CN109948855B - Heterogeneous hazardous chemical transportation path planning method with time window - Google Patents

Heterogeneous hazardous chemical transportation path planning method with time window Download PDF

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CN109948855B
CN109948855B CN201910222496.XA CN201910222496A CN109948855B CN 109948855 B CN109948855 B CN 109948855B CN 201910222496 A CN201910222496 A CN 201910222496A CN 109948855 B CN109948855 B CN 109948855B
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蒋鹏
门金坤
郑松
孔亚广
吕跃华
张良军
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Hangzhou Dianzi University
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Abstract

The invention discloses a heterogeneous hazardous chemical transportation path planning method with a time window. The invention provides a dynamic load transportation risk assessment model considering vehicle types and parking time by fully considering the types of transportation vehicles, transportation loads, transportation road information, population distribution and hazardous chemical substance information, and a multi-objective optimization model for heterogeneous hazardous chemical substance transportation path planning with a time window is constructed. According to the model characteristics, a mixed multi-objective evolutionary algorithm solving problem based on variable neighborhood search is designed, and finally the heterogeneous hazardous chemical substance vehicle path planning method with the time window is established. According to the method, risk factors of dangerous chemical transportation are considered on the basis of a traditional vehicle path planning method by combining with the transportation characteristics of the dangerous chemicals, a heterogeneous dangerous chemical transportation path multi-objective optimization model with a time window closer to the actual condition of dangerous chemical transportation is constructed, and finally a mixed multi-objective algorithm based on variable neighborhood searching is designed to solve the model.

Description

Heterogeneous hazardous chemical transportation path planning method with time window
Technical Field
The invention belongs to the field of risk management of hazardous chemicals, relates to an automation technology, and particularly relates to a heterogeneous hazardous chemical transportation path planning method with a time window.
Background
The transportation of dangerous chemicals is an important component of the chemical industry in China, and the proportion of the transportation of the dangerous chemicals in the whole transportation industry is higher and higher along with the enlargement of the scale of the chemical industry. Due to the special nature of hazardous chemicals, any activity associated with their use is accompanied by a significant risk.
In the transportation process of hazardous chemicals, the probability of hazardous chemical leakage accidents caused by common traffic accidents is very high, and the hazardous chemical transportation accidents can cause large-scale casualties, environmental deterioration and property loss. Due to the needs of industrial development, the risk of dangerous chemical transportation cannot be avoided, the accident probability and the accident consequence can be reduced only through a series of risk management measures, and the planning of the transportation path of the dangerous chemical is one of the main transportation risk management measures.
Many traditional hazardous chemical substance transportation path planning methods only adopt a single vehicle type for transportation and do not consider the time window requirements of users, so a large gap exists between the practical application, in addition, when a plurality of optimization targets are integrated into a single-target optimization problem by adopting a linear weighting function, the importance of each optimization target is difficult to evaluate for weighting, and dimension disasters are easy to generate when the large-scale optimization problem is solved by accurate algorithms such as a branch-and-bound method, a cut plane method, a PILP (pitch image projection and translation phase) method, so that the hazardous chemical substance transportation path planning is very difficult.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a heterogeneous hazardous chemical substance vehicle path planning method with a time window.
The object of the present invention is to determine the size and route of a heterogeneous transport fleet to transport a specific hazardous chemical from one storage center to a set of customers with time windows, minimizing the total transport cost, transport risk and average vehicle redundancy, in the context of meeting all given constraints, for some of the challenges in hazardous chemical transport path planning.
The technical scheme of the invention is that a dynamic load transportation risk assessment model considering vehicle types and parking time is provided by fully considering the types of transportation vehicles, transportation loads, transportation road information, population distribution and hazardous chemical substance information, and a multi-objective optimization model with a time window for heterogeneous hazardous chemical substance transportation path planning is constructed. According to the model characteristics, a mixed multi-objective evolutionary algorithm solving problem based on variable neighborhood search is designed, and finally the heterogeneous hazardous chemical substance vehicle path planning method with the time window is established.
The invention has the beneficial effects that: according to the method, risk factors of hazardous chemical transportation are considered on the basis of a traditional vehicle path planning method in combination with the transportation characteristics of the hazardous chemical, a heterogeneous hazardous chemical transportation path multi-objective optimization model with a time window closer to the actual condition of hazardous chemical transportation is constructed, and finally a mixed multi-objective algorithm based on variable neighborhood searching is designed to solve the model; the method has the characteristics of openness, flexibility, low calculation complexity and the like.
Drawings
FIG. 1 is a flow chart of an algorithm;
FIG. 2 is a diagram of a pareto ranking strategy;
fig. 3 is a schematic diagram of a routing exchange crossover operator.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention comprises the following steps:
step 1: and acquiring basic data including transport vehicle information, transport road information, population distribution and hazardous chemical substance information.
Step 2: and constructing a multi-objective optimization model for heterogeneous hazardous chemical transportation path planning with a time window.
The invention defines a multi-objective optimization model in a complete directed graph G ═ N, L. N ═ 0,1,2 …, N } is the set of nodes in the directed graph, node 0 is the warehouse node, C ═ 1,2 …, N } is the set of customer nodes, and L is the set of arcs in the directed graph. q. q.siI ∈ C is the nonnegative demand of client i, [ Ta ∈ Ci,Tbi]I ∈ C as client time window, TaiRepresenting the earliest time that the customer can accept the service, TbiRepresenting the latest time that the customer can accept the service.
The transport motorcade consists of K vehicle types, QkK ∈ K is the maximum load, fc, of model KkFixed use cost, V, for k ∈ Ks model kkK ∈ K is the number of usable vehicles of model K, ARkAnd K ∈ K is the vehicle accident rate of the vehicle type K. arcijE L represents the transport path between nodes i, j e N,alijfor the distance of transit between nodes i, j ∈ N, tijFor the transit time between nodes i, j e N,
Figure BDA0002004077070000021
k belongs to K is the non-negative unit distance transportation cost from the node i belongs to N to the node j belongs to N of the vehicle with the vehicle type K, and pdijThe exposure population density between nodes i, j ∈ N.
For the sake of closeness to practical operating conditions, the present invention assumes that each vehicle model has a uniform transportation cost per unit distance and an infinite number of available vehicles, i.e.,
Figure BDA0002004077070000022
k ∈ K and VkInfinity, K ∈ K. In addition, the present invention assumes that population density and leakage incident probability are uniform on each arc for purposes of calculating transportation risk. The model constraints are: each transport vehicle must start from the storage node and finally return to the storage node; each customer can only be served once within a time window, and split delivery is not allowed; the transport vehicle is allowed to be in the earliest service time TaiArrive before, in which case it must wait until time TaiThe client can be supplied with goods only after the arrival; the vehicle is not allowed to overload.
The invention defines the optimization objective function as a multi-objective three-dimensional vector, namely minimize (Z) ═ Z1,Z2,Z3]Wherein Z is1Is an objective function for minimizing the total cost of transportation; z2Is an objective function for minimizing the risk of transportation; z3Is an objective function for minimizing average vehicle redundancy. The optimization model requires two sets of variables, where SivkIs a first set of variables defined as vehicles V ∈ V of type K ∈ KkTime to reach customer node i ∈ C; the second group of variables is decision variables defined as the supply sequence of the vehicle to the customer node:
Figure BDA0002004077070000023
in the formula (I), the compound is shown in the specification,
Figure BDA0002004077070000024
is a decision variable i, j belongs to N; k belongs to K; v < Vk
Objective function Z1
Figure BDA0002004077070000031
Objective function Z2
Figure BDA0002004077070000032
In the formula (I), the compound is shown in the specification,
Figure BDA0002004077070000033
for a vehicle V ∈ V with the type K ∈ KkIn the arcijThe probability of dangerous chemical leakage accidents caused by the E L is left; csijIs an arcijThe consequence of the leakage accident on the L is left, and is expressed as the number of people affected within one kilometer from the incident place; in order to calculate the probability of dangerous chemical accidents, the invention combines the corresponding vehicle accident rate, the conditional probability of the given accident, the arc length, the vehicle load and the waiting time as follows:
Figure BDA0002004077070000034
in the formula, PRijIs an arcijThe conditional probability of a given accident on the L belongs to; beta and alpha are standard coefficients established according to the types of dangerous chemicals;
Figure BDA0002004077070000035
for a vehicle V ∈ V with the type K ∈ KkIn the arcijBelongs to the load on L;
Figure BDA0002004077070000036
is a vehicle V ∈ V of the type K ∈ KkWaiting time at node j for N; the accident rate of the vehicle in the parking state is lower than that in the driving state, so that τ is a correction factor smaller than 1.
Objective function Z3
One of the common optimization objectives of the conventional time windowed vehicle path planning problem is to optimize the number of vehicles. However, for heterogeneous vehicle path planning problems with unlimited number of vehicles with time windows, average vehicle redundancy is more appropriate because the optimization objective involves, but is not limited to, a reduction in the number of vehicles.
Figure BDA0002004077070000037
In the formula (I), the compound is shown in the specification,
Figure BDA0002004077070000038
is a vehicle V ∈ V of the type K ∈ KkThe degree of redundancy of;
Figure BDA0002004077070000039
is the number of all vehicles in use.
The model constraints are:
Figure BDA00020040770700000310
the above equation indicates that each customer site can only be accessed once by the transport vehicle.
Figure BDA00020040770700000311
The above equation indicates that all vehicles are not permitted to overload.
Figure BDA00020040770700000312
Figure BDA00020040770700000313
Figure BDA00020040770700000314
The above three equations indicate that all vehicles must start from the warehousing node 0 and return to the warehousing node 0 after visiting several non-repeat customers.
Figure BDA00020040770700000315
The above equation indicates that each customer must be satisfied within a predefined time window, allowing the vehicle to arrive early, but not late.
And step 3: and (4) model solving, namely designing a hybrid multi-objective evolutionary algorithm based on variable neighborhood search.
The invention follows a framework of a hybrid multi-target evolutionary algorithm, and provides a hybrid multi-target evolutionary algorithm based on variable neighborhood search, which solves the problem of path planning of multi-target heterogeneous vehicles with time windows in hazardous chemical transportation. The algorithm integrates a two-stage forward insertion algorithm for initial population construction, a special evolutionary operator for optimizing different targets, and a variable neighborhood search meta-heuristic for local search development. The algorithm flow is shown in figure 1.
Initial population construction
In order to meet the requirements and specifications of the model constructed in the step 2, the invention designs a two-stage forward insertion method on the basis of the traditional forward insertion algorithm. Vehicles of various types are infinitely available. Thus, in the first stage, the fixed fleet is used to relax the model constraints. In order to serve as many customers as possible, the vehicle model with the largest load capacity is adopted to form a fixed cluster. The heterogeneous vehicle path planning problem with the time window is converted into a vehicle path planning problem with the time window.
Figure BDA0002004077070000041
The above formula is used to define the initial customer point, al, of each path0iThe distance from the node i to the warehousing node 0 is shown; angleiIs the polar angle of node i; csA set of client nodes that have not been accessed. The current path selects the initial customer point, forward insertion from CsTo select a customer that minimizes the total cost of insertion between each edge in the current route without violating time and capacity constraints. When the current route does not have a feasible insertion location for the unassigned client, a new route is established. When all clients have been allocated, the first phase ends. In the second stage, the current stationary fleet is replaced by the fleet of vehicles with the minimum average degree of redundancy, i.e., the transport vehicle type k for each route is such that the degree of redundancy VR for that vehicle isvkAnd minimum. And converting the vehicle path planning problem with the time window into a heterogeneous vehicle path planning problem with the time window again.
② pareto sorting
After the initial population construction is completed, the population levels are divided by adopting a pareto sorting method. The pareto sorting method adopts the pareto domination relation to compare the advantages and disadvantages among individuals in the population. Assuming the population to be P, the pareto ranking method needs to calculate two parameters n of each individual P E P in the populationpAnd Sp,npIs the number of individuals in the population that dominate the individual p, SpIs the set of individuals dominated by individual p in the population. After traversing all individuals in the population, all npAn individual equal to 0 will be divided into the first layer P of the population1For P1The individual within l ∈ P1The dominant set of individuals is SlGo through Slm.epsilon.S of the individual in (1)lExecute nm=nm-1, all nmAn individual equal to 0 will be divided into a second level P of the population2And so on until the entire population is stratified. Hierarchy P with sequence number 11As a non-dominant layer, P1All individuals in the population are pareto optimal solutions for the current population. As shown in fig. 2, a solution assigned rank 1 is prioritized over a solution assigned rank 2, i.e., a solution assigned rank 1 is better than the remaining solutions at any optimization goal. Thus, is assigned toThe level 1 solution is non-dominant.
③ evolution operator
And selecting individuals in the current population to perform cross variation operation through a binary system champion algorithm to generate a new population, wherein the probability of the selected individuals performing the cross variation operation is higher when the hierarchical serial number is smaller.
Because the standard evolutionary operator can not ensure to generate a feasible sub-solution, the performance is possibly poor, and the hybrid multi-objective evolutionary algorithm based on the variable neighborhood search adopts a route exchange crossover operator and a route elimination mutation operator.
The route-switching crossover operator is designed for optimization objectives 1 and 2, as shown in FIG. 3, and allows good routes or gene sequences in one chromosome to be shared with other individuals in the population. The gene sequences to be exchanged travel less costly and perfectly match the time window. The optimization objective 3 reflects the average cost per unit of transportation, meaning that the optimization objective can reduce average vehicle redundancy by eliminating a particular route altogether or eliminating a customer and deploying a fixed cost less vehicle. Therefore, the hybrid multi-objective evolutionary algorithm based on variable neighborhood search adopts a route elimination mutation operator to improve the optimization objective 3.
Development of local search
To further improve individuals within the population, hierarchy P with sequence number 1 is randomized1And selecting a non-dominant solution as an initial solution of a Variable Neighborhood Search (VNS) meta-heuristic algorithm for local search. The basic idea of the VNS is a process of expanding a search range by systematically changing a neighborhood structure set in a search process to obtain a local optimal solution, then changing the neighborhood structure set based on the local optimal solution, expanding the search range and finding another local optimal solution. By "neighborhood" is meant the set of all solutions that are adjacent to the initial solution, obtained by some method (e.g., Exchange, Or-opt, etc.). The VNS is a meta-heuristic algorithm based on local search, is particularly excellent when used for solving NP-difficult problems, and is particularly suitable for solving large-scale problems. General meta-heuristic algorithms, such as tabu search algorithm, hill climbing method, simulated annealing method, etc.,a single neighborhood structure is used for searching. The VNS is based on an initial solution, a neighborhood structure is transformed according to a certain mechanism, and the search range is continuously enlarged to enable the algorithm to jump out of local optimization, so that a global optimal solution is obtained.
The VNS meta-heuristic algorithm mainly comprises four stages of initialization, dithering, local search and moving. The algorithm initialization phase defines an initial solution x and a set of neighborhood structures Nμ,μ=1,2,...,μmax. In the algorithm dithering phase, a solution x' is randomly selected from the μ -th neighborhood of the initial solution x. The algorithm local search phase uses the relocation operator (relocation) to generate a new solution x "from x'. If x 'dominates x, x' will replace x to become a new initial solution, otherwise, the algorithm adopts a new neighborhood structure N in the moving phaseμThe above process is repeated. If all neighborhood structures cannot further improve the initial solution, the VNS meta-heuristic algorithm stops the oscillation process.
Iteration of algorithm
Repeating the second to the fourth until the maximum iteration number of the algorithm is met. Finally, a group of pareto optimal solutions meeting different preferences is given out by a mixed multi-objective evolutionary algorithm based on variable neighborhood search.

Claims (1)

1. A heterogeneous hazardous chemical transportation path planning method with a time window is characterized by comprising the following steps:
acquiring basic data including transportation vehicle information, transportation road information, population distribution and hazardous chemical substance information;
step 2: constructing a multi-objective optimization model for heterogeneous hazardous chemical transportation path planning with a time window;
the multi-objective optimization model is defined in a complete directed graph G ═ N, L; n ═ 0,1,2 …, N } is the node set in the directed graph, node 0 is the warehousing node, C ═ 1,2 …, N } is the customer node set, L is the arc set in the directed graph; q. q.siIs the non-negative demand of client i, i belongs to C, Tai,Tbi]For the client time window, TaiRepresenting the earliest time that the customer can accept the service, TbiIs acceptable on behalf of the customerThe latest time of the transaction;
the transport motorcade consists of K vehicle types, QkIs the maximum load of the vehicle model K, K belongs to K, fckIs a fixed use cost of vehicle type k, VkNumber of usable vehicles, AR, of vehicle type kkIs the vehicle accident rate for model k; arcijRepresenting the transport path between nodes i, j, alijIs the distance of transit between nodes i, j, tijThe transit time between nodes i, j,
Figure FDA0002004077060000011
is the non-negative unit distance transportation cost, pd, from node i to node j for a vehicle of type kijIs the exposed population density between nodes i, j;
assuming that each vehicle model has a uniform cost per unit distance for transportation and an unlimited number of available vehicles, i.e.,
Figure FDA0002004077060000012
and VkInfinity; meanwhile, the population density and the leakage accident probability on each arc are assumed to be uniform; the model constraints are: each transport vehicle must start from the storage node and finally return to the storage node; each customer can only be served once within a time window, and split delivery is not allowed; the transport vehicle is allowed to be in the earliest service time TaiArrive before, in which case it must wait until time TaiSupplying goods to the customer only after the arrival; the vehicle is not allowed to overload;
defining the optimization objective function as a multi-objective three-dimensional vector, minimize (Z) ═ Z1,Z2,Z3]Wherein Z is1Is an objective function for minimizing the total cost of transportation; z2Is an objective function for minimizing the risk of transportation; z3Is an objective function for minimizing average vehicle redundancy; the optimization model requires two sets of variables, where SivkIs a first set of variables defined as the time at which a vehicle v of type k arrives at customer node i; the second group of variables is decision variables defined as the supply sequence of the vehicle to the customer node:
Figure FDA0002004077060000013
in the formula (I), the compound is shown in the specification,
Figure FDA0002004077060000014
is a decision variable i, j belongs to N; k belongs to K; v. of<Vk
Objective function Z1
Figure FDA0002004077060000015
Objective function Z2
Figure FDA0002004077060000016
In the formula (I), the compound is shown in the specification,
Figure FDA0002004077060000021
is a vehicle of type k v in arcijThe probability of causing dangerous chemical leakage accidents is increased; csijIs an arcijUp-leakage incident consequences, expressed as the number of affected people within one kilometer of the incident site; to calculate the probability of a hazardous chemical accident, the corresponding vehicle accident rate, conditional probability of a given accident, arc length, vehicle load and waiting time are combined as follows:
Figure FDA0002004077060000022
in the formula, PRijIs an arcijThe conditional probability of the given accident; beta and alpha are standard coefficients established according to the types of dangerous chemicals;
Figure FDA0002004077060000023
is of typek vehicle v is in arcijA load on the rotor; wt. ofjvkIs the waiting time of vehicle v of type k at node j;
objective function Z3
Figure FDA0002004077060000024
In the formula (I), the compound is shown in the specification,
Figure FDA0002004077060000025
is the degree of redundancy of vehicle v of type k;
Figure FDA0002004077060000026
is the number of all vehicles in use;
the model constraints are:
Figure FDA0002004077060000027
the above formula indicates that each customer site can only be accessed once by the transport vehicle;
Figure FDA0002004077060000028
the above equation indicates that all vehicles are not permitted to overload;
Figure FDA0002004077060000029
Figure FDA00020040770600000210
Figure FDA00020040770600000211
the third expression shows that all vehicles need to start from the warehousing node 0 and return to the warehousing node 0 after visiting a plurality of non-repeated customers;
Figure FDA00020040770600000212
the above equation indicates that each customer must be satisfied within a predefined time window, allowing the vehicle to arrive ahead, but not to be delayed;
step 3, model solution is carried out, and a hybrid multi-target evolutionary algorithm based on variable neighborhood search is designed;
initial population construction
In order to meet the requirements and specifications of the model constructed in the step 2, a two-stage forward insertion method is designed on the basis of the traditional forward insertion algorithm; in the first stage, a fixed cluster is adopted to relax model constraints; in order to serve as many clients as possible, the vehicle type with the largest load capacity is adopted to form a fixed cluster; the heterogeneous vehicle path planning problem with the time window is converted into a vehicle path planning problem with the time window;
Figure FDA00020040770600000213
the above formula is used to define the initial customer point, al, of each path0iThe distance from the node i to the warehousing node 0 is shown; angleiIs the polar angle of node i; csA set of client nodes that have not been accessed; the current path selects the initial customer point, forward insertion from CsTo select a customer that minimizes the total cost of insertion between each edge in the current route without violating time and capacity constraints; establishing a new route when the current route has no feasible insertion position for the unallocated client; when all the clients are distributed, the first stage is finished; in the second phase, the current stationary fleet is replaced with a fleet of vehicles with a minimum average degree of redundancy, i.e., each route has a transport vehicle type kMaking the redundancy level VR of the vehiclevkMinimum; converting the vehicle path planning problem with the time window into a heterogeneous vehicle path planning problem with the time window again;
② pareto sorting
After the initial population construction is completed, dividing the population levels by adopting a pareto sorting method; comparing the advantages and disadvantages of individuals in the population by adopting a pareto domination relation in a pareto sorting method; assuming the population to be P, the pareto ranking method needs to calculate two parameters n of each individual P E P in the populationpAnd Sp,npIs the number of individuals in the population that dominate the individual p, SpIs a set of individuals governed by an individual p in the population; after traversing all individuals in the population, all npAn individual equal to 0 will be divided into the first layer P of the population1For P1The individual within l ∈ P1The dominant set of individuals is SlGo through Slm.epsilon.S of the individual in (1)lExecute nm=nm-1, all nmAn individual equal to 0 will be divided into a second level P of the population2And so on until the whole population is layered; hierarchy P with sequence number 11As a non-dominant layer, P1All individuals in the population are pareto optimal solutions of the current population;
③ evolution operator
Selecting individuals in the current population to perform cross variation operation through a binary system champion algorithm to generate a new population, wherein the probability of the selected individuals to perform the cross variation operation is higher when the hierarchical serial number is smaller;
because the standard evolutionary operator can not ensure to generate a feasible sub-solution, the performance is possibly poor, and the hybrid multi-target evolutionary algorithm based on variable neighborhood search adopts a route exchange crossover operator and a route elimination mutation operator; the route exchange cross operator aims at the optimization target Z1And optimization target Z2Designed, this operator allows a good route or gene sequence in one chromosome to be shared with other individuals in the population; the gene sequences to be exchanged have a low travel cost and are perfectly matched with the time window; optimization objective Z3Reflecting the average cost per unit of transportation, the optimization objective can be generalAverage vehicle redundancy is reduced by completely eliminating a particular route or eliminating customers and deploying a fixed cost smaller vehicle; therefore, the hybrid multi-objective evolutionary algorithm based on variable neighborhood search adopts a route mutation elimination operator to improve the optimized objective Z3
Development of local search
To further improve individuals within the population, hierarchy P with sequence number 1 is randomized1Selecting a non-dominated solution as an initial solution of a variable neighborhood search meta-heuristic algorithm for local search; the basic idea of variable neighborhood search is a process of expanding a search range by systematically changing a neighborhood structure set in a search process to obtain a local optimal solution, then changing the neighborhood structure set based on the local optimal solution, expanding the search range and finding another local optimal solution;
the variable neighborhood search meta-heuristic algorithm mainly comprises four stages of initialization, dithering, local search and movement; the algorithm initialization phase defines an initial solution x and a set of neighborhood structures Nμ,μ=1,2,…,μmax(ii) a In the algorithm dithering stage, randomly selecting a solution x' from the mu neighborhood of the initial solution x; in the algorithm local search stage, a new solution x 'is generated from x' by adopting a repositioning operator; if x 'dominates x, x' will replace x to become a new initial solution, otherwise, the algorithm adopts a new neighborhood structure N in the moving phaseμRepeating the above process; if all neighborhood structures can not further improve the initial solution, stopping the oscillation process by the VNS meta-heuristic algorithm;
iteration of algorithm
Repeating the second step to the fourth step until the maximum iteration number of the algorithm is met; finally, a group of pareto optimal solutions meeting different preferences is given out by a mixed multi-objective evolutionary algorithm based on variable neighborhood search.
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