CN107133375A - It is a kind of that the facility addressing optimal method approached is linearized based on Euclidean distance - Google Patents
It is a kind of that the facility addressing optimal method approached is linearized based on Euclidean distance Download PDFInfo
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Abstract
The present invention provides a kind of facility addressing optimal method for linearizing and approaching based on Euclidean distance, and its step is as follows：Step 1: data prediction prepares；Step 2: setting up linear math plan model；Step 3: solving model；Step 4: result is exported：Determine optimal warehouse point position coordinates；By above step, the present invention provides global optimum's site selecting method for the warehouse point location problem of logistics centers location, more efficiently solves the Facility Location in real life.
Description
First, art
The present invention provides a kind of method based on the optimal addressing of facility for linearizing Euclidean distance, and it can be used in city
Public facilitiesplanning, for the distribution of existing city dweller, solves optimal rubbish warehouse point coordinates addressing and corresponding
Resident distributes, with the cost of transportation for reducing resident between its allocated rubbish warehouse, belongs to logistic facilities planning and addressing
Field.
2nd, background technology
In logistic facilities planning field, Warehouse Location problem is to influence the key issue of cost of transportation and efficiency..In economy
In evolution, we are frequently necessary to set one or more collecting and distributing materials, transmission information or performed in certain " warehouse " for servicing
Point, so as to the node-node transmission information for its periphery or offer service.For example, urban construction and planning commercial center, hospital,
During the communal facilitys such as fire station, parking lot, garbage reclamation website, it is often necessary to which where just central point is selected in by consideration can make
City system Operating ettectiveness is optimal.Therefore, in practical problem, these location problems namely asking on the optimal addressing of facility
Topic.How the address of services sites is selected, on the premise of ensureing that each client's point is assigned to suitable station services so that
Total distance of all client's points to its corresponding service point is most short, is a problem in logistics centers location field.
The design problem is to be calculated using tradition k- averages (i.e. k-means) at present, but this method needs are previously given
Initial center point, result of calculation is influenceed by initial center point selection, and the averaging method calculating central point of this method can not
Optimal distance center is ensured of, so optimal solution can not be calculated.Present invention proposition is a kind of to be linearized most based on Euclidean distance
Excellent site selecting method, this method is a kind of method of global optimization, it is ensured that result of calculation can be controlled in arbitrarily small error model
Within enclosing, and avoid influence of the initial solution to final result.
3rd, the content of the invention
3.1 goal of the invention
The mesh of this invention is to provide a kind of facility addressing optimal method for linearizing and approaching based on Euclidean distance, and it is
Efficient optimal case system of selection is provided for the warehouse optimal location problem of point of logistics centers location, it is surrounding to meet warehouse point
Client's point provides the requirement of service, while making total distance in all client's points to its allocated warehouse most short.
3.2 technical scheme
Standardization description is carried out to the problem first：There are n scattered clients in somewhere, and the coordinate and demand of client are
Know.Need to set up m warehouse (or service facility), each warehouse/facility has corresponding total capacity/service ability upper limit.Ask
The optimal warehouse coordinate addressing of solution and client's distribution so that total distance of all client's points to its allocated warehouse/facility is most
It is short.The decision variable of problem is exactly that where to build warehouse point and each warehouse point, to be which client's point carry for the selection
For service so that total distance of all client's points to its allocated warehouse is most short.
Euclidean distance between 2 points is expressed asWhereinWithRepresent respectively between 2 points
X and y-axis are to distance.Because this apart from expression formula is nonlinear, Warehouse Location problem is set to be difficult to obtain optimal solution.This patent is set
The method approached with one group of section has been counted, to replace non-linear Euclidean distance formula, and has ensured that the error replaced can be pre-
First within given arbitrarily small error range ε.The expression formula that this group of section is approached is as follows：
Wherein, q is the quantity in section, and θ is the rotation angle in two adjacent sections, is constant, dependent on given
Small number epsilon.When ε values are to regularly, q and θ calculation formula are as follows：
In above formula, symbol is calculatedRepresent to take the smallest positive integral more than or equal to x.ε, θ and q part relations data such as table 1 below：
Table 1 ε, θ and q relation table
Some symbols of first collection definition, are easy to carry out accurate description to the implementation steps of this patent below：
Based on above symbol definition,
The present invention is a kind of to linearize the facility addressing optimal method approached based on Euclidean distance, by four rapid completions step by step,
It is as follows respectively：
Step 1: data prediction prepares
In the present invention, client's point in two dimensional surface is numbered first, number value is from 1 to N；Secondly, it is necessary to provide client
The coordinate of point, that is, use XiRepresent client's point i abscissa, YiRepresent client's point i ordinate；Then warehouse/facility to be selected is provided
Numbering, number value is from 1 to K；It is finally given positive integer q and given angle radian θ assignment；
Step 2: setting up linear math plan model
According to the thought of optimal location problem, the coordinate of finally selected warehouse point is calculated so that cost of transportation is minimum,
I.e. so that warehouse point and the client's point distance and minimum that are serviced, here, by warehouse point and the client's point distance serviced and title
For object function；The facility site selecting method approached is linearized based on Euclidean distance, linear math plan model is set up；
Wherein, described " setting up linear math plan model ", the way that it is set up is as follows：
(1) optimize the distance and minimum of warehouse point in location problem each client's point being subordinate to it, and by this
Individual distance and it is defined as object function；With the object function of this linear math plan model for setting up the problem, i.e., each visitor
The distance between family point i and its affiliated warehouse point k dikSum up, and cause the distance and as small as possible.Build based on this
Object function under Liru：
(2) each client's point in the two-dimensional coordinate plane in invention is demand point, warehouse point it is intended that client's point
There is provided service, so restrictive condition need ensure each client's point i there is a warehouse point k to provide service for it, i.e., for
Any one client point i, it and can only be assigned to a warehouse point k.Set up constraints 1)：
1)
(3) distance restraint in the present invention enters row constraint using Euclidean distance, so existing in client point i and warehouse point k
, it is necessary to meet client point i and affiliated warehouse point k x/y axial distances not less than client point i and affiliated warehouse point during service relation
K horizontal stroke/Diff N, sets up constraints 2)~5)：
2)
3)
4)
5)
(4) the rotation angle theta in the quantity q in regulation section quantity section and two adjacent sections, and by the above
Restrictive condition 2)~d 5) can be obtainedik xdik yValue, it is possible thereby to provide client point i and warehouse point k Euclidean distance dik, i.e.,
Set up constraints 6)：
6)
Therefore it can summarize and show that linear math plan model is as follows：
Object function：
Constraints：
1)
2)
3)
4)
5)
6)
Step 3: solving model
Solved for above-mentioned linear math plan model, it is considered to a variety of solution modes：(1) direct solution, utilizes list
Pure shape method, branch and bound method, cutting plane algorithm are solved to the linear math plan model；(2) business software is utilized, such as
Lingo, CPLEX etc., are solved；
Because this mathematical programming model is linear, possesses optimal solution completely and solve feasibility；
Wherein, described " model ", refers to the object function set up in step 2 and constraints 1)~6) constituted
Linear math plan model；
Wherein, described " solving model ", Selection utilization AMPL language call CPLEX solver solving models, it is solved
Specific practice it is as follows：
(1) data of cluster required for inputting and cluster basic parameter, set up AMPL data files xxx.dat；
(2) AMPL model file xxx.mod are set up, linear math plan model is set up；
(3) AMPL autoexecs xxx.sh is set up；
(4) autoexec xxx.sh is called using AMPL, starts to solve；
Step 4: result is exported：Determine optimal warehouse point position coordinates
According to final result of calculation, by the decision variable x of modelk、ykAnd uikCan determine warehouse point coordinate and
Corresponding client's membership is (if uik=1, then it represents that client point i provides service by warehouse/facility k), so as to try to achieve optimal
Target function value (i.e. Total_Dis), i.e. total distance in warehouse and client.
By above step, the present invention provides global optimum's site selecting method for the warehouse point location problem of logistics centers location,
More efficiently solve the Facility Location in real life.
Effect and advantage of 3.3 present invention
The present invention has 2 advantages：
(1) compared with traditional K-means, the problem of being influenceed this method avoids locally optimal solution by initial solution；
(2) this method is optimized using linear programming, it is ensured that output result is globally optimal solution.
4th, illustrate
Fig. 1 the method for the invention flow charts.
The numerical results figure of Fig. 2 tradition k-means clustering methods.
Numerical results figures of the Fig. 3 based on this patent method.
Sequence number, symbol, code name are described as follows in figure：
Blockage represents to calculate obtained warehouse point coordinates using new method
Circle represents known client's point coordinates in two dimensional surface
Triangular representation calculates obtained warehouse point coordinates using traditional k-means methods
Line segment represents the belonging relation of the warehouse point and client's point calculated
5th, embodiment
Illustrate the embodiment of the inventive method with specific example below.The example is：In two-dimensional coordinate plane
It is interior, there is client known to 10 coordinate points, it is necessary to set up 3 positions service station undetermined and distribute service relation, make total distance
It is most short, it is assumed that service point ability is without constraint.
The present invention is a kind of to linearize the facility addressing optimal method approached based on Euclidean distance, and as shown in Figure 1, its is specific
Implementation steps are as follows：
Step 1: data prediction
The coordinate data of 10 client's points in two dimensional surface is collected into following table：
The client's point coordinates value of table 2
Then to warehouse point assignment 3, finally provide given positive integer q=18 and determine the assignment of angle radian θ=0.0895.
In order to fully show the feasibility of mathematical modeling, we are using description and solve building for large-scale complex mathematical problem
Mould language (i.e. AMPL)/mathematical programming model solver (i.e. CPLEX) solves software and solved.AMPL is a kind of powerful
Synthesis algebraic language, linear mathematical programming model can be solved.AMPL softwares are read in after model and data file, according to holding
Row strategy, calls the solver of correlation to be solved, and the solver used herein is CPLEX solvers.
Step 2: setting up linear math plan model
Object function：
Constraints：
1)
2)
3)
4)
5)
6)
Step 3: solving model
On the basis of AMPL language, we set up the data file p.dat of above-mentioned case:
The model file p.mod of the case is write according to given mathematical modeling：
Because this mathematical modeling is linear, feasibility is solved with optimal solution.This example is solved using AMPL.Compile
Write corresponding autoexec p.sh：
Finally autoexec p.sh is called to proceed by solution using AMPL.
Step 4: result is exported
The final calculation result run using AMPL is as follows：
The final calculation result run according to AMPL, can obtain final warehouse point coordinates and client's point and warehouse
Corresponding relation between supply and demand, as shown in Figure 2.Result of calculation shows, the target function value come out using the model solution after improvement, i.e. institute
There is client's point with the distance of the warehouse point belonging to it and for 1.61633, and the mesh obtained using traditional k-means clustering methods
Offer of tender numerical value is 1.654592, final warehouse point coordinates and client's point relation between supply and demand corresponding to warehouse, as shown in Figure 3.
Finally, for the ease of observation, the model after improvement and tradition k-means are calculated and tied by we using Tecplot mapping softwares
Fruit warehouse plots scatter diagram with the distribution of client's point with belonging relation figure.
Based on identical client point, result of calculation and the result of calculation of traditional k-means models are compared, can be with
Find out that total distance that new method is obtained is less than the obtainable total distance of tradition k-means methods.In scatter diagram it is also seen that
The position coordinates that two methods calculate obtained warehouse is different, and the method that this patent is provided can find more preferably Optimizing Site Selection
Scheme.
Claims (3)
1. a kind of linearize the facility addressing optimal method approached based on Euclidean distance, it is characterised in that：Its step is as follows：
Step 1: data prediction prepares
In the present invention, client's point in two dimensional surface is numbered first, number value is from 1 to N；Secondly, it is necessary to provide client's point
Coordinate, that is, use XiRepresent client's point i abscissa, YiRepresent client's point i ordinate；Then the volume of warehouse/facility to be selected is provided
Number, number value is from 1 to K；It is finally given positive integer q and given angle radian θ assignment；
Step 2: setting up linear math plan model
According to the thought of optimal location problem, the coordinate of finally selected warehouse point is calculated so that cost of transportation is minimum, even if
Warehouse point and the client's point distance and minimum that are serviced, here, by warehouse point and the client's point distance serviced and referred to as mesh
Scalar functions；The facility site selecting method approached is linearized based on Euclidean distance, linear math plan model is set up；
Step 3: solving model
Solved for above-mentioned linear math plan model, it is considered to a variety of solution modes：(1) direct solution, utilizes simplex
Method, branch and bound method, cutting plane algorithm are solved to the mathematical modeling；(2) business software, such as Lingo and CPLEX are utilized,
Solved；
Because this mathematical programming model is linear, possesses optimal solution completely and solve feasibility；
Step 4: result is exported：Determine optimal warehouse point position coordinates
According to final result of calculation, by the decision variable x of modelk、ykAnd uikDetermine the coordinate of warehouse point and corresponding client
Membership, if uik=1, then it represents that client point i provides service by warehouse/facility k, so as to try to achieve optimal target function value
That is Total_Dis, i.e. warehouse and client total distance；
By above step, the present invention provides global optimum's site selecting method for the warehouse point location problem of logistics centers location, higher
Solve to effect the Facility Location in real life.
2. a kind of facility addressing optimal method approached based on Euclidean distance linearisation according to claim 1, it is special
Levy and be：" setting up linear math plan model " described in step 2, the way that it is set up is as follows：
(1) optimize the distance and minimum of warehouse point in location problem each client's point being subordinate to it, and by this away from
From be defined as object function；With the object function of this linear math plan model for setting up the problem, i.e., each client's point i
With the distance between its affiliated warehouse point k dikSum up, and cause the distance and as small as possible；Set up based on this as follows
Object function：
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<mi>k</mi>
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<mn>1</mn>
</mrow>
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</mrow>
</msub>
</mrow>
(2) each client's point in the two-dimensional coordinate plane in invention is demand point, warehouse point it is intended that client's point is provided
Service, so restrictive condition needs to ensure that each client's point i has a warehouse point k to provide service for it, i.e., for any
One client point i, it and can only be assigned to a warehouse point k, set up constraints 1)：
1)
(3) distance restraint in the present invention enters row constraint using Euclidean distance, so in client point i and warehouse point k presence services
, it is necessary to meet client point i and affiliated warehouse point k x/y axial distances not less than client point i and affiliated warehouse point k's during relation
Horizontal stroke/Diff N, sets up constraints 2)~5)：
2)
3)
4)
5)
(4) the rotation angle theta in the quantity q in regulation section quantity section and two adjacent sections, and being limited more than
Condition 2)~5) obtain dik xdik yValue, thus provide client point i and warehouse point k Euclidean distance dik, that is, set up constraints
6)：
6)
Therefore summarize and show that linear math plan model is as follows：
Object function：
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<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mo>.</mo>
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</mrow>
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</mrow>
</msub>
</mrow>
Constraints：
1)
2)
3)
4)
5)
6)
The symbol referred to above arrived, its connotation is all checked in from the symbol table in specification.
3. a kind of facility addressing optimal method approached based on Euclidean distance linearisation according to claim 1, it is special
Levy and be：" model " described in step 3, refers to object function and the constraints 1 set up in step 2)~6) institute
The linear math plan model of composition；" solving model " described in step 3, Selection utilization AMPL language calls CPLEX is asked
Device solving model is solved, the specific practice that it is solved is as follows：
(1) data of cluster required for inputting and cluster basic parameter, set up AMPL data files xxx.dat；
(2) AMPL model file xxx.mod are set up, linear math plan model is set up；
(3) AMPL autoexecs xxx.sh is set up；
(4) autoexec xxx.sh is called using AMPL, starts to solve.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107633358A (en) * | 2017-09-14 | 2018-01-26 | 北京京东尚科信息技术有限公司 | Facility addressing and the method and apparatus of distribution |
| CN107679810A (en) * | 2017-10-20 | 2018-02-09 | 北京航空航天大学 | A kind of generation method, the device and system of article migration scheme |
| CN109685244A (en) * | 2018-11-08 | 2019-04-26 | 北京交通大学 | The continuous site selecting method of reliability of return is considered under limited information scene |
| CN110826753A (en) * | 2018-08-09 | 2020-02-21 | 阿里巴巴集团控股有限公司 | Resource processing method, device and equipment |
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Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107633358A (en) * | 2017-09-14 | 2018-01-26 | 北京京东尚科信息技术有限公司 | Facility addressing and the method and apparatus of distribution |
| CN107633358B (en) * | 2017-09-14 | 2022-04-12 | 北京京东尚科信息技术有限公司 | Facility site selection and distribution method and device |
| CN107679810A (en) * | 2017-10-20 | 2018-02-09 | 北京航空航天大学 | A kind of generation method, the device and system of article migration scheme |
| CN107679810B (en) * | 2017-10-20 | 2020-10-13 | 北京航空航天大学 | Method, device and system for generating article migration scheme |
| CN110826753A (en) * | 2018-08-09 | 2020-02-21 | 阿里巴巴集团控股有限公司 | Resource processing method, device and equipment |
| CN110826753B (en) * | 2018-08-09 | 2024-04-23 | 阿里巴巴集团控股有限公司 | Resource processing method, device and equipment thereof |
| CN111144675A (en) * | 2018-11-05 | 2020-05-12 | 顺丰科技有限公司 | Partition planning method, device, equipment and storage medium |
| CN109685244A (en) * | 2018-11-08 | 2019-04-26 | 北京交通大学 | The continuous site selecting method of reliability of return is considered under limited information scene |
| CN111598359A (en) * | 2020-06-04 | 2020-08-28 | 上海燕汐软件信息科技有限公司 | Logistics station site selection method and system |
| CN111598359B (en) * | 2020-06-04 | 2023-11-21 | 上海燕汐软件信息科技有限公司 | Logistics station site selection method and system |
| CN114742593A (en) * | 2022-04-22 | 2022-07-12 | 北京信息科技大学 | Logistics storage center optimal site selection method and system |
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