CN110689155B - Multi-constraint scheduling method of card collection reservation system considering congestion and emission - Google Patents

Abstract

The invention discloses a multi-constraint scheduling method for a collector reservation system considering congestion and emission. The method comprises the following steps: S1. Set the iteration number iter=0, and initialize all collector reservation schemes Q ^iter of the collector; S2. All collection card reservation schemes Q ^iter of step S1 carry out real number coding; S3, decode all collection card reservation schemes Q ^iter generated by step S2 encoding; S4, calculate the fitness value f of each kind of collection card reservation scheme; S5, when the number of iterations When iter is equal to the preset maximum number of iterations iter _max , the set card reservation scheme corresponding to the maximum fitness value f is output as the best reservation scheme. Its advantages are: this method improves the initialization speed of the algorithm through the combination of real number and qubit encoding; at the same time, this method adopts the strategy of dynamic quantum revolving gate and mutation probability self-adjusting according to evolutionary algebra, which can improve the accuracy of set cards. The accuracy of the reservation plan solution, and the best reservation plan can be selected at a faster speed.

Description

A multi-constraint scheduling method for truck reservation system considering congestion and emissions

technical field

The invention relates to the field of truck reservation, in particular to a multi-constraint scheduling method for a truck reservation system considering congestion and emission.

Background technique

In 2018, Shanghai Port completed a container throughput of 42.01 million TEU (TEU), a growth rate of 4.4% compared to the past, and the container throughput reached a new high. Shanghai Port has been the world's largest container port for 9 consecutive years, and the increase in container operations is Container terminals bring opportunities as well as more challenges. In May 2017, serious port congestion occurred in Shanghai Port. After that, the congestion of container terminals quickly spread to other domestic ports, and Qingdao Port and Ningbo Port also faced congestion and shortage of storage yard. In 2018, the Port of Los Angeles-Long Beach in the United States experienced an unusual period of congestion that prevented collection cards from picking up and returning empty boxes on time, resulting in thousands of dollars in detention and demurrage fees per day.

In order to alleviate the problem of truck congestion at terminals, some ports at home and abroad, such as Los Angeles and Long Beach in the United States, Vancouver in Canada, and Tianjin in my country, have successively implemented the Truck Appointment System (TAS). The truck reservation system is a relatively advanced solution, which is mainly used for the external truck operations related to port operations. Different truck reservation methods are used in the truck reservation system.

According to the pre-arranged working hours of the truck, the truck company will reserve a time window for each truck. The port company pre-determines the allocation of yard equipment based on the quota for each time window. Through the combination of mathematical formula and simulation, Huynh et al. proposed a method to determine the maximum number of collectors that the port can accept in each time window. Huynh et al. proposed an improved method for ports, which is to improve the reservation system by assigning different reservation time windows to each truck. In order to integrate the truck reservation system with the internal operation of the port, Zehendner et al. proposed a mixed integer linear programming model to determine the number of reservations to provide and allocate trucks for different transportation modes according to the overall workload and available processing capacity. Phan et al. took into account the impact of the change of the arrival time of the truck, and established a model combining mathematical formulas and decentralized decision-making to support the negotiation between the truck company and the port company, so that the truck can arrive at the port more evenly. . Chen et al. proposed a method called "vessel-dependent time window" to control the arrival of trucks, which makes the trucks reach the gate more uniformly and significantly reduces the congestion at the gate. Schulte et al. established an optimization model based on the multi-travelling salesman problem with a time window, which can effectively use the cooperation between sets of cards to reduce costs and emissions. Mohammad et al. established a mixed integer nonlinear model, which can serve both truck companies and port companies at the same time, which can alleviate the congestion of trucks at the gate on the basis of effectively reducing transportation costs.

However, at present, the actual performance of many card reservation systems applying each of the above methods is not consistent with the expected performance. The study by Giuliano et al. found that when Long Beach and Los Angeles ports implemented the truck reservation system, due to disruptive events that hindered the smooth operation of the truck reservation system, the congestion of trucks at the gate was not significantly relieved, and the emission of heavy-duty diesel trucks was not affected. been significantly reduced. The study by Islam et al. concluded that the implementation of the truck reservation system in New Zealand ports has increased the limitations of truck companies in the arrangement of truck work schedules.

The above solutions are all aimed at reducing the waiting time of trucks at the gate or yard, thereby reducing idle emissions. Although the research on the truck reservation system is becoming more and more mature, the existing research does not consider the impact of urban traffic on the arrival time of the truck, which greatly limits the practical application value of the truck reservation system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a multi-constraint scheduling method for a truck reservation system that considers congestion and emissions. The method considers the impact of urban traffic congestion on the arrival time of trucks in the morning and evening rush hours, and the impact of trucks in deceleration and idling states. Therefore, a multi-constraint scheduling model for collector reservation based on mixed integer nonlinear programming is established, and an improved adaptive quantum genetic algorithm is used to optimize the solution. Companies and ports reduce operating costs.

In order to achieve the above object, the present invention realizes through the following technical solutions:

A multi-constraint scheduling method for a truck reservation system considering congestion and emissions, the method includes the following steps:

S1, set the number of iterations iter=0, initialize all the collection card reservation schemes Q ^iter of the collection card;

S2, perform real number coding on all the card reservation schemes Q ^iter of step S1;

S3, decoding step S2 coding and generating all card reservation schemes Q ^iter ;

S4. Calculate the fitness value f of each collection card reservation scheme;

S5. When the number of iterations iter is equal to the preset maximum number of iterations iter _max , output the card reservation scheme corresponding to the maximum fitness value f as the optimal reservation scheme;

In the step S5, when the number of iterations iter is less than the preset maximum number of iterations iter _max , step S6 is performed;

S6. Use the quantum revolving gate U ^iter to update all the collection card reservation schemes Q ^iter of the collection card;

S7, using quantum multi-point crossover and adaptive mutation to update all the collection card reservation schemes Q ^iter of the collection card;

S8. Let iter=iter+1, and go to step S2.

Preferably, in the step S1, all the card collection reservation schemes Q ^iter for initializing the card collection are as follows:

一个完整的第 n个预约方案编码为

一辆集卡所有集卡预约方案的集合为

其中，α、β为两个复常数，分别表示量子取偏下限态和取偏上限态的几率幅，且满足归一化条件|α|²+|β|²＝1。The maximum number of appointments per day is S, the maximum time window number of the company for each appointment is X, the number of the time window for the s-th appointment is x _s , and the n-th appointment plan of the iter generation The qubit encoding method corresponding to the middle time window number x _s is:

A complete nth reservation scheme is encoded as

The collection of all the truck reservation plans for a truck is:

Among them, α and β are two complex constants, which represent the probability amplitudes of the quantum deviated lower state and deviated upper state respectively, and satisfy the normalization condition |α| ² +|β| ² =1.

Preferably, the real number encoding performed in the step S2 is specifically:

若

则该位取

态，否则取

态，其中，

和

分别为时间窗号码x_s的取值上限和取值下限；Generate a random number of [0, 1] for the time window number x _s of each reservation in each card reservation scheme

like

then the bit takes

state, otherwise take

state, where,

and

are the upper limit and lower limit of the time window number x _s , respectively;

一辆集卡实数编码的所有集卡预约方案的集合为

The real code of a complete nth card reservation scheme is expressed as

The set of all truck reservation schemes encoded by a truck real number is:

Preferably, the decoding in the step S3 is specifically:

和

对应于时间窗号码x_s的两个取值区域，令

每个区域的大小为Δx_s/2，在每个时间窗配额及集卡公司的约束下生成集卡的集卡预约方案，具体解码规则如下：The bound encoding of the time window number x _s is expressed as one of two cases:

and

Corresponding to the two value areas of the time window number x _s , let

The size of each area is Δx _s /2, and the collection card reservation plan of the collection card is generated under the constraints of each time window quota and the collection card company. The specific decoding rules are as follows:

时，x_s偏取值下限取值，可取时间窗号码为0～X/2，此时

r为0～1内的随机数；(1) When

When , the lower limit of the x _s offset value is the value, and the number of the time window can be 0~X/2. At this time

r is a random number between 0 and 1;

时，x_s偏取值上限取值，可取时间窗号为X/2+1～X，此时

r为0～1内的随机数。(2) When

, the upper limit of the offset value of x _s is taken as the upper limit value, and the time window number can be taken as X/2+1～X. At this time

r is a random number within 0-1.

Preferably, the fitness value f in the step S4 is the inverse of the cost of each card reservation scheme.

Preferably, the cost of each pickup reservation scheme includes: the total cost of all pickup companies to change the reservation, the average waiting cost of pickup at the port gate, the extra time cost of pickup congestion during morning and evening peak hours, the cost of pickup at The additional environmental pollution costs caused by deceleration and idling in the morning and evening rush hour congestion and waiting in line at the gate.

Preferably, the step S6 is specifically:

其中，U_n，s为量子旋转门，α′、β′均为更新后的复函数，构成更新之后的预约方案，用于更新种群，χθ_n,s＝▽(α,β)·θ_n,s，χ＝▽(α,β)，θ_n,s为旋转角度，用于控制算法的收敛速度，

r'为0～1之间的常数，▽(α,β)为旋转方向，用于保证算法的收敛。A mechanism of dynamically adjusting the rotation angle is adopted, and the rotation angle gradually decreases with the increase of algebra. For each reservation time window number x _s of each card reservation scheme, the following operations are performed:

Among them, U _{n, s} is the quantum revolving gate, α′ and β′ are both updated complex functions, which constitute the updated reservation scheme for updating the population, χθ _n,s =▽(α,β)·θ _{n ,s} , χ=▽(α,β), θ _{n, s} is the rotation angle, which is used to control the convergence speed of the algorithm,

r' is a constant between 0 and 1, and ▽(α, β) is the rotation direction, which is used to ensure the convergence of the algorithm.

Preferably, the step S7 is specifically:

Perform crossover and mutation operations on the scheduling time window number x _s of each collector reservation scheme to update all collector reservation schemes Q ^iter ;

Select two intersections randomly from the two multi-point crossover and mutual pairing reservation schemes, and exchange the part between the intersections, thereby generating two new collection reservation schemes;

At the same time, adaptive mutation is adopted, and the amount of change is set to a random integer and opposite to each other. The mutation probability p _m is automatically adjusted according to the evolutionary algebra. The calculation formula is as follows:

其中p_max为最大变异概率，p_min为最小变异概率。

where p _max is the maximum mutation probability and p _min is the minimum mutation probability.

Compared with the prior art, the present invention has the following advantages:

(1) The multi-constraint scheduling method of the collector reservation system considering congestion and emission of the present invention forms an adaptive quantum genetic algorithm by improving the quantum genetic algorithm. The speed of algorithm initialization;

(2) This method adopts the strategy of dynamic quantum revolving gate and mutation probability self-adjusting according to evolutionary algebra, which can improve the accuracy of solving the reservation scheme of the set card, and select the best reservation scheme at a faster speed;

(3) This method takes into account the impact of urban traffic congestion on the arrival time of trucks in the morning and evening peak hours, as well as the environmental pollution cost caused by trucks in deceleration and idling states. While obtaining the optimal scheduling scheme, it effectively reduces the Comprehensive operating costs of truck companies and port companies;

(4) The solution speed of this method is obviously better than that of the traditional genetic algorithm, especially when solving large-scale problems, the calculation time has been greatly improved.

Description of drawings

1 is a schematic flowchart of a multi-constraint scheduling method for a card reservation system considering congestion and emissions of the present invention;

2 is a schematic diagram of the range of the value region of x _s during rule (1) in an embodiment of the present invention;

3 is a schematic diagram of the value area range of x _s during rule (2) in an embodiment of the present invention;

Fig. 4 is the schematic diagram of PSFFA method;

5 is a schematic diagram of a container port network in an embodiment of the present invention;

Figure 6 shows the changes and comparative experimental results of the operating costs of the three card booking systems under different customer time windows;

Figure 7 is a schematic diagram showing the influence of the duration of each time window on the operating cost of the entire port and the truck company in three different truck reservation systems;

Figure 8 is a schematic diagram showing the influence of the turnaround time of trucks in the port on the overall operating cost in four different truck reservation systems.

Detailed ways

The present invention will be further elaborated below by describing a preferred specific embodiment in detail with reference to the accompanying drawings.

In the model of the truck reservation system of this embodiment, the truck company submits the reservation application for the next day before 5:00 pm every day, and the port company submits the quota for each time window of the next day before 5:00 pm every day. For each reservation application of the collection card, the collection card ID and the corresponding container number must be provided, so that the collection card reservation system will determine the respective expected time difference between the successive reservations of the collection card. This embodiment assumes that the time difference is constant. When all the input data (reservation request and time window quota) are completed, the truck reservation system finally determines the reservation time window for each truck, in order to minimize the comprehensive operation cost of the port company and the truck company. Finally, the truck reservation system sends the best reservation time window for each truck to the truck company. If the last specified appointment time window is different from the appointment time window submitted by the collecting company, the collecting company will reschedule the itinerary of the collecting card.

The main factors affecting the card collection reservation are: reservation share, reservation time, and collection card arrival regularity. In this embodiment, taking into account the influence of the peak period and the arrival volume of the next day, the reservation share is distributed unevenly; the length of the reservation period will affect the arrival distribution of the collection card, and the length of the reservation is the management of the arrival of the collection card It is beneficial, but it will reduce the probability of the collection card arriving on time within the reservation period. Therefore, in this embodiment, every day from 8:00 am to 6:00 pm is divided into 10 time windows, and the duration of each time window is 1 hour; the arrival law of the collector has a law that changes with time, and this embodiment uses a non-stationary arrival queuing model to describe the arrival of the collector.

The scheduling problem of truck reservations is an NP-hard problem, which belongs to the extension of the multiple Traveling Salesman Problem with Time-Windows (m-TSPTW) based on time windows. The increased waiting time and the increased pollutant emissions in deceleration and idling states increase the difficulty of solving and make the multi-constraint scheduling problem of the truck reservation system more complicated. The genetic algorithm can approach the global optimal point well in a short generation time, but when the problem scale is large, the genetic algorithm is prone to fall into "prematurity". In order to solve this problem and further improve the accuracy of solving the problem, Narayanan proposed the Quantum Genetic Algorithm (QGA), which is a probabilistic optimization method based on the principle of quantum computing, which is a combination of quantum computing and genetic algorithm. product. The invention proposes an improved self-adaptive quantum genetic algorithm (Improved Self-Adaptive Quantum Genetic Algorithm, ISQGA), and proposes a coding method combining real number and quantum bit coding, a dynamic quantum revolving gate, and a mutation probability that is independently adjusted according to evolutionary algebra. strategy, which greatly reduces the code length and improves the accuracy of solving the problem. The multi-constraint scheduling method of the truck reservation system considering congestion and emission of the present invention is applied to the truck reservation system to determine the truck reservation scheme of one truck, so as to coordinately determine the truck reservation scheme of all the trucks.

As shown in FIG. 1 , it is a multi-constraint scheduling method for a collector reservation system considering congestion and emission of the present invention, and the method includes the following steps:

S1. Set the number of iterations iter=0, and initialize all the collection card reservation schemes Q ^iter of the collection card.

All the card reservation schemes of the initialized card collection are as follows:

The maximum number of appointments per day for the collection card is S, the maximum time window number of the collection card company for each reservation of the collection card is X, and the time window number for the sth reservation of the collection card is x _s . In this embodiment, the maximum number of reservations S=4, the maximum time window number X=10, that is, there are 10 time windows, so there are 4 variables in each reservation scheme of each truck, such as the first variable Indicates the time window number for the first reservation of the collection card.

A qubit is represented as follows: |φ>=α·|x ^min >+β·|x ^max >. Among them, α and β are two complex constants, which represent the probability amplitudes of the quantum deviated lower state and deviated upper state respectively, and satisfy the normalization condition |α| ² +|β| ² =1. The maximum time window number in this embodiment is 10, so the sequence number of the reservation time window for each truck is in the range of 0 to 10, for example, 0 means no reservation, and 10 means the tenth time window is reserved. Take the time window number reserved by each truck as its variable, namely x _s .

一个完整的第n个预约方案编码为

设定种群规模N，在本实施例中，N＝10，n＝10，则一辆集卡所有集卡预约方案的集合即种群为

The qubit encoding method corresponding to the time window number x _s in the nth reservation scheme of the iter generation is:

A complete nth reservation scheme is encoded as

Set the population size N, in this embodiment, N=10, n=10, then the set of all pickup reservation schemes for a pickup truck, that is, the population is

S2. Perform real coding on all the card reservation schemes Q ^iter in step S1, that is, generate real coding chromosomes.

若

则该位取

态，否则取

态，其中，

和

分别为时间窗号码x_s的取值上限和取值下限(即时间窗号码的最大值和最小值，分别为0和10)；In order to make the reservation scheme of each truck more intuitive, the present invention proposes to apply real number coding to the algorithm. The real number encoding in the step S2 is specifically: generating a random number of [0,1] for the time window number x _s of each reservation in each card reservation scheme

like

then the bit takes

state, otherwise take

state, where,

and

are the upper limit and lower limit of the time window number x _s (that is, the maximum and minimum values of the time window number, which are 0 and 10, respectively);

一辆集卡实数编码的所有集卡预约方案的集合为

The real number code of a complete collection reservation scheme of the nth collection reservation scheme of the collection card is:

The set of all truck reservation schemes encoded by a truck real number is:

S3. Decoding all the card reservation schemes Q ^iter generated by the encoding in step S2.

The decoding in the step S3 is specifically:

和

对应于时间窗号码x_s的两个取值区域，令

每个区域的大小为Δx_s/2，在每个时间窗配额及集卡公司的约束下生成集卡的集卡预约方案，具体解码规则如下：As shown in the combination of Figure 2 and Figure 3, the limit encoding of the time window number x _s is expressed as one of the following two cases:

and

Corresponding to the two value areas of the time window number x _s , let

The size of each area is Δx _s /2, and the collection card reservation plan of the collection card is generated under the constraints of each time window quota and the collection card company. The specific decoding rules are as follows:

时，x_s偏取值下限取值，即可取时间窗号码为0～5，如图2所示区域，此时

r为0～1内的随机数；(1) When

When the value of x _s is the lower limit of the offset value, the time window number can be taken as 0 to 5, as shown in Figure 2, at this time

r is a random number between 0 and 1;

时，x_s偏取值上限取值，即可取时间窗号为6～10，如图3所示区域，此时

r为0～1内的随机数。(2) When

, the upper limit of the x _s offset value can be taken as the upper limit value, and the time window number can be taken as 6 to 10, as shown in the area shown in Figure 3, at this time

r is a random number within 0-1.

S4. Calculate the fitness value f of each collection card reservation scheme.

The fitness value f in the step S4 is the inverse of the cost of each card reservation scheme.

The cost of each pickup reservation scheme described above includes: the total cost of changing the reservation of all pickup companies, the average waiting cost of pickup at the port gate, the additional time cost of pickup congestion during the morning and evening peak hours, and the pickup during the morning and evening peak hours. Congestion and additional environmental pollution costs caused by slowing down and idling when waiting in line at gates.

来决策，该决策变量表示了具有i次预约的集卡k在时间窗t_w内的第b次预约的状态。The present invention establishes a multi-constraint scheduling model based on Mixed Integer Nonlinear Programming (MINLP). Since the time window of the port is discrete, a binary decision variable is established in the model

to make a decision, the decision variable represents the status of the b-th appointment of the set card k with i appointments within the time window _tw .

The objective function of the present invention, that is, the cost of each card reservation scheme, is shown in formula (2):

Restrictions:

Therefore, the calculation formula of the fitness value f of the present invention is as follows:

The first term of the objective function is the total cost of changing an appointment for all the trucking companies. Each formula is each constraint condition. Equation (3) calculates the cost of changing an appointment for each trucking company. The first term indicates that for a trucking company with multiple appointments in one day, the time difference between consecutive appointments after the change is greater than the expected time difference (unit cost). It is represented by Y ₁ ); the second item represents the change cost (unit cost is represented by Y ₂ ) when the time difference between consecutive appointments after the change is less than the expected time difference; the third item represents the change cost of changing to a later time window (unit The cost is represented by Y ₃ ); the fourth term represents the cost of the change to an earlier time window (unit cost is represented by Y ₄ ). Equations (4) and (5) are linearized representations of the maximum value of dt _kib -dt _pkib . Equations (6) and (7) are linearized representations of the maximum value of dt _pkib - dt _kib . Equations (8) and (9) are linearized representations of the maximum difference between the actual arrival time window and the expected arrival time window. Equations (10) and (11) are linearized representations of the maximum difference between the expected arrival time window and the actual arrival time window. Equation (12) is to ensure that the cost increase of each card company's change time window does not exceed a predetermined threshold, and the threshold is determined by formula (13). Collector companies with more cards have lower thresholds. Among them, parameter a represents the minimum threshold for all truck companies from the port, parameter c represents the initial threshold of truck companies with relatively few reservations, and parameter h represents the slope or the rate of decline of the threshold. Equations (14) and (15) respectively calculate the time difference between two actual consecutive appointments and the time difference between two expected consecutive appointments for a set card with multiple appointments in one day. Equation (16) represents the condition that the reservation request should be satisfied. Equation (17) is a capacity constraint that requires the number of reservations in each time window to be less than the specified quota. The pre-specified quota is calculated as formulas (27) and (28). where AQ is the average quota for each time window, and all experiments in this example are performed within 10 time windows, except for the experiments related to the sensitivity analysis of the port time window duration. Equation (28) sets the quota for each time window. Equation (18) ensures that the order of reservations after adjustment is the same as the order in which the cards are requested with multiple reservations.

t _w = [0.9 AQ, 0.9 AQ, 1.1 AQ, 1.1 AQ, 1.1 AQ, 1.1 AQ, 1.1 AQ, 1.1 AQ, 0.9 AQ, 0.9 AQ] (28)

开始到时间间隔

结束的平均队列长度乘以等待队列长度的成本。式(19)是将一个时间窗内到达的所有集卡数量除以该时间窗内的时间间隔个数，得到每个时间间隔内集卡到达的平均数量，时间间隔这一术语仅用于队列长度估计。式(19)～(22)中使用的逐点平稳流体流动近似(PSFFA)方法所需持续时间比时间窗更短，PSFFA方法说明如图4所示。The second term of the objective function is the average waiting cost of the set card at the terminal gate (the unit cost is represented by Y ₅ ), which is calculated from the time interval.

start to time interval

The average queue length at the end multiplied by the cost of waiting for the queue length. Equation (19) is to divide the number of all collectors arriving in a time window by the number of time intervals in the time window to obtain the average number of collectors arriving in each time interval. The term time interval is only used for queues length estimate. The point-by-point smooth fluid flow approximation (PSFFA) method used in equations (19) to (22) requires a shorter duration than the time window. The description of the PSFFA method is shown in Figure 4.

For example: the average queue length for time interval _t5 is

In this embodiment, the gate collector queue is regarded as an M/G/1 queue, and is represented by a corresponding queuing function, as shown in formula (20). Constraints (20) and (21) are used to define the departure rate from gate to container yard in each time interval as

和

的最小值。

and

the minimum value of .

Equation (22) is used to calculate the stacker queue length for each time interval. Equation (23) is the representation of the value of the decision variable.

The third term of the objective function is the extra time cost (unit cost is represented by Y ₆ ) of truck congestion during the morning and evening peak hours, where η is about 2. In the model, urban roads are divided into three grades: expressway, main road and sub-arterial road. The time cost of truck congestion of trucks of different road levels under different congestion intensity conditions is calculated respectively, and the critical speed of trucks in different time states is used as a reference. Classification criteria for different types of road traffic conditions in cities. Equation (24) is the traffic flow of trucks on different grades of roads during peak periods.

The fourth item of the objective function is the additional environmental pollution cost (unit cost represented by Y ₇ ) caused by deceleration and idling when the truck is congested during the morning and evening peak hours and waiting in line at the gate. The calculation method is the difference between the environmental cost of exhaust emissions under the basic clear road and the environmental cost of exhaust emissions under congestion conditions. Equation (25) is the extra time for the truck to be congested. The pollutant emission coefficients W _g and W _g ' are obtained from the emission factor, and the emission factor can refer to China's truck exhaust emission standard (National VI Standard).

parameter definition

(1) Symbols: t _w = port time window; t _i = time interval of each time window; k = truck ID; i = number of appointments for a truck; b = number of appointments for a truck; d = ID of the collector company.

(2) Collection:

_Tw = set of time windows, _Tw ={1,...,10}; for example: Tw =1 represents the time window of 8:00 _AM-9:00AM ;

T _i = a set of time intervals within a time window; for example: T ₁ ={1,...,10}, T ₂ ={1,...,10}, etc.; T ₁ =1 represents the first time The time interval of 8:00AM-8:06AM in the window;

I = the set of reservation times for each collection card (set as 1 to 4 times in this article), I = {1,...,4}; for example: I = 3 means that the collection card has 3 reservations;

Ri = reservation set of cards with _i reservations, Ri = 1,..., _i ; such as: Ri ₌ {1 _} , Ri ={1,2}, etc.;

D=collection of card companies, D={1,2,...}, for example: D=1 means No. 1 card company;

K _d = the set of all the trucks of the No. d truck company; for example: K ₁ ={1,2,...}, K ₁ =1 means the first truck of the No. 1 truck company;

j = set of urban road grades, j = {1, 2, 3}; for example: j = 1 means expressway, j = 2 means main road, j = 3 means secondary arterial road;

g=set of exhaust pollutants, g={1,2,3}; for example: g=1 represents carbon monoxide (CO), g=2 represents hydrocarbons, and g=3 represents PM.

(3) Parameters:

P _kib = the expected time window for the b-th appointment of a card k with i appointments;

σ = the number of time intervals in a time window;

e=variance coefficient of gate service time;

C _l = the penalty value that the actual time difference is greater than the expected time difference;

C _s = the penalty value that the actual time difference is less than the expected time difference;

C _p = penalty value that the actual arrival time is earlier than the expected arrival time;

C _n = penalty value for the actual arrival time later than the expected arrival time;

C _q = penalty value for the card to wait in line at the gate;

n _d = the total number of appointments submitted by the trucking company d;

TH _d = the threshold value of the difference between the transportation costs of each trucking company;

dt _pkib = the time difference between the b-th appointment and the b+1-th appointment of the card k with i appointments;

η=conversion factor of economic loss under truck congestion;

L _j = the length of the j-type road;

K _j = the number of trucks on the j-type road;

V _j = critical speed when the truck is congested on the j-type road;

V _j '= the speed of the collection card on the j-type road when the truck is unblocked;

W _g = emission coefficient of class g pollutants when the truck is congested;

W _g '= emission coefficient of class g pollutants when the collector is unblocked;

CE _g = the environmental cost of each additional g pollutant.

(4) Decision variables:

dt _kib = the time difference between the b-th arrival and the b+1-th arrival of the set card k with i reservations;

N _kib = the difference of dt _kib -dt _pkib ;

Q _kib = the difference of dt _pkib -dt _kib ;

_Skib = the difference between the actual arrival time window and the expected arrival time window of the collector;

Z _kib = the difference between the expected arrival time window and the actual arrival time window of the collector;

T _d = total cost of change of reservation of trucking company d;

TC=Additional congestion time of trucks;

Q _j = the peak flow of the truck on the j-type road.

S5. When the iteration number iter of the algorithm is equal to (reaches) the preset maximum iteration number iter _max , output the card reservation scheme corresponding to the maximum fitness value f as the optimal reservation scheme, and the algorithm ends. In this embodiment, the preset maximum number of iterations iter _max is 500 times, that is, iter _max =500.

In the step S5, when the number of iterations iter is less than the preset maximum number of iterations iter _max , the iteration is continued. The iterative loop operation can calculate the fitness value of all the truck reservation schemes of a truck, so that the final output optimal reservation scheme has the best effect. The specific process of the shown iteration is as follows:

S6. Use the quantum revolving gate U ^iter to update all the collection card reservation schemes Qi ^iter of the collection card.

The step S6 is specifically:

In order to improve the running speed of the whole card reservation system, a dynamic adjustment mechanism of rotation angle is adopted, and the rotation angle gradually decreases with the increase of algebra. For each reservation time window number x _s of each card reservation scheme, perform the following operations:

其中U_n，s为量子旋转门(′为量子旋转门更新的方向，是量子旋转门更新的一部分)，α′、β′为更新后的复函数，构成更新之后的预约方案，用来更新种群(即集卡预约方案)，χθ_n,s＝▽(α,β)·θ_n,s，χ＝▽(α,β)，▽(α,β)为旋转方向，用于保证算法的收敛，θ_n,s为旋转角度，用来控制算法的收敛速度，

其中 r'为0～1之间的常数，本实施例r'取值1/e(e为自然常数)。

Among them, U _{n, s} is the quantum revolving door (' is the update direction of the quantum revolving door, which is a part of the quantum revolving door update), and α' and β' are the updated complex functions, which constitute the updated reservation scheme for updating Population (i.e. card reservation scheme), χθ _n,s =▽(α,β)·θn _,s , χ=▽(α,β), ▽(α,β) is the rotation direction, which is used to ensure the algorithm Convergence, θ _{n, s} is the rotation angle, which is used to control the convergence speed of the algorithm,

r' is a constant between 0 and 1, and in this embodiment, r' takes a value of 1/e (e is a natural constant).

S7, utilize quantum multi-point crossover and self-adaptive mutation to update all collector reservation schemes ^Qiter of collectors.

The step S7 is specifically:

Crossover and mutation operations are performed on the scheduling time window number x _s of each collector reservation scheme to update all the collector reservation schemes Q ^iter .

Two intersections are randomly selected from the two multi-point cross and mutual matching reservation schemes, and then the parts between the intersections are exchanged, thereby generating two new collection reservation schemes. Preferably, a collection card reservation scheme with a high fitness value f is selected as the two collection card reservation schemes of the experiment.

At the same time, the present invention also adopts self-adaptive mutation, and the amount of change is set as a random integer between [-0.9, 1.2] and is opposite to each other, and the mutation probability p _m is automatically adjusted according to the evolutionary algebra, and the calculation formula is as follows:

其中p_max为最大变异概率，p_min为最小变异概率。

where p _max is the maximum mutation probability and p _min is the minimum mutation probability.

S8. Let iter=iter+1, and go to step S2 until the best reservation scheme is obtained.

In order to verify the feasibility of the established model and the solution method, the multi-constraint scheduling method of the collector reservation system considering the congestion and emission of the present invention is used to conduct a simulation experiment. The experiment is generated on a square network with a container port with an annual throughput of 5 million TEU as an example, which has one container port, multiple empty container yards and multiple card pools, as shown in Figure 5. The chosen square network is large enough that the travel time of the collector card along the edge of the network is 160 minutes. The size of the network and the location of the container ports are provided for each experiment. The locations of the truck warehouse and empty container warehouse are randomly selected for different shipping companies. Customer locations are randomly placed in the network, customer pickup and delivery time windows are from 4:00 am to 10:00 pm, container ports operate from 8:00 am to 6:00 pm, using ten port time windows, each Each time window is 1 hour. All experiments are performed on a computer with Intel Core i7, 1.8GHz CPU and 8GB RAM.

The basic data of this embodiment are as follows: the turnaround time of trucks in the port is 43.2 minutes; the daily working time of the port is 10 hours, and the number of time windows is 10; the average queuing time of the port yard is 10 minutes; The time to unload the container is 5 minutes.

For the five penalty values involved in this embodiment, the value range of each of them is an integer from 1 to 10, they are arranged and combined, and the objective function of the unconstrained set card scheduling model under each group of penalty values is calculated. The difference between the value and the objective function value of the constrained set card scheduling model, the penalty value corresponding to the smallest difference is the optimal penalty value. Finally, the optimal penalty values are determined as C _l =1, C _s =3, C _p =1, C _n =3, C _q =1.

Simulation Experiment of Reservation Scheduling of Collectors in Different Scales

Table 1 is an experiment for an optimal solution provided by the reservation and reservation system of a card collection company. This embodiment uses the experiment to explain the inner working principle of the reservation system for collection cards. In the table, Y ₁ to Y ₇ represent the larger time difference after the change, the smaller time difference after the change, the delay of the time window after the change, the advance of the time window after the change, the average waiting time at the gate, the morning and evening peak congestion time and the unit cost of emission. In Experiment 1, the truck company makes a reservation for a truck, and the expected time windows are 1, 3, 6 and 8, and the optimal time windows provided by the truck reservation system are 1, 4, 6 and 8. The reason is that the cargo allocation of time window 3 is 0, and the reservation of time window 3 is extended to time window 4. Experiment 2 and Experiment 3 are both scheduling of two trucks. The optimal time window provided by the truck reservation system in Experiment 3 is the expected time window. The total target value is the unit cost of trucks queuing at the gate, the morning and evening peak hours The sum of the unit time cost and the unit environmental pollution cost in deceleration and idling states.

Table 1 The time window of a card-collecting company and the optimal solution provided by the card-collecting reservation system

Table 2 summarizes the parameters of 28 additional experiments. Based on the experimental parameters in Table 2, simulation experiments are carried out on the truck reservation system that only considers the problem of gate congestion, the truck reservation system that considers the cost of changing reservations and the problem of gate congestion, and the target truck reservation system in this paper. Table 3 is the experiment. result. Among them, experiments 4-18 are small-scale problems, experiments 19-25 are medium-scale problems, and experiments 26-31 are large-scale problems (the average amount of goods that each truck company needs to handle exceeds 10TEU). The card collecting company hopes to reduce the number of collecting cards as much as possible to reduce the cost. Through the experimental comparison of the three card collecting reservation systems, the card collecting reservation system of this embodiment has the least requirement on the number of collecting cards, which can meet the needs of the collecting card companies. . For the entire restricted transportation problem, the target value of the truck reservation system designed in this embodiment is the smallest, that is, the entire transportation time is the least, which shows that the truck reservation system makes full use of the time of each truck, and improves the efficiency of the entire system. In the entire operating system, reducing the comprehensive operating cost as much as possible can better serve the truck companies and ports. Considering the impact of the city’s morning and evening rush hours on the truck’s travel time, the reasonable allocation of the appointment time window can make the entire operating cost reduce.

Table 2 Experimental parameters

Experiment number Quantity of Goods (TEU) Quota per time window Number of card companies Port coordinates (min) transport area X Y (min×min) 4 4 (1,1,1,1,1,1,1,1,1,1,1) 1 0 80 160×160 5 8 (2,2,2,2,2,2,2,2,2,2) 1 0 80 160×160 6 11 (2,2,3,3,3,3,3,3,2,2) 2 0 80 160×160 7 15 (3,3,4,4,4,4,4,4,3,3) 2 0 80 160×160 8 18 (4,4,4,4,4,4,4,4,4,4) 3 0 80 160×160 9 twenty two (4,4,5,5,5,5,5,5,4,4) 3 0 80 160×160 10 26 (5,5,6,6,6,6,6,6,6,5,5) 4 0 80 160×160 11 32 (6,6,8,8,8,8,8,8,6,6) 4 0 80 160×160 12 36 (7,7,8,8,8,8,8,8,8,7,7) 5 0 80 160×160 13 37 (7,7,9,9,9,9,9,9,7,7) 5 0 80 160×160 14 50 (9,9,11,11,11,11,11,11,9,9) 6 0 80 160×160 15 55 (10,10,13,13,13,13,13,13,10,10) 7 0 80 160×160 16 100 (18,18,22,22,22,22,22,22,18,18) 13 0 80 160×160 17 157 (29,29,35,35,35,35,35,35,29,29) twenty one 0 80 160×160 18 209 (38,38,46,46,46,46,46,46,38,38) 27 0 80 160×160 19 257 (47,47,57,57,57,57,57,57,47,47) 32 0 80 160×160 20 324 (59,59,72,72,72,72,72,72,59,59) 38 0 80 160×160 twenty one 417 (76,76,92,92,92,92,92,92,76,76) 47 0 80 160×160 twenty two 492 (89,89,109,109,109,109,109,109,89,89) 60 0 80 160×160 twenty three 569 (103,103,126,126,126,126,126,126,103,103) 67 0 80 160×160 twenty four 602 (109,109,133,133,133,133,133,133,109,109) 71 0 80 160×160 25 663 (120,120,146,146,146,146,146,146,120,120) 74 0 80 160×160 26 701 (131,131,160,160,160,160,160,160,131,131) 62 0 80 160×160 27 754 (136,136,166,166,166,166,166,166,136,136) 70 0 80 160×160 28 827 (149149182182182182182182149149) 75 0 80 160×160 29 1032 (186,186,228,228,228,228,228,228,186,186) 82 0 80 160×160 30 1782 (321,321,393,393,393,393,393,393,321,321) 90 0 80 160×160 31 2438 (439,439,537,537,537,537,537,537,439,439) 157 0 80 160×160

Table 3 Experimental results

Table 4 Comparison of Algorithms

Table 4 is a comparison of algorithms for small-scale, medium-scale and large-scale problems. Based on 5 sets of experiments on small-scale, medium-scale and large-scale problems, the improved adaptive quantum genetic algorithm proposed by the present invention (ie the multi-constraint scheduling method of the card reservation system considering congestion and emission of the present invention) and the traditional genetic algorithm Algorithm comparison. The experimental results show that the solving speed of the algorithm proposed by the present invention is obviously better than that of the traditional genetic algorithm, especially when solving large-scale problems, the calculation time is greatly improved. At the same time, the final target value of the optimal solution obtained by the algorithm of the present invention is obviously better than the target value obtained by the traditional algorithm, which is more in line with the goal of reducing the comprehensive operation cost of the truck company and the port company.

Analysis of the impact of operating costs

The impact of different customer time windows on operating costs

In order to examine the impact of customer working time windows on operating costs, five experiments were carried out on different customer working time windows based on the above model, and the card reservation system of the present invention was compared with that of CHEN et al. (Document 1: CHEN G, GOVINDAN K , YANG Z.Managing truck arrivals with time windows to alleviate gatecongestion at container terminals[J].International Journal of ProductionEconomics,2013,141(1):179–188), MOHAMMAD et al. (Document 2: MOHAMMAD T, NATHAN H, SAMANEH S. Truck appointment systems considering impact to drayage truck tours [J]. Transportation Research Part E: Logistic and Transportation Review, 2018, 116: 208-228) for comparison, Figure 6 shows different customer time windows Changes in operating costs of three card reservation systems and comparative experimental results. It can be seen from Figure 6 that the operating costs of the three card reservation systems increase with the reduction of the time window, and the growth rate of operating costs will also be higher and higher. However, due to the consideration of the morning and evening traffic peaks, the truck reservation system in this paper allocates the reservation truck more reasonably, and the total operating cost is lower than the operating cost of the other two truck reservation systems.

Effects of different durations of time windows on operating costs

The number of port time windows in this paper is 10, and the time of each time window is 1 hour. In order to analyze the impact of the duration of each time window of the port on the operating cost of the entire port and the truck company, experiments were conducted on the above three different truck booking systems (TAS), and the results are shown in Figure 7. For these three truck booking systems, increasing the duration of the port time window will lead to lower operating costs. For the port, the short duration of the time window makes the time error of the truck arriving at the port relatively small, which improves the control of the port. For trucking companies, a long time window will reduce the overall operating cost. However, taking into account uncertain factors such as changes in transportation routes, a time window with a longer duration is more beneficial to the entire system. Compared with the reduction value of the operation cost of the collection card reservation system of Document 1 and the collection card reservation system of Document 2, the reduction value of the operation cost of the collection card reservation system of this paper and the collection card reservation system of Document 2 is smaller, because the duration of the time window It is large enough. The cost considered by the truck reservation system in Reference 2 is for the entire time window, while the truck reservation system in this paper considers the impact on the journey time and emissions of trucks in the morning and evening peak hours. The time window in which the expiry time is approaching. At the same time, when the duration of the time window is greater than 120min, the operating cost of the card reservation system in Reference 2 and the card reservation system in this paper hardly changes. The impact of the arrival time of the collection card is reduced, and at the same time, the possibility of the collection card making an appointment on time can be increased, and the possibility of changing the reservation will also be reduced. However, under the time windows of different durations, the overall operation cost of the card collection reservation system of this embodiment is lower than that of the other two collection card reservation systems.

The impact of different truck turnaround times on operating costs

In order to analyze under different scheduling strategies (Reference 3: PHAN M H, KIM K H. Negotiating truck arrival times among trucking companies and a container terminal [J]. Transportation Research Part E: Logistic and Transportation Review, 2015, 75: 132–144) , the effect of the turnaround time of the truck in the port on the overall operating cost, by dividing the truck turnaround time into five groups (20min, 30min, 40min, 50min, 60min), respectively, for experimental analysis and comparison, the results are shown in Figure 8 . It can be seen from Figure 8 that, under the turnaround time of 20min-60min, the operating cost increases continuously with the increase of the turnaround time. However, when the turnaround time is close to 60 minutes, it can be seen that the operating costs of each card reservation system are approaching. Therefore, when the turnaround time becomes larger and larger, the impact of the turnaround time of the truck on the overall operating cost will decrease. For the same truck reservation system, the longer the truck turnaround time, the higher the comprehensive operating cost. The reason is that the longer the turnaround time is, the less the number of truck operations in one day, which leads to the increase in truck transportation costs and the overall operation of the port. The efficiency is reduced; for different truck reservation systems, since the truck reservation system of this embodiment takes into account the congestion during morning and evening peak periods and the emission under congestion conditions, under the same truck turnaround time, the comprehensive truck reservation system of this embodiment can The operating cost is the lowest, and as the turnaround time of the truck is reduced, the overall operating cost is reduced more. Therefore, the congestion time cost of trucks in the morning and evening peak hours and the environmental pollution costs of truck deceleration and idling cannot be ignored in the design of the entire truck reservation system.

To sum up, the multi-constraint scheduling method of the truck reservation system of the present invention that considers congestion and emissions takes into account the impact of urban traffic congestion on the arrival time of trucks during morning and evening rush hours, and the environment caused by trucks in deceleration and idling states. To solve the pollution cost, a multi-constraint scheduling model for truck reservation based on mixed integer nonlinear programming was established, and an improved adaptive quantum genetic algorithm was used to optimize the solution. The port reduces operating costs. At the same time, the algorithm improves the initialization speed of the algorithm through the combination of real number and qubit encoding. The algorithm adopts a dynamic quantum revolving gate and a strategy of autonomous adjustment of mutation probability according to evolutionary algebra, which can improve the accuracy of the algorithm. Set the accuracy of the card reservation plan solution, and select the best reservation plan at a faster speed.

While the content of the present invention has been described in detail by way of the above preferred embodiments, it should be appreciated that the above description should not be construed as limiting the present invention. Various modifications and alternatives to the present invention will be apparent to those skilled in the art upon reading the foregoing. Accordingly, the scope of protection of the present invention should be defined by the appended claims.

Claims (7)

1. A multi-constraint scheduling method for a card reservation system considering congestion and discharge, characterized in that the method comprises the following steps: S1, set the number of iterations iter=0, initialize all the collection card reservation schemes Q ^iter of the collection card; S2, perform real number coding on all the card reservation schemes Q ^iter of step S1; S3, decoding step S2 coding and generating all card reservation schemes Q ^iter ; S4. Calculate the fitness value f of each collection card reservation scheme; S5. When the number of iterations iter is equal to the preset maximum number of iterations iter _max , output the card reservation scheme corresponding to the maximum fitness value f as the optimal reservation scheme; In the step S5, when the number of iterations iter is less than the preset maximum number of iterations iter _max , step S6 is performed; S6. Use the quantum revolving gate U ^iter to update all the collection card reservation schemes Q ^iter of the collection card; S7, using quantum multi-point crossover and adaptive mutation to update all the collection card reservation schemes Q ^iter of the collection card; S8, make iter=iter+1, go to step S2; In the step S1, all the card-collecting reservation schemes Q ^iter for initializing card-collecting cards are specifically: The maximum number of appointments per day is S, the maximum time window number of the company for each appointment is X, the number of the time window for the s-th appointment is x _s , and the n-th appointment plan of the iter generation The qubit encoding method corresponding to the middle time window number x _s is:

A complete nth reservation scheme is encoded as

The collection of all the truck reservation plans for a truck is:

Among them, α and β are two complex constants, which represent the probability amplitudes of the quantum deviated lower state and deviated upper state respectively, and satisfy the normalization condition |α| ² +|β| ² =1. 2. The multi-constraint scheduling method for a card reservation system considering congestion and discharge as claimed in claim 1, wherein the real number coding in the step S2 is specifically: Generate a random number of [0, 1] for the time window number x _s of each reservation in each card reservation scheme

like

then the bit takes

state, otherwise take

state, of which,

and

are the upper limit and lower limit of the time window number x _s , respectively; The real code of a complete nth card reservation scheme is expressed as

The set of all truck reservation schemes encoded by a truck real number is:

3. The multi-constraint scheduling method for a card reservation system considering congestion and emissions as claimed in claim 2, wherein the decoding described in the step S3 is specifically: The bound encoding of the time window number x _s is expressed as one of two cases:

and

Corresponding to the two value areas of the time window number x _s , let

The size of each area is Δx _s /2, and the collection card reservation plan of the collection card is generated under the constraints of each time window quota and the collection card company. The specific decoding rules are as follows: (1) When

When , the lower limit of the x _s offset value is the value, and the number of the time window can be 0~X/2. At this time

r is a random number between 0 and 1; (2) When

, the upper limit of the offset value of x _s is taken as the upper limit value, and the time window number can be taken as X/2+1～X. At this time

r is a random number within 0-1. 4. The multi-constraint scheduling method for a card reservation system considering congestion and emissions as claimed in claim 3, characterized in that, The fitness value f in the step S4 is the inverse of the cost of each card reservation scheme. 5. The multi-constraint scheduling method for a card reservation system considering congestion and emissions as claimed in claim 4, characterized in that, The cost of each pickup reservation scheme described above includes: the total cost of changing the reservation of all pickup companies, the average waiting cost of pickup at the terminal gate, the additional time cost of pickup congestion during the morning and evening peak hours, and the pickup during the morning and evening peak hours. Congestion and additional environmental pollution costs caused by slowing down and idling when waiting in line at gates. 6. The multi-constraint scheduling method for a card reservation system considering congestion and emissions as claimed in claim 5, wherein the step S6 is specifically: A mechanism of dynamically adjusting the rotation angle is adopted, and the rotation angle gradually decreases with the increase of algebra. For each reservation time window number x _s of each card reservation scheme, the following operations are performed:

Among them, U _{n, s} is the quantum revolving gate, α′ and β′ are the updated complex functions, which constitute the updated reservation scheme for updating the population,

θ _{n, s} is the rotation angle, which is used to control the convergence speed of the algorithm,

r' is a constant between 0 and 1,

is the rotation direction, which is used to ensure the convergence of the algorithm. 7. The multi-constraint scheduling method for a card reservation system considering congestion and emissions as claimed in claim 6, wherein the step S7 is specifically: Perform crossover and mutation operations on the scheduling time window number x _s of each collector reservation scheme to update all collector reservation schemes Q ^iter ; Select two intersections randomly from the two multi-point crossover and mutual pairing reservation schemes, and exchange the part between the intersections, thereby generating two new collection reservation schemes; At the same time, adaptive mutation is adopted, and the amount of change is set to a random integer and opposite to each other. The mutation probability p _m is automatically adjusted according to the evolutionary algebra. The calculation formula is as follows:

where p _max is the maximum mutation probability and p _min is the minimum mutation probability.

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