A container liner transportation scheduling control method considering environmental pollution and transportation efficiency

Abstract

The application discloses a container liner transportation scheduling control method considering environmental pollution and transportation efficiency, relates to the technical field of ship deployment control in shipping, and comprises the following steps: collecting the number of inbound containers on each route served by a ship company, the number of containers that need to be exported, the number of each type of ship, the ship wear and tear and pollution discharge generated by each type of ship during operation; based on the number of routes served by the ship company and the ports that need to be served on each route, a homogeneous ship container liner transportation deployment and scheduling control model VDS1 is constructed; the transportation scheduling control method in the application can reasonably allocate each ship of the ship company, maximize the utilization of ship capacity and port resources, realize efficient ship scheduling between different ports, significantly improve shipping efficiency, reduce shipping time, and reduce the discharge of environmental pollutants.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship deployment control in shipping, and particularly relates to a container liner transportation scheduling control method considering environmental pollution and transportation efficiency. BACKGROUND

[0002] In recent years, the development of international trade has driven the rapid growth of the container transportation industry. According to statistics, container transportation has become one of the most important transportation methods in international trade, and its proportion continues to grow. At the same time, with the deepening of globalization, people increasingly need to obtain more extensive goods and services through international trade. Therefore, the container shipping industry must continuously improve the operational efficiency of container ships to meet the growing demand for freight transportation. With the increase in the number of container ships and the expansion of their capacity, the number of container transportation companies is increasing. Therefore, the competition between them is becoming more and more fierce. In order to maintain competitiveness, container transportation companies need to continuously control their operational technology and improve efficiency to meet customer demand. Therefore, the study of container liner deployment and scheduling has become increasingly important. In order to achieve the effectiveness of freight transportation, shipping companies must reasonably allocate each ship, maximize the use of ship capacity and port resources to ensure efficient operation and customer satisfaction.

[0003] At present, domestic and foreign researchers have relatively maturely studied the deployment and scheduling control of container liner transportation ships. Wang et al. (2012) studied the optimal sailing speed of container ships on each section of each route in liner transportation networks, Branchini et al. (2015) established a mixed integer linear programming model by representing contract shipping and spot shipping as nodes of a directed graph, and finally obtained the optimal solution through the CPLEX solver, Wang et al. (2021) considered selecting the most suitable ship from different candidate ships in terms of capacity, operational technology and fuel consumption to participate in operation, and improved transportation efficiency by adjusting their order, timetable and sailing speed in the route. The research results of the above scholars have made corresponding contributions to the deployment and scheduling of container liner transportation, but the factors considered are not comprehensive enough and precise algorithms cannot be used to solve the model. Based on the above research background and actual problems, in order to comprehensively consider various factors, improve transportation efficiency, reduce pollutant emissions and control ship operation, it is urgent to solve the problem of ship deployment and scheduling control in container liner transportation. SUMMARY

[0004] The present application aims to provide a container liner transportation scheduling control method considering environmental pollution and transportation efficiency to solve the problems existing in the prior art proposed in the background.

[0005] To achieve the above object, the present application provides the following technical scheme:

[0006] A container liner transportation scheduling control method considering environmental pollution and transportation efficiency, comprising the following steps:

[0007] S1: collecting the number of imported containers, the number of containers to be exported, the number of each type of ship, the ship wear and tear and pollution emission generated by each type of ship during operation on each route served by the ship company;

[0008] S2: based on the number of routes served by the ship company and the ports to be served on each route, a homogeneous ship container liner transportation deployment and scheduling control model I VDS1 is constructed, and the type, number and speed scheme of each voyage of the ship to be invested by the ship company on each route are calculated based on the collected data;

[0009] S3: based on the control model I VDS1, the constraints of different ship types are added, and the sailing speed interval of different types of ships is uniformly constrained according to the specifications, and a container liner transportation deployment and scheduling control model II VDS2 considering different specifications of ships is constructed based on the control model I VDS1;

[0010] S4: according to the established container liner transportation deployment and scheduling control model, seven algorithms are designed to solve, and the optimal scheme is obtained after comparative analysis, so as to obtain the optimal ship deployment and scheduling scheme, wherein the seven algorithms are genetic algorithm, simulated annealing algorithm, branch and bound algorithm, genetic algorithm combined with branch and bound algorithm, simulated annealing algorithm combined with branch and bound algorithm, Gurobi solver and Gurobi solver combined with branch and bound algorithm.

[0011] Preferably, in S2, the type, number and speed scheme of each voyage of the ship to be invested by the ship company on each route are obtained by the formula P k =M k -D k +E r -F r -B r -G r ; wherein M k represents the value generated by allocating the ship to other ship companies due to the fact that the capacity of the ship is too small or too large to be suitable for operation on the route of the ship company, D k represents the loss of the ship company due to the fact that the number of existing ships does not meet the transportation capacity, E r represents the value brought by the efficient transportation of containers by the ship company, F r represents the ship wear and tear generated during the operation of the ship, B r represents the pollution emission, and G rpenalty due to the fact that the shipping company is not able to transport the containers by itself, k represents the type of the ship, and r represents the route of the ship service.

[0012] Preferably, in S3, according to the capacity data of the ship, the various types of ships can be divided into three specifications: if the capacity of the ship is less than M, then if the capacity of the ship is greater than M and less than L, then if the capacity of the ship is greater than L, then wherein M is the capacity of the smallest medium-sized ship, and L is the capacity of the smallest large-sized ship, is a binary decision variable representing that the specification of the ship is a small-sized ship, is a binary decision variable representing that the specification of the ship is a medium-sized ship, is a binary decision variable representing that the specification of the ship is a large-sized ship, and k represents the type of the ship.

[0013] Preferably, in S2, the number of k-type ships owned by the shipping company l k , the number of k-type ships needed to be rented by the shipping company j k , the number of ships that can be rented q k , the number of k-type ships owned by the shipping company deployed on the rth route x rk , the number of k-type ships needed to be rented by the shipping company deployed on the rth route z rk , and the total number of k-type ships operating on the route b rk ;

[0014] First, the number of k-type ships needed to be rented by the shipping company j k is set as follows: j k ≤ L k This is to achieve the effectiveness of the cargo transportation, and the shipping company must reasonably allocate each ship, and is not allowed to exceed the limit of renting ships, wherein L k represents the maximum number of k-type ships allowed to be rented, and further the loss D k of the shipping company due to the fact that the existing number of ships does not meet the transport capacity can be calculated by the formula , wherein represents the value brought to the third-party shipping company by renting a k-type ship;

[0015] Then, the number of ships rented q k in step 2 is calculated by the formula q k = l k -∑ r x rk +j kThe value M generated by allocating the type of ship to other ship companies for use can be calculated k The value M generated by allocating the type of ship to other ship companies for use can be calculated The value M generated by allocating the type of ship to other ship companies for use can be calculated The value M generated by allocating the type of ship to other ship companies for use can be calculated rk The following constraints are set to limit the number of k-type ships owned by the ship company deployed on route r to the total number of k-type ships owned by the ship company: In addition, the number z of k-type ships rented by the ship company deployed on route r rk The following constraints are set: The number z of k-type ships rented by the ship company deployed on route r cannot exceed the total number of k-type ships rented by the ship company, and also involves the number b of ships operating on the route rk The constraint is: 1≤∑ r b rk ≤l k +j k Further, the total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated r The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated

[0016] Preferably, the S2 involves a penalty G generated by the ship company's inability to transport containers itself for some reason r This part is mainly generated by the purchase of non-company-operated ship container slots, and the number n of purchased non-company-operated ship container slots od The number n of purchased non-company-operated ship container slots is calculated by the formula n od =ξ od -g od And the following constraints: Further, the total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated r The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated od The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated od The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated od The total amount of ship wear and tear and pollution emissions F generated by the ship during operation can be calculated

[0017] The value E brought by the high-efficient container transportation of the shipping company is also involved in S2 r , which is calculated by the formula , where, represents the number of containers actually transported from the port o to the destination port d along the rth route, represents the value brought by the shipping company for transporting a unit of container from the port o to the destination port d along the rth route;

[0018] Finally, the pollution discharge is also involved, which is calculated by the linear formula , and the time required for the ship to sail through the ith segment is calculated by the formula , thus having the following constraints: Further, the pollution discharge B of the ship during the operation is calculated by the formula r , where, , where, represents the slope of the tangent line of the ith segment, τ i represents the pollution discharge of the ship after sailing through the ith segment, represents the intersection of the tangent line and the y-axis, represents the fuel consumption of the ship for sailing through the ith segment at the speed of τ i , i represents the segment of the route, and p represents the fuel consumption of the ship for sailing through the ith segment at the speed of τ represents the time when the kth ship departs from the ith port along the rth route, represents the time when the kth ship arrives at the (i-1)th port along the rth route, represents the time when the kth ship stays at the ith port along the rth route, η r,i is a binary variable, which is 1 if the ith port is the starting port of the rth route, and 0 otherwise, C bunk represents the pollution discharge per unit of fuel consumption.

[0019] In the preferred container liner transportation deployment and scheduling control model VDS1 for homogeneous ships, the type of ship deployed on each route is first constrained, and the constraint condition is: k f rk = 1 , and x rk ≤ Mf rk , where f rk is a binary variable, which is 1 if the kth ship is deployed on the rth route, and 0 otherwise, R represents the set of routes, and M is a maximum number;

[0020] Secondly, the number of ships deployed on each route is constrained so that it cannot be greater than the sum of the number of ships of that type owned by the shipping company and the number of ships that can be rented, while also ensuring that the number of each type of ship rented cannot be greater than the number of ships rented from other shipping companies. At the same time, the number of ships is constrained to ensure that the service frequency of the shipping company meets the service frequency required by the ports on the route, ensuring efficient transportation of goods so that the goods can be delivered to customers in a timely manner, i.e. the following constraints need to be met:

[0021]

[0022] wherein u ri represents the distance of the i-th leg on route r, v ri represents the speed of travel on the i-th leg on route r, δ r,i,k represents the stopover time of a k-type ship at the i-th port on route r, b rk represents the number of k-type ships deployed on route r, but this constraint is not linear, so a decision variable O ri = 1 / v ri is introduced, then the above constraint condition will become the following equation:

[0023]

[0024] wherein O ri represents the inverse of the speed of travel on the i-th leg on route r;

[0025] In terms of penalties, the number of slots purchased needs to be limited so that the number of slots is greater than 0 and less than the number of containers that need to be shipped out of the port, while ensuring that ships entering the port must leave the port and the number of containers flowing in and out must be balanced, so the flow conservation constraint for containers and the flow conservation constraint for service variables are set;

[0026] The flow conservation constraint for containers is as follows: and wherein, represents the number of containers stored on the ship that travels on the i-1th leg on route r from the oth port of origin for a k-type ship, represents the number of containers loaded at the jth stopover port on route r for a k-type ship starting from the oth port of origin, represents the number of containers unloaded at the jth stopover port on route r for a k-type ship starting from the oth port of origin, I rd represents a set of port indices pointing to a specific port d in route r;

[0027] The flow conservation constraint of service variables is subject to: and k∈K, where, is a binary variable, 1 if a k-type ship sails from port o to port d, otherwise 0, and the time of ship arriving at port i is linked to the time of ship arriving at port i+1, with the following constraint: where, denotes the time of k-type ship arriving at j port on route r, denotes the time of k-type ship staying at j port on route r, denotes the sailing time of k-type ship from j port on route r;

[0028] In terms of sailing speed, the following constraints are made: where, denotes the fastest sailing speed of ship on the i-th leg of route r, denotes the slowest sailing speed of ship on the i-th leg of route r, ri denotes the sailing speed of ship on the i-th leg of route r, r denotes the set of all ports on route r;

[0029] Finally, the following non-negativity constraints are made for all other decision variables:

[0030]

[0031] Preferably, in S3, first, the constraints on speed in control model VDS1 are rewritten as the following constraints:

[0032]

[0033] where, denotes the sailing speed of k-type ship on the i-th leg of route r, denotes the minimum sailing speed of small, medium and large ships, respectively, denotes the maximum sailing speed of small, medium and large ships, respectively;

[0034] Then, the model sets the non-negativity constraints on variables variable variable , and the constraint that each type of ship is only allowed to be one ship specification: and

[0035] Preferably, the control model VDS1 and the control model VDS2 are solved by genetic algorithm.

[0036] First, the genetic algorithm uses real-number encoding to randomly generate chromosomes. The encoding method is as follows: one gene represents a feasible ship deployment scheme, where each sub-encoder is denoted as Y. i , representing the i-th deployment scheme, each gene consists of three parts, where Y i1 ,Y i2, Y i3 It is the first part of the gene, used to control the service route number, the number of ships deployed on the route, and the type of ships deployed on the route; Y i4 The second part of the gene controls the order in which shipping companies arrive at ports during a particular voyage; the third part is the Y chromosome. i5 This is used to describe the speed of a ship on its route. These parts are then repeated, only the functions are repeated, not the values, until all route deployment schemes have been generated.

[0037] Secondly, in the calculation of the fitness function, the randomly generated genes are first decoded to obtain the number of services each ship type provides for the i-th route and the ship's speed in each segment. Once the number of ships deployed on the route is determined, the number of ships leased in and whether any ships are leased out can be determined. If ships are leased out, the value brought to the shipping company by the leased-out ships can be calculated using the formula in the model. Using the calculation formula in the model, the pollution emissions are calculated based on the known ship speeds and port visit order. At the same time, the value brought to the shipping company by efficient container transportation can be calculated based on the number of containers transported at each port. Finally, based on the cargo demand between given ports, it is calculated whether there is a penalty for each port, thus obtaining the fitness value of the gene. In terms of selection operations, the roulette wheel selection method is used to design the genetic algorithm selection operator.

[0038] Roulette wheel selection is a commonly used selection operation in genetic algorithms. It normalizes the fitness value of an individual into a selection probability and creates a mechanism similar to a roulette wheel to select individuals. Individuals with higher fitness values ​​have a greater probability of being selected during the selection process, thus having a greater chance of being retained in the next generation. Roulette wheel selection is relatively simple and easy to implement, and it can effectively retain excellent individuals and promote the evolution of the population. The process of roulette wheel selection is as follows:

[0039] (1) Calculate the fitness value of each individual, because the fitness value reflects the individual's quality;

[0040] (2) Normalize the fitness values ​​of all individuals so that their sum is 1. The purpose of normalization is to convert the fitness values ​​into selection probabilities, for example, using... To represent an individual with chromosome j, use where j should not exceed the maximum population size MAX size , i.e. size j∈{1,2,3,…,MAX n}, can be expressed as The probability of a chromosome being selected to pass to the next generation:

[0041]

[0042] (3) Create a roulette wheel. The length of the roulette wheel is equal to the number of individuals in the population, and the size of the roulette area occupied by each individual is proportional to its fitness value;

[0043] (4) In the selection process, several selection operations are performed, and one individual is selected each time;

[0044] (5) A random number between 0 and 1 is randomly generated, and then the individual is selected according to the roulette area where the random number is located; the larger the roulette area, the greater the probability of the individual being selected;

[0045] (6) Repeat steps (4) and (5) until a sufficient number of individuals are selected;

[0046] The crossover operation considers that longer driving distances produce more pollutant emissions and ship rental fees, and the specific crossover strategy is:

[0047] The present application sets two genes A: (a1, a2, …, a n ) and B: (b1, b2, …, b n ), wherein a1, a2, …, a n ∈I r and b1, b2, …, b n ∈I r , and a1≠a2≠…≠a n , b1≠b2≠…≠b n . If there are three ports x, y, z, define a triangular distance function F(x, y, z) = d(x, y) + d(y, z) - d(x, z), wherein d(x, z) represents the distance from port x to port z. The order crossover step is as follows:

[0048] (1) Identify A as the basic gene, and set B as the reference gene, and find a reference port b i (i = 1, 2, …, I r ) in B;

[0049] (2) Find a port a j = b i , a k = bi+1 Then, the defined triangular distance function is used to calculate F(a j ,b i+1 ,a j+1 ) and F(a k-1 ,a k ,a k+1 ), and the two results are compared, if F(a j ,b i+1 ,a j+1 ) ≥ F(a k-1 ,a k ,a k+1 ), the gene A remains unchanged, if F(a j ,b i+1 ,a j+1 ) < F(a k-1 ,a k ,a k+1 ), then the port a k is deleted in the gene A, then the port b j is added in a j+1 and a i+1 to obtain a new gene

[0050] (3) the reference ports b i+1 ,…,b n ,b1,…,b i-1 are taken in the reference gene in turn, and step 2 is repeated until the final gene A1 is generated;

[0051] (4) the gene B is taken as the basic gene, the gene A is taken as the reference gene, and steps 1-3 are repeated;

[0052] (5) the gene after the crossover is judged, if the port in the gene after the crossover is not the port in a certain route of the ship company, i.e. the port in two routes exists, the gene is deleted to ensure that the ship serves a complete route;

[0053] Finally, in the mutation operation, the present application adopts the crossover adjustment mutation method in the port stopping sequence, but only the genes of the same route are selected for mutation in the mutation process.

[0054] Preferably, the control model one VDS1 and the control model two VDS2 are solved by the simulated annealing algorithm:

[0055] The idea of solving the container liner shipping fleet deployment and scheduling problem by the simulated annealing algorithm is as follows: firstly, an initial solution is generated by using the designed coding rule, then the rule of generating a new solution is designed, and finally the final solution is obtained by combining the acceptance function, annealing strategy and ending strategy of the simulated annealing algorithm; the specific implementation method is as follows:

[0056] In the simulated annealing algorithm, the encoding and decoding process is the process of determining the order of the ports to be accessed and the number and type of ships serving the route. Assuming that 12 ships are deployed on Route 1 and ships of type 2 are selected to serve the route, and the port numbers on the route are 2, 5, 11, 9, and 8, and the random speed values of each section are initialized within a reasonable range, then the encoding is [1, 2, 12, 5, 9, 2, 8, 11, 22, 25, 20, 19];

[0057] Based on the above encoding and decoding rules, an initial solution can be generated. Next, a new solution is generated. In designing the new solution generation rule, it is divided into two parts: the first part is the order of serving the ports, and the strategy adopted in this part is to randomly select the order of a number of ports on the route to exchange; the second part is the generation of the speed on each route section, and the speed on part of the route section is randomly generated based on the distance within a certain reasonable range;

[0058] Finally, the acceptance function, annealing strategy, and ending strategy of the simulated annealing algorithm. The acceptance function in the simulated annealing algorithm is used to judge whether to accept a new solution as the current solution. It allows to accept inferior solutions with a certain probability in the search process to avoid falling into local optimum. The simulated annealing algorithm selects the Metropolis criterion as the acceptance function:

[0059]

[0060] where E(n+1) represents the newly calculated allocation of ship types and quantities of the ship company on each route, E(i) represents the last calculated allocation of ship types and quantities of the ship company on each route, when E(i)≤E(n+1), it means that the current solution of ship type and quantity allocation is more reasonable and the transportation efficiency of goods is faster, then the current solution is adopted, otherwise, if E(i)>E(n+1), it means that the ship type and quantity allocation or the transportation efficiency of goods in the current solution is not as good as the last solution, then θ=∪(0,1), if then the current solution is adopted, i.e. the inferior solution is adopted;

[0061] Exponential annealing refers to the temperature decreasing exponentially, for example, T j =T0·α k , where T j is the temperature after the jth iteration, T0 is the initial temperature set, and α is the annealing factor and α<1; the simulated annealing algorithm adopts this way to construct the annealing function, i.e. T j+1 =T j ·s, where s∈[0.95, 0.99];

[0062] Finally, the end strategy of the simulated annealing algorithm is to set the maximum iteration number, i.e., to end when the termination temperature is reached.

[0063] Preferably, the control model one VDS1 and the control model two VDS2 are solved by a branch and bound algorithm.

[0064] The branch and bound algorithm can effectively solve the mixed integer linear programming MILP problem; in order to quickly obtain a global optimal solution, two auxiliary methods are embedded on the basis of the algorithm: the first is to use Gurobi solver as a preprocessor, and the second is to combine it with a heuristic algorithm.

[0065] In the first method of using Gurobi solver as a preprocessor, Gurobi solver is used to solve the relaxation model, and this process is carried out before using the branch and bound algorithm, which aims to greatly reduce the time required for the branch and bound algorithm search; the relaxation of the model mainly focuses on the selection of ship types, which is changed from binary decision variable f rk Relaxation to real number decision variable, so there will be a non-integer possibility in the solving process, which is one of the parts to be branched by the branch and bound algorithm, wherein f rk Indicates 1 if the k type of ship is used to serve the route r, otherwise 0; in the ship type part, only the non-integer ship types need to be branched; and in the second branch and bound algorithm combined with the heuristic algorithm, in order to speed up the search efficiency, the heuristic method is used to obtain a relatively optimal solution as the initial solution of the branch and bound algorithm, and then the branch and bound algorithm is used for solving.

[0066] In the branch and bound algorithm, the pruning process is necessary, so special pruning rules are developed for the algorithm, in the branch and bound algorithm, the search strategy used is the depth-first search strategy, which is used because the depth-first search strategy can definitely find the global optimal solution, and the depth-first search is more efficient in memory usage than the breadth-first search because it only needs to store the nodes on the branch path, not the nodes of the entire layer; then the integer judgment of the ship selection part in the code will be carried out, if it is a non-integer, the upper bound value will be updated, otherwise the lower bound will be updated; then the constraints in the model will be judged, for example, the constraints of speed and service frequency, if the above conditions are not met, the algorithm will take pruning; after calculating the target value, the integer judgment of the corresponding code part will be carried out, if they are all integers and the target value is less than the lower bound, it means that branching down will not appear a better solution, so it is pruned, thereby stopping this branch.

[0067] Compared with the prior art, the present application has the following beneficial effects:

[0068] The transportation scheduling and control method in this invention enables shipping companies to rationally allocate each vessel, maximize the utilization of vessel capacity and port resources, achieve efficient vessel scheduling between different ports, significantly improve shipping efficiency, reduce shipping time, and reduce emissions of environmental pollutants. Attached Figure Description

[0069] Figure 1 This is a flowchart of a ship deployment and scheduling control method applied to container liner shipping operations in an embodiment of the present invention.

[0070] Figure 2 This is a chromosome coding design diagram for the genetic algorithm in an embodiment of the present invention.

[0071] Figure 3 This is an example diagram of the encoding and decoding of the simulated annealing algorithm in an embodiment of the present invention.

[0072] Figure 4 This is a flowchart of the genetic algorithm in an embodiment of the present invention.

[0073] Figure 5 This is a flowchart of the simulated annealing algorithm in an embodiment of the present invention.

[0074] Figure 6 This is a flowchart of the branch and bound algorithm in an embodiment of the present invention.

[0075] Figure 7 Efficiency and accuracy data for solving model VDS1 using seven algorithms are presented in the table.

[0076] Figure 8 Efficiency and accuracy data for solving model VDS2 using seven algorithms are presented in the table.

[0077] Figure 9 Error data tables for solving model VDS1 using seven algorithms.

[0078] Figure 10 Error data tables for solving model VDS2 using seven algorithms.

[0079] Figure 11 A comparison table of efficiency data for solving model VDS1 using seven algorithms.

[0080] Figure 12 A comparison table of efficiency data for solving the VDS2 model using seven algorithms.

[0081] Figure 13 A table showing the speed ranges of different ship types and the corresponding value data for each allocation scheme. Detailed Implementation

[0082] In order to make the technical means, creative features, purposes and effects of the present application easy to understand, the present application is further described below in conjunction with specific embodiments.

[0083] Please refer to Figures 1-13 The present application provides the following technical solutions:

[0084] In order to evaluate the effectiveness of the two proposed models and six algorithms, a real route between Asia and Northern Europe is used as the first scenario for experiment. First, the number of inbound containers at each port and the number of containers that need to be exported on each route served by the shipping company are collected in real time, and then the capacity and speed interval of different types of ships owned by the shipping company are collected as input. Subsequently, the homogeneous ship container liner transportation deployment and scheduling control model VDS1 and the container liner transportation deployment and scheduling control model VDS2 considering different ship specifications are established.

[0085] Further, referring to Figures 4-6 , genetic algorithm, simulated annealing algorithm and branch and bound based combination algorithm are used to solve the model VDS1 and the model VDS2 respectively, and then the solution accuracy and efficiency of all algorithms are analyzed and evaluated. The evaluation is carried out through 10 different scenarios. In the present application, these instances are named as "K / R / Imax", wherein K, R and Imax represent the number of ship types, the number of segments and the maximum number of ports on the route respectively. Figure 7 and Figure 8 The results obtained by the six algorithms for each scenario and the corresponding running time are shown. The "Obj" column represents the value of the optimal ship deployment type, number and optimal route speed scheme for each segment calculated by the shipping company using the above six algorithms. The "time" column represents the CPU running time (in seconds), which is measured from the start of the algorithm calculation.

[0086] Further, referring to Figure 9 and Figure 10 The present application finds that in terms of solution accuracy, heuristic algorithms often cannot achieve the optimal solution and there is a certain gap from the optimal solution. Specifically, compared with the optimal result, the gap of genetic algorithm is 13% on average, and the gap of simulated annealing algorithm is 8%. In fact, in scenarios other than scenario 2, the simulated annealing algorithm is superior to the genetic algorithm in solution accuracy.

[0087] On the other hand, the computation time of the simulated annealing algorithm was reduced by an average of 55.5% compared to the genetic algorithm in solving model VDS1. In model VDS2, the simulated annealing algorithm was faster by an average of 53.6% compared to the genetic algorithm. Nevertheless, this rule did not exist in smaller cases. For example, in instance 2 based on model VDS1, the execution time of the simulated annealing algorithm was 4% more than the genetic algorithm. Likewise, in instance 2 testing model VDS2, the genetic algorithm was 6% faster than the simulated annealing algorithm. However, as the model size increased, it was found that the solution speed of the simulated annealing algorithm gradually exceeded that of the genetic algorithm, which was consistent with the average solution speed trend mentioned initially. This is because the genetic algorithm performed more operations (such as crossover / variation) than the simulated annealing algorithm, thus taking longer to run.

[0088] Overall, the simulated annealing algorithm saved 44% to 76% of the time in solving model VDS1. For solving model VDS2, the simulated annealing algorithm saved computation time ranging from 4% to 71%. Compared to the optimal solution of model VDS2, the simulated annealing algorithm had an error of only 0.4% in the best case. However, the error of the better solution calculated by the genetic algorithm was slightly higher (1%), which was less accurate than the simulated annealing algorithm.

[0089] Referring to Figure 9 and Figure 10 , respectively, show the gap between the seven algorithms in solving the two models VDS1 and VDS2. The gap of the heuristic algorithms (i.e., GA and SA) was quite large, ranging from 0.4% to 38%. In particular, B&B sometimes produced a small gap, such as 0.001% (K8 / R5 / Imax) and 0.002% (K5 / R3 / Imax), while the gap of the other algorithms was zero. Further, the solving efficiency of Gurobi solver and Gurobi+B&B was compared. In the case of small-scale instances, such as the first 5 scenarios of solving model VDS1 and model VDS2, the speed of Gurobi solver was always superior to Gurobi+B&B. In the case of the largest gap, Gurobi solver was 1.84 seconds faster than Gurobi+B&B, saving 82.5% of the time. However, in the case of very small scenarios, it was found that the efficiency of Gurobi solver and Gurobi+B&B was similar. As the case size increased, it was observed that the solving efficiency of Gurobi+B&B gradually exceeded that of Gurobi. Specifically, when the model size expanded to the last three instances of model VDS2, the solving efficiency of Gurobi+B&B improved significantly. The 6th instance saved 0.14 seconds, accounting for 31.8% of the total time, the 7th instance saved 0.65 seconds, accounting for 51.6% of the total time, and the 8th instance saved 5.71 seconds, accounting for 87.7% of the total time.

[0090] Further, the solution results of the other three algorithms, B&B, GA+B&B and SA+B&B, are analyzed. In large-scale cases, i.e., the 6th to 10th instances of model VDS1 and the 5th to 8th scenarios of model VDS2, the B&B algorithm outperforms GA+B&B and SA+B&B, saving 7.4% and 11.6% of solution time on average, respectively. Specifically, the B&B algorithm performs better in solving some small-scale instances, such as the 3rd, 4th, 5th instances of model VDS1 and the 4th instance of model VDS2. Compared with GA+B&B, it saves 51.7% of time on average, and compared with SA+B&B, it saves 54.3% of time on average. For the solutions of model VDS1, it saves 0.6% to 99.4% of time compared with GA+B&B and 1.1% to 99.8% of time compared with SA+B&B. For the solutions of model VDS2, it saves 0.8% to 92.1% of time compared with GA+B&B and 2.9% to 98.8% of time compared with SA+B&B.

[0091] Further, referring to Figure 11 and Figure 12 , the present application can also be used to derive and compare the computational efficiency of all algorithms. Taking the running time of GA as the benchmark, for small-scale transportation scenarios, the branch-and-bound algorithm outperforms other algorithms (0.004% for VDS1 and 0.052% for VDS2). The Gurobi solver significantly outperforms other algorithms in medium-scale cases (from 0.006% to 0.05% for VDS1 and from 0.023% to 0.214% for VDS2). For large-scale transportation scenarios, Gurobi+B&B is the most efficient (from 0.053% to 0.065% in the VDS2 model). The second model VDS2 further estimates the adaptability of multi-type ships characterized by changes in sailing speed. Specifically, small, medium, and large ships perform [3-23] knots / nautical mile, [13-33] knots / nautical mile, and [23-42] knots / nautical mile, respectively. The three speed intervals are divided into six levels to test effectiveness. The present application finds that even if the speed continues to increase, the value rate corresponding to the allocation scheme cannot maintain a high growth. That is, the value rate corresponding to the allocation scheme decreases from 41.9% (the first speed level) to 4.9% (the highest speed level).

[0092] Whether the sailing speed of the ship is fixed or different, two models VDS1 and VDS2 are formed respectively. Although the latter leads to a more complex problem, the speed dynamics can make the ship deployment more superior. Therefore, further, the present application can quantitatively compare the two models, and can find out whether the speed dynamics can generate revenue according to the objective function. The data of the first 8 scenarios in the comparison model VDS1 and all scenarios in the model VDS2 are selected. By observing the comparison of the revenue calculated by the two models in the 8 scenarios, with the increase of the route and the type of ship, the proportion of additional value revenue is also rapidly increasing, from 15% to 85%.

[0093] The present application can also analyze the influence of sailing speed on the type and number of ships deployed on each route of the shipping company's operation route and the sailing speed of each leg. The ship size is set from small to large, the speed gradient of ±2 knots per nautical mile is implemented, and six different shipping speed intervals are designed. The present application finds that with the increase of speed, the growth of the value corresponding to the type and number of ships deployed on each route and the sailing speed of each leg is not linear. At the beginning, the growth rate (41.9%) is faster when the speed level is 2. As for the 3rd, 4th and 5th speed categories, the growth rate is slightly higher than 10% respectively. Finally, if the actual speed increases to the maximum, i.e. the 6th speed category, the percentage of value corresponding to each allocation scheme is the smallest, which is 4.9%. This finding shows that when the speed of the ship is slow, a slight increase in speed can greatly save the size of the fleet. Therefore, the shipping company achieves significant value on the allocation scheme corresponding to the 1st speed category. Obviously, the growth percentage of each knot of sailing speed is 8.3%. However, the high-speed solution shows that the number of ships cannot be saved again. Therefore, as the last speed category, the value rate of the allocation scheme corresponding to each increase of one knot of sailing speed decreases to 0.9%.

[0094] Finally, the application can also analyze all the algorithm to calculate the type of ship deployed on each route, the number of ships and the value of the difference of the speed distribution scheme of each leg of the voyage, and find that only the heuristic algorithm (i.e. GA and SA) has a large gap, ranging from 0.4% to 38%. Occasionally, B&B will produce a small gap, such as 0.001% and 0.002%. In addition, the gap of other algorithms is zero. Take the running time of GA as the benchmark, compare the computing efficiency of all solutions. For small-scale cases, B&B algorithm is better than other algorithms (0.004% for VDS1 and 0.052% for VDS2). However, for medium-sized cases, Gurobi solver is significantly better than other algorithms (from 0.006% to 0.05% for VDS1 and from 0.023% to 0.214% for VDS2). Finally, for larger cases, Gurobi+B&B achieves the best efficiency (from 0.053% to 0.065% for VDS2). In conclusion, the application applied to the background of container liner shipping operation in which each ship must be reasonably allocated, maximize the use of ship capacity and port resources, to ensure efficient operation and customer satisfaction, the ship deployment and scheduling control effect, first, real-time acquisition of the number of inbound containers at each port on each route served by the ship company and the number of containers that need to be exported, then collect the capacity and speed interval of different types of ships owned by the ship company. According to the number of routes served by the ship company and the ports that need to be served on each route, a container liner shipping deployment and scheduling control model is constructed, by controlling the number of each type of ship serving each route and the speed interval, combined with the algorithm designed in the application, to obtain the best ship type used on each route, the minimum number of ships deployed and the best speed of each leg of the route and the ship deployment and scheduling scheme that minimizes environmental pollution on the route operated by the ship company; Compared with the prior art, the application considers more control factors, can more accurately control the ship deployment and scheduling scheme, improve the transportation efficiency and reduce the emission of environmental pollutants.

[0095] Although embodiments of the application have been shown and described, it is to be understood that various modifications, substitutions, replacements and changes can be made to these embodiments without departing from the principles and spirit of the application, the scope of the application being defined by the appended claims and their equivalents.

Claims

1. A container liner shipping dispatch control method considering environmental pollution and transportation efficiency, characterized by, The method comprises the following steps: S1: Collect the number of inbound containers, the number of containers that need to be exported, the number of each type of ship, the ship wear and tear and pollution emissions generated by each type of ship in operation on each route served by the shipping company; S2: constructing a homogeneous ship container liner transport deployment and dispatch control model based on the number of routes served by the shipping company and the ports that need to be served on each route According to the collected data, the type and number of ships that need to be invested by the shipping company on each route and the speed scheme of each voyage are calculated. Through formula Obtain the shipping company's required vessel types and quantities for each route, as well as the speed plan for each leg of the journey; among which, This indicates the value generated from the allocation of our company's vessels to other shipping companies. This refers to the losses incurred by a shipping company when it charters ships from other companies because its existing fleet is insufficient to meet its transport capacity. This indicates the value brought by the shipping company's efficient transport of containers. This refers to the wear and tear incurred by a ship during its operation. Indicates pollution emissions. This refers to the penalties imposed on shipping companies for failing to transport containers themselves. Indicates the type of ship. Indicates the shipping routes; Regarding pollution emissions From the formula The calculation uses a linearized formula. Calculate the length of the voyage completed by the ship. The required time is expressed by the formula The calculation has the following constraints: ,in, Indicates flight segment The slope of the upper tangent, Indicates the completion of a voyage segment. The amount of pollution emitted, This indicates the intersection of the tangent line and the y-axis. Indicates Time to complete the flight segment The amount of fuel required, where i represents a segment of the route. The dividing line indicates the amount of fuel. This indicates the departure time of type k vessels on route r from port i. This indicates the time when a type k vessel on route r arrives at port i-1. This indicates the dwell time of type k vessels on route r at port i. It is a binary variable; if port i is the starting port of shipping route r, it is 1; otherwise, it is 0. This indicates the amount of pollutants emitted per unit of fuel. The ship type deployed on each route is constrained by the following constraint: and wherein, is a binary variable, which is 1 if a k-type ship is deployed on the rth route, otherwise 0, represents a set of routes, and M is a large number; The number of ships deployed on each route is constrained, that is, the following constraints need to be met: wherein, represents the distance of the i-th leg on the route r, represents the speed of the i-th leg on the route r, represents the time of the k-th ship type to stay at the i-th port on the route r, represents the number of the k-th ship type deployed on the route r, which is not a linear constraint, a decision variable The above constraint will become the following equation: wherein, represents the inverse of the speed at which the i-th leg on route r is driven; S3: On the basis of the control model one , increase the constraints of different ship types, different types of ships are uniformly constrained in the speed interval according to their specifications, and on the basis of the control model one , build a container liner transport deployment and scheduling control model two considering different specifications of ships ; According to the capacity data of the ship, the various types of ships are divided into three sizes: if the capacity of the ship is less than , then ; if the capacity of the ship is greater than but less than , then ; and if the capacity of the ship is greater than , then , where is the capacity of the smallest medium-sized ship, is the capacity of the smallest large-sized ship, is a binary decision variable indicating that the ship size is small ship, is a binary decision variable indicating that the ship size is medium ship, is a binary decision variable indicating that the ship size is large ship, and is the ship type. Rewrite the speed constraints in the control model VDS1 into the following constraints: wherein denotes the speed of a type ship on a leg of a route, denote the minimum speed of a small, medium and large ship, respectively, denote the maximum speed of a small, medium and large ship, respectively.​​​​​​ The model sets non-negativity constraints on the variables , the variables , the variables , and constraints that each type of vessel is allowed to be only one vessel specification: and ; S4: According to the established container liner transportation deployment and scheduling control model, combined with the designed seven algorithms, the optimal scheme is obtained after comparison and analysis.

2. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that: The S2, involving the number of k-type ships owned by the shipping company itself , the number of k-type ships that the shipping company needs to rent , the number of rented ships , the number of k-type ships owned by the shipping company deployed on route r , the number of k-type ships that the shipping company needs to rent deployed on route r , and the number of deployed k-type ships ; The number of k-type vessels that the shipping company needs to charter The following constraints are set: where, represents the maximum number of k-type vessels allowed to be chartered, calculated by the formula is calculated as where, represents the value brought to the third-party shipping company by chartering one k-type vessel; Number of chartered vessels is calculated by the formula is calculated by the formula wherein, represents the value that a chartered k-type vessel can bring to the shipping company; the number of k-type vessels owned by the shipping company deployed on route r The following constraint is set to limit the number of k-type vessels owned by the shipping company deployed on route r to be no more than the total number of k-type vessels owned by the shipping company: ; the number of k-type vessels chartered by the shipping company deployed on route r The following constraint is set: to limit the number of k-type vessels chartered by the shipping company deployed on route r to be no more than the total number of k-type vessels chartered by the shipping company; the constraint on is: Further, the ship wear and tear generated in the process of operation of the ship is calculated by the formula wherein, K represents the type set of all available ships, represents the ship wear and tear generated in the process of operation of a k-type vessel on route r.​ 3. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that: S2 in the above equation, The number of purchased non-company-operated container slots generated by purchasing non-company-operated container slots, calculated by the formula with the following constraints: , calculated by the formula where, represents the number of containers that need to be shipped from port o to port d on route r, represents the amount of slot purchase per unit container from port o to port d, represents the number of containers shipped from port o to port d on route r by k-type ships, o and d represent the ports on route r, and V represents the set of all ports; is calculated by the formula wherein, represents the number of containers actually transported along route r from port o to destination port d, represents the value brought to the shipping company by transporting one unit of container from origin port o to destination port d on route r.

4. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that: In a container liner transport deployment and dispatch control model of homogeneous ships In the container liner transport deployment and dispatch control model of homogeneous ships, a flow conservation constraint for containers and a flow conservation constraint for service variables are set, and the flow conservation constraint for containers is specifically as follows: and wherein, represents the number of containers stored on the ship of the k type ship originating from the oth port on the ith-1 segment of the rth route, represents the number of containers loaded on the jth port of call of the rth route by the k type ship originating from the oth port, represents the number of containers unloaded on the jth port of call of the rth route by the k type ship originating from the oth port, represents a set of port indexes pointing to a specific port d in the rth route; The flow conservation constraint of service variables is subject to: and where, is a binary variable, 1 if a k-type ship sails from port o to port d, otherwise 0, and the time of the ship arriving at port i is linked to the time of the ship arriving at port i+1, and the specific constraint is: where, denotes the time of the k-type ship on route r arriving at port j, denotes the stay time of the k-type ship on route r at port j, denotes the sailing time of the k-type ship on route r to port j. In terms of speed, the following constraints are imposed: , where, Vr,i is the maximum speed of the ship on the i-th leg of the r-th route, Vr,i is the minimum speed of the ship on the i-th leg of the r-th route, Vr,i is the speed of the ship on the i-th leg of the r-th route, R is the set of all ports on the r-th route. Finally, the following non-negativity constraints are made for all other decision variables: 。 5. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that, The control model VDS1 and the control model VDS2 are solved by using a genetic algorithm: First, the genetic algorithm uses real number coding, randomly generates chromosomes, and the coding method is as follows: using a gene to represent a feasible ship deployment scheme, where each sub-coding is denoted as , representing the th deployment scheme, and each gene consists of three parts, where is the first part of the gene, used to control the service route number, the number of ships deployed on the route, and the type of ships deployed on the route; is the second part of the gene, used to control the order of arrival of a certain route of the ship company at the port; the third part is , used to describe the sailing speed of the ship on the route, and these parts are repeated only for the function, not for the value, until all the route deployment schemes are generated. Secondly, in the calculation process of the fitness function, firstly, the randomly generated genes are decoded to obtain the number of services of each ship type on the ith route and the speed of the ship on each voyage section; Once the number of ships deployed on the route is determined, the number of rented and leased ships can be determined, and whether there is a leased ship; If there is a leased ship, the value brought to the shipping company by the leased ship can be calculated using the formula in the model; Using the calculation formula in the model, the pollution emissions can be calculated according to the known speed of the ship and the port access sequence, and at the same time, the value brought to the shipping company by efficient transportation of containers can be calculated according to the number of containers transported in each port; Finally, according to the given cargo demand between ports, it is calculated whether there is a part of the penalty in each port, so as to obtain the fitness value of the gene; In the selection operation, the roulette method is used to design the genetic algorithm selection operator.

6. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that, The control model VDS1 and the control model VDS2 are solved by using a simulated annealing algorithm, and the specific implementation method is as follows: In the simulated annealing algorithm, the coding and decoding process is to determine the order of the ports to be visited and the number and type of ships serving the route. It is assumed that 12 ships are deployed on route 1, and ships of type 2 are selected to serve the route. If the port numbers on the route are 2, 5, 11, 9, and 8, initialize the random speed values of each section within a reasonable range, then the code is [1, 2, 12, 5, 9, 2, 8, 11, 22, 25, 20, 19]; The new solution generation rule includes two parts: the first part is the order of the service port, and the strategy adopted in this part is to randomly select the order of a number of ports on the route to exchange; The second part is the generation of the speed on each voyage section, which is to randomly generate the speed on some voyage sections based on the distance within a certain reasonable interval; The Metropolis criterion is selected as the acceptance function in the simulated annealing algorithm: wherein, represents the newly calculated allocation of ship types and numbers of ships of the shipping company on each route, represents the last calculated allocation of ship types and numbers of ships of the shipping company on each route, when the current solution is adopted if the allocation of ship types and numbers of ships of the current solution is more reasonable and the transport of goods is more efficient, otherwise if the allocation of ship types and numbers of ships of the current solution or the transport of goods is not as good as the last solution, then a new solution is generated, the current solution is adopted, i.e. the worse solution is adopted. The annealing strategy is exponential annealing, which means that the temperature is exponentially decreased, wherein is the temperature after the th iteration, is the initial temperature set, is the annealing factor and ; the simulated annealing algorithm uses this way to construct the annealing function, that is, , wherein ; The end strategy of the simulated annealing algorithm is to set the maximum number of iterations, that is, to end when the termination temperature is reached.

7. The container liner shipping dispatch control method considering environmental pollution and transportation efficiency according to claim 1, characterized in that, The control model VDS1 and the control model VDS2 are solved by using a branch and bound algorithm: Gurobi solver is used as a preprocessor to solve the problem by using a branch and bound algorithm, or the branch and bound algorithm is combined with a heuristic algorithm to solve the problem; In the first method using Gurobi solver as a pre-processor, Gurobi solver is used to solve the relaxed model, which is done before using the branch-and-bound algorithm, the relaxation of the model is focused on the selection of the ship type, which is turned from binary decision variable to real number decision variable, which is also one of the parts to be branched by the branch-and-bound algorithm, where, denotes 1 if the ship of type k is used to serve route r, otherwise 0; in the ship type part, only the non-integer ship types need to be branched; For the branch and bound algorithm combined with heuristic algorithm, the relative optimal solution obtained by the heuristic algorithm is used as the initial solution of the branch and bound algorithm, and then the branch and bound algorithm is used for solving; in the branch and bound algorithm, the search strategy used is the depth-first search strategy, then the integer judgment is performed on the part of the ship selection in the code, if it is a non-integer, the upper bound value is updated, otherwise the lower bound is updated; then the constraints in the model are judged, for the speed constraint, if the above conditions are not met, the algorithm will take pruning; after calculating the target value, the integer judgment is performed on the corresponding code part, if they are all integers and the target value is less than the lower bound, then branching down will not appear a better solution, so it is pruned, thereby stopping this branch.

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