CN113780676A - Method for optimizing distribution path of bottled liquefied gas vehicle - Google Patents

Method for optimizing distribution path of bottled liquefied gas vehicle Download PDF

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CN113780676A
CN113780676A CN202111116863.1A CN202111116863A CN113780676A CN 113780676 A CN113780676 A CN 113780676A CN 202111116863 A CN202111116863 A CN 202111116863A CN 113780676 A CN113780676 A CN 113780676A
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吴庆涛
贾新宇
谢萍
冀治航
王琳
刘牧华
张明川
朱军龙
邢玲
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Abstract

A bottled liquefied gas vehicle delivery path optimization method relates to the technical field of vehicle path optimization, combines the actual condition of vehicle transportation, establishes a multi-objective mathematical model of a vehicle path problem with a time window more closely related to the actual problem according to the transportation characteristics of liquefied gas, limits the model constraint aiming at the particularity of the liquefied gas, refines the targets, selects three targets of minimum risk, minimum cost and minimum vehicle redundancy after analyzing various influence factors and determination principles influencing the liquefied gas delivery path, and solves the three targets by using a hybrid coevolution optimization algorithm. The invention has the beneficial effects that: the liquefied gas transport vehicle avoids the transport risk, reduces the probability of accidents, reduces the probability of liquefied gas transport accidents, helps the carrying enterprises to solve the key difficult problem of completing the transport task at low risk and low cost, and ensures that the liquefied gas distribution has higher safety, economy and high efficiency.

Description

Method for optimizing distribution path of bottled liquefied gas vehicle
Technical Field
The invention belongs to the technical field of vehicle path optimization, and particularly relates to a method for optimizing a distribution path of a bottled liquefied gas vehicle.
Background
At present, the transportation and distribution of liquefied gas companies mostly adopt the traditional method, routes are manually selected according to the experience of drivers, the transportation cost is high, liquefied gas cannot arrive in time due to unreasonable route planning, and the service quality is greatly reduced. Moreover, liquefied gas distribution belongs to dangerous material transportation, has dangerous characteristics such as inflammability, explosiveness and the like, and once an accident occurs in the transportation process, serious casualties and property loss are often brought. Risk and cost are two important factors to be considered for a carrier enterprise. Therefore, according to the multi-objective vehicle path problem (MOVRP), an effective optimization method is researched and designed, and the low-risk and low-cost completion of the transportation task of dispatching the transportation fleet is a key problem to be solved by a carrier enterprise.
The multi-target vehicle path problem (MOVRP) is a classical combinatorial optimization problem, belongs to NP-Hard problem, and an accurate algorithm cannot give an optimal solution in a limited time, and the solving difficulty is exponentially increased along with the increase of the scale. In order to effectively meet the delivery requirements of liquefied gas enterprises on customers, a multi-objective evolutionary optimization algorithm can be used for giving a relatively better solution within a limited time. However, the distribution path of the liquefied gas needs to meet two strict constraints of a customer time window and a maximum vehicle load, so that the feasible domain of the problem model is small, and a general multi-objective evolutionary algorithm usually shows poor convergence and diversity.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for optimizing a distribution path of a bottled liquefied gas vehicle, and solve the problem of path optimization in the distribution process of the conventional bottled liquefied gas vehicle.
The technical scheme adopted by the invention for solving the technical problems is as follows: a bottled liquefied gas vehicle delivery path optimization method comprises the following steps:
step one, establishing a mathematical model according to the description of the liquefied gas distribution vehicle path problem:
defining a complete graph G ═ N, A ═ N {0,1,2, …, N } as a distribution center and a set of customer points, { arc (i, j) | i, j ∈ N, i ≠ j } as a set of paths, a node 0 is a distribution center node, a node C is a set of customer points not including the distribution center node 0, and knowing the position of each customer point i, the demand and the distribution time window requirements are G respectivelyiAnd [ Tai,Tbi]The distribution center reaches all customer points from the distribution center by K vehicles at most, each vehicle starts from the distribution center and finally returns to the distribution center, and the maximum cargo capacity of each vehicle is Q and TikTime of vehicle k to customer i, wikFor the waiting time of vehicle k at customer i, a ═ { arc (i, j) | i, j ∈ N, i ≠ j } is the set of edges, defining dijIs the distance of arc (i, j), i.e., the distance from client point i to client point j, and dij＝dji，tijThe real-time loading of the vehicle k from the customer i to the customer j is al for the transport time from the customer i to the customer jijkThe path failure rate is pijAnd the exposure population associated therewith is
Figure BDA0003275818470000021
Liquefied gas delivery contains three targets, the risk is low, the cost is low, the vehicle redundancy is low, and the target function is established as follows:
Figure BDA0003275818470000022
Figure BDA0003275818470000023
Figure BDA0003275818470000024
decision variables:
Figure BDA0003275818470000025
Figure BDA0003275818470000026
the constraints that must be satisfied by a feasible solution to this problem are:
Figure BDA0003275818470000031
Figure BDA0003275818470000032
Figure BDA0003275818470000033
Figure BDA0003275818470000034
Figure BDA0003275818470000035
Figure BDA0003275818470000036
Figure BDA0003275818470000037
Figure BDA0003275818470000038
Figure BDA0003275818470000039
where k is a vehicle for transporting liquefied gas, CVCost of departure for a single transport vehicle, CLIs unit distance fuel cost, CTIs the driver's cost per unit time, DijRepresenting the actual distance or transit time from customer i to customer j; constraint (4) means that each customer site has only one vehicle to serve it; constraint (5) indicates that each customer is visited once and returned to the distribution center; constraint (6) indicates that each vehicle can only access one client at most when departing; constraint (7) indicates that each vehicle can only deliver a maximum of one customer when it arrives; the constraint (8) represents a vehicle load constraint; constraint (9) indicates that after the vehicle arrives at a certain customer node and the delivery is completed, the vehicle must leave the customer and go to the next customer; the constraint (10) indicates that the reduced load of the vehicle after servicing a customer must equal the customer's demand; the constraint (11) represents the time of arrival of the vehicle at the customer; constraints (12) impose a hard time window constraint on each customer, allowing earlier arriving vehicles to wait for the start of the customer time window, although requiring vehicles to have to start delivery within the customer time window.
And step two, solving the model to obtain an optimal solution which is an optimal route.
The method for solving the model in the first step comprises the following steps:
(1) make F1Representing the model in step one, F2A model representing the removal of (3), (11) and (12) in step one;
(2) coding;
step 2.1, setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
step 2.2, encoding: the chromosome is coded in the form of integer coding, the number 0 represents the distribution center, 1,2,3, …, and N represents the customer point, then the distribution route can be coded as (0,1,2,3,0,4,5,6,7,0, …, N, 0);
(3) initializing a population P1And P2：
Step 3.1, respectively using forward insertion heuristic algorithm to construct F1And F2Two viable individuals of (a);
step 3.2, selecting partial individuals in the neighborhood of the individuals in the step 3.1, and forming the initial population P together with other randomly generated individuals1And P2；
(4) Based on sequence crossing operation:
step 4.1, respectively from offspring population Off1And Off2One chromosome was selected as the parent chromosome, designated chrom1 and chrom2, resulting in a chromosome that is [0,1 ]]Random number r 'of segments, if r'<PC, performing the cross operation of the step 4.2 to the step 4.6, otherwise, directly keeping the two chromosomes to the next generation;
step 4.2, randomly selecting a path from parent chromosomes chrom1 and chrom2, and marking the path as L1 and L2;
4.3, randomly selecting a breakpoint from each path, and recording the breakpoint as Node1 and Node 2;
step 4.4, linking the part before the Node1 in the L1 and the part after the Node2 in the L2 into a new path, deleting one of the two repeated clients if the two repeated clients appear, checking whether the new path meets the constraint, if the constraint is met, performing the step 4.5, if the constraint is not met, returning to the step 4.3, and if the number of times of returning to the step 4.3 reaches the product of the number of the clients in the L1 and the number of the clients in the L2, abandoning the cross performing step (5);
step 4.5, adding the new path in the step 4.4 into the chrom1, and if one client appears in the new path and appears in other old paths, deleting the repeated client in the old path;
step 4.6, if a client is not allocated with a path in the second half of the L1, the client is inserted into a feasible insertion position of other paths in the chrom1, if no feasible insertion position exists, the step (5) is abandoned, if all feasible, the chrom1 is updated to chrom1', and a second descendant chrom2' can be generated by reversing the parent roles;
(5) mutation operation: at Off1And Off2Each of which is generated at [0,1 ]]Random number of interval r ', if r'<PM, randomly selecting two customer point codes in the chromosome, and interchanging positions; otherwise, directly keeping the current chromosome to the next generation; updating the offspring population Off after traversing all chromosomes1And Off2；
(6) From updated Off2Of the original liquefied gas distribution problem, i.e., satisfying the time window constraint2_feasible；
(7) And (3) population merging: merging population P1，Off2Feasible and updated offspring population Off1Become new P1(ii) a Merging population P2Updated offspring population Off1And Off2Become new P2；
(8) Calculating a fitness value: separately calculating the population P1And P2Fitness of each chromosome in each dimension of the target;
(9) non-dominant ordering: the population P1All individuals in the system are divided into a plurality of layers according to the dominating relation for each dimension fitness value, the first layer is R0Of non-dominant individuals F1The second layer is at R0The non-dominant individual set F obtained after removing the first layer of individuals2And so on, producing all sort order subsets F ═ F (F)1,F2…), population P2The same process is carried out;
(10) computingP1Crowding distance of individual: let P [ x ]]distanceA crowding distance of individual x, P [ x ]]M is the function value f of the individual x on the sub-target mkThen calculate the population P1Crowding distance of all individuals:
Figure BDA0003275818470000051
group P2The same process is carried out;
(11) calculating P2Individual violation constraint value: for P2Calculates its time window constraint value, i.e., cv (x), that violates the original liquefied gas delivery problem;
(12) to P1And P2Performing elite selection operation: defining a classification number x for each individualrank，xrankIf and only if x ∈ Fk(ii) a When two individuals belong to different sorting subsets, the sequence number x is preferentially selectedrankSmall individuals enter Pt+1(ii) a At P1In (b), when x isrankWhen the same, the gathering distance P [ x ] is selected preferentially]distanceLarge Individual entry Pt+1(ii) a At P2In (b), when x isrankIf the values are the same, the individual with smaller violation constraint value CV (x) is selected to enter Pt+1(ii) a Up to Pt+1The scale of (A) is N;
(13) iterating the steps 4 to 11, and obtaining a population P by the maximum iteration times G1And selecting one solution from the optimal solutions according to the priority of the decision maker to each target to make a decision, so as to obtain the optimal distribution route of the bottled liquefied gas vehicle.
The invention has the beneficial effects that: the method combines the actual situation of vehicle transportation, considers three targets of transportation risk, transportation cost and minimum carbon emission according to the transportation characteristics of liquefied gas, establishes a multi-target mathematical model of the vehicle path problem with a time window more closely to the actual problem, and limits the model constraint aiming at the specificity of the liquefied gas. Refining the targets, selecting three targets of minimized risk, minimized cost and minimized vehicle redundancy after analyzing various influence factors and determination principles influencing the liquefied gas distribution path, and solving by using a hybrid coevolution optimization method; the liquefied gas transport vehicle avoids the transport risk, reduces the probability of accidents, reduces the probability of liquefied gas transport accidents, helps the carrying enterprises to solve the key difficult problem of completing the transport task at low risk and low cost, and ensures that the liquefied gas distribution has higher safety, economy and high efficiency.
Drawings
FIG. 1 is a diagram of a multi-objective vehicle path problem system model of the present invention;
FIG. 2 is a schematic flow chart of the hybrid co-evolution optimization method of the present invention;
fig. 3 is a schematic diagram of a sequence-based interleaving operation in an embodiment of the present invention.
Detailed Description
In the present invention, a multi-objective vehicle routing problem Model (MOVRP) is designed based on the characteristics of bottled liquefied gas delivery. The liquefied gas distribution characteristics are divided into two characteristics of distribution safety and distribution cost. The impact factors on delivery safety can be divided into the probability of an accident per path, the consequences of the accident (expressed in human exposure), and the real-time loading of the vehicle. Distribution costs include departure costs for the vehicle, vehicle fuel costs, and personnel service costs. In the optimization process of the algorithm, a vehicle may not meet the time window of the client, and a new transport vehicle is preferably added to transport the client, so that the utilization rate of the vehicle is low, and the redundancy of the vehicle is considered. Accordingly, three goals of the multi-objective vehicle path problem model of the present invention are to minimize transportation risk, minimize delivery costs, and minimize vehicle redundancy.
A multi-objective vehicle path problem Model (MOVRP) optimizes by comprehensively considering multiple objectives, but no optimal solution can satisfy simultaneous optimization of multiple conflicting objectives, so we aim to find a compromise solution that can approximate simultaneous optimization of three objectives. Moreover, the delivery path of the liquefied gas needs to meet both the strict constraints of the customer time window and the maximum vehicle load, making the feasible domain of the problem model smaller. This makes the problem model challenging, and a general multi-objective evolutionary algorithm tends to show poor convergence and diversity in solving the problem model. The invention solves the problem of liquefied gas delivery by initializing two populations, one population solving the problem of liquefied gas delivery and the other population solving an auxiliary problem model derived from the problem of liquefied gas delivery, and the two populations co-evolve and cooperate with each other to solve the problem of liquefied gas delivery.
A method for optimizing a distribution path of a bottled liquefied gas vehicle comprises the following specific steps:
(I) modeling
1. Model assumptions
And defining a complete graph G as (N, A), wherein N is {0,1,2, …, N } to be a distribution center and a client node set. A ═ arc (i, j) | i, j ∈ N, i ≠ j } is a set of paths, the node 0 is a distribution center node, C is a subset that does not include the distribution center node 0, and the travel distance, the accident probability, and the number of exposure population between the distribution center and the demand point are known. The demand for each liquefied gas demand point is known and relatively stable over a period of time. The method is characterized in that a group of vehicles of the same type with the same maximum loading capacity complete liquefied gas distribution service for a customer site, the vehicles cannot exceed the maximum loading capacity when the vehicles are served at the customer site, each vehicle visits each customer at most once, the demand and time window requirements of each customer node can be known in advance and cannot be split, and liquefied gas is required to be transported to each demand place on time within the time period required by the customer. The service of each customer is performed within a specified time window and the vehicle waits until it reaches the customer site before the time window. The target number is multiple targets, and the met targets are the lowest risk, the lowest transportation cost and the lowest vehicle redundancy.
2. Model building
Before constructing the model, firstly, the decision variables of the model are given:
Figure BDA0003275818470000071
Figure BDA0003275818470000072
(1) multi-objective model building
According to the characteristics of liquefied gas as inflammable and explosive dangerous goodsThe risk in the transportation and distribution process is reduced, and the safety of personnel in the whole transportation process is ensured, which is an object to be considered. When the model is built, a dangerous accident occurrence probability is selected to be small, and once an accident occurs, the influence on the population within the minimum range is ensured. Conventional risk metric model to
Figure BDA0003275818470000073
To measure the road risk on the edge (i, j), where pij，
Figure BDA0003275818470000074
The probability of the vehicle accident on the path (i, j) and the result (expressed by human exposure) caused by the accident are respectively, the relationship between the cargo capacity and the accident influence result is not considered, and the path risk cannot be accurately measured. Thus assuming a linear relationship between the risk impact consequences and the cargo capacity of the hazardous material, the objective function for the risk of vehicular transport is:
Figure BDA0003275818470000081
wherein alijkFor the load of vehicle k from customer i to customer j, Q represents the maximum load of the vehicle to transport liquefied gas.
Liquefied gas distribution is a logistic process, and no matter what product is transported and distributed, the cost is always a core factor considered by distributors. The cost of logistics vehicle distribution mainly comprises: vehicle departure costs, vehicle fuel costs, and personnel service costs.
Objective function of vehicle delivery cost:
Figure BDA0003275818470000082
where k is a vehicle for transporting liquefied gas, CVCost of departure for a single transport vehicle, CLIs unit distance fuel cost, CTIs the driver's cost per unit time, DijRepresenting the actual distance or transit time from customer i to customer j。
The liquefied gas distribution essentially belongs to the problem of vehicle paths with time windows, and the time windows of customers can be avoided in the algorithm evolution process to increase the number of vehicles, so that the utilization rate of the vehicles is low, and the cost is increased. Thus, the third optimization objective minimizes the average vehicle redundancy:
Figure BDA0003275818470000083
wherein, giFor customer demand, Q is the vehicle maximum load.
(2) Model constraint conditions
Each customer is to be serviced by a vehicle, and there is only one:
Figure BDA0003275818470000084
each customer is accessed once and returned to the distribution center:
Figure BDA0003275818470000091
each vehicle can only visit one client at most when departing, and can only deliver one client when arriving:
Figure BDA0003275818470000092
the restriction of the capacity of the vehicles for transporting the liquefied gas meets the condition that the actual transportation volume of each vehicle running on each road section does not exceed the safe transportation capacity:
Figure BDA0003275818470000093
in the liquefied gas transportation process, after a vehicle arrives at a certain customer node to complete delivery, the vehicle must leave the customer and go to the next customer:
Figure BDA0003275818470000094
the reduced load of a vehicle after servicing a customer must equal the customer's demand, where giIndicating the customer's liquefied gas demand. This constraint may avoid abnormal situations such as repetitive distribution.
Figure BDA0003275818470000095
The transport vehicle must comply with the customer's time window requirements, i.e., wait before the time window arrives, but not later.
Figure BDA0003275818470000096
(II) multi-objective optimization method
The essence of the multi-objective optimization problem is to balance the conflict situation between the sub-targets, so that each sub-target function is optimized as much as possible. The optimal solution is therefore not likely to be a single solution, but a set of solutions, i.e. a Pareto solution set. The Pareto solution is only a non-inferior solution, and multiple Pareto optimal solutions are mostly generated in the multi-objective problem. The fast non-dominated sorting genetic algorithm with the elite strategy is to perform operation on the whole population in parallel, and a plurality of Pareto optimal solutions of the multi-objective optimization problem can be found by operation once. However, the feasible domain of the liquefied gas distribution problem with time window constraints is small, and it may be difficult to search the Pareto solution set in the feasible domain using only NSGA-II. Two populations co-evolution are therefore used, the first one to solve the original liquefied gas delivery problem and the other one to solve the liquefied gas delivery problem without a time window, which enhances the convergence and diversity of the first one and finds the Pareto solution set.
The flow design of the hybrid coevolution method is shown as a second drawing; the specific process is as follows:
the first step is as follows: generating two initial populations P of size N1And P2；
The second step is that: let P1Solving the problem of liquefied gas delivery, P2Solving the problem of liquefied gas distribution without time window constraint and calculating the function values of the two populations;
the third step: respectively carrying out evolution operations, namely crossing and mutation, on the two populations to generate offspring population Off with the size of N1And Off2；
The fourth step is from Off2Of the available solutions forming Off that can solve the original liquefied gas delivery problem2_feasible；
The fourth step is to merge P1，Off1And Off2Feasible forms a new P1Merge P2，Off1And Off2Formation of a new P2；
The fifth step is to calculate P1，P2A fitness value of;
sixth step according to P1，P2Respectively selecting N individuals through an NSGA-II-based environment selection strategy to form a new population P1And P2；
And sixthly, jumping to the third step and circulating until the ending condition is met.
Examples
During the dynamic distribution process of liquefied gas, the analysis of targets and constraint conditions needs to be performed according to the characteristics of the liquefied gas, and a reasonable mathematical model is given through a specific analysis result. And solved by the MOA.
Step 1: establishing a mathematical model according to the description of the liquefied gas distribution vehicle path problem:
define complete graph G ═ (N, a). N ═ {0,1,2, …, N } is the set of distribution centers and customer nodes. Node 0 is a distribution center node, and C is a set that does not include distribution center node 0. Knowing the location of each customer site i, the demand and delivery time window requirements are giAnd [ Tai,Tbi]The distribution center reaches all customer points from the distribution center by K vehicles at most, each vehicle starts from the distribution center and finally returns to the distribution center, and the maximum cargo capacity of each vehicle is Q and TikIs a vehicleTime of vehicle k to customer i, wikThe waiting time of the vehicle k at the customer i. A ═ arc (i, j) | i, j ∈ N, i ≠ j } is a set of edges, and d is definedijIs the distance of arc (i, j), i.e., the distance from client point i to client point j, and dij＝djiTime of transport tijReal-time loading al of vehicle k from customer i to customer jijkRate of path failure pijAnd the exposure population associated therewith
Figure BDA0003275818470000111
And the like.
Liquefied gas delivery comprises three goals, low risk, low cost and low vehicle redundancy. The objective function is as follows:
Figure BDA0003275818470000112
Figure BDA0003275818470000113
Figure BDA0003275818470000114
decision variables:
Figure BDA0003275818470000115
Figure BDA0003275818470000116
the constraints that must be satisfied by a feasible solution to this problem are:
Figure BDA0003275818470000121
Figure BDA0003275818470000122
Figure BDA0003275818470000123
Figure BDA0003275818470000124
Figure BDA0003275818470000125
Figure BDA0003275818470000126
Figure BDA0003275818470000127
Figure BDA0003275818470000128
Figure BDA0003275818470000129
wherein the constraint (4) indicates that each customer site has only one vehicle to serve it; constraint (5) indicates that each customer is visited once and returned to the distribution center; constraint (6) indicates that each vehicle can only access one client at most when departing; constraint (7) indicates that each vehicle can only deliver a maximum of one customer when it arrives; the constraint (8) represents a vehicle load constraint; constraint (9) indicates that after the vehicle arrives at a certain customer node and the delivery is completed, the vehicle must leave the customer and go to the next customer; the constraint (10) indicates that the reduced load of the vehicle after servicing a customer must equal the customer's demand; the constraint (11) represents the time of arrival of the vehicle at the customer; constraints (12) impose a hard time window constraint on each customer, allowing earlier arriving vehicles to wait for the start of the customer time window, although requiring vehicles to have to start delivery within the customer time window.
Make F1Representing the above model, F2The above model excluding (3), (11) and (12) is shown.
Step 2: and (3) encoding:
step 2.1: setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
step 2.2: and (3) encoding: the chromosome is encoded in the form of integer coding, the number 0 represents the distribution center, 1,2,3, …, and N represents the customer points, the distribution route can be encoded as (0,1,2,3,0,4,5,6,7,0, …, N, 0).
And step 3: initializing a population P1And P2：
Step 3.1: construction of F Using Forward insertion heuristic algorithms separately1And F2Two viable individuals of (a);
step 3.2: selecting partial individuals in the neighborhood of the individual in step 3.1, and forming the initial population P together with other randomly generated individuals1And P2。
And 4, step 4: based on the sequence interleaving operation, as shown in fig. three:
step 4.1: from offspring population Off separately1And Off2One chromosome from each of them was selected as the parent chromosome, designated chrom1 and chrom2, resulting in a chromosome in [0,1]Random number r 'of segments, if r'<PC, performing the following cross operation, otherwise, directly keeping the two chromosomes to the next generation;
step 4.2: randomly selecting a path from parent chromosomes chrom1 and chrom2, and marking the path as L1 and L2;
step 4.3: randomly selecting a breakpoint from each path, and recording the breakpoint as Node1 and Node 2;
step 4.4: linking the part before the Node1 in the L1 and the part after the Node2 in the L2 into a new path, deleting one of the two repeated clients if the two repeated clients appear, checking whether the new path meets the constraint, returning to the step 4.3 if the constraint is not met, and abandoning the intersection to carry out the step 5 if the number of times of returning to the step 4.3 reaches the product of the number of the clients in the L1 and the number of the clients in the L2;
step 4.5: adding the new path in the step 4.4 into the chrom1, and if any client appears once in the new path and appears once in other old paths, deleting the duplicate clients in the old paths;
step 4.6: if there is a customer in the second half of L1 that has no path assigned, then the customer is inserted into a feasible insertion location for the other path in chrom1, and if there is no feasible insertion location, then step 5 is aborted. If all is feasible, chrom1 is updated to chrom1', a second descendant chrom2' may be generated by reversing the parent role.
And 5: mutation operation: at Off1And Off2Each of which is generated at [0,1 ]]Random number of intervals r "; if r "<PM, randomly selecting two customer point codes in the chromosome, and interchanging positions; otherwise, directly keeping the current chromosome to the next generation; updating the offspring population Off after traversing all chromosomes1And Off2。
Step 6: from the updated offspring population Off2Of the original liquefied gas distribution problem, i.e., satisfying the time window constraint2_feasible。
And 7: and (3) population merging: merging population P1Updated offspring population Off1And Off2Feasible becomes a new P1(ii) a Merging population P2Updated offspring population Off1And Off2Become new P2。
And 8: calculating a fitness value: separately calculating the population P1And P2The fitness of each chromosome in each dimension of the target.
And step 9: non-dominant ordering: the population P1All individuals in the system are divided into a plurality of layers according to the dominating relation for each dimension fitness value, the first layer is R0Of non-dominant individuals F1The second layer is at R0The non-dominant individual set F obtained after removing the first layer of individuals2And so on, producing all sorted subsetsF＝(F1,F2…); group P2The same is true.
Step 10: calculating P1Crowding distance of individual: let P [ x ]]distanceA crowding distance of individual x, P [ x ]]M is the function value f of the individual x on the sub-target mk(ii) a Then calculate the population P1Crowding distance of all individuals:
Figure BDA0003275818470000141
group P2The same is true.
Step 11: calculating P2Individual violation constraint value: for P2Calculates its time window constraint value, cv (x), that violates the original liquefied gas delivery problem.
Step 12: to P1And P2Performing elite selection operation: defining a classification number x for each individualrank，xrankIf and only if x ∈ Fk(ii) a When two individuals belong to different sorting subsets, the sequence number x is preferentially selectedrankSmall individuals enter Pt+1(ii) a At P1In (b), when x isrankWhen the same, the gathering distance P [ x ] is selected preferentially]distanceLarge Individual entry Pt+1(ii) a At P2In (b), when x isrankIf the values are the same, the individual with smaller violation constraint value CV (x) is selected to enter Pt+1(ii) a Up to Pt+1The scale of (a) is N.
Step 13: iterating the step 4 to the step 11 for the maximum iteration times G to obtain a population P1And selecting one of the solutions according to the priority of the decision maker on each target to make a decision.

Claims (2)

1. A method for optimizing a delivery path of a vehicle containing liquefied gas in bottles, comprising:
step one, establishing a mathematical model according to the description of the liquefied gas distribution vehicle path problem:
defining a complete graph G ═ N, a ═ {0,1,2, …, N } as a set of distribution centers and customer points, { arc (i, j) | i, j ∈ N, i ≠ j } as a set of paths, node 0 as a distribution center node,c is a set of customer points not including the distribution center node 0, and knowing the location of each customer point i, the demand and the distribution time window requirements are giAnd [ Tai,Tbi]The distribution center reaches all customer points from the distribution center by K vehicles at most, each vehicle starts from the distribution center and finally returns to the distribution center, and the maximum cargo capacity of each vehicle is Q and TikTime of vehicle k to customer i, wikFor the waiting time of vehicle k at customer i, a ═ { arc (i, j) | i, j ∈ N, i ≠ j } is the set of edges, defining dijIs the distance of arc (i, j), i.e., the distance from client point i to client point j, and dij＝dji，tijThe real-time loading of the vehicle k from the customer i to the customer j is al for the transport time from the customer i to the customer jijkThe path failure rate is pijAnd the exposure population associated therewith is
Figure FDA0003275818460000011
Liquefied gas delivery contains three targets, the risk is low, the cost is low, the vehicle redundancy is low, and the target function is established as follows:
Figure FDA0003275818460000012
Figure FDA0003275818460000013
Figure FDA0003275818460000014
decision variables:
Figure FDA0003275818460000015
Figure FDA0003275818460000016
the constraints that must be satisfied by a feasible solution to this problem are:
Figure FDA0003275818460000021
Figure FDA0003275818460000022
Figure FDA0003275818460000023
Figure FDA0003275818460000024
Figure FDA0003275818460000025
Figure FDA0003275818460000026
Figure FDA0003275818460000027
Figure FDA0003275818460000028
Figure FDA0003275818460000029
where k is a vehicle for transporting liquefied gas, CVCost of departure for a single transport vehicle, CLIs unit distance fuel cost, CTIs the driver's cost per unit time, DijRepresenting the actual distance or transit time from customer i to customer j; constraint (4) means that each customer site has only one vehicle to serve it; constraint (5) indicates that each customer is visited once and returned to the distribution center; constraint (6) indicates that each vehicle can only access one client at most when departing; constraint (7) indicates that each vehicle can only deliver a maximum of one customer when it arrives; the constraint (8) represents a vehicle load constraint; constraint (9) indicates that after the vehicle arrives at a certain customer node and the delivery is completed, the vehicle must leave the customer and go to the next customer; the constraint (10) indicates that the reduced load of the vehicle after servicing a customer must equal the customer's demand; the constraint (11) represents the time of arrival of the vehicle at the customer; constraints (12) impose a hard time window constraint on each customer, allowing earlier arriving vehicles to wait for the start of the customer time window, although requiring vehicles to have to start delivery within the customer time window;
and step two, solving the model by using a hybrid coevolution optimization method to obtain an optimal solution which is an optimal route.
2. The method for optimizing the distribution path of the vehicle containing liquefied gas according to claim 1, wherein the method for solving the model in the first step by using the hybrid co-evolution optimization method in the second step comprises the following steps:
(1) make F1Representing the model in step one, F2A model representing the removal of (3), (11) and (12) in step one;
(2) coding;
step 2.1, setting parameters: the method comprises the following steps of (1) counting the number N of customer points, the maximum load capacity Q of a vehicle, a demand list T of the customer points, a cross probability PC, a variation probability PM, a population size NP and iteration times G;
step 2.2, encoding: the chromosome is coded in the form of integer coding, the number 0 represents the distribution center, 1,2,3, …, and N represents the customer point, then the distribution route can be coded as (0,1,2,3,0,4,5,6,7,0, …, N, 0);
(3) initializing a population P1And P2：
Step 3.1, respectively using forward insertion heuristic algorithm to construct F1And F2Two viable individuals of (a);
step 3.2, selecting partial individuals in the neighborhood of the individuals in the step 3.1, and forming the initial population P together with other randomly generated individuals1And P2；
(4) Based on sequence crossing operation:
step 4.1, respectively from offspring population Off1And Off2One chromosome was selected as the parent chromosome, designated chrom1 and chrom2, resulting in a chromosome that is [0,1 ]]Random number r 'of segments, if r'<PC, performing the cross operation of the step 4.2 to the step 4.6, otherwise, directly keeping the two chromosomes to the next generation;
step 4.2, randomly selecting a path from parent chromosomes chrom1 and chrom2, and marking the path as L1 and L2;
4.3, randomly selecting a breakpoint from each path, and recording the breakpoint as Node1 and Node 2;
step 4.4, linking the part before the Node1 in the L1 and the part after the Node2 in the L2 into a new path, deleting one of the two repeated clients if the two repeated clients appear, checking whether the new path meets the constraint, if the constraint is met, performing the step 4.5, if the constraint is not met, returning to the step 4.3, and if the number of times of returning to the step 4.3 reaches the product of the number of the clients in the L1 and the number of the clients in the L2, abandoning the cross performing step (5);
step 4.5, adding the new path in the step 4.4 into the chrom1, and if one client appears in the new path and appears in other old paths, deleting the repeated client in the old path;
step 4.6, if a client is not allocated with a path in the second half of the L1, the client is inserted into a feasible insertion position of other paths in the chrom1, if no feasible insertion position exists, the step (5) is abandoned, if all feasible, the chrom1 is updated to chrom1', and a second descendant chrom2' can be generated by reversing the parent roles;
(5) mutation operation: at Off1And Off2Each of which is generated at [0,1 ]]Random number of interval r ', if r'<PM, randomly selecting two customer point codes in the chromosome, and interchanging positions; otherwise, directly keeping the current chromosome to the next generation; updating the offspring population Off after traversing all chromosomes1And Off2；
(6) From updated Off2Of the original liquefied gas distribution problem, i.e., satisfying the time window constraint2_feasible；
(7) And (3) population merging: merging population P1，Off2Feasible and updated offspring population Off1Become new P1(ii) a Merging population P2Updated offspring population Off1And Off2Become new P2；
(8) Calculating a fitness value: separately calculating the population P1And P2Fitness of each chromosome in each dimension of the target;
(9) non-dominant ordering: the population P1All individuals in the system are divided into a plurality of layers according to the dominating relation for each dimension fitness value, the first layer is R0Of non-dominant individuals F1The second layer is at R0The non-dominant individual set F obtained after removing the first layer of individuals2And so on, producing all sort order subsets F ═ F (F)1,F2…), population P2The same process is carried out;
(10) calculating P1Crowding distance of individual: let P [ x ]]distanceA crowding distance of individual x, P [ x ]]M is the function value f of the individual x on the sub-target mkThen calculate the population P1Crowding distance of all individuals:
Figure FDA0003275818460000041
group P2The same process is carried out;
(11) calculating P2Individual violation constraint value: for P2Calculates its time window constraint value, i.e., cv (x), that violates the original liquefied gas delivery problem;
(12) to P1And P2Performing elite selection operation: defining a classification number x for each individualrank，xrankIf and only if x ∈ Fk(ii) a When two individuals belong to different sorting subsets, the sequence number x is preferentially selectedrankSmall individuals enter Pt+1(ii) a At P1In (b), when x isrankWhen the same, the gathering distance P [ x ] is selected preferentially]distanceLarge Individual entry Pt+1(ii) a At P2In (b), when x isrankIf the values are the same, the individual with smaller violation constraint value CV (x) is selected to enter Pt+1(ii) a Up to Pt+1The scale of (A) is N;
(13) iterating the steps 4 to 11, and obtaining a population P by the maximum iteration times G1And selecting one solution from the optimal solutions according to the priority of the decision maker to each target to make a decision, so as to obtain the optimal distribution route of the bottled liquefied gas vehicle.
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