CN116485062B - Method and device for dispatching strip mine trucks - Google Patents
Method and device for dispatching strip mine trucks Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/12—Computing arrangements based on biological models using genetic models
- G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
- G06Q50/02—Agriculture; Fishing; Mining
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Abstract
The invention discloses a method and a device for dispatching a strip mine truck, comprising the following steps: step 1, obtaining a target flow rate by using a multi-target strip mine truck dispatching traffic flow planning model according to a strip mine truck application dispatching instruction; step 2, taking the path with the maximum deviation between the actual flow rate and the target flow rate of each path in actual production at the same moment as the target flow rate as a truck dispatching path to form a truck dispatching scheme; step 3, encoding a truck dispatching scheme gene, generating a chromosome and initializing; step 4, setting a fitness function; step 5, decoding the chromosome into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, and calculating a chromosome fitness function value; step 6, selecting a chromosome with the best adaptability in the previous iteration, and searching an optimal solution; and 7, repeating the steps 5 and 6 until the ending condition is met, and outputting the optimal solution of the truck scheduling scheme. The invention can realize the efficient and energy-saving scheduling target. The invention is suitable for the mining automation of the area where the large-scale strip mine is located.
Description
Technical Field
The invention relates to the technical field of industrial automation, in particular to a method and a device for dispatching a truck in a strip mine.
Background
The mining process of the area where the large-scale strip mine is located generally comprises the steps of explosion penetration, loading, transportation, discharging and the like. The transportation process generally refers to a process that after a strip mine truck loads materials at a loading point by an electric shovel, the materials are transported to a corresponding unloading point for unloading, and after the unloading is completed, the materials continue to return to the loading point for preparing for the next round of transportation, and the process also comprises a process of queuing the strip mine truck at the loading point and the unloading point, and the like.
Research shows that the cost occupied by the transportation process accounts for 60% of the total operation cost of the strip mine, so that the cost reduction in the transportation process is a key point for reducing the operation cost of the area where the strip mine is located. Under ideal conditions, when the strip mine truck reaches the electric shovel at the loading point, the last strip mine truck which is working at the loading point finishes loading at the same time, and the truck and the electric shovel do not need to wait to waste energy and time.
In actual production, due to the fact that the number of motorcades and the number of electric shovels may not be perfectly matched and random events occur, such as uncertainty of truck driving time, uncertainty of loading time and uncertainty of unloading time, idle waiting conditions of some loading point electric shovels or trucks may be caused, reasonable scheduling of the truck transportation process of the strip mine is very important for improving the production efficiency of the strip mine and reducing the production cost. Meanwhile, the conventional manual scheduling method has great randomness, so that the route selection of the strip mine trucks is not necessarily optimal, and the situations of low effective utilization rate of the strip mine trucks and the like cannot be avoided.
Disclosure of Invention
It is an object of the present invention to provide a strip mine truck scheduling method and apparatus that overcomes or at least alleviates at least one of the above-mentioned drawbacks of the prior art.
To achieve the above object, the present invention provides a strip mine truck scheduling method, which includes:
step 1, calculating the optimal flow rate of each path by using a multi-target strip mine truck dispatching traffic flow planning model according to a strip mine truck application dispatching instruction, and taking the flow rate as a target flow rate; the multi-objective strip mine truck dispatching traffic flow planning model is used for simultaneously taking the maximization of the ore production yield in shifts, the minimization of the strip mine truck running cost and the minimization of the production equipment waiting time as optimization objectives;
step 2, acquiring the actual flow rate of each path in actual production at the same time as the target flow rate through a strip mine truck scheduling system, and taking a path corresponding to the maximum difference between the actual flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme;
step 3, carrying out gene coding on the truck dispatching scheme in the step 2, generating a chromosome, and initializing;
step 4, setting a fitness function;
step 5, decoding the chromosome in the step 3 into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, and calculating a chromosome fitness function value;
Step 6, selecting a chromosome with the best adaptability in the previous iteration, and searching an optimal solution through crossover and mutation;
and 7, repeating the step 5 and the step 6 until the ending condition is met, and outputting the optimal solution of the truck scheduling scheme.
Further, the method for acquiring the multi-target strip mine truck dispatching traffic flow planning model in the step 1 specifically comprises the following steps:
step 11, determining basic information of each production element and historical operation data of equipment in the area where the strip mine is located;
step 12, a multi-target strip mine truck dispatching traffic flow planning model is established, a random variable is determined, the random variable is fitted according to collected historical operation data, and the expected value of the variable is substituted into an objective function for calculation;
the step 12 specifically includes:
step 121, taking the ore production yield in the shift as a first sub-target;
step 122, taking the running cost of the strip mine trucks in the shift as a second sub-target;
step 123, taking the wait time of the production equipment in the shift as a third sub-target;
step 124, normalizing the first sub-target, the second sub-target and the third sub-target;
step 125, determining a multi-target strip mine truck dispatching traffic flow planning objective function according to the first sub-objective, the second sub-objective and the third sub-objective;
Step 126, determining constraint conditions of an objective function according to actual mining conditions of the area where the strip mine is located;
in step 127, in the objective function of step 125, the first sub-objective, the second sub-objective and the third sub-objective are maximized, minimized and the multi-objective strip mine truck dispatching traffic planning model is set according to the constraint conditions determined in step 126.
Further, the multi-objective strip mine truck dispatch traffic flow planning model is set as follows:
the constraint settings were as follows:
in the method, in the process of the invention,representation purposeMark function->Indicating total truck traffic of strip mine in shift, < + >>Representing the cost of truck operation in strip mine in shift, < + >>Indicating production equipment waiting time in shift +.>、/>、/>Respectively indicate->、/>、/>Normalized results,/->、/>、/>Respectively indicate->、/>、/>Weight coefficient of>，/>Representing a strip mine truck->Rated load capacity,/>Is a strip mine truck->Total number of->For unloading points->Total number of->For loading point->Total number of->Representing loading point->Storage of ore and waste soil +.>Representing unloading point->Production requirements yield of->Representing loading point->Is tolerant of->Representing unloading point->Is tolerant of->Representing a strip mine truck- >From parking area->To the loading point->Is used for the number of times of driving,representing a strip mine truck->From parking area->To the unloading point->Is>Representing a strip mine truck->From the loading point->To the unloading point->Is a running number of times of the vehicle.
Further, the "determining random variable" in step 12 includes: parameters of the strip mine trucks and electric shovel in the strip mine truck dispatching process are set to random variables.
Further, the specific steps of the step 3 are as follows:
step 31, setting a chromosome as a solution of a truck dispatching scheme, wherein each gene represents a decision variable and uses a real number code, each gene corresponds to a non-negative integer, the numerical value represents the number of times a strip mine truck travels from a starting point to a destination, and meanwhile, the chromosome is divided into 4 gene segments respectively representing the number of times the truck travels from a loading point to an unloading point, from the unloading point to the loading point, from a parking area to the loading point and from the unloading point to the parking area;
step 32, generatingBar chromosomes as an initializing population.
Further, for inclusion ofLoading points,/->Unloading points, < >>In the case of a truck for a strip mine, a region of the strip mine of 1 parking area, the chromosome length is +. >The chromosome is divided into 4 gene segments, the first gene segment is from sequence number 1 to sequence number +.>Representing the number of runs of all strip mine trucks transporting ore and waste from each loading point to each unloading point +.>The method comprises the steps of carrying out a first treatment on the surface of the The second gene fragment in the chromosome is selected from the group consisting of SEQ ID NO->To serial numberRepresenting the number of times of travel of all strip mine trucks from empty to each loading point>The method comprises the steps of carrying out a first treatment on the surface of the The third gene fragment in the chromosome is designated by the sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from the parking area to each loading point +.>Sequence number of the fourth gene fragment in chromosomeTo the serial number->Indicating the number of times of travel of all strip mine trucks from each unloading point to the parking area +.>。
The invention also provides a strip mine truck dispatching device, which comprises:
the real-time monitoring module is used for monitoring the real-time production condition of the area where the strip mine is located;
the scheduling module is used for firstly calculating the optimal flow rate of each path by using a multi-target strip mine truck scheduling traffic flow planning model according to a strip mine truck application scheduling instruction, taking the flow rate as a target flow rate, then obtaining the actual flow rate of each path in actual production at the same moment as the target flow rate, taking the path with the largest difference between the actual flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme, finally carrying out genetic coding on the truck scheduling scheme to generate a chromosome, initializing, decoding the chromosome into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, calculating a chromosome fitness function value, selecting the chromosome with the best fitness in the previous iteration, and searching the optimal solution through crossover and mutation;
The multi-objective strip mine truck dispatching traffic flow planning model takes maximized ore production yield, minimized strip mine truck running cost and minimized production equipment waiting time in shifts as optimization targets;
the method for acquiring the multi-target strip mine truck dispatching traffic flow planning model specifically comprises the following steps:
step 11, determining basic information of each production element and historical operation data of equipment in the area where the strip mine is located;
step 12, a multi-target strip mine truck dispatching traffic flow planning model is established, a random variable is determined, the random variable is fitted according to collected historical operation data, and the expected value of the variable is substituted into an objective function for calculation;
the step 12 specifically includes:
step 121, taking the ore production yield in the shift as a first sub-target;
step 122, taking the running cost of the strip mine trucks in the shift as a second sub-target;
step 123, taking the wait time of the production equipment in the shift as a third sub-target;
step 124, normalizing the first sub-target, the second sub-target and the third sub-target;
step 125, determining a multi-target strip mine truck dispatching traffic flow planning objective function according to the first sub-objective, the second sub-objective and the third sub-objective;
Step 126, determining constraint conditions of an objective function according to actual mining conditions of the area where the strip mine is located;
step 127, in the objective function of step 125, using the maximized first sub-objective, the minimized second sub-objective and the minimized third sub-objective as optimization objectives, and simultaneously, setting a multi-objective strip mine truck dispatching traffic planning model according to the constraint conditions determined in step 126;
the communication module is used for establishing communication connection between the strip mine truck and the background of the dispatching system, dispatching application is carried out on the dispatching module by the communication module after the strip mine truck finishes loading or unloading tasks, and the dispatching module generates a dispatching instruction and then issues the dispatching instruction to the strip mine truck.
Further, the method comprises the steps of,
the multi-target strip mine truck dispatching traffic flow planning model is set as follows:
the constraint settings were as follows:
in the method, in the process of the invention,representing an objective function +.>Indicating total truck traffic of strip mine in shift, < + >>Representing the cost of truck operation in strip mine in shift, < + >>Indicating production equipment waiting time in shift +.>、/>、/>Respectively indicate->、/>、/>Normalized results,/->、/>、/>Respectively indicate->、/>、/>Weight coefficient of>，/>Representing a strip mine truck->Rated load capacity,/ >Is a strip mine truck->Total number of->For unloading points->Total number of->For loading point->Total number of->Representing loading point->Storage of ore and waste soil +.>Representing unloading point->Production requirements yield of->Representing loading point->Is tolerant of->Representing unloading point->Is tolerant of->Representing a strip mine truck->From parking area->To the loading point->Is used for the number of times of driving,representing a strip mine truck->From parking area->To the unloading point->Is>Representing a strip mine truck->From the loading point->To the unloading point->Is a running number of times of the vehicle.
Further, the scheduling module specifically includes:
a chromosome setting subunit for setting a chromosome as a solution of a truck dispatching scheme, each gene representing a decision variable and using real numbers for coding, each gene corresponding to a non-negative integer, the numerical value representing the number of times a strip mine truck travels from a start point to a destination, and dividing the chromosome into 4 gene segments representing the number of times the truck travels from a loading point to an unloading point, from an unloading point to a loading point, from a parking area to a loading point, and from the unloading point to a parking area, respectively;
a population initialization subunit for generatingBar chromosomes as an initializing population.
Further, for inclusion ofLoading points,/->Unloading points, < >>In the case of a truck for a strip mine, a region of the strip mine of 1 parking area, the chromosome length is +.>The chromosome is divided into 4 gene segments, the first gene segment is from sequence number 1 to sequence number +.>Representing the number of runs of all strip mine trucks transporting ore and waste from each loading point to each unloading point +.>The method comprises the steps of carrying out a first treatment on the surface of the The second gene fragment in the chromosome is selected from the group consisting of SEQ ID NO->To serial numberRepresenting the number of times of travel of all strip mine trucks from empty to each loading point>The method comprises the steps of carrying out a first treatment on the surface of the The third gene fragment in the chromosome is designated by the sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from the parking area to each loading point +.>The fourth gene fragment in the chromosome is from sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from each unloading point to the parking area +.>。
Aiming at production targets with high efficiency and low energy consumption in an area where the strip mine is located, a multi-target strip mine truck scheduling traffic flow planning model which simultaneously fuses the maximum production target yield, the minimum production cost and the minimum equipment waiting time as optimization targets is constructed, a truck scheduling scheme is obtained through the multi-target strip mine truck scheduling traffic flow planning model, finally, an optimal solution of the truck scheduling scheme is generated by utilizing a genetic algorithm, after the loading of the strip mine truck is completed, heavy truck scheduling is applied to a strip mine truck scheduling system, and the strip mine truck is sent to the most suitable unloading point for unloading; after the strip mine trucks are unloaded, the empty car dispatching system is applied for empty car dispatching, and the strip mine trucks are dispatched to the most suitable loading points for loading, so that the efficient energy-saving dispatching target can be realized.
Drawings
Fig. 1 is a schematic diagram of a chromosome crossover operation according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of chromosome mutation operation according to an embodiment of the present invention.
Fig. 3 is a block diagram of a strip mine truck scheduling system according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
The method for dispatching the strip mine trucks provided by the embodiment of the invention comprises the following steps:
and step 1, calculating the optimal flow rate of each path by using a multi-target strip mine truck dispatching traffic flow planning model according to a strip mine truck application dispatching instruction, and taking the flow rate as a target flow rate. The multi-objective strip mine truck dispatching traffic planning model takes maximization of ore production yield, minimization of strip mine truck running cost and minimization of production equipment waiting time in shifts as optimization targets.
And 2, acquiring the actual flow rate of each path in actual production at the same time as the target flow rate through a strip mine truck scheduling system, and taking the path with the largest deviation of the actual flow rate, the target flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme.
And 3, carrying out gene coding on the truck dispatching scheme in the step 2, generating a chromosome, and initializing.
And 4, setting a fitness function reflecting the size of the objective function. And selecting the reciprocal of the objective function of the multi-objective strip mine truck dispatching traffic flow planning model as an adaptability function to evaluate the advantages and disadvantages of the feasible solution, wherein the larger the adaptability function is, the smaller the objective function is, and the feasible solution meets the optimization objective.
And 5, decoding the chromosome in the step 3 into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, and calculating a fitness function value of the chromosome, wherein the higher the fitness is, the smaller the objective function is, and the closer the objective function is to an optimization target.
And 6, selecting a chromosome with the best adaptability in the previous iteration, and searching an optimal solution through crossover and mutation.
And 7, repeating the step 5 and the step 6 until the ending condition is met, and outputting an optimal solution of the truck dispatching scheme in a chromosome structure scheme of the step 31. The end condition may be the iteration number, or the end condition of the iteration of the genetic algorithm may be set to be that the fitness function reaches the maximum value, that is, the iteration is ended when the objective function of the multi-objective strip mine truck dispatching traffic flow planning model reaches the minimum value, and the optimal chromosome at this time is the optimal solution of the strip mine truck dispatching problem.
In one embodiment, the method for acquiring the multi-target strip mine truck dispatching traffic flow planning model in the step 1 specifically includes:
And step 11, determining basic information of each production element and historical operation data of equipment in the area where the strip mine is located.
In one embodiment, the basic information of each production element in the area of the strip mine comprises basic production parameters and historical production data of the strip mine, and the basic information comprises the basic production parameters and the historical production data of the strip mineThe representation is performed. Wherein (1)>The sequence numbers indicating the unloading points of the area of the strip mine (the area of the strip mine comprises loading points, unloading points, crushing stations, dumping grounds, parking areas), the following will>The unloading points are simply called unloading points->，/>，/>Indicating the total number of unloading points of the area of the strip mine, < +.>Representing the total number of crushing stations>Representing the total number of the dumping sites; a number indicating the loading point of the area of the strip mine, hereinafter +.>The individual loading points are simply referred to as loading points->，/>，/>Representing the total number of loading points in the area of the strip mine, wherein the loading points generate ores and rocks after blasting operation, and each loading point is provided with an area for loading the strip mine and a soil loading area after separation of the ores and the rocks, so that the area for loading the strip mine and the soil loading area are the same in number; />Representing loading point->To the unloading point->Is the shortest path of (a); />A serial number indicating the vehicle of the transportation fleet in the area of the strip mine, hereinafter +. >The transportation fleet vehicles in the area of the strip mine are simply referred to as strip mine trucks +.>，/>，/>Representing a strip mine truck->Total number of->Total number of strip mine trucks representing first model,/-for the first model of the vehicle>Representing the total number of strip mine trucks of the second model; /> =1，…，/>，/>A parking area number indicating the area of the strip mine, the number of parking areas in the area of one strip mine being one +.>Representing the total number of crushing stations.
In one embodiment, the strip mine equipment historical operating data is composed ofThe representation is performed. Wherein, the liquid crystal display device comprises a liquid crystal display device,representing a strip mine truck->Idle speed in historical production data, +.>Representing a strip mine truck->Full rate in historical production data, < >>Representing a strip mine truck->The amount of loading time in the historical production data, +.>Representing a strip mine truck->Unloading time in the historical production data.
In one embodiment, in order to improve the accuracy of the model, the parameters that change may be represented by random variables on the basis of the parameters given in the above embodiment.
And 12, establishing a multi-target strip mine truck dispatching traffic flow planning model, determining a random variable, fitting the random variable according to the collected historical operation data, and substituting the expected value of the variable into an objective function for calculation. The random variable is obtained by fitting the collected historical production data through a probability distribution function.
In one embodiment, the "determining random variables" in step 12 includes: parameters of the strip mine trucks and electric shovel in the strip mine truck dispatching process are set to random variables. Step 12 specifically includes:
step 121, taking the ore production yield in the shift as the first sub-objective.
In one embodiment, the ore production yield of step 121 may be based on the total amount of open pit truck transport in a shift, since both the ore and the rock produced in a shift in open pit production are transported by open pit trucks to the corresponding unloading pointsExpressed as follows, formula (1):
（1）
in the formula (1), the components are as follows,representing a strip mine truck->Rated load capacity,/>Representing a strip mine truck->From the loading point->To the unloading point->Is a number of times of transportation.
Of course, the ore production yield of step 121 may be expressed by other parameters, and the number of idle runs may be usedThe representation is performed.
Step 122, taking the in-shift strip mine truck operating cost as the second sub-objective.
In one embodiment, within a production shift, the strip mine trucks travel from the parking area to the loading point, loading ore and rock by the electric shovel, transporting the ore and rock to the crushing station or dump, and returning to the loading point for the next round of loading and transporting. Typically, a strip mine truck will return to the parking area after the end of a shift. Thus, the present embodiment may include the second sub-object may include:
Cost of operating a strip mine truck from a parking area to a loading point。
In one embodiment, the costs of driving a strip mine truck from a parking area to a loading pointTaking into account the fuel consumption costs of different types of strip mine trucks and the fixed costs of different types of strip mine trucks in operation, the following formula (2) is calculated:
（2）
in the formula (2), the amino acid sequence of the compound,representing a strip mine truck->From parking area->To the loading point->Is>Indicating parking area +.>And loading point->Shortest path distance between ∈>Representing a strip mine truck->The fuel consumption costs at idle are reduced,representing a strip mine truck->The fixed cost in no-load process can be considered, and meanwhile, the loss cost and the maintenance cost of the strip mine truck can be considered separately, and only the fuel cost can be considered.
Transportation cost of strip mine trucks from loading point to unloading point。
In one embodiment of the present invention, in one embodiment,as shown in the following formula (3), which considers the transportation cost of the strip mine truck from the loading point to the unloading point:
（3）
in the formula (3), the amino acid sequence of the compound,representing a strip mine truck->From the loading point->To the unloading point->Is>Representing +.>To the unloading point->Shortest path distance between ∈ >Representing a strip mine truck->Fuel consumption costs at full load,/-)>Representing a strip mine truck->The fixed cost at full load, which considers both the loss cost and the maintenance cost of the strip mine truck, can be considered separately, and can also only consider the fuel cost.
Cost of empty travel of strip mining trucks from unloading to loading points。
In one embodiment of the present invention, in one embodiment,as shown in the following equation (4), which considers the empty driving cost of the strip mine truck from the unloading point to the loading point:
（4）
in the formula (4), the amino acid sequence of the compound,representing a strip mine truck->From the unloading point->To the loading point->Is a running number of times of the vehicle.
(IV) cost of travel of the strip mine truck from the unloading point back to the parking area。
In one embodiment of the present invention, in one embodiment,is represented by the following formula (5):
（5）
in the formula (5), the amino acid sequence of the compound,representing a strip mine truck->From parking area->To the unloading point->Is>Indicating parking areasAnd unloading point->The shortest path distance between them.
In summary, the calculation formula of the second sub-object is shown in the following formula (6), while taking into consideration the occurrence in the above embodiment、/>、/>And->：
（6）
The objects of the invention may also be achieved by considering only the transportation costs of the strip mine trucks circulating between the loading and unloading points, as in the prior art, and by one or both of the other costs.
Step 123, taking the production equipment waiting time in shift as the third sub-objective.
In one embodiment, production equipment in shifts always operates in a circulating mode, in an ideal state, one strip mine truck reaches a loading point when the last strip mine truck just finishes loading, the last strip mine truck just finishes unloading reaches an unloading point, the utilization rates of the strip mine truck and an electric shovel are 100%, in actual production, the fact that the strip mine truck reaches the loading point and the unloading point too early or too late due to random variables often occurs, the condition that the production equipment waits occurs at the moment, and the production equipment waiting time can reflect the utilization rate of the production equipment. Thus, the present embodiment may include the third sub-object may include:
waiting time of strip mine truck in shift。
In one embodiment, for each strip mine truck, the waiting time in the shift is the total time of the shift minus the working operation time, and the working operation time includes the time from the parking area to the loading point, the round trip time between the loading points, the time from the unloading point to the parking area, the loading time and the unloading time, so the strip mine truck waiting time in the shift is calculated as shown in the following formula (7):
（7）
In the formula (7), the amino acid sequence of the compound,indicating total time of shift->The expression number is->Unloading time of strip mine truck, +.>The expression number is->Full load speed of the strip mine truck, (-)>The expression number is->Idle speed of strip mine truck, +.>The expression number is->Is a loading time for the strip mine truck.
(II) waiting time of electric shovel in shift。
In one embodiment, for each shovel, the wait time for the shovel in the shift is the total time of the shift minus the working time for the shovel to load the strip mine truck, and therefore, the wait time for the shovel in the shift is calculated as shown in equation (8) below:
（8）
open pit truckIdle speed->Is a random variable.
In one embodiment, a strip mine truckIdle speed +.>The historical statistical data of the formula (2) accords with a normal distribution rule, and the formula (9) is as follows:
（9）
in the formula (9), the amino acid sequence of the compound,for idle speed +.>Probability density function of>Is a strip mine truck->Idle speed +.>Mean value of historical statistics of +.>Is a strip mine truck->Idle speed->Variance of historical statistics of (a).
Generating 12 [0,1 ] by approximate distribution]Interval ofInternally uniformly distributed random numbersAccording to the central limit theorem, the strip mine truck +. >Idle speed +.>Can be calculated from the following formula (10):
（10）
open pit truckFull load speed->Is a random variable.
In one embodiment, a strip mine truckFull load speed->The historical statistical data of (2) accords with a normal distribution rule, and the following formula (11) is shown:
（11）
in the formula (11), the amino acid sequence of the compound,is a strip mine truck->Full load speed->Probability density function of>Is a strip mine truck->Full load speed->Mean value of historical statistics of +.>Is a strip mine truck->Full load speed->Variance of historical statistics of (a).
Generating 12 [0,1 ] by approximate distribution]Random numbers uniformly distributed in intervalRandom variable strip mine truck->Is +.>Can be calculated from the following formula (12):
（12）
open pit truckLoading time of +.>Is a random variable.
In one embodiment, a strip mine truckIs loaded with (a)Time->The historical statistical data of (1) accords with a negative index distribution rule, namely:
（13）
in the formula (13), the amino acid sequence of the compound,for loading time +.>Probability density function of>Is a strip mine truck->At loading time->Inverse of the historical statistical data average of (c).
Generate [0,1 ]]Random numbers uniformly distributed in intervalRandom variable strip mine truck>Loading time of +.>Can be calculated from the following formula (14):
（14）
Open pit truckIs +.>Is a random variable.
In one embodiment, a strip mine truckIs +.>The historical statistics of (a) conform to a negative exponential distribution law, as shown in the following formula (15):
（15）
in the formula (15), the amino acid sequence of the compound,for unloading time->Inverse of the historical statistical data average of (c).
Generate [0,1 ]]Random numbers uniformly distributed in intervalRandom variable strip mine truck>The unloading time is as follows:
（16）
in summary, the calculation formula of the third sub-objective is shown in the following formula (17), while taking into account the waiting time of the strip mine truck in the above embodimentWaiting time with electric shovel->And (2) sum:
（17）
in one embodiment, the third sub-objective may be based on equation (17) above, and may also take into account the waiting time of the crushing station within a shiftThe working time of the crushing station is subtracted from the total shift time;
at this time, the liquid crystal display device,
。
and 124, normalizing the first sub-target, the second sub-target and the third sub-target.
Since the 3 sub-objective functions have different dimensions and dimension units, data normalization processing is required in order to eliminate the dimensional influence between indexes. By taking the usual methodsNormalization method for normalizing sub-objective functions to obtain +. >、/>、/>The following formula (18) shows:
（18）
in the formula (18), the amino acid sequence of the compound,respectively->The maximum value which can be reached, decision variables can be set manually, so that each sub-objective function can reach the extreme case of the maximum value respectively,/for>Respectively->The minimum achievable, decision variables can be set manually, respectively to bring each sub-objective function to the extreme of the minimum.
Step 125, determining a multi-target strip mine truck dispatch traffic flow planning objective function according to the first sub-objective, the second sub-objective, and the third sub-objective.
The objective function consists of three sub-objectives: maximizing throughput, minimizing shipping costs, and minimizing equipment waiting time can be described as represented by the following formula (19):
（19）
in the formula (19), the amino acid sequence of the compound,the weight coefficient representing each sub-target can be adjusted according to the actual operation condition and production requirement, and +.>。/>
And 126, determining constraint conditions of the objective function according to actual mining conditions of the area where the strip mine is located.
In one embodiment, the constraint condition needs to be designed according to the actual mining situation of the area where the strip mine is located, and the following condition can be considered:
1. load point storage constraints.
For example: the transportation quantity of the ore and the waste soil at the loading point is smaller than that at the loading point Storage of ore and waste soil +.>The following formula (20) shows:
（20）
2. unloading point production requires constraints.
For example: the output of the unloading point is not lower than that of the unloading pointProduction requirement yield of->The following formula (21) shows:
（21）
3. the operational capacity of the loading point is constrained.
For example: the loading number of the loading point cannot exceed the bearing capacity of the loading pointThe following formula (22) shows:
（22）
4. the capacity constraints of the unloading point.
For example: the unloading number of the unloading point cannot exceed the bearing capacity of the unloading pointThe following formula (23):
（23）
5. departure scheduling constraints.
For example: each strip mine truck is launched at most once and up to one loading point per shift, as shown in formula (24) below:
（24）
6. and (5) vehicle receiving scheduling constraint.
For example: each strip mine truck receives at most one truck and at most one truck from one unloading point, as shown in formula (25) below:
（25）
7. integer constraints.
For example: decision variables、/>、/>Are integers, and are represented by the following formula (26):
（26）
also for example: at the position ofConsider->At the time of (1), then, decision variable +.>、/>、/>、/>Are integers, at this time +.>。
In one embodiment, constraints may be based on the above embodiments, and other factors such as ore grade deviation may be considered.
Step 127, in the objective function of step 125, maximizing the first sub-objective, minimizing the second sub-objective and minimizing the third sub-objective are used as optimization objectives, and at the same time, according to the constraint conditions determined in step 126, setting
The multi-target strip mine truck dispatching traffic flow planning model is set as follows:
the constraint settings were as follows:
in the above embodiment, similar effects can be achieved by using the opportunity constraint model, the related opportunity planning when processing random variables through steps 1, 2 and 3.
In one embodiment, step 3 is specifically as follows:
in step 31, a chromosome is set as a solution of the truck dispatching scheme, each gene represents a decision variable and uses a real number code, each gene corresponds to a non-negative integer, the numerical value represents the number of times of driving a strip mine truck from a starting point to a destination, and meanwhile, the chromosome is divided into 4 gene segments respectively representing the number of times of driving from a loading point to an unloading point, from the unloading point to the loading point, from a parking area to the loading point and from the unloading point to the parking area, so that the calculation is convenient, and the occurrence of infeasible solutions is avoided.
Step 31, the method for encoding the chromosome specifically includes:
Setting a chromosome as a solution of a truck dispatching scheme, wherein each gene represents a decision variable and uses real number coding, each gene corresponds to a non-negative integer, and the numerical value represents the number of times a strip mine truck travels from a starting point to a destination. For inclusion ofLoading point(s)>Unloading point->Chromosomal length for the area of the strip mine where the strip mine truck is located in 1 parking areaDegree is->The chromosome is divided into 4 gene segments, the first gene segment is from sequence number 1 to sequence number +.>Representing the number of runs of all strip mine trucks transporting ore and waste from each loading point to each unloading point +.>The method comprises the steps of carrying out a first treatment on the surface of the The second gene fragment in the chromosome is selected from the group consisting of SEQ ID NO->To the serial number->Representing the number of times of travel of all strip mine trucks from empty to each loading point>The method comprises the steps of carrying out a first treatment on the surface of the The third gene fragment in the chromosome is designated by the sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from the parking area to each loading point +.>Sequence number of the fourth gene fragment in chromosomeTo the serial number->Indicating the number of times of travel of all strip mine trucks from each unloading point to the parking area +.>。
Step 31 reflects the number of times of traveling between any two points of the strip mine truck, is convenient to calculate, and avoids the occurrence of infeasible solutions. Of course, real and binary coding implementations of the prior art may also be employed.
In the above embodiment, in the chromosome coding of the genetic algorithm, binary coding is used instead of real coding to achieve the similar effect of the above embodiment, and similarly, a plurality of chromosomes, each of which represents a scheduling scheme of a strip mine truck, is used to achieve the similar effect.
Step 32, generatingBar chromosomes as an initializing population.
In one embodiment, step 6 specifically includes:
step 61, performing a selection operation on the chromosome. Using the roulette algorithm, individuals with large values are more easily selected based on the ratio of the value of the fitness function of the individuals to the sum of the fitness of all individuals in the population. Has a degree of adaptation ofIs->In other words, the probability of being selected is +.>I.e. the higher its fitness, the greater the probability of being selected.
At step 62, crossover operations are performed on the chromosomes. In the iterative process, certain gene values of chromosomes of a parent individual are changed with a certain probability to form a new individual, so that the local search category can be jumped out, and the whole-region search can be realized.
As shown in FIG. 1, the present example uses two-point crossover, two crossover points are randomly set in the chromosome of an individual, and then partial gene exchange is performed, and crossover operations are performed on the 2 nd to 5 th genes in a pair of chromosomes.
Step 63, mutation operation is performed on the chromosome. New individuals are generated with a certain probability by interchanging part of the chromosomes of two parent individuals with the aim of further expanding the coverage area of limited individuals on the basis of superior parent genes.
As shown in fig. 2, in this example, mutation was performed on the 4 th gene of the chromosome by using a random number to replace the gene value at the point by a random real number, and mutation was performed on the mutated individual by using a multi-point mutation.
The invention provides a strip mine truck scheduling system applying the method, which comprises the following specific processes:
as shown in fig. 3, the truck dispatching system mainly comprises a real-time monitoring module, a dispatching module and a communication module.
The real-time monitoring module can monitor real-time production conditions of the area where the strip mine is located, and the real-time production conditions comprise real-time parameters such as the running times of the strip mine trucks on each path, the quantity of ore and waste soil produced at the loading point and the unloading point, and the like. And can receive the open pit truck status data through the communication module, provide data support for scheduling algorithm.
The scheduling module is used for calculating the optimal flow rate of each path by using a multi-target strip mine truck scheduling traffic flow planning model according to the strip mine truck application scheduling instruction and the input data of the real-time monitoring module, taking the flow rate as a target flow rate, acquiring the actual flow rate of each path in actual production at the same moment as the target flow rate, taking the path with the largest difference between the actual flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme, carrying out gene coding on the truck scheduling scheme to generate a chromosome, initializing, decoding the chromosome into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, calculating a chromosome fitness function value, selecting the chromosome with the best fitness in the previous iteration, and searching the optimal solution through intersection and variation. The scheduling module is also used for issuing scheduling instructions to the strip mine trucks through the communication module to enable the strip mine trucks to go to the next destination.
The communication module establishes communication connection for the strip mine truck and a background of the dispatching system, the communication module conducts dispatching application to the dispatching module after the strip mine truck finishes loading or unloading tasks, and the dispatching module issues the dispatching instruction to the strip mine truck after generating the dispatching instruction.
Compared with the prior art, the invention has the advantages that: the method fully considers the production targets of high efficiency and low energy consumption required by the area of the strip mine, calculates the cost, time and yield concerned by the strip mine production as optimization targets, thereby realizing multi-target simultaneous optimization, improving the productivity, improving the equipment utilization rate and reducing the production energy consumption. Meanwhile, the method considers random variables such as the running speed of the strip mine truck, the loading and unloading time of the strip mine truck and the like in the dispatching process of the strip mine truck, can reduce calculation deviation, and enables the optimization calculation result to be more in line with the actual condition of strip mine production.
Finally, it should be pointed out that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting. Those of ordinary skill in the art will appreciate that: the technical schemes described in the foregoing embodiments may be modified or some of the technical features may be replaced equivalently; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A method of scheduling a strip mine truck, comprising:
step 1, calculating the optimal flow rate of each path by using a multi-target strip mine truck dispatching traffic flow planning model according to a strip mine truck application dispatching instruction, and taking the flow rate as a target flow rate; the multi-objective strip mine truck dispatching traffic flow planning model is used for simultaneously taking the maximization of the ore production yield in shifts, the minimization of the strip mine truck running cost and the minimization of the production equipment waiting time as optimization objectives;
step 2, acquiring the actual flow rate of each path in actual production at the same time as the target flow rate through a strip mine truck scheduling system, and taking a path corresponding to the maximum difference between the actual flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme;
step 3, carrying out gene coding on the truck dispatching scheme in the step 2, generating a chromosome, and initializing;
step 4, setting a fitness function;
step 5, decoding the chromosome in the step 3 into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, and calculating a chromosome fitness function value;
step 6, selecting a chromosome with the best adaptability in the previous iteration, and searching an optimal solution through crossover and mutation;
Step 7, repeating the step 5 and the step 6 until the end condition is met, and outputting an optimal solution of the truck scheduling scheme;
the multi-target strip mine truck dispatching traffic flow planning model is set as follows:
the constraint settings were as follows:
in the method, in the process of the invention,representing an objective function +.>Indicating total truck traffic of strip mine in shift, < + >>Representing the cost of truck operation in strip mine in shift, < + >>Indicating production equipment waiting time in shift +.>、/>、/>Respectively indicate->、/>、/>Normalized results,/->、/>、/>Respectively indicate->、/>、/>Weight coefficient of>，/>Representing a strip mine truck->Rated load capacity,/>Is a strip mine truck->Total number of->For unloading points->Total number of->For loading point->Total number of->Representing loading pointsStorage of ore and waste soil +.>Representing unloading point->Production requirements yield of->Representing loading point->Is tolerant of->Representing unloading point->Is tolerant of->Representing a strip mine truck->From parking area->To the loading point->Is>Representing a strip mine truck->From parking area->To the unloading point->Is>Representing a strip mine truck->From the loading point->To the unloading point->Is a running number of times of the vehicle.
2. The strip mine truck dispatching method of claim 1, wherein the method for acquiring the multi-target strip mine truck dispatching traffic flow planning model in step 1 specifically comprises the following steps:
Step 11, determining basic information of each production element and historical operation data of equipment in the area where the strip mine is located;
step 12, a multi-target strip mine truck dispatching traffic flow planning model is established, a random variable is determined, the random variable is fitted according to collected historical operation data, and the expected value of the variable is substituted into an objective function for calculation;
the step 12 specifically includes:
step 121, taking the ore production yield in the shift as a first sub-target;
step 122, taking the running cost of the strip mine trucks in the shift as a second sub-target;
step 123, taking the wait time of the production equipment in the shift as a third sub-target;
step 124, normalizing the first sub-target, the second sub-target and the third sub-target;
step 125, determining a multi-target strip mine truck dispatching traffic flow planning objective function according to the first sub-objective, the second sub-objective and the third sub-objective;
step 126, determining constraint conditions of an objective function according to actual mining conditions of the area where the strip mine is located;
in step 127, in the objective function of step 125, the first sub-objective, the second sub-objective and the third sub-objective are maximized, minimized and the multi-objective strip mine truck dispatching traffic planning model is set according to the constraint conditions determined in step 126.
3. The strip mine truck scheduling method of claim 2, wherein determining the random variable in step 12 comprises: parameters of the strip mine trucks and electric shovel in the strip mine truck dispatching process are set to random variables.
4. A strip mine truck scheduling method according to any one of claims 1-3, characterized in that step 3 comprises the following specific steps:
step 31, setting a chromosome as a solution of a truck dispatching scheme, wherein each gene represents a decision variable and uses a real number code, each gene corresponds to a non-negative integer, the numerical value represents the number of times a strip mine truck travels from a starting point to a destination, and meanwhile, the chromosome is divided into 4 gene segments respectively representing the number of times the truck travels from a loading point to an unloading point, from the unloading point to the loading point, from a parking area to the loading point and from the unloading point to the parking area;
step 32, generatingBar chromosomes as an initializing population.
5. The strip mine truck scheduling method of claim 4, whereinIn that for inclusion ofLoading points,/->Unloading points, < >>In the case of a truck for a strip mine, a region of a strip mine with 1 parking area, the chromosome length is The chromosome is divided into 4 gene fragments, the first gene fragment is from sequence number 1 to sequence numberRepresenting the number of runs of all strip mine trucks from each loading point to each unloading pointThe method comprises the steps of carrying out a first treatment on the surface of the The second gene fragment in the chromosome is selected from the group consisting of SEQ ID NO->To the serial number->Representing the number of times of travel of all strip mine trucks from empty to each loading point>The method comprises the steps of carrying out a first treatment on the surface of the The third gene fragment in the chromosome is designated by the sequence number +.>To the serial number->Indicating that all strip mine trucks are traveling from the parking area to eachNumber of runs at loading point ∈ ->The fourth gene fragment in the chromosome is from sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from each unloading point to the parking area +.>。
6. A strip mine truck dispatching apparatus, comprising:
the real-time monitoring module is used for monitoring the real-time production condition of the area where the strip mine is located;
the scheduling module is used for firstly calculating the optimal flow rate of each path by using a multi-target strip mine truck scheduling traffic flow planning model according to a strip mine truck application scheduling instruction, taking the flow rate as a target flow rate, then obtaining the actual flow rate of each path in actual production at the same moment as the target flow rate, taking the path with the largest difference between the actual flow rate and the target flow rate as a truck scheduling path to form a truck scheduling scheme, finally carrying out genetic coding on the truck scheduling scheme to generate a chromosome, initializing, decoding the chromosome into an original scheduling scheme, substituting the original scheduling scheme into an fitness function, calculating a chromosome fitness function value, selecting the chromosome with the best fitness in the previous iteration, and searching the optimal solution through crossover and mutation;
The multi-objective strip mine truck dispatching traffic flow planning model takes maximized ore production yield, minimized strip mine truck running cost and minimized production equipment waiting time in shifts as optimization targets;
the method for acquiring the multi-target strip mine truck dispatching traffic flow planning model specifically comprises the following steps:
step 11, determining basic information of each production element and historical operation data of equipment in the area where the strip mine is located;
step 12, a multi-target strip mine truck dispatching traffic flow planning model is established, a random variable is determined, the random variable is fitted according to collected historical operation data, and the expected value of the variable is substituted into an objective function for calculation;
the step 12 specifically includes:
step 121, taking the ore production yield in the shift as a first sub-target;
step 122, taking the running cost of the strip mine trucks in the shift as a second sub-target;
step 123, taking the wait time of the production equipment in the shift as a third sub-target;
step 124, normalizing the first sub-target, the second sub-target and the third sub-target;
step 125, determining a multi-target strip mine truck dispatching traffic flow planning objective function according to the first sub-objective, the second sub-objective and the third sub-objective;
Step 126, determining constraint conditions of an objective function according to actual mining conditions of the area where the strip mine is located;
step 127, in the objective function of step 125, using the maximized first sub-objective, the minimized second sub-objective and the minimized third sub-objective as optimization objectives, and simultaneously, setting a multi-objective strip mine truck dispatching traffic planning model according to the constraint conditions determined in step 126;
the communication module is used for establishing communication connection between the strip mine truck and a background of the dispatching system, dispatching application is carried out on the dispatching module by the communication module after the strip mine truck finishes loading or unloading tasks, and the dispatching module generates a dispatching instruction and then sends the dispatching instruction to the strip mine truck by the communication module;
the multi-target strip mine truck dispatching traffic flow planning model is set as follows:
the constraint settings were as follows:
in the method, in the process of the invention,representing an objective function +.>Indicating total truck traffic of strip mine in shift, < + >>Representing the cost of truck operation in strip mine in shift, < + >>Indicating production equipment waiting time in shift +.>、/>、/>Respectively indicate->、/>、/>Normalized results,/->、/>、/>Respectively indicate->、/>、/>Weight coefficient of>，/>Representing a strip mine truck->Rated load capacity,/ >Is a strip mine truck->Total number of->For unloading points->Total number of->For loading point->Total number of->Representing loading pointsStorage of ore and waste soil +.>Representing unloading point->Production requirements yield of->Representing loading point->Is tolerant of->Representing unloading point->Is tolerant of->Representing a strip mine truck->From parking area->To the loading point->Is>Representing a strip mine truck->From parking area->To the unloading point->Is>Representing a strip mine truck->From the loading point->To the unloading point->Is a running number of times of the vehicle.
7. The strip mine truck scheduling apparatus of claim 6, wherein the scheduling module specifically comprises:
a chromosome setting subunit for setting a chromosome as a solution of a truck dispatching scheme, each gene representing a decision variable and using real numbers for coding, each gene corresponding to a non-negative integer, the numerical value representing the number of times a strip mine truck travels from a start point to a destination, and dividing the chromosome into 4 gene segments representing the number of times the truck travels from a loading point to an unloading point, from an unloading point to a loading point, from a parking area to a loading point, and from the unloading point to a parking area, respectively;
A population initialization subunit for generatingBar chromosomes as an initializing population.
8. The strip mine truck scheduling apparatus of claim 7, wherein for the inclusionLoading points,/->Unloading points, < >>In the case of a truck for a strip mine, a region of a strip mine with 1 parking area, the chromosome length isThe chromosome is divided into 4 gene fragments, the first gene fragment is from sequence number 1 to sequence numberRepresenting the number of runs of all strip mine trucks from each loading point to each unloading pointThe method comprises the steps of carrying out a first treatment on the surface of the The second gene fragment in the chromosome is selected from the group consisting of SEQ ID NO->To the serial number->Representing the number of times of travel of all strip mine trucks from empty to each loading point>The method comprises the steps of carrying out a first treatment on the surface of the The third gene fragment in the chromosome is designated by the sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from the parking area to each loading point +.>The fourth gene fragment in the chromosome is from sequence number +.>To the serial number->Indicating the number of times of travel of all strip mine trucks from each unloading point to the parking area +.>。
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| CA2957708A1 (en) * | 2016-02-12 | 2017-08-12 | Suncor Energy Inc. | Method and system for dispatching a haulage vehicle at a mining site |
| CN112488441A (en) * | 2020-10-23 | 2021-03-12 | 湖南大学 | Intelligent dispatching method and system for strip mine truck |
| CN113222462A (en) * | 2021-05-31 | 2021-08-06 | 西安建筑科技大学 | Strip mine multi-energy truck dispatching optimization method based on co-evolution |
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