CN114707693A - Vehicle distribution path planning method and system - Google Patents
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Abstract
The invention relates to a vehicle distribution path planning method and a system, firstly, acquiring and acquiring node position information, customer information and vehicle information of a distribution center, and establishing a target function by taking the shortest total distribution vehicle mileage as a target; and then, obtaining an initial solution through a scanning algorithm, taking the objective function as a target value, and selecting an optimal vehicle distribution path by combining an improved large-scale neighborhood search algorithm and a Metropolis criterion. The optimal distribution path of the vehicle can be screened out by utilizing the improved large-scale neighborhood search algorithm, so that a more reasonable distribution path scheme is formulated, the distribution efficiency is improved, the total distribution mileage of the vehicle is greatly reduced, and the working intensity of manually formulating the scheme is reduced.
Description
Technical Field
The invention relates to the field of goods distribution, in particular to a large-scale vehicle distribution path planning method and system based on an improved self-adaptive large-scale neighborhood search algorithm.
Background
The study of vehicle paths is a hot problem in the last decade, and has become a development trend of logistics distribution. The method is closely related to resource distribution and path planning in actual life, and mainly solves the problem of how to reasonably plan and determine the optimal vehicle path when a plurality of distribution vehicles with capacity limitation serve a plurality of client nodes. With the increase of the scale of the distribution problem, that is, the number of the distribution client nodes increases, the preparation of the distribution scheme becomes more complex, and the existing scheme generally depends on manual experience, but the distribution scheme with a better vehicle route is difficult to obtain only by the manual experience, which causes waste of labor and time.
Therefore, there is a need in the art for a planning scheme for optimal delivery paths of vehicles that can be used for large-scale customers.
Disclosure of Invention
The invention aims to provide a vehicle distribution path planning method and a vehicle distribution path planning system, which select the distribution limit of the maximum load capacity of a vehicle, take a vehicle path problem with capacity constraint as a model of vehicle distribution, aim at the shortest distribution mileage of each vehicle in a distribution scheme, and introduce an improved large-scale neighborhood search algorithm to select an optimal distribution path, thereby making a reasonable distribution path scheme and reducing the working intensity of manually making the scheme.
In order to achieve the purpose, the invention provides the following scheme:
a vehicle delivery path planning method, the method comprising:
acquiring node position information, customer information and vehicle information of a distribution center; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: vehicle number and vehicle maximum load information;
establishing an objective function taking the shortest total vehicle delivery mileage as a target according to the distribution center node position information, the customer information and the maximum vehicle load information; the constraint condition of the objective function is that each customer is served by one vehicle and the total amount of customer demand served by each vehicle does not exceed the load of the vehicle;
determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node;
calculating a target value of the initial coding sequence according to the target function;
calculating the initial temperature of the Metropolis criterion according to the target value of the initial coding sequence, and starting the iteration of the optimal distribution path;
the iteration of the optimal delivery path specifically includes:
selecting a removal operator and an insertion operator by using a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; the current solution in the first iteration process is the initial coding sequence;
if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is an initial temperature value;
updating the corresponding operator weights according to the use times and preset scores of each insert operator and each removal operator, wherein the updating interval is the preset iteration times;
and stopping iteration until the target value of the local solution is not less than the iteration frequency of the current solution and reaches a preset frequency, and outputting the optimal coding sequence of the vehicle.
In some embodiments, the objective function targeting the shortest total delivered vehicle range is:
wherein F represents an objective function; m is the maximum number of vehicles that can be used for delivery; n is the number of customers; dijRepresents the distance between any two nodes i and j; x is the number ofijkA plan for 0-1 indicates whether vehicle k passes nodes i and j, 0 indicates that vehicle k does not pass nodes i and j, and 1 indicates that vehicle k passes nodes i and j.
In some embodiments, the determining the initial coding sequence specifically includes:
establishing a polar coordinate system by taking the position of a distribution center node as a pole and taking a ray where the distribution center node and a customer node closest to the distribution center node are located as a polar axis, and converting the position coordinates of the distribution center node and the customer node into polar coordinates;
sequencing the client nodes according to the polar angle size;
on the premise of meeting the constraint condition, sequentially inserting each client node into the solution according to the objective function; the solution comprises a plurality of delivery paths; in the inserting process, if a client node which does not satisfy the constraint condition is encountered and the client node which does not satisfy the constraint condition is not the last client node, skipping the client node which does not satisfy the constraint condition;
searching whether a client node j is not inserted, and if so, sequentially calculating the insertion cost c of the client node j inserted between every two client nodes in each distribution pathijAnd inserting between two client nodes corresponding to the lowest cost; wherein, cij＝di,j+dj,i+1-di,i+1(ii) a In the formula (d)i,jRepresents the distance between client node i and client node j, dj,i+1Represents the distance between client node j and client node i +1, di,i+1Representing the distance between the client node i and the client node i + 1;
and traversing all the client nodes which are not inserted until all the client nodes are inserted into the solution to obtain an initial coding sequence.
In some embodiments, the calculating the initial temperature of the Metropolis criterion according to the target value in the initial coding sequence specifically includes:
calculating the initial temperature T of Metropolis criterion according to the target value in the initial coding sequence0；
The initial temperature T0When the reception probability of the poor solution is η, the poor solution is received by β% from the current target value f (x), and the corresponding temperature is T0。
In some embodiments of the present invention, the,
the random client node removal specifically includes: if the current solution has the infeasible subpath solution, randomly removing the client nodes in the infeasible subpath until the sum of the client demands does not exceed the maximum load of the vehicle; if the number of the removed client nodes does not exceed the removal upper limit, selecting random client nodes to remove the client nodes until the number of the removed client nodes reaches the removal upper limit; the unfeasible sub-path solution, namely the sum of the customer demands of the sub-paths is larger than the maximum load of the vehicle; the removal upper limit is generated by a random function;
the random sub-path removal specifically includes: if the current solution has the solution of the non-feasible sub-path, removing the non-feasible sub-path; if the number of the removed client nodes does not exceed the removal upper limit, selecting a random sub-path for removal until the number of the removed client nodes reaches the removal upper limit;
the similar client node removing specifically includes: randomly selecting a client node i in the current solution, calculating the similarity between the client node i and other client nodes j, and sequentially removing the client nodes with the maximum similarity until the number of the removed client nodes reaches the removal upper limit;
the ring region similarity removal specifically comprises: calculating similarity based on three spatial relations among the annular regions where the sub paths are located in the current solution;
the similarity between the two sub-paths is:
wherein σ1>σ2>σ3，siAnd sjRepresenting two sub-paths r in the current solutioniAnd rjCorresponding to the ring region, then a single sub-path riThe similarity coefficient of (a) is:
in that
The sub-path r with the maximum similarity coefficient is selectedm xSelecting sub-paths r of non-maximum similarity coefficient by roulettedThen removing rm xAnd rdThe Chinese herbal medicineThere is a client node that is connected to the client node,
representing the similarity coefficient set of all sub-paths, wherein l represents the total number of sub-paths in the current solution;
the cost greedy insertion specifically comprises: inserting each removed customer node into a sub-path of the current solution, wherein each insertion selects the sub-path with the minimum insertion cost and meeting load limitation;
the regret value insertion specifically includes: inserting each removed client node into a sub-path of the current solution, and selecting the sub-path with the maximum regret value to insert each time; the regret value is as follows: Δ c ═ cm2-cm1Wherein c ism1Denotes the minimum insertion cost, cm2Representing the next smallest insertion cost.
In some embodiments, the update formula of the operator weight is:
where τ denotes the interval τ iterations, y denotes the ith iteration interval, q denotes the qth operator,
representing the number of times of use of the operator q in tau iterations, with a corresponding predetermined score
In the y iteration interval, the operator weight corresponding to the q operator is as follows
In the (y + 1) th iteration interval, the operator weight corresponding to the q-th operator is as
μ∈[0,1]The factor is used for controlling the influence of the operator, and the smaller the value is, the greater the influence of the weight of the y iteration interval on the weight updating of the y +1 iteration interval is; if μ is 0, the weight is completely dependent on the weight of the last iteration interval; if μ is 1, only the intra-iteration interval score is considered, if 0<μ<1, the score in the iteration interval and the previous weight value are considered simultaneously.
In some embodiments, before said determining the initial coding sequence, further comprising:
and carrying out chromosome coding on the distribution center node and each client node.
In some embodiments, the updated formula for the temperature value is: t ═ α
Wherein T' represents the updated temperature, T represents the current temperature before updating, alpha belongs to (0,1) as the cooling speed, and the value of alpha is a preset constant parameter.
In some embodiments, the probabilistically accepting a local solution according to Metropolis criterion in combination with the temperature value of the iteration includes:
according to Metropolis criterion, combining the temperature value of the iteration, and receiving a local solution with probability of receiving the local solution
Wherein, PΔValue of (1) and [0,1]Random number r in between, if PΔAnd r, receiving a poor solution as a current solution of the next iteration, wherein T represents the current temperature, f (x) represents a target value of the current solution x, and f (x ') represents a target value of the local solution x'.
The invention also provides a vehicle delivery path planning system, which comprises:
the information acquisition module is used for acquiring the position information, the customer information and the vehicle information of the distribution center node; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: vehicle number and vehicle maximum load information;
the target function determining module is used for establishing a target function taking the shortest total vehicle delivery mileage as a target according to the distribution center node position information, the customer information and the maximum vehicle load information; the constraint condition of the objective function is that each customer is served by one vehicle and the total amount of customer demand served by each vehicle does not exceed the load of the vehicle;
the initial solution construction module is used for determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node;
the initial solution target value calculation module is used for calculating a target value of the initial coding sequence according to the target function;
the optimal distribution path iteration module is used for calculating the initial temperature of the Metropolis criterion according to the target value of the initial coding sequence and starting the optimal distribution path iteration;
the iteration of the optimal delivery path specifically includes:
selecting a removal operator and an insertion operator by using a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; the current solution in the first iteration process is the initial coding sequence;
if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is an initial temperature value;
updating the corresponding operator weights according to the using times and preset scores of each insert operator and each removal operator, wherein the updating interval is the preset iteration times;
and stopping iteration until the target value of the local solution is not less than the iteration frequency of the current solution and reaches a preset frequency, and outputting the optimal coding sequence of the vehicle.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a vehicle distribution path planning method and a system, firstly, acquiring and acquiring node position information, customer information and vehicle information of a distribution center, and establishing a target function by taking the shortest total distribution vehicle mileage as a target; and then, obtaining an initial solution through a scanning algorithm, determining a target value of an initial coding sequence by using a target function, and selecting an optimal vehicle distribution path by using an improved large-scale neighborhood search algorithm in combination with a Metropolis criterion. The invention can screen the optimal distribution path of the vehicle by utilizing the improved large-scale neighborhood search algorithm, thereby formulating a more reasonable distribution path scheme, improving the distribution efficiency, greatly reducing the total distribution mileage of the vehicle and reducing the working intensity of manually formulating the scheme.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a vehicle distribution route planning method according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a distribution center and positions of nodes according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a spatial relationship between two sub-paths and an annular region according to an embodiment of the present invention.
Fig. 4 is a schematic view of a client node for completing all delivery tasks and services required by 4 vehicles according to an embodiment of the present invention.
Fig. 5 is a block diagram of a vehicle distribution route planning system according to a second embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious 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.
The invention aims to provide a vehicle distribution path planning method and a vehicle distribution path planning system, which select the distribution limit of the maximum load capacity of a vehicle, take a vehicle path problem with capacity constraint as a model of vehicle distribution, aim at the shortest distribution mileage of each vehicle in a distribution scheme, and introduce an improved large-scale neighborhood search algorithm to select an optimal distribution path, thereby making a reasonable distribution path scheme and reducing the working intensity of manually making the scheme. Firstly, acquiring basic information for determining a vehicle path; the basic information comprises the geographical positions of the distribution center nodes and the customer nodes, the number of customers, the cargo demand of the customers and the maximum load of the vehicle; then establishing an objective function taking the shortest mileage of a vehicle distribution path as a target; determining an initial solution of the model through a scanning algorithm; and finally, determining the optimal vehicle distribution path by using the target function as a target value and utilizing an improved large-scale neighborhood search algorithm.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The first embodiment is as follows:
as shown in fig. 1, the present embodiment provides a vehicle distribution path planning method, where the method includes:
s1, acquiring the position information, the customer information and the vehicle information of the distribution center node; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: number of vehicles and maximum load information of vehicles. The location of the distribution center and each customer node is shown in fig. 2.
S2, establishing an objective function taking the shortest total vehicle distance as a target according to the distribution center node position information, the customer information and the maximum vehicle load information; the constraint of the objective function is that each customer is served by one and only one vehicle and that the total amount of customer demand served by each vehicle does not exceed the vehicle load.
The objective function with the shortest total vehicle mileage for delivery as the target is:
wherein F represents an objective function; m is the maximum number of vehicles that can be used for delivery; n is the number of customers; d is a radical ofijRepresents the distance between any two nodes i and j; x is the number ofijkThe plan is 0-1, which indicates whether the vehicle k passes through the nodes i and j, 1 indicates that the vehicle k passes through the nodes i and j, 0 indicates that the vehicle k does not pass through the nodes i and j, and 0 indicates that the nodes i and j are not communicated, that is, the vehicle k does not pass through a path between the nodes i and j, namely, does not pass through two end points of the road section, namely, the nodes i and j.
In order to obtain a more optimal distribution route, certain constraints need to be set on the objective function, considering that the distribution between the vehicles and the customers and the loading capacity of the distribution vehicles influence the selection of the vehicle distribution route. That is, the constraint of the objective function is that each customer is served by one and only one vehicle and that the total amount of customer demand served by each vehicle does not exceed the vehicle load.
Then, the distribution center node and each client node are chromosomally encoded, and for the convenience of distinguishing the distribution center from the client node, the distribution center, i.e., the departure place of the distribution vehicle is represented by 0, and each client node is represented by a natural number.
S3, determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node. The dispatch order is the sub-path and order of the dispatch. Illustratively, the initial code sequence includes a distribution center (here, indicated by 0), and ordered customer points (indicated by natural numbers such as 1, 2, 3, etc.). For example, for the vehicle routing problem with a distribution center and 6 distribution points, an initial code sequence of the code can be represented as {0, 3, 4, 2, 0, 5, 1, 6, 0}, { } is a code of a solution, which indicates that the vehicle starts from the distribution center (0), sequentially passes through the client points 3, 4, 2 and then returns to the distribution center, and then sequentially passes through the clients 5, 1, 6 and then returns to the distribution center from the distribution center (0). For the distribution center 0, the customer sites 1, 2, 3, 4, 5, 6 go through step S3 to form {0, 3, 4, 2, 0, 5, 1, 6, 0 }.
The step of determining the initial coding sequence specifically comprises:
and S31, establishing a polar coordinate system by taking the position of the distribution center node as a pole and the ray of the distribution center node and the customer node closest to the distribution center node as a polar axis, and converting the position coordinates of the distribution center node and the customer node into polar coordinates.
And S32, sorting the client nodes according to the polar angle size. The ordering rules are from small to large or from large to small.
S33, sequentially inserting each client node into the solution according to the objective function on the premise of meeting the constraint condition; the solution comprises several delivery paths. I.e., the delivery of a customer node is completed, the resolved customer node and path are placed into the solution.
And in the inserting process, if a client node which does not satisfy the constraint condition is encountered and the client node which does not satisfy the constraint condition is not the last client node, skipping the client node which does not satisfy the constraint condition.
S34, searching whether a client node j is not inserted, if yes, calculating the insertion cost c of the client node j inserted between every two client nodes in each distribution path in sequenceijAnd inserting between two client nodes corresponding to the lowest cost; wherein, cij＝di,j+dj,i+1-di,i+1(ii) a In the formula (d)i,jRepresenting customer segmentsDistance between point i to client node j, dj,i+1Represents the distance between client node j and client node i +1, di,i+1Representing the distance between client node i to client node i + 1.
For example, {0, 3, 4, 2, 0, 5, 1, 6, 0}, the solution is only {0} at the beginning, then considering the insertion costs of several points, 1, 2, 3, 4, 5, 6, and determining which point is put to 0 based on the comparison of the insertion costs, if 3 is inserted, then it becomes {0, 3}, and so on, until {0, 3, 4, 2 } is inserted, then 5 is inserted, the sum of the customer demands of points 3, 4, 2, 5 is found to exceed the load, so 5 cannot be inserted, so 0 is inserted first, it becomes {0, 3, 4, 2, 0}, then 5 is inserted, forming {0, 3, 4, 2, 0, 5}, until all points are inserted, forming {0, 3, 4, 2, 0, 5, 1, 6, 0 }.
And S35, traversing all the client nodes which are not inserted until all the client nodes are inserted into the solution, and obtaining an initial coding sequence.
And S4, calculating the target value of the initial coding sequence according to the target function.
The target value refers to the total vehicle path length. Using {0, 3, 4, 2, 0, 5, 1, 6, 0} solution as an example, the target value f (x) ═ d03+d34+d42+d20+d05+d51+d16+d60Wherein d isijIs the distance between point i and point j. The target value here can also be understood as the fitness of a chromosome in a genetic algorithm, which is essential to evaluate a solution.
And S5, calculating the initial temperature of the Metropolis criterion according to the target value of the initial coding sequence, starting the iteration of the optimal distribution path, and outputting the optimal coding sequence of the vehicle after the iteration is finished.
Initial temperature T of Metropolis guidelines0The calculation formula of (2) is as follows:
the initial temperature T0A bad solution having a bad solution acceptance probability of η, which is different from the current target value f (x) by β%The temperature should be T0Where η and β are generally specified by man, and there is no fixed range, and in this embodiment, η is 50 and β is 20.
The iteration of the optimal delivery path specifically includes:
a1, selecting a removal operator and an insertion operator by a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; and the current solution is the initial coding sequence in the first iteration process. At the beginning: the weight of each operator (4 removal operators and 2 insertion operators in this embodiment) is 1 at the beginning of the algorithm, and this weight is initially predetermined by a person.
Step S3 has already constructed an initial solution of the vehicle path problem, which can actually be used as the final answer to the problem, but the quality of the initial solution is generally poor, so the following steps are mainly the optimization of the initial solution, and this optimization process belongs to the subject of an adaptive large-scale neighborhood search algorithm (ALNS for short). The algs algorithm itself does not include a description of the initial solution generation method, and therefore the initial solution needs to be constructed by other methods, and here, a scanning algorithm is selected, and the method can also be a saving algorithm, a proximity insertion algorithm, and the like. The optimization idea of the ALNS algorithm can be understood as that the solution is continuously destroyed and recombined, and the solution is transformed to a better direction in the process.
Removal and insertion are inherent operational and core features of the ALNS algorithm, as the current temperature would be calculated in each iteration in the simulated annealing algorithm. The optimization process of the ALNS algorithm can be simply described as: a complete solution (in the form of an initial solution containing complete path information) → performing a removal operator (removing some points or some sub-paths in the complete solution, the solution after removal may be referred to as an incomplete solution) → performing an insertion operator (reinserting the points removed above into the incomplete solution according to the process described by the removal operator, forming a complete solution again) → the complete solution, thus forming a closed loop, and continuously iterating the optimization. Wherein, one removing operator and one inserting operator form one iteration, and only one removing operator and one inserting operator are selected in each iteration.
The selection of the removal operator (one of the removal operators is selected) and the selection of the insertion operator (one of the insertion operators is selected) are all roulette, and the selections of the removal operator and the insertion operator are not interfered with each other.
Roulette selection is a common method in algorithms, and is commonly used in genetic algorithms for chromosome selection, where operator selection is similar.
Taking the example of selecting 1 removal operator from h removal operators, let the weights corresponding to h removal operators be w1，w2，…，whThen the u-th operator corresponds to the individual probability
Wherein, wuP before the equationuCorrespondingly, the weight of the u-th operator (the u-th operator is taken as an example for the purpose of explaining the calculation method of the individual probability) wgAnd in the formula
Corresponds to, means wgW from 1 to h of middle ggThe sum, where g is only within the sum symbol, refers to the sum range symbol, and where h is h in the paragraph, i.e., the total number of removal operators. The cumulative probability of an operator is
Wherein, PgIs the probability of the individual,
is the cumulative probability; the individual probability and the accumulated probability are the original values in the common method of roulette. Similar to g in the previous problem, Pg is in the formula
Where P is the individual probability and g is its index, which indicates the sequence sign in the summation symbol, i.e. Pg is the individual probability of the g-th operator (found by the previous individual probability formula), which means theoretically the probability that the g-th operator is selected among all operators (from the 1 st to h-th operators).
Representing the sum of individual probabilities of the first n operators, e.g.
Representing the sum of the probabilities of operator 1 and operator 2. Generating a random number r ∈ [0,1 ]]Starting from n equal to 1, r is compared with r
When it first appears
And when the selection process is finished, the u-th operator is the selected operator.
And executing a removal operator and then an insertion operator on the current solution. The removing operator is used for removing some client points from the current solution until the removed client points reach a preset removing upper limit, so that an incomplete solution is obtained; and the insert operator is used for reinserting the removed client points into the incomplete solution according to the rule described by the insert operator so as to obtain a new local solution, thereby achieving the purpose of searching a more optimal solution.
The random client node removal specifically includes: if the current solution has the infeasible subpath solution, randomly removing the client nodes in the infeasible subpath until the sum of the client demands does not exceed the maximum load of the vehicle; if the number of the removed client nodes does not exceed the removal upper limit, selecting random client nodes to remove the client nodes until the number of the removed client nodes reaches the removal upper limit; the unfeasible sub-path solution, namely the sum of the customer demands of the sub-paths is larger than the maximum load of the vehicle; the removal ceiling is generated by a random function. The upper removal limit is typically a random number between 20% and 30% of the number of customer nodes. The random number is typically generated by a random function in the program.
The random sub-path removal specifically includes: if the current solution has the solution of the non-feasible sub-path, removing the non-feasible sub-path; if the number of the removed client nodes does not exceed the removal upper limit, selecting a random sub-path for removal until the number of the removed client nodes reaches the removal upper limit;
the similar client node removing specifically includes: randomly selecting a client node i in the current solution (if the current solution has the infeasible subpath solution, preferentially selecting the client node i in the infeasible subpath solution), calculating the similarity between the client node i and other client nodes j, and sequentially removing the client nodes with the maximum similarity until the number of the removed client nodes reaches the removal upper limit. Distance d between two customer points i and jijAs a basis for removing the similarity points, dijThe smaller the value, the higher the similarity of the client points i and j.
The ring region similarity removal specifically comprises: and calculating the similarity of the current solution sub-paths based on three spatial relations among the annular regions in which the sub-paths are located by considering the spatial relations among the sub-paths. The three spatial relations are respectively overlapped, intersected and separated, and as shown in FIG. 3, two sub-paths in the solution correspond to an annular region s1And S2Schematic diagram of the spatial relationship of (1). Each annular area is a minimum annular area which can cover the complete sub-path by taking the distribution center as a circle center, and the shadow area is a part of the two sub-paths corresponding to the overlapped annular areas.
Calculating similarity based on the three spatial relationships in fig. 3;
the similarity between the two sub-paths is:
wherein σ1>σ2>σ3(the value is a fixed constant and is a fixed value that is artificially predetermined during the execution of the algorithmIn the present embodiment, σ may be set without the fixed range criterion1＝20，σ2＝5，σ3＝1)，siAnd sjRepresenting two sub-paths r in the current solutioniAnd rjCorresponding to the ring region, then a single sub-path riThe similarity coefficient is:
using an elite strategy to remove sub-paths in
The sub-path r with the maximum similarity coefficient is selectedm xSelecting sub-paths r of non-maximum similarity coefficient by roulettedThen removing rm xAnd rdAll of the client nodes in (a) are,
and representing the similarity coefficient set of all sub-paths, and l represents the total number of sub-paths in the current solution.
The cost greedy insertion specifically comprises: each removed client node is inserted into the best position in the sub-path of the current solution. After the client node i to be inserted is inserted into the client node j in the sub-path, the insertion cost c is obtainedij＝di,j+dj,i+1-di,i+1And selecting the sub-path which has the minimum insertion cost and meets the load limit for each insertion. If there is a non-inserted point after the above steps, the insertion is performed only in consideration of the insertion cost until there is no remaining point.
The regret value insertion specifically includes: inserting each removed client node into a sub-path of the current solution, and selecting the sub-path with the maximum regret value to insert each time; the regret value is: Δ c ═ cm2-cm1Wherein c ism1Denotes the minimum insertion cost, cm2Representing a next lowest insertion cost. The significance is that the larger the regret value delta c is, the more the client node can not insert the optimal position, the suboptimal position is selectedThe larger the rise in insertion cost due to insertion.
A2, if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is the initial temperature value.
The probability of acceptance of a local solution is
Wherein, PΔValue of (1) and [0,1]Random number r in between, if PΔAnd r, receiving a poor solution as a current solution of the next iteration, wherein T represents the current temperature, f (x) represents a target value of the current solution x, and f (x ') represents a target value of the local solution x'. The random number r is generated by a programmed random function.
The update formula of the temperature value is as follows: t ═ α
Wherein T' represents the updated temperature, T represents the current temperature before updating, α e (0,1) is the cooling rate, α is a preset constant parameter whose value is generally close to 1 (e.g. 0.95, 0.99, 0.999, etc., where it can be made 0.99), and the closer to 1 represents the slower the temperature decrease.
And A3, updating the corresponding operator weight according to the use times and the preset scores of each insert operator and each remove operator, wherein the updating interval is the preset iteration time. The preset number of iterations is generally manually specified, and there is no hard requirement, and is set to 20 in this embodiment, which means that 20 iterations are performed, and the weight of each operator is adjusted based on the expression of each operator in the 20 iterations. The adjusted weight is used as the selection basis of the next 20 times of iteration operators.
The updating formula of the operator weight is as follows:
where τ denotes the interval τ iterations, y denotes the yth iteration interval, and q denotes the qth operator，
Representing the using times of the operator q in tau iterations, and corresponding preset score is
In the y iteration interval, the operator weight corresponding to the q operator is as follows
In the (y + 1) th iteration interval, the operator weight corresponding to the q-th operator is as
μ∈[0,1]The smaller the value is, the greater the influence of the weight of the y iteration interval on the weight update of the y +1 iteration interval is; if μ is 0, the weight is completely dependent on the weight of the last iteration interval; if μ equals 1, only the score within the iteration interval is considered, if 0<μ<1, the score and the previous weight value in the iteration interval are considered at the same time, and the value of mu is preset artificially.
The rule of the preset scoring of the operator is as follows: if a new global optimal solution is found, the operator score is increased by theta1(ii) a If the new solution is only better than the current solution and is worse than the global optimal solution, the operator score is increased by theta2(ii) a If the new solution is inferior to the current solution, but is accepted by the Metropolis criterion as the next iteration initial solution, then the operator score is increased by θ3(ii) a If the new solution is inferior to the current solution and is not accepted by the Metropolis criterion, the operator score is increased by θ4. General theta1>θ2>θ3>θ4And the person is preset without a fixed standard, in this embodiment, θ1＝5，θ2＝3，θ3＝1.5，θ4＝1.8。
And A4, stopping iteration until the target value of the local solution is not less than the iteration number of the current solution and reaches the preset number, and outputting the optimal coding sequence of the vehicle. And decoding the optimal vehicle coding sequence to obtain the optimal vehicle distribution path.
The preset times can be 2000 generations, and the iteration times without the improved solution can be adjusted according to requirements. In addition, the recorded optimal solution is selected and decoded, and then vehicles required for completing all distribution tasks and customers served by the vehicles can be obtained. As shown in fig. 4, the process of completing all delivery tasks by 4 vehicles and the customer nodes that each vehicle needs to service are shown in fig. 4.
The embodiment provides a vehicle delivery path planning method, which comprises the following steps: acquiring basic information of a vehicle path; the basic information comprises the geographical positions of the distribution center nodes and the customer nodes, the number of customers, the cargo demand of the customers and the maximum load of the vehicle; establishing an objective function based on a distribution model; obtaining an initial solution of the model through a scanning algorithm; and selecting the optimal vehicle distribution path by using the improved large-scale neighborhood search algorithm by taking the target function as a target value. The optimal distribution path of the vehicle can be screened out by utilizing the improved large-scale neighborhood search algorithm, so that a more reasonable distribution path scheme is formulated, the distribution efficiency is improved, and the total distribution mileage of the vehicle is greatly reduced. The improved large-scale neighborhood search algorithm in the embodiment considers the geographical position correlation of single distribution in the distribution scheme, improves the local search capability of the algorithm, has better applicability to the formulation of large-scale vehicle distribution schemes, can provide a solution for the general vehicle distribution path problem with capacity constraint, and provides reference for the decision of managers.
Example two:
as shown in fig. 5, the present embodiment provides a vehicle delivery path planning system, which includes:
the information acquisition module M1 is used for acquiring the distribution center node position information, the customer information and the vehicle information; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: vehicle number and vehicle maximum load information;
an objective function determination module M2, configured to establish an objective function with the shortest total vehicle mileage for distribution as a target according to the distribution center node location information, the customer information, and the vehicle maximum load information; the constraint condition of the objective function is that each customer is served by one vehicle and the total amount of customer demand served by each vehicle does not exceed the load of the vehicle;
an initial solution construction module M3 for determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node;
an initial solution target value calculation module M4, configured to calculate a target value of the initial coding sequence according to the objective function;
an optimal distribution path iteration module M5, configured to calculate an initial temperature of the Metropolis criterion according to the target value of the initial coding sequence, and start an optimal distribution path iteration;
the iteration of the optimal delivery path specifically includes:
selecting a removal operator and an insertion operator by using a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; the current solution is the initial coding sequence in the first iteration process;
if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is an initial temperature value;
updating the corresponding operator weights according to the use times and preset scores of each insert operator and each removal operator, wherein the updating interval is the preset iteration times;
and stopping iteration until the target value of the local solution is not less than the iteration times of the current solution and reaches a preset time, and outputting the optimal vehicle coding sequence.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A vehicle delivery path planning method, the method comprising:
acquiring node position information, customer information and vehicle information of a distribution center; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: the number of vehicles and the maximum load information of the vehicles;
establishing an objective function taking the shortest total vehicle delivery mileage as a target according to the distribution center node position information, the customer information and the maximum vehicle load information; the constraint condition of the objective function is that each customer is served by one vehicle and the total amount of customer demand served by each vehicle does not exceed the load of the vehicle;
determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node;
calculating a target value of the initial coding sequence according to the target function;
calculating the initial temperature of the Metropolis criterion according to the target value of the initial coding sequence, and starting the iteration of the optimal distribution path;
the iteration of the optimal delivery path specifically includes:
selecting a removal operator and an insertion operator by using a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; the current solution in the first iteration process is the initial coding sequence;
if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is an initial temperature value;
updating the corresponding operator weights according to the use times and preset scores of each insert operator and each removal operator, wherein the updating interval is the preset iteration times;
and stopping iteration until the target value of the local solution is not less than the iteration frequency of the current solution and reaches a preset frequency, and outputting the optimal coding sequence of the vehicle.
2. The vehicle delivery path planning method according to claim 1, wherein the objective function targeting the shortest total delivery vehicle mileage is:
wherein F represents an objective function; m is the maximum number of vehicles that can be used for delivery; n is the number of customers; dijRepresents the distance between any two nodes i and j; x is the number ofijkPlanning for 0-1, indicating whether the vehicle k passes through the nodes i and j, 0 indicating that the vehicle k does not pass throughPassing nodes i and j, 1 represents vehicle k passing nodes i and j.
3. The vehicle distribution path planning method according to claim 1, wherein the determining an initial code sequence specifically includes:
establishing a polar coordinate system by taking the position of a distribution center node as a pole and taking a ray where the distribution center node and a customer node closest to the distribution center node are located as a polar axis, and converting the position coordinates of the distribution center node and the customer node into polar coordinates;
sequencing the client nodes according to the polar angle size;
on the premise of meeting the constraint condition, sequentially inserting each client node into the solution according to the objective function; the solution comprises a plurality of delivery paths; in the inserting process, if a client node which does not satisfy the constraint condition is encountered and the client node which does not satisfy the constraint condition is not the last client node, skipping the client node which does not satisfy the constraint condition;
searching whether a client node j is not inserted, and if so, sequentially calculating the insertion cost c of the client node j inserted between every two client nodes in each distribution pathijAnd inserting between two client nodes corresponding to the lowest cost; wherein, cij＝di,j+dj,i+1-di,i+1(ii) a In the formula (d)i,jRepresents the distance between client node i and client node j, dj,i+1Represents the distance between client node j and client node i +1, di,i+1Representing the distance between the client node i and the client node i + 1;
and traversing all the non-inserted client nodes until all the client nodes are inserted into the solution to obtain an initial coding sequence.
4. The vehicle distribution path planning method according to claim 1, wherein the calculating an initial temperature of Metropolis criterion according to the target values in the initial code sequence specifically comprises:
calculating the initial temperature T of Metropolis criterion according to the target value in the initial coding sequence0；
The initial temperature T0When the probability of accepting the poor solution is η, the temperature corresponding to the poor solution is T0。
5. The vehicle delivery path planning method according to claim 1,
the random client node removal specifically includes: if the current solution has the infeasible subpath solution, randomly removing the client nodes in the infeasible subpath until the sum of the client demands does not exceed the maximum load of the vehicle; if the number of the removed client nodes does not exceed the removal upper limit, selecting random client nodes to remove the client nodes until the number of the removed client nodes reaches the removal upper limit; the unfeasible sub-path solution, namely the sum of the customer demands of the sub-paths is larger than the maximum load of the vehicle; the removal upper limit is generated by a random function;
the random sub-path removal specifically includes: if the current solution has the solution of the non-feasible sub-path, removing the non-feasible sub-path; if the number of the removed client nodes does not exceed the removal upper limit, selecting a random sub-path for removal until the number of the removed client nodes reaches the removal upper limit;
the similar client node removing specifically includes: randomly selecting a client node i in the current solution, calculating the similarity between the client node i and other client nodes j, and sequentially removing the client nodes with the maximum similarity until the number of the removed client nodes reaches the removal upper limit;
the ring region similarity removal specifically comprises: calculating similarity based on three spatial relations among the annular regions where the sub paths are located in the current solution;
the similarity between the two sub-paths is:
wherein σ1>σ2>σ3，siAnd sjRepresenting two sub-paths r in the current solutioniAnd rjCorresponding to the ring region, then a single sub-path riThe similarity coefficient is:
in that
The sub-path r with the maximum similarity coefficient is selectedmaxSelecting sub-paths r of non-maximum similarity coefficient by roulettedThen removing rm xAnd rdAll of the client nodes in (a) are,
representing the similarity coefficient set of all sub-paths, wherein l represents the total number of sub-paths in the current solution;
the cost greedy insertion specifically comprises: inserting each removed customer node into a sub-path of the current solution, wherein each insertion selects the sub-path with the minimum insertion cost and meeting load limitation;
the regret value insertion specifically includes: inserting each removed client node into a sub-path of the current solution, and selecting the sub-path with the maximum regret value to insert each time; the regret value is as follows: Δ c ═ cm2-cm1Wherein c ism1Denotes the minimum insertion cost, cm2Representing the next smallest insertion cost.
6. The vehicle distribution path planning method according to claim 1, wherein the update formula of the operator weight is:
where τ denotes the interval τ iterations, y denotes the ith iteration interval, q denotes the qth operator,
representing the number of times of use of the operator q in tau iterations, with a corresponding predetermined score
In the y iteration interval, the operator weight corresponding to the q operator is as follows
In the (y + 1) th iteration interval, the operator weight corresponding to the q-th operator is as
μ∈[0,1]The factor is used for controlling the influence of the operator, and the smaller the value is, the greater the influence of the weight of the y iteration interval on the weight updating of the y +1 iteration interval is; if μ is 0, the weight is completely dependent on the weight of the last iteration interval; if μ is 1, only the intra-iteration interval score is considered, if 0<μ<1, the score in the iteration interval and the previous weight value are considered simultaneously.
7. The vehicle delivery path planning method according to claim 1, further comprising, before the determining the initial code sequence:
and carrying out chromosome coding on the distribution center node and each client node.
8. The vehicle distribution path planning method according to claim 1, wherein the update formula of the temperature value is: t ═ α
Wherein T' represents the updated temperature, T represents the current temperature before updating, alpha belongs to (0,1) as the cooling speed, and the value of alpha is a preset constant parameter.
9. The vehicle distribution path planning method according to claim 1, wherein the probabilistically accepting a local solution according to Metropolis' criterion in combination with the temperature value of the iteration includes:
according to Metropolis criterion, combining the temperature value of the iteration, and receiving a local solution with probability of receiving the local solution
Wherein, PΔValue of (1) and [0,1]Random number r in between, if PΔAnd r, accepting the inferior solution as the current solution of the next iteration, wherein T represents the current temperature, f (x) represents the target value of the current solution x, and f (x ') represents the target value of the local solution x'.
10. A vehicle delivery path planning system, the system comprising:
the information acquisition module is used for acquiring the position information, the customer information and the vehicle information of the distribution center node; the customer information includes: the number of customers, the cargo demand of each customer and the position of each customer node; the vehicle information includes: the number of vehicles and the maximum load information of the vehicles;
the target function determining module is used for establishing a target function taking the shortest total vehicle delivery mileage as a target according to the distribution center node position information, the customer information and the maximum vehicle load information; the constraint condition of the objective function is that each customer is served by one vehicle and the total quantity of the customer demands served by each vehicle does not exceed the load of the vehicle;
the initial solution construction module is used for determining an initial coding sequence; the initial coding sequence is a coded representation of an initial distribution path, and the initial coding sequence comprises each client node on the initial distribution path and a distribution sequence of each client node;
the initial solution target value calculation module is used for calculating a target value of the initial coding sequence according to the target function;
the optimal distribution path iteration module is used for calculating the initial temperature of the Metropolis criterion according to the target value of the initial coding sequence and starting the optimal distribution path iteration;
the iteration of the optimal delivery path specifically includes:
selecting a removal operator and an insertion operator by using a roulette method according to the weights of the removal operators and the insertion operators, and respectively performing operator removal operation and operator insertion operation on the current solution according to the selected removal operator and insertion operator to obtain a local solution; the removal operator includes: random client node removal, random sub-path removal, similar client node removal and ring region similarity removal; the insertion operator includes: cost greedy insertion and regret value insertion; the current solution in the first iteration process is the initial coding sequence;
if the target value of the local solution is smaller than the target value of the current solution, taking the local solution as the current solution; if the target value of the local solution is larger than the target value of the current solution, according to the Metropolis criterion, combining the temperature value of the iteration, probabilistically receiving the local solution, and updating the temperature value; the temperature value in the first iteration process is an initial temperature value;
updating the corresponding operator weights according to the use times and preset scores of each insert operator and each removal operator, wherein the updating interval is the preset iteration times;
and stopping iteration until the target value of the local solution is not less than the iteration frequency of the current solution and reaches a preset frequency, and outputting the optimal coding sequence of the vehicle.
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| CN116384869A (en) * | 2023-03-20 | 2023-07-04 | 深圳市大数据研究院 | Vehicle path planning method, path planning device, electronic equipment and storage medium |
| CN116629586A (en) * | 2023-07-24 | 2023-08-22 | 青岛民航凯亚系统集成有限公司 | Airport guarantee vehicle scheduling method and system based on ALNS |
| CN117933513A (en) * | 2024-01-17 | 2024-04-26 | 山东科技大学 | Vehicle path determining method and system for simultaneously taking and delivering goods in common delivery mode |
| CN118134372A (en) * | 2024-02-28 | 2024-06-04 | 南开大学 | Urban E-commerce takeout distribution path optimization method based on single-commerce and multi-commerce conditions |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116384869A (en) * | 2023-03-20 | 2023-07-04 | 深圳市大数据研究院 | Vehicle path planning method, path planning device, electronic equipment and storage medium |
| CN116384869B (en) * | 2023-03-20 | 2024-09-03 | 深圳市大数据研究院 | Vehicle path planning method, path planning device, electronic equipment and storage medium |
| CN116629586A (en) * | 2023-07-24 | 2023-08-22 | 青岛民航凯亚系统集成有限公司 | Airport guarantee vehicle scheduling method and system based on ALNS |
| CN117933513A (en) * | 2024-01-17 | 2024-04-26 | 山东科技大学 | Vehicle path determining method and system for simultaneously taking and delivering goods in common delivery mode |
| CN118134372A (en) * | 2024-02-28 | 2024-06-04 | 南开大学 | Urban E-commerce takeout distribution path optimization method based on single-commerce and multi-commerce conditions |
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