CN111445084B - Logistics distribution path optimization method considering traffic conditions and double time windows - Google Patents
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Abstract
The invention discloses a logistics distribution path optimization method considering traffic conditions and double time windows, wherein the logistics distribution path comprises a primary distribution path from a distribution center to a plurality of transfer stations and a secondary distribution path from each transfer station to a plurality of demand points; based on the current two-stage logistics distribution mode, the logistics distribution model with double time windows under the traffic condition is established, then the mixed firework algorithm is used for solving the model, an initial population is generated through an insertion algorithm in the solving process, and individuals are updated through cross operation and explosion operation, so that an optimized logistics distribution path can be obtained in a short time, and the effectiveness and the rationality of the logistics distribution path are greatly improved.
Description
Technical Field
The invention belongs to the technical field of logistics management, relates to logistics distribution path planning and vehicle scheduling, and particularly relates to a method for establishing a logistics distribution model with double time windows under a traffic condition by taking the maximum customer satisfaction degree and the minimum distribution cost as targets and obtaining a reasonable logistics distribution scheme by processing through a mixed firework algorithm.
Background
With the development of electronic commerce, logistics plays an important role in people's daily life. In the logistics distribution process, in order to avoid other factors such as damage and unnecessary resource waste caused by large vehicles entering a city, logistics enterprises generally adopt a secondary logistics distribution mode, wherein large vehicles transport goods to various suburbs transfer stations, and then small vehicles transport the goods from the transfer stations to various customers, so as to complete basic logistics distribution, as shown in fig. 1.
After meeting the basic logistics distribution requirements, the logistics enterprises are striving to reduce the distribution cost and improve the customer satisfaction. By summarizing the existing logistics distribution scheme, the factors influencing the customer satisfaction are mainly found to be package breakage and the distribution time, so that many scholars propose a path optimization method with a hard time window and a soft time window based on the limitation of the distribution time. With the continuous development of society, people put higher requirements on logistics distribution, which not only requires the total logistics distribution time, but also requires the time window of the logistics time desired by customers (called as the logistics time window); and meanwhile, the order taking time is required to be within a time range of the day of distribution, namely the time window of customer order taking (called order taking time window). The two time windows constitute a double time window, as shown in FIG. 2, with the horizontal axis representing all times of day and the vertical axis representing the total time taken for the package to pick up orders from the shipments to the customers. Especially, in the bad road condition period, not only the logistics distribution efficiency is reduced and the logistics distribution cost is increased, but also the double time window of the customer requirements is more difficult to meet, thereby influencing the customer satisfaction.
Therefore, how to achieve reasonable distribution under time-varying traffic and double time windows required by customers is a difficult problem for logistics enterprises to reduce distribution cost and improve customer satisfaction. Therefore, it is of great practical significance to research the logistics distribution path optimization with double time windows based on traffic conditions.
Disclosure of Invention
The invention provides a logistics distribution path optimization method considering traffic conditions and double time windows aiming at the technical situations of low logistics distribution efficiency, high distribution cost and poor customer satisfaction under poor traffic conditions and considering double time windows meeting customer requirements.
The invention idea is as follows: based on the current two-level logistics distribution mode, a logistics distribution model with double time windows under the traffic condition is established, the logistics distribution model is processed by utilizing a designed mixed firework algorithm to obtain a logistics distribution path, in order to improve the convergence rate of the mixed firework algorithm, the initial logistics population of the logistics distribution path is further generated by adopting an insertion algorithm, the idea of cross operators is introduced, so that firework individuals can learn each other, and the local position optimizing capability of the logistics distribution path is improved by utilizing the diversity of explosion operators in the firework algorithm.
In order to achieve the above object, the present invention is achieved by the following technical solutions.
The invention provides a logistics distribution path optimization method considering traffic conditions and double time windows, wherein the logistics distribution path comprises a primary distribution path from a distribution center to a plurality of transfer stations and a secondary distribution path from each transfer station to a plurality of demand points; the determination of the logistics distribution path comprises the following steps:
s1 constructs the objective function according to the following formula:
minC＝λ(C1+C2)-(1-λ)CS；
wherein C is the total cost, C1Cost incurred for the distance traveled by the vehicle, C2For penalty cost generated when the vehicle is not in a time window expected by a client or the vehicle is waited to a demand point in advance until the client is satisfied with the expected time window, CS is the average satisfaction degree of the client; lambda is a set control parameter;
s2 generating an initial population
Inserting the demand points into the vehicle in sequence by using an insertion algorithm, taking an insertion position which meets the total route increment requirement when each demand point is inserted, generating a secondary distribution path for completing distribution of all the demand points, then determining a corresponding primary distribution path by an enumeration method according to an objective function, wherein the secondary distribution path and the corresponding primary distribution path form a logistics distribution path, repeating the process to obtain a plurality of logistics distribution paths which serve as initial populations, and each logistics distribution path corresponds to one individual in the initial populations;
s3 obtaining fitness value of each individual in initial population
Constructing a fitness function according to the target function, and calculating the fitness value of each individual in the initial population:
F(L)＝λ(C1+C2)-(1-λ)CS；
f (L) is the fitness value of the Lth individual;
s4 obtaining group optimality
Taking the individual with the minimum fitness value in the initial population as the optimal individual in the initial population, namely the initial optimal delivery path, then entering step S5, and setting the parameter Gen as 1;
s5 obtaining the number of each individual explosion spark in the population
The number of explosion sparks of each individual in the population is obtained according to the following formula:
in the formula, SLNumber of sparks generated for the L-th individual, m being the set maximum number of sparks, F (L) being a fitness value for the L-th individual, FmaxMax { f (L) }, L1, 2, …, n, n is the number of individuals in the population, and epsilon is a very small set constant;
s6 individual updating operation in population
Firstly, performing cross operation on each individual in the population and the optimal individual, and then performing explosion operation on each vehicle of each individual after the cross operation according to the corresponding individual explosion spark number obtained in the step S5 to finish individual updating;
s7 obtaining each individual fitness value again
Constructing a fitness function according to the objective function, and calculating the fitness value of each individual updated in step S6:
F(L′)＝λ(C1+C2)-(1-λ)CS；
f (L ') is the fitness value of the L' th updated individual;
s8 updating population optimality
Taking the individual with the minimum fitness value obtained in the step S7 as an updated optimal individual in the population, namely the current optimal delivery path, then judging whether the parameter Gen reaches the set maximum value, if the Gen does not reach the set maximum value, adding 1 to the current Gen, taking the population formed by the current updated individual as a processing object, and repeating the steps S5-S8; if Gen reaches the maximum value, go to step S9;
s9 output logistics distribution path
And taking the current optimal individual as the logistics distribution path of the final output.
The logistics distribution path optimization method is characterized in that the cost C caused by the running distance of the vehicle1Determined according to the following formula:
wherein D is a distribution center, S is a transfer station set, P is a demand point set, M, N is any two nodes respectively in the union of the distribution center D and the transfer station set S, and c1For first-class vehicle unit distance transportation cost, dMNIs the distance from node M to node N, rMNuIf the first-level vehicle u accesses the node M and then accesses the node N, if yes, 1 is selected, otherwise 0 is selected, I, J are any two nodes in the union set of the demand point set P and the transfer station set S respectively, and c2For second-level vehicle unit distance transportation costs, dIJIs the distance from node I to node J, xIJkAnd if the second-level vehicle k accesses the node J after accessing the node I, 1 is selected, and otherwise, 0 is selected.
The logistics distribution path optimization method generates the penalty cost C which is not generated in the time window expected by the customer or in the time window that the vehicle waits to the time window expected by the customer in advance2Determined according to the following formula:
C2＝c3max(ETi′-t i ,0)+ c3max(ti-LTi′,0)+ c4max(Ti-HTi″,0)；
wherein, c3Penalty cost per unit time for not being in the customer order-receiving time window, c4Penalty cost per time, t, for exceeding the time window of the logistics duration expected by the customeriThe order receiving time of the ith demand point, i belongs to P and ETi′、LTi' lower and upper limits, T, of order taking time window corresponding to the lowest customer satisfaction for demand point iiThe logistics time length of a demand point i belongs to P and HTi"demand point i corresponds to the upper limit of the logistics time window corresponding to the customer satisfaction degree b.
In the method for optimizing the logistics distribution path, the average satisfaction degree CS of the customer is determined according to the following formula:
CSirepresenting the average customer satisfaction of the ith demand point, wherein P is the size of the demand point set P;
wherein, ETi、LTiThe lower limit and the upper limit of the order receiving time window corresponding to the highest customer satisfaction degree corresponding to the demand point i; HTiThe upper limit of the logistics time length time window corresponding to the highest customer satisfaction corresponding to the demand point i, HTi' is the upper limit of a logistics time window corresponding to the demand point i and the customer satisfaction degree a, and beta is a set weight; HTi"is the upper limit of the logistics time window corresponding to the customer satisfaction degree b corresponding to the demand point i, and β is the set weight.
In the logistics distribution path optimization method, in step S2, the demand points are sequentially inserted into the vehicle by using an insertion algorithm, and when a demand point is inserted, one of the positions where the total distance cost is smaller than the increment before the insertion is not performed is taken, so as to generate the secondary distribution path for completing the distribution of all the demand points, thereby avoiding the occurrence of too many repeated paths and affecting the optimization effect. After the second-level distribution path is determined, the demand of each transfer station can be known, and then the corresponding first-level distribution path is determined by an enumeration method to form a solution of the logistics distribution path problem, namely an individual. Solutions to multiple problems were constructed in this way as the initial population. The generation of the initial population specifically comprises the following sub-steps:
s21, newly building a secondary vehicle for each transfer station;
s22, selecting a demand point to be inserted;
s23, judging whether a secondary vehicle can load the goods at the demand point, if so, going to step S24, and if not, going to step S26;
s24, judging whether the number of demand points continuously completing insertion is larger than S, if so, entering step S25, and if not, entering step S27;
s25 generating a random number, if the generated random number is larger than 1/2, go to step S26; if the generated random number is not greater than 1/2, go to step S27;
s26, building a secondary vehicle, and building a secondary vehicle at the transfer station closest to the insertion demand point;
s27 selecting a demand point insertion position, constructing a plurality of secondary distribution paths according to the demand point insertion position, calculating distance cost increment of the plurality of secondary distribution paths relative to the demand point when the demand point is not inserted, and taking one of the first l secondary distribution paths with smaller distance cost increment according to the sequence from small to large; l is a set secondary distribution path selection parameter;
s28, judging whether the insertion of the demand point is finished, if so, entering step S29, and if not, returning to step S22;
s29 individual generation, determining a secondary distribution path between each transfer station and a demand point according to the insertion sequence of the demand point, determining the demand quantity of each transfer station according to the insertion position of the demand point, then determining a primary distribution path between a distribution center and each transfer station according to the demand quantity of each transfer station by using an enumeration method and a target function, wherein the secondary distribution path and the primary distribution path form a logistics distribution path, namely an individual is generated; then, the process goes to step S210;
s210, judging whether the number of individuals reaches a set upper limit, if not, returning to the step S21; if the number of individuals reaches the set upper limit, the generation of the initial population is finished, and the next step S3 is entered.
In the above step S23, if the number of the insertion positions of the demand point is H, the insertion position w of the demand pointzIs determined by:
randperm (H,1) indicates that a natural number from 1 to H is randomly taken one;
randperm (l,1) is from 1 tolOne is randomly taken.
In the method for optimizing a distribution route, in step S5, in order to avoid an excessive or insufficient number of explosion sparks, the number of sparks per individual explosion is further corrected according to the following formula, and the corrected number of sparks is SL′：
In the formula, round () is a rounding function;
and
is a given constant.
In the method for optimizing the logistics distribution path, in step S6, each individual in the population is first crossed with the optimal individual, the individuals learn each other through the crossing operation, and the local position optimizing capability of the logistics distribution path is improved by combining the self-diversity generated by the explosion operation. The method comprises the following steps:
s61 performing cross operation on each individual and the optimal individual in the population
Randomly taking out any sequence in the optimal individuals, replacing any sequence with the same length in other individuals except the optimal individuals in the population by the taken-out sequence, then deleting repeated demand points, and reinserting the demand points which are not served into the vehicle by using an insertion algorithm to form new individuals;
s62 explosion operation for each individual
And (5) carrying out explosion operation on each vehicle of each new individual obtained after the crossing operation in the step (S61) according to the corresponding individual explosion spark number obtained in the step (S5) to finish individual updating.
In step 61, the demand points that are not served need to be inserted at the position where the distance increment after insertion is the minimum according to the insertion algorithm given in step S23.
In step 62, the distribution cost of the new vehicle route is calculated after the vehicle is subjected to the explosion operation, and the new vehicle route with the minimum distribution cost is used to replace the old vehicle route with the higher distribution cost. If the cost of the new vehicle path is higher after the explosion, the vehicle path before the explosion is reserved.
In the logistics distribution path optimization method, in step S8, an iterative loop is implemented by setting a parameter Gen. Through multiple iterations, a more reasonable and effective logistics distribution path can be obtained.
Compared with the prior art, the logistics distribution path optimization method considering the traffic condition and the double time windows has the following beneficial effects:
1. according to the invention, the improved firework algorithm is utilized to process the logistics distribution model with double time windows, the optimized logistics distribution path is obtained, the traffic condition, the logistics duration and the customer order receiving time are taken into consideration, and the effectiveness and the rationality of the logistics distribution path are greatly improved.
2. The initial population of the logistics distribution model is obtained by adopting the insertion algorithm, so that the convergence speed of the firework algorithm is improved.
3. The invention processes the firework units by introducing the cross operation and the explosion operation, so that the firework units can learn each other, and the local position optimizing capability of the logistics distribution path is improved by combining the diversity of the explosion operation.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other embodiments and drawings can be obtained according to the embodiments shown in the drawings without creative efforts.
Fig. 1 is a logistics distribution model.
Fig. 2 is a schematic diagram of distribution of logistics duration time windows and customer order receiving time windows.
Fig. 3 is a schematic flow chart of a logistics distribution path optimization method considering traffic conditions and dual time windows according to an embodiment of the present invention.
Fig. 4 shows the variation of customer satisfaction with order receiving time window (a) and logistics time duration time window (b) according to the embodiment of the invention.
Fig. 5 is a representation of a logistics distribution path model solution according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of a flow of generating an initial population by an insertion algorithm according to an embodiment of the present invention.
FIG. 7 is a schematic diagram of a crossover operation performed by two individuals according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a vehicle undergoing an explosive operation in an individual embodiment of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is to be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
In the embodiment, the optimal delivery path is obtained by constructing a multi-target path planning model with the goals of minimum delivery cost and maximum customer satisfaction. Based on the current secondary logistics distribution mode, the logistics distribution path comprises a primary distribution path from a distribution center to a plurality of transfer stations and a secondary distribution path from each transfer station to a plurality of demand points. The primary distribution path is completed by the primary vehicle, and the secondary distribution path is completed by the secondary vehicle. The present embodiment considers the vehicle path problem in the general case: a total of several transfer stations and demand points, and there is one and only one distribution center in the area, and make the following assumptions:
(2.1) the vehicles distributed in the same level have the same type and enough vehicles;
(2.2) starting the primary vehicles from the distribution center and finally returning to the distribution center;
(2.3) starting secondary vehicles from the transfer station and finally returning to the transfer station at the starting time;
(2.4) the first-level demand can be split and distributed;
(2.5) the goods of the secondary demand point can be distributed by one vehicle only once;
(2.6) exceeding the logistics duration time window, exceeding the order receiving time window and arriving at the demand point in advance for waiting all generate high penalty cost;
(2.7) if the vehicle reaches the demand point in advance, the vehicle needs to wait until the time window with the highest customer satisfaction to be served;
(2.8) once the vehicle has confirmed the demand point serviced, it cannot be changed.
Description of the symbols:
d: a distribution center;
s: a transfer station set;
p: a demand point set;
c: the total cost;
c1: first-class vehicle unit distance transportation cost;
c c 2: second-level vehicle unit distance transportation cost;
c c3: punishment cost per unit time is not carried out in the client order receiving time window;
c c4: penalty cost per unit time exceeding the logistics time duration window expected by the customer;
c Q1: the maximum load of the first-level vehicle;
c Q2: maximum load of the secondary vehicle;
c U: a primary vehicle set;
c K: a set of secondary vehicles;
c qi: demand for demand point i;
c Ti: the logistics time for the goods to reach the demand point i from the distribution center;
c ti: the specific time when the goods arrive at the demand point i (i.e. the order receiving time when the goods are received by the customer);
c HTi: the demand point i corresponds to the upper limit of the logistics time length time window corresponding to the highest customer satisfaction (namely the longest logistics time which can be accepted by the customer corresponding to the demand point i);
c HTi': the customer satisfaction corresponding to the demand point i is the upper limit of the logistics time duration window corresponding to the a;
c HTi"a: the customer satisfaction corresponding to the demand point i is the upper limit of the logistics time duration window corresponding to the customer satisfaction b;
c ETi: the demand point i corresponds to the lower limit of the order receiving time window corresponding to the highest customer satisfaction;
c LTi: the order receiving time upper limit of the order receiving time window corresponding to the highest customer satisfaction degree corresponding to the demand point i
c ETi': the demand point i corresponds to the lower limit of the order receiving time window corresponding to the lowest customer satisfaction;
c LTi': the demand point i corresponds to the upper limit of the order receiving time window corresponding to the lowest customer satisfaction;
c eM′: the demand of the transfer station M';
c zM′u: the traffic of the first-level vehicle u to the transfer station M';
c v1: a first level vehicle speed;
c v2: a secondary vehicle speed;
c 
；
the primary vehicle set U, the secondary measurement set K and the order receiving time t in the related logistics distribution informationiDuration of logistics TiThe required quantity e of the transfer station MMThe amount of traffic z from the first-class vehicle u to the transfer station MMuAnd rMNu、xIJkAnd yikAnd (4) the parameters in the process of optimizing the logistics distribution path are all known conditions.
In logistics distribution, the speed of distribution vehicles is influenced by the quality of traffic conditions. Therefore, the embodiment describes the traffic condition by the parameter, and reflects the actual speed of the vehicle by the product of the maximum speed of the normal running of the vehicle and the traffic condition parameter; given its traffic condition parameter α, the actual speed of the vehicle can be described as equation (1) and equation (2), where V1And V2Maximum speed, v, of normal operation of the primary and secondary vehicles, respectively1And v2The actual speeds of travel of the primary and secondary vehicles are respectively.
v1＝V1×α(1)；
v2＝V2×α(2)。
According to the symbolic illustration and the above scenario description, the method for optimizing logistics distribution paths considering both traffic conditions and dual time windows according to the embodiment is shown in fig. 3, and includes the following steps:
s1 construction of an objective function
Since the present embodiment needs to consider both the dual time windows and the traffic conditions that satisfy the customer requirements, the present embodiment establishes the objective function according to the following formula:
minC＝λ(C1+C2)-(1-λ)CS (3)；
wherein C is the total cost, C1Cost incurred for the distance traveled by the vehicle, C2For penalty cost generated when the vehicle is not in a time window expected by a client or the vehicle is waited to a demand point in advance until the client is satisfied with the expected time window, CS is the average satisfaction degree of the client; lambda is a set control parameter; λ and 1- λ are used to control C1+C2And the specific gravity of CS.
Cost C due to the above-mentioned running distance of the vehicle1Determined according to the following formula:
the penalty cost C generated when the vehicle does not arrive at the demand point in advance within the time window expected by the customer or the vehicle waits until the customer is satisfied with the time window expected by the customer2Determined according to the following formula:
C2＝c3max(ETi′-t i ,0)+ c3max(ti-LTi′,0)+ c4max(Ti-HTi″,0) (5)。
the relationship between the two time windows of the demand point i corresponding to the customer and the customer satisfaction is shown in fig. 4. The following customer satisfaction is established based on the dual time window:
in the formula (6), the first term is the satisfaction degree of the logistics time length, the second term is the satisfaction degree of the order receiving time, beta is a set control parameter, and beta and 1-beta are used for controlling the proportion of the two terms. The customer satisfaction a, b can be set according to the actual demands of the customers.
Thus, the average customer satisfaction for all needs:
the constraint conditions of the objective function are as follows (the following M ', N', f represent transfer stations, i, j, h represent demand points, u represents a primary vehicle, k represents a secondary vehicle, and g represents a distribution center):
tMu+dMN/v1+M0*(1-rMNu)≥tNu,M∈DUS,N∈S,u∈U (23)；
tMu+ dMN/v1-M0*(1-rMNu)≤ tNu,M∈DUS,N∈S,u∈U (24)；
tIk+dIJ/v2+max(ETI′-tIk,0)+max(tMu)+ M0* (1-xIJk)≥tJk,I∈SUP,J∈P,k∈K,u∈U (25)；
tIk+dIJ/v2+max(ETI′-tIk,0)+max(tMu)-M0* (1-xIJk) ≤tJk ,I∈SUP,J∈P,k∈K,u∈U (26)；
equation (8) indicates that the primary vehicle cannot be overloaded. Equation (9) indicates that the secondary vehicle cannot be overloaded. Equations (10) and (11) indicate that the paths of the primary vehicles are consecutive. Equations (12) and (13) indicate that each demand point can only be serviced once by one secondary vehicle. Equation (14) represents that the distribution of the demanded quantity of the transfer station is completed. Equations (15) to (18) indicate that each primary vehicle returns to the departure transfer station through a plurality of demand points after departing from the departure transfer station. Equations (19) to (22) indicate that each secondary vehicle starts from the distribution center and returns to the distribution center through a plurality of transfer stations. Expressions (23) to (29) represent order receiving time t of the customer corresponding to the demand point iiDuration of logistics TiA constraint of (2), wherein tMuIndicating the time of use of the transit station node M of the primary vehicle u (when M is a distribution center node, t)Mu＝0)，tNuTime of arrival of the first-class vehicle u at the transfer station node N, M0Given a sufficiently large number, tIkRepresenting the time of use of the secondary vehicle k to the demand point node I (when I is the transfer station node, t)IkEqual to 0, at this time ETI′＝0)，tJkTime of use, T, representing the arrival of the Secondary vehicle k at the demand Point node J0Indicating the duration of operation of a day (e.g. taking 24h), t0Representing the time (e.g., 8 o' clock) at which the day starts working, floor () representing a floor function, ceil () representing a floor function; for any demand point i in the demand point set P, the time t for the cargo to reach the demand point i can be determined according to the formulas (23) to (27)i' then determining the order taking time t of the customer corresponding to the demand point i according to the formula (28)iFurther determining the logistics time length T of the client corresponding to the demand point i according to the formula (29)i. Equation (30) represents a constraint condition of the demand amount of the transfer station M'.
The expression method of the objective function solution adopts a matrix form, each row represents the distribution sequence of the demand points of one transfer station and the number of the required secondary vehicles or the distribution sequence of the transfer stations of one distribution center and the number of the required primary vehicles, and the size of the matrix is determined according to the number of the vehicles and the number of the demand points served by the vehicles. For a more clear explanation, the explanation is given with reference to fig. 5. In fig. 5, the first row represents that the transfer station 1 needs one secondary vehicle to distribute the packages to 3 demand points, the second row represents that the transfer station 2 needs two secondary vehicles to distribute the packages to 5 demand points, and the third row represents that the distribution center needs two primary vehicles to transport the packages to two transfer stations.
S2 generating an initial population
To solve the vehicle path problem, the embodiment designs a hybrid fireworks algorithm (HFWA) optimized from bottom to top, which first generates the path of the secondary vehicle to determine the demand of the transfer station, and then optimizes the path of the primary vehicle.
In order to improve the convergence rate of the algorithm, the step of generating a better initial population by adopting an insertion algorithm specifically comprises the following steps: and sequentially inserting the demand points into the vehicle by using an insertion algorithm, and taking an insertion position which meets the total distance cost increment requirement when each demand point is inserted so as to generate a secondary distribution path for completing distribution of all the demand points, and then determining a corresponding primary distribution path by an enumeration method according to an objective function, wherein the secondary distribution path and the corresponding primary distribution path form a solution of a logistics distribution path problem, namely an individual. By repeating the above process, a plurality of feasible solutions to the problem, i.e. a plurality of individuals, can be obtained, and when the number of individuals reaches a certain number, an initial population is formed.
The specific process of generating the initial population, as shown in fig. 6, includes the following sub-steps:
s21 creates a new secondary vehicle for each transfer station.
When all the demand points are inserted into the secondary vehicles according to the set insertion sequence, the vehicles are fixed, and the corresponding transfer stations are determined. Therefore, a second-class vehicle is first newly built for each transfer station to facilitate the insertion of the subsequent demand points.
S22 selects a demand point to be inserted.
The first demand point to be inserted in the step is inserted randomly, and the selection of the subsequent demand point takes the closest distance from the last demand point to be inserted as a criterion; of course, the insertion may be performed in accordance with a set order of insertion of the demand points.
S23 judges whether or not there is a secondary vehicle capable of loading the demand point cargo, and if so, the process proceeds to step S24, and if not, the process proceeds to step S26.
The secondary vehicle capable of loading the goods at the demand point is determined according to the constraint conditions, and when no secondary vehicle capable of loading the goods at the demand point exists, the vehicle needs to be newly built. When there is a secondary vehicle capable of loading the cargo at the point of demand, it is also necessary to select an appropriate position for insertion.
S24 judges whether the number of demand points for completing insertion is larger than S, if so, the step S25 is executed, and if not, the step S27 is executed.
S25 generating a random number, if the generated random number is larger than 1/2, go to step S26; if the generated random number is not greater than 1/2, the process proceeds to step S27.
In order to avoid falling into local optimization, the embodiment randomly generates a random number after inserting a plurality of demand points by using an insertion algorithm, and then determines whether a new secondary vehicle is needed according to whether the random number is greater than 1/2.
S26, building a secondary vehicle, and building a secondary vehicle at the transfer station closest to the insertion demand point.
In this embodiment, when a secondary vehicle is newly built, in view of transportation cost, a secondary vehicle is newly built at a transfer station closest to a demand point to be inserted.
S27 selecting insertion position of demand point, constructing multiple secondary distribution paths according to the insertion position of demand point, and calculating multiple secondary distribution pathsThe distance is relative to the distance cost increment when the demand point is not inserted, and the front with smaller distance cost increment is taken according to the sequence from small to largelOne of the secondary distribution paths;land selecting parameters for the set secondary distribution path.
For each demand point, any secondary vehicle in the transfer station meeting the requirement can be selected according to the constraint condition corresponding to the objective function, so that multiple choices are generated, multiple secondary distribution paths are provided, in order to improve the convergence speed, in the embodiment, the total distance cost increment of all the demand points before and after the demand point is inserted is chosen to be chosen, and the front distance cost increment is smallerlOne of the secondary distribution paths.lCan be set and adjusted according to the initial population size and the number of demand points, and is generally 3 or 4.
If the number of the demand point insertable positions to be inserted is H, the insertion position w z of the demand point is determined by:
randperm (H,1) indicates that a natural number from 1 to H is randomly taken one;
randperm (l,1) is from 1 tolOne is randomly taken.
That is, the number of insertable positions H when the required point to be inserted is not more than the setting parameterlThen, the pluggable position takes one of the front H according to the total distance cost increment sequence; when the number H of the insertion-capable positions of the demand point to be inserted is more than the set parameterlThe insertable position is taken forward according to the total distance cost increment sequencelThereby completing the insertion of one demand point.
S28 judges whether the insertion of the demand point is completed, if so, the process goes to step S29, and if not, the process returns to step S22.
After all the demand points are inserted, the demand quantity of each transfer station and the secondary distribution path from each transfer station to the demand points can be determined.
S29 individual generation, determining a secondary distribution path between each transfer station and a demand point according to the insertion sequence of the demand point, determining the demand quantity of each transfer station according to the insertion position of the demand point, then determining a primary distribution path between a distribution center and each transfer station according to the demand quantity of each transfer station by using an enumeration method and a target function, wherein the secondary distribution path and the primary distribution path form a logistics distribution path, namely an individual is generated; and then proceeds to step S210.
After all the demand points are inserted, the demand of the secondary distribution path and each transfer station can be determined, and then the primary distribution path needs to be determined. In this embodiment, an enumeration method is adopted, that is, all possible primary distribution paths are listed one by one, the default distribution time starts from 0, and then the primary distribution path that minimizes the objective function is determined according to the objective function and the corresponding constraint condition. And forming a corresponding solution matrix (namely a feasible logistics distribution path) by the secondary distribution paths and the corresponding primary distribution paths, wherein each row in the matrix represents the distribution sequence of each demand point of one transfer station and the number of required secondary vehicles or the distribution sequence of each transfer station of one distribution center and the number of required primary vehicles, namely forming a solution of the logistics distribution problem.
S210, judging whether the number of individuals reaches a set upper limit, if not, returning to the step S21; if the number of individuals reaches the set upper limit, the generation of the initial population is finished, and the next step S3 is entered.
In order to improve the effectiveness and the reasonableness of optimizing the logistics distribution path by using a firework algorithm, enough initial individuals are still needed to serve as initial populations, and then firework individuals are learned mutually. For this reason, the present embodiment sets the initial population size (i.e., the upper limit of the number of individuals in the initial population) according to the required point number. And then repeating the steps S21-S29, constructing a plurality of feasible solutions for solving the problem, and taking all the possible solutions as an initial population, wherein each solution is an individual in the initial population.
For example: comprising a distribution center D and two transfer stations
And
the demand point is
Set uplThe upper limit of the number of individuals in the initial population is 300, with s being 5. From which the demand point (S) is selected as the first insertion demand point (assuming that the constraints are all satisfied), the selectable insertion positions include, according to steps S21-S27
A first step of
Two (i.e., H-2), H < l, and thus, from the secondary vehicle path
First, and
selecting one, e.g.
First, add it to solution matrix to get the last page
(r) then continue to insert the next demand point. When the demand point nearest to the first is
To be provided with
As the second demand point to be inserted (assuming that the constraints are all satisfied), the second demand point insertable position includes, in accordance with steps S21 to S27
① 
A first step of
Thus, there are three insertable positions for the second demand point (i.e., H-3), H-l, where the secondary vehicle path is followed
①
A first step of
Optionally one selected, e.g.
And adding it to the solution matrix to obtain
……。
After the demand point to be inserted is selected or five demand points (i.e. s is 5) are inserted, whether a secondary vehicle is newly built needs to be judged, and if the secondary vehicle needs to be newly built, the point to be inserted is continuously inserted by adopting the insertion algorithm after the secondary vehicle is completely newly built. And repeating the steps until all the demand points are inserted, obtaining a plurality of secondary distribution paths for completing distribution of all the demand points, and adding the secondary distribution paths into corresponding solution matrixes.
After all the demand points are inserted, the demand of the secondary distribution path and each transfer station can be determined, and then the primary distribution path is determined. In this embodiment, an enumeration method is adopted, that is, all possible primary distribution paths are listed one by one, and then the primary distribution path with the minimum objective function is determined according to the objective function and the corresponding constraint condition. And adding the determined first-level distribution path into a corresponding solution matrix to obtain a feasible logistics distribution path, namely a solution for forming the logistics distribution problem. A plurality of feasible solutions for solving the problem are constructed by the method, and all the possible solutions are used as an initial population, wherein each solution is an individual in the initial population.
S3, obtaining the fitness value of each individual in the initial population.
Constructing a fitness function according to the target function, and calculating the fitness value of each individual in the initial population:
F(L)＝λ(C1+C2)-(1-λ)CS (30)；
f (L) is the fitness value of the Lth individual.
Each individual is a determined logistics distribution path, the default distribution time is started from 0, and the demand point i at the time corresponds to the order receiving time t of the clientiDuration of logistics TiCan be calculated from the running distance and the running speed of the vehicle according to the required point insertion position, and thus can obtain C according to the foregoing equations (4) to (7)1，C2And CS, and thus a fitness value of each individual can be obtained according to equation (30).
S4 obtaining population optima.
The individual with the smallest fitness value f (l) in the initial population is used as the optimal individual in the initial population, i.e., the initial optimal delivery route, and then the process proceeds to step S5, and the parameter Gen is set to 1.
The following steps S5 and S6 are to perform the updating operation on the individuals in the initial population, and it is necessary to perform the crossing operation on each individual in the population and the optimal individual, and then perform the explosion operation on each individual after the crossing operation.
S5 obtains the number of explosive sparks per individual in the population.
The number of explosion sparks per individual in the population is obtained according to the following equation (31):
in the formula, SLNumber of sparks generated for the L-th individual, m being the set maximum number of sparks, F (L) being a fitness value for the L-th individual, Fmax＝max{F (L) }, L ═ 1, 2, …, n, n is the number of individuals in the population, and epsilon is a very small set constant to avoid denominations of zero.
Further, in the present embodiment, in order to limit the number of sparks from being too large or too small, the number of sparks is corrected by the following equation (32) so that the corrected number of sparks is SL′：
In the formula, round () is a rounding function;
and
is a given constant.
And S6, updating the individuals in the population.
Firstly, each individual in the population is subjected to cross operation with the optimal individual, then each vehicle of each individual after the cross operation is subjected to explosion operation according to the corresponding individual explosion spark number obtained in the step S5, and the individual updating is completed, wherein the method specifically comprises the following steps:
and (S61) performing cross operation on each individual in the population and the optimal individual.
Randomly taking out any segment of sequence in the optimal individual, replacing any segment of sequence with the same length in other individuals except the optimal individual in the population by the taken-out sequence, then deleting repeated demand points, and reinserting the demand points which are not served into the vehicle by using an insertion algorithm to form a new individual.
For example: fig. 7 shows two individuals: individual 1 and individual 2, with individual 1 being the optimal individual. Three demand points (2, 3, 4) in the virtual frame of the individual 1 and three demand points (1, 5, 4) in the individual 2 are mutually replaced. Since the demand points (1, 5) originally exist in the original individual 1, the demand points (5, 1) in the original individual 1 need to be deleted, and two demand points (2, 3) which are not served are generated, so that the demand points (2, 3) need to be reinserted into the individual 1, and a new individual 1 is obtained. Similarly, since the demand points (2, 3) originally exist in the original individual 2, the demand points (2, 3) in the original individual 2 need to be deleted, and two demand points (1, 5) which are not served are generated, so that the demand points (1, 5) need to be reinserted into the individual 2, thereby obtaining a new individual 2.
For the generated demand points which are not served, any position which can be inserted, and the position where the repeated demand points are deleted is not necessary. At this time, the demand points which are not served need to be inserted at the position with the minimum distance cost after insertion according to the insertion algorithm given in the previous steps S23 to S29.
S62 performs an explosion operation for each individual.
And (5) carrying out explosion operation on each vehicle of each new individual obtained after the crossing operation in the step (S61) according to the corresponding individual explosion spark number obtained in the step (S5) to finish individual updating.
In the embodiment, for an individual, each primary vehicle and each secondary vehicle comprise the explosion spark number (S) calculated according to the front of the individualLOr SL') performing an explosive operation. The explosion operation of the vehicle is to randomly displace a plurality of random positions of corresponding quantity on the vehicle according to the spark number to obtain a new vehicle path, wherein the displacement is not limited. Then, the distribution cost of the new vehicle route is calculated, and the new vehicle route with the minimum distribution cost is used for replacing the old vehicle route with the higher distribution cost. If the cost of the new vehicle path is higher after the explosion, the vehicle path before the explosion is reserved.
For example: as shown in fig. 8, for a vehicle, the number of explosion sparks is 2, and the position 1 (corresponding to the demand point 2) and the position 2 (corresponding to the demand point 8) on the vehicle are randomly displaced, in this embodiment, the demand point 8 is moved to the position 1, and the demand point 2 is moved to the position 2, so that a new vehicle path is obtained. Mainly for explaining the explosion process, in actual operation, the position shift displacement of the demand point may be random.
S7 acquires each individual fitness value again.
After each vehicle of each individual is subjected to explosion operation, updating of each individual is completed, and a new individual, namely a solution of a new logistics distribution path, is obtained.
At this time, the updated fitness value for each new individual needs to be recalculated.
Here, the fitness function is still constructed according to the objective function, and the fitness value of each individual after being updated in step S6 is calculated:
F(L′)＝λ(C1+C2)-(1-λ)CS (33)；
f (L ') is the fitness value of the L' th updated individual.
Each individual is the determined logistics distribution path, the default distribution time starts from 0, and the demand point i at the time corresponds to the order receiving time t of the clientiDuration of logistics TiCan be calculated from the running distance and the running speed of the vehicle according to the demand point insertion position, and thus can obtain C according to the above equations (4) to (7)1，C2And CS, and thus the fitness value for each new individual can be obtained according to equation (33).
S8 updates population optimal.
Taking the individual with the minimum fitness value obtained in the step S7 as an updated optimal individual in the population, namely the current optimal delivery path, then judging whether the parameter Gen reaches the set maximum value, if the Gen does not reach the set maximum value, adding 1 to the current Gen, taking the population formed by the current updated individual as a processing object, and repeating the steps S5-S8; if Gen reaches the maximum value, the process proceeds to step S9.
In this embodiment, an iterative loop is implemented by setting a parameter Gen. Through multiple iterations, a more reasonable and effective logistics distribution path can be obtained. One skilled in the art can select an appropriate upper limit for the number of iterations as desired.
S9 outputs the logistics distribution path.
When the parameter Gen reaches the maximum value (i.e. the iterative loop is completed), the currently optimal individual is taken as the logistics distribution path of the final output.
The embodiment establishes a logistics distribution model with double time windows under the condition of traffic conditions, processes the logistics distribution model by utilizing a designed mixed firework algorithm to obtain a logistics distribution path, and improves the convergence speed of the mixed firework algorithm by an insertion algorithm, so that the optimized logistics distribution path can be obtained in a short time; and the individual cross operation is introduced, so that fireworks individuals can learn each other, and the local position optimizing capability of the logistics speed distribution path is improved by utilizing the diversity of the explosion operators in the fireworks algorithm. The method provided by the invention not only can obtain the optimized logistics distribution path, ensure the effectiveness and rationality of logistics distribution, but also can greatly reduce the number of iterative cycles, thereby improving the optimization efficiency of the logistics distribution path.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (5)
1. A logistics distribution route optimization method considering traffic conditions and double time windows comprises a primary distribution route from a distribution center to a plurality of transfer stations and a secondary distribution route from each transfer station to a plurality of demand points; characterized in that the determination of the logistics distribution path comprises the following steps:
s1 constructs the objective function according to the following formula:
minC＝λ(C1+C2)-(1-λ)CS；
wherein C is the total cost, C1Cost incurred for the distance traveled by the vehicle, C2For penalty cost generated when the vehicle is not in a time window expected by a client or the vehicle is waited to a demand point in advance until the client is satisfied with the expected time window, CS is the average satisfaction degree of the client; lambda is a set control parameter;
wherein D is a distribution center, S is a transfer station set, P is a demand point set, M, N is any two nodes respectively in the union of the distribution center D and the transfer station set S, and c1For first-class vehicle unit distance transportation cost, dMNIs the distance from node M to node N, rMNuIf the first-level vehicle u accesses the node M and then accesses the node N, if yes, 1 is selected, otherwise, 0 is selected, I, J is any two nodes in the union set of the demand point set P and the transfer station set S, and c2For second-level vehicle unit distance transportation costs, dIJIs the distance from node I to node J, xIJkIf the second-level vehicle k accesses the node J after accessing the node I, 1 is selected if the second-level vehicle k accesses the node I, and 0 is selected if the second-level vehicle k accesses the node J;
C2＝c3max(ETi′-ti,0)+ c3max(ti-LTi′,0)+ c4max(Ti-HTi″,0)；
in the formula, c3Penalty cost per unit time for not being in the customer order-receiving time window, c4Penalty cost per time, t, for exceeding the time window of the logistics duration expected by the customeriThe order receiving time of the ith demand point, i belongs to P and ETi′、LTi' lower and upper limits, T, of order taking time window corresponding to the lowest customer satisfaction for demand point iiThe logistics time length of a demand point i belongs to P and HTi"is the upper limit of the logistics time duration time window corresponding to the customer satisfaction degree of the demand point i as b;
in the formula, CSiThe average customer satisfaction of the demand points i, and P is the size of the demand point set P;
in the formula, ETi、LTiThe lower limit and the upper limit of the order receiving time window corresponding to the highest customer satisfaction degree corresponding to the demand point i; HTiThe upper limit of the logistics time length time window corresponding to the highest customer satisfaction corresponding to the demand point i, HTi' the customer satisfaction corresponding to the demand point i is the upper limit of the logistics time duration window corresponding to a, and beta is a set weight;
s2 generating an initial population
Inserting the demand points into the vehicle in sequence by using an insertion algorithm, taking an insertion position which meets the total route increment requirement when each demand point is inserted, generating a secondary distribution path for completing distribution of all the demand points, then determining a corresponding primary distribution path by an enumeration method according to an objective function, wherein the secondary distribution path and the corresponding primary distribution path form a logistics distribution path, repeating the process to obtain a plurality of logistics distribution paths which serve as initial populations, and each logistics distribution path corresponds to one individual in the initial populations;
s3 obtaining fitness value of each individual in initial population
Constructing a fitness function according to the target function, and calculating the fitness value of each individual in the initial population:
F(L)＝λ(C1+C2)-(1-λ)CS；
f (L) is the fitness value of the Lth individual;
s4 obtaining group optimality
Taking the individual with the minimum fitness value in the initial population as the optimal individual in the initial population, namely the initial optimal delivery path, then entering step S5, and setting the parameter Gen as 1;
s5 obtaining the number of explosion sparks of each individual in the population
The number of explosion sparks of each individual in the population is obtained according to the following formula:
in the formula, SLFor L individual to give birthNumber of sparks generated, m is the set maximum number of sparks, F (L) is the fitness value of the L-th individual, FmaxMax { f (L) }, L1, 2, …, n, n is the number of individuals in the population, and epsilon is a very small set constant;
s6 individual updating operation in population
Firstly, performing cross operation on each individual in the population and the optimal individual, and then performing explosion operation on each vehicle of each individual after the cross operation according to the corresponding individual explosion spark number obtained in the step S5 to finish individual updating;
s7 again obtains each individual fitness value
Constructing a fitness function according to the objective function, and calculating the fitness value of each individual updated in step S6:
F(L′)＝λ(C1+C2)-(1-λ)CS；
f (L ') is the fitness value of the L' th updated individual;
s8 updating population optimality
Taking the individual with the minimum fitness value obtained in the step S7 as an updated optimal individual in the population, namely the current optimal delivery path, then judging whether the parameter Gen reaches the set maximum value, if the Gen does not reach the set maximum value, adding 1 to the current Gen, taking the population formed by the current updated individual as a processing object, and repeating the steps S5-S8; if Gen reaches the maximum value, go to step S9;
s9 output physical distribution path
And taking the current optimal individuals as the logistics distribution path of the final output.
2. The method for optimizing logistics distribution path with consideration of traffic conditions and dual time windows as claimed in claim 1, wherein the step S2 comprises the following sub-steps:
s21, newly building a secondary vehicle for each transfer station;
s22, selecting a demand point to be inserted;
s23, judging whether a secondary vehicle can load the goods at the demand point, if so, going to step S24, and if not, going to step S26;
s24, judging whether the number of demand points continuously completing insertion is larger than S, if so, entering step S25, and if not, entering step S27;
s25 generating a random number, if the generated random number is larger than 1/2, go to step S26; if the generated random number is not greater than 1/2, go to step S27;
s26, building a secondary vehicle, and building a secondary vehicle at the transfer station closest to the insertion demand point;
s27 selecting insertion position of demand point, constructing multiple secondary distribution paths according to the insertion position of demand point, calculating distance cost increment of multiple secondary distribution paths relative to the demand point when the demand point is not inserted, and taking front with smaller distance cost increment according to the sequence from small to biglOne of the secondary distribution paths;lselecting parameters for the set secondary distribution path;
s28, judging whether the insertion of the demand point is finished, if so, entering step S29, and if not, returning to step S22;
s29 individual generation, determining a secondary distribution path between each transfer station and a demand point according to the insertion sequence of the demand point, determining the demand quantity of each transfer station according to the insertion position of the demand point, then determining a primary distribution path between a distribution center and each transfer station according to the demand quantity of each transfer station by using an enumeration method and a target function, wherein the secondary distribution path and the primary distribution path form a logistics distribution path, namely an individual is generated; then, the process goes to step S210;
s210, judging whether the number of individuals reaches a set upper limit, if not, returning to the step S21; if the number of individuals reaches the set upper limit, the generation of the initial population is finished, and the next step S3 is entered.
3. The method for optimizing logistics distribution paths with consideration of traffic conditions and dual time windows as claimed in claim 2, wherein in step S23, if the number of insertion positions of demand points is H, the insertion position w of the demand point iszIs determined by:
randperm (H,1) indicates that a natural number from 1 to H is randomly taken one;
randperm (l,1) is from 1 tolOne is randomly taken.
4. The method as claimed in claim 1, wherein the number of sparks per individual explosion is further modified according to the following formula in step S5, and the modified number of sparks is SL′：
In the formula, round () is a rounding function;
and
is a given constant.
5. The method for optimizing logistics distribution paths with consideration of traffic conditions and dual time windows according to any one of claims 1 to 4, wherein the step S6 comprises the following sub-steps:
s61 performing cross operation on each individual and the optimal individual in the population
Randomly taking out any sequence in the optimal individuals, replacing any sequence with the same length in other individuals except the optimal individuals in the population by the taken-out sequence, then deleting repeated demand points, and reinserting the demand points which are not served into the vehicle by using an insertion algorithm to form new individuals;
s62 explosion operation for each individual
And (5) carrying out explosion operation on each vehicle of each new individual obtained after the crossing operation in the step (S61) according to the corresponding individual explosion spark number obtained in the step (S5) to finish individual updating.
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