space as an optimization result when a preset termination condition is reached.

[0256] Preferably, the embodiment of the present application further provides a specific implementation of an electronic device capable of implementing all steps of the low-carbon cold-chain logistics path optimization method based on the improved marine predator algorithm in the above embodiment, and the electronic device specifically includes the following contents:

[0257] a processor, a memory, a communications interface, and a bus;

[0258] The processor, the memory, and the communications interface complete mutual communication through the bus; the communications interface is configured to realize information transmission between a server-side device, a metering device, a user-side device, and other related devices.

[0259] The processor is configured to call a computer program in the memory, and the processor implements all steps of the low-carbon cold-chain logistics path optimization method based on the improved marine predator algorithm in the above embodiment when executing the computer program.

[0260] The embodiment of the present application further provides a computer-readable storage medium capable of implementing all steps of the low-carbon cold-chain logistics path optimization method based on the improved marine predator algorithm in the above embodiment, and the computer-readable storage medium stores a computer program, and the computer program is executed by the processor to implement all steps of the low-carbon cold-chain logistics path optimization method based on the improved marine predator algorithm in the above embodiment.

[0261] The various embodiments in this specification are described in a progressive manner. Similar portions between the various embodiments can be referenced to each other. Each embodiment focuses on the differences between the other embodiments. In particular, the hardware + program embodiments are generally similar to the method embodiments, so their description is relatively simple. For relevant portions, refer to the description of the method embodiments.

[0262] The foregoing description of this specification describes specific embodiments. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different from that described in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or the sequential order to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0263] Although the present application provides method operation steps such as embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-creative work. The order of steps listed in the embodiments is only one way of executing the steps among many steps and does not represent the only execution order. When an actual device or client product is executed, it can be executed in the order shown in the embodiments or the drawings or in parallel (for example, in a parallel processor or multi-threaded processing environment).

[0264] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0265] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0266] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0267] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, those skilled in the art may make various specific modifications based on the teachings of the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A low-carbon cold chain logistics path optimization method based on an improved marine predator algorithm, characterized in that: include: S1. Establish a multi-objective distribution path optimization model based on the cold chain logistics distribution task requirements and the urban transportation network conditions. The multi-objective distribution path optimization model considers factors such as vehicle fixed costs, vehicle transportation costs, cargo damage costs, refrigeration costs, carbon emission costs, time window penalty costs, and customer satisfaction. S2. Minimize the total delivery cost and maximize customer satisfaction as the comprehensive optimization objective function, and determine the constraints; S3, applying the Tent chaotic mapping method to randomly generate an initialized candidate solution space, where the candidate solution space represents a set consisting of several path planning solutions; S4. Iteratively optimize the candidate solution space. In each iteration, the path planning scheme in the group is updated according to the global search and local search mechanism of the marine predator algorithm. The fitness of each path planning scheme is evaluated according to the comprehensive optimization objective function, and the candidate solution space is updated according to the evaluation results. S5. When the preset termination condition is reached, the path planning solution with the highest fitness in the candidate solution space is output as the optimization result.

2. The low-carbon cold chain logistics path optimization method according to claim 1 is characterized in that: In step S1, each influencing factor in the multi-objective delivery path optimization model is modeled as follows: 1) Vehicle fixed costs; Vehicle fixed costs refer to the expenses incurred by a refrigerated truck to complete a single mission, including driver salaries, training costs, and vehicle maintenance and depreciation costs. They are represented by C1, as shown in the following formula: Among them, H is the fixed cost of starting the vehicle, G k is whether the kth vehicle is enabled, K is the scale of the transport vehicle, k=1, 2, ..., K; 2) Vehicle transportation costs; Vehicle transportation costs consist of fuel costs and tolls, which are proportional to the distance traveled. As the mileage increases, the transportation costs also increase. This is represented by C2, as shown in the following formula: Among them, N is a node set, 0 represents the distribution center, and the remaining nodes represent customers. is the unit transportation cost of vehicle k traveling from node i to node j, d ij is the distance from node i to node j, If vehicle k travels from node i to node j, the value is 1, otherwise it is 0; 3) Cargo damage costs; Cargo damage cost C3 includes cargo loss during transportation C 3a and cargo loss during loading and unloading 3b , as shown below: C3=C 3a +C 3b ; Among them, p1 is the unit value of cold chain products, q i is the demand of node i, ε1 is the cargo damage rate per unit time during vehicle transportation, ε2 is the cargo damage rate per unit time when the vehicle is unloading, is the time it takes for vehicle k to arrive at node i, is the departure time of vehicle k from the distribution center, w i is the service time of node i, Takes a value of 0 or 1, if node i is served by vehicle k then The value is 1, otherwise it is 0; 4) Refrigeration costs; The cooling cost C4 includes the loss of cooling efficiency in the vehicle compartment during transportation. 4a and additional refrigeration demand caused by loading and unloading of goods C 4b , as shown below: C4=C 4a +C 4b ; Among them, p2 is the unit cooling cost, B1 is the heat load coefficient when the door is closed, is the time it takes for vehicle k to reach delivery point i, is the departure time of vehicle k from the distribution center, B2 is the heat load coefficient when the door is open, t si is the service time of vehicle k at node i; 5) Carbon emission costs; The carbon emission cost C5 includes the carbon emission generated by fuel consumption during transportation C 5a and carbon emissions generated by refrigeration equipment during operation C 5b , the carbon emissions generated by the vehicle during transportation and refrigeration at point (i, j) are as follows: C 5a =θ1×η(Q)×d ij ; C 5b =θ2×Q ij ×d ij ; There is a linear relationship between the fuel consumption per unit distance η and the vehicle load, as shown in the following formula: η(Q)=e(Q O +Q ij )+f; Among them, the load capacity of the transport vehicle is Q ij , e and f are constants, the vehicle's own weight is Q0, and the vehicle's maximum load is Q m ; The carbon tax method is used to estimate the carbon emission costs generated by vehicles during the delivery process as follows: Among them, θ0 is the carbon tax, θ1 is the carbon emissions generated by each unit of fuel consumption of the vehicle, and θ2 is the carbon emissions generated by the operation of the refrigeration equipment per unit distance traveled by the vehicle; 6) Time window penalty cost; Customers have a psychological preset time range for product delivery and hope to receive the product within the corresponding time range. This time range is the expected time window. Set the time penalty cost function γ(t i ) is as follows: Among them, M is the maximum penalty cost, μ1 is the penalty cost coefficient for early arrival of vehicles, μ2 is the penalty cost coefficient for late arrival of vehicles, and ET i is the earliest time that the vehicle is expected to arrive at node i, LT i is the latest time that the vehicle is expected to arrive at node i, ET′ i is the earliest time for the receiving vehicle to arrive at node i, LT′ i is the latest time for the vehicle to arrive at node i, t i is the time when the vehicle arrives at node i; The time penalty cost C6 is obtained as follows: 7) Customer satisfaction; The customer satisfaction function is set as follows:

3. The low-carbon cold chain logistics path optimization method according to claim 2, characterized in that: In step S2, the comprehensive optimization objective function is as follows: Setting decision variables The values ​​are as follows: Set the constraints as follows: 201) Vehicle size constraint: The number of vehicles used in the distribution process cannot exceed the vehicle size K of the distribution center, that is, the maximum number of vehicles. This constraint is expressed as: Where N is the node set, 0 represents the distribution center, and the remaining nodes represent customers; Indicates that vehicle k travels from the distribution center to node j; 202) Customer access constraint: Each customer point can be visited by one and only one transport vehicle once. This constraint is expressed as: 203) Distribution center round-trip constraint: Each transport vehicle must start from the distribution center and return to the distribution center, and each vehicle cannot have more than one predecessor node and successor node at the distribution center. This constraint is expressed as: Indicates that vehicle k travels from node j to the distribution center; 204) Customer point penalty cost function: The time penalty cost function of the vehicle at customer point i. This constraint is expressed as: 205) Customer point load constraint: The load of vehicle k when it leaves customer point j. This constraint is expressed as: in, represents the vehicle load when vehicle k leaves node i, q j is the demand of node j; 206) Vehicle load limit constraint: The load of vehicle k at any time must not exceed its load limit. This constraint is expressed as: Q m The maximum load capacity of the vehicle is; 207) Service time constraint: the time t at which the vehicle arrives at customer point j j , w i represents the service time of node i, c ij is the congestion or delay risk factor, is the time required for customer point i to customer point j. The constraint is expressed as: 208) Travel time constraint: the travel time of vehicle k from customer point i to customer point j This constraint is expressed as: 209) Total number of vehicles constraint: The total number of vehicles m used in the entire delivery process is expressed as: 210) Initial load constraint: The initial load of vehicle k when it leaves the distribution center This constraint is expressed as:

4. The low-carbon cold chain logistics path optimization method according to claim 3 is characterized in that: 208), d ij represents the distance from node i to node j, and the vehicle speed represents the average vehicle speed, ζ con Indicates the impact rate of different weather conditions on vehicle speed at different time periods; different weather conditions include sunny, rainy, snowy and foggy days, con = sun, rain, snow, fog; ζ sun ,ζ rain ,ζ snow ,ζ fog They represent the impact rate of different time periods on vehicle speed under sunny, rainy, snowy and foggy conditions. The specific mathematical expressions are as follows:

5. The low-carbon cold chain logistics path optimization method according to claim 1, characterized in that: In the iterative update process of step S4, an elite retention strategy is introduced to directly retain the path planning solution with the highest fitness value in each iteration to the next generation candidate solution space to accelerate the convergence speed of the algorithm.

6. The low-carbon cold chain logistics path optimization method according to claim 1 or 5, characterized in that: During the iterative update process of step S4, a greedy algorithm is also combined to perform mutation operations on some path planning solutions to achieve local optimization, so as to improve the quality of the solution and the search speed.

7. The low-carbon cold chain logistics path optimization method according to claim 1 or 5, characterized in that: The specific steps of step S4 are as follows: (401) Setting the candidate solution space range, number of predators and number of iterations in the marine predator algorithm; (402) Calculating the fitness of each path planning solution; (403) Based on the elite retention strategy, the path planning solution with the highest fitness value in each iteration is directly retained in the next generation candidate solution space to accelerate the convergence of the algorithm. (404) The path planning scheme moves in the candidate solution space and explores new solutions by simulating the predation behavior of marine organisms such as sharks and whales, that is, exploring new path planning schemes. In each iteration, the moving direction and step size of the path planning scheme are adjusted according to the current position and the surrounding environment; the number of iterations is increased by 1. If the maximum number of iterations is not reached, go to step (402), otherwise go to step (405); (405) Output the final path planning solution.

8. A low-carbon cold chain logistics path optimization device based on an improved marine predator algorithm, characterized in that: include: A multi-objective optimization model building module is used to establish a multi-objective distribution path optimization model based on the cold chain logistics distribution task requirements and urban transportation network conditions. The multi-objective distribution path optimization model considers vehicle fixed costs, vehicle transportation costs, cargo damage costs, refrigeration costs, carbon emission costs, time window penalty costs, and customer satisfaction factors; The objective function setting module is used to minimize the total delivery cost and maximize customer satisfaction as the comprehensive optimization objective function, and to determine the constraints; The initial candidate solution space setting module is used to randomly generate an initialized candidate solution space based on the Tent chaotic mapping method, where the candidate solution space represents a set of several path planning solutions; Iterative optimization module is used to iteratively optimize the candidate solution space. In each iteration, the path planning scheme in the group is updated according to the global search and local search mechanisms of the marine predator algorithm. The fitness of each path planning scheme is evaluated according to the comprehensive optimization objective function, and the candidate solution space is updated according to the evaluation results. The output module is used to output the path planning solution with the highest fitness in the candidate solution space as the optimization result when the preset termination condition is reached.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the low-carbon cold chain logistics path optimization method based on the improved marine predator algorithm as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the low-carbon cold chain logistics path optimization method based on the improved marine predator algorithm described in any one of claims 1 to 7 are implemented.

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