CN109886493A - A kind of Logistics System Design method based on improvement multi-objective particle swarm algorithm - Google Patents
A kind of Logistics System Design method based on improvement multi-objective particle swarm algorithm Download PDFInfo
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Abstract
Intelligent logistics application field is belonged to based on the Logistics System Design method for improving multi-objective particle swarm algorithm the present invention provides a kind of, mainly solves the problems, such as while handling the low of logistics system to build cost and high conevying efficiency.This method first by logistics system build cost and conevying efficiency is described as corresponding objective function and carries out mathematical description to the form of solution；Then the bound of target function value is expanded using the method for dilatation, and grid is built according to this bound, calculate the mesh coordinate of particle；Then guidance particle is picked out using the method for dual range decision, and population formula is combined to generate follow-on population, filter out optimal solution set preservation；Finally according to the demand of client, suitable logistics system is selected from optimal solution set.The logistics system of the method for the present invention design, which had not only been able to satisfy, to be built into originally low but also is able to satisfy the high demand of conevying efficiency, has actual use value well.
Description
Technical field
The invention belongs to Intelligent logistics application field, it is related to determining to the method and dual range of target function value bound dilatation
The method of plan；The Logistics System Design side of specifically a kind of multi-objective particle swarm algorithm based on dilatation and dual range decision
Method can be used for the design etc. of Intelligent logistics and transport hub.
Background technique
With the rapid development of Intelligent logistics technology, the design of logistics system seems of crucial importance.Logistics system is by crowd
More express delivery points and logistics center's composition, the design method of the system select the express delivery of certain amount from all express delivery points first
Point is used as logistics center, and remaining express delivery point is then distributed to logistics center again.Each express delivery point is only under the jurisdiction of a logistics
Center is completely interconnected between multiple logistics centers, and between each express delivery point also can only by logistics center come
Connection, so logistics center plays the key effect for connecting each express delivery point.Currently, the design of logistics system has become intelligent object
A hot spot of area research is flowed, the especially research to logistics center position has been subjected to the extensive concern of domestic and foreign scholars.
For Logistics System Design problem, traditional mode when designing logistics system only by low cost for the purpose of, which includes each
Freight and logistics center between express delivery point establish expense, but nowadays only consider that expense cost can not meet
How huge market competition then designs a kind of inexpensive and efficient, quick logistics system and has become Intelligent logistics
Challenging project in field.
Then many domestic and foreign scholars continuously improve optimization to the design scheme of logistics system, and propose new theoretical sight
Point: mixed integer programming, Bi-level Programming Models and Based on Entropy theory etc., and with the extensive use of intelligent algorithm, it is right
It solves problems and also provides new scheme, such as the addressing based on ant group algorithm.It is most of in these methods only to consider
Cost factor (including expense is built by freight and logistics center) although some methods increase other factors, and gives this
The specified weight coefficient of a little factor distribution forms a kind of new synthesis sexual factor, but since there may be lances between these factors
Shield constraint, the feature of these factors respectively cannot be highlighted by being formed integral with one another, to cannot carry out very well to entire logistics system
Optimal improvements affect the value of its actual use.
Summary of the invention:
In view of the above-mentioned problems, the present invention proposes a kind of Logistics System Design side based on improvement multi-objective particle swarm algorithm
Method is built and high efficiency transport with solving the problems, such as while handling the low cost of logistics system.
Realizing the key technology of the method for the present invention is: first by logistics system build cost and haulage time is described as pair
The objective function answered and the form progress mathematical description to solution；Then by target function value by the way of dilatation
Bound is expanded, and builds grid using bound, calculates the mesh coordinate of particle；Then the side of dual range decision is used
Method picks out guidance particle, and population formula is combined to generate follow-on population, filters out optimal solution set preservation；Last root
According to the demand of client, suitable logistics system is selected from optimal solution set.
To realize above-mentioned target, the technical solution of the present invention is as follows:
A kind of Logistics System Design method based on improvement multi-objective particle swarm algorithm, specific implementation step include the following:
(1) position of n express delivery point is stored in [X, Y], wherein X=[x1,x2,…,xi,…,xn], Y=[y1,
y2,…,yi,…,yn],xiIndicate the abscissa of i-th of express delivery point, yiThe ordinate for indicating i-th of express delivery point, is stored with Matrix C
Freight between all express delivery points stores haulage time between each express delivery point with matrix T, is stored with the row vector F of a 1*n
The expense of vertical logistics center, binary column vector H (h are set up in each express delivery point1,h2,…hi,…,hn) in each element table
Show whether each express delivery point is logistics center, if hi=1, then express delivery point i is logistics center, and the number for preparing to establish logistics center is used
P is indicated.Solution (i.e. particle) is the binary matrix of a n*n, and diagonal line upper value is the row (column) where 1 in the matrix
For logistics center, each column refers to an express delivery point in logistics system in matrix, the behavior express delivery point where numerical value is 1 in each column
The number of logistics center subjected.For convenience of use, express delivery point logistics center subjected all in solution is deposited
Enter in array hub, the subscript of array corresponds to express delivery point number, as hub (i) indicates the logistics center that express delivery point i is subordinate to；
(2) logistics system objective function build it is as follows:
Wherein i and j is the number of express delivery point, and k and l are respectively express delivery point i and j logistics center subjected, express delivery point and
The corresponding relationship of logistics center is hub.Since the transport between each logistics center is relatively convenient, so the traffic expense between them
With and haulage time all multiplied by a discount factor β (0 < β < 1).f1In first half be entire logistics system traffic expense
With wherein Cik+βCkl+CljIndicate express delivery point i to logistics center k, logistics center k to logistics center l, logistics center l to express delivery
The sum of the freight of point j, f1Latter half F*H be the expense for establishing logistics center；f2For entire logistics system cargo transport
Time；
(3) location information, that is, solution of nPOP particle of random initializtion, the location information set note of these particles
For POP, nPOP speed of random initializtion, these sets of speeds are denoted as V, initialize maximum number of iterations gmax, external archival
Per one-dimensional grid dividing number nGrid in capacity nRep, object space, the number of objective function is 2, current iteration number is t；
(4) target function value for calculating all particles, is indicated with Epa, enables each particle individual optimal for its own.Then
It filters out in Pareto optimal particle deposit external archival, location information is denoted as APOP, and corresponding target function value is denoted as Arc；
(5) grid is carried out using the particle in external archival to build, then calculate the mesh coordinate at object space midpoint；
(6) particle sizing operation is guided by dual range decision-making technique.After selecting guidance particle, calculated using population
Method more new formula generates new particle, then generates random number r, as r > 0.8, carries out differential variation to the new particle of generation,
Otherwise without mutation operation.If the new particle generated dominates current particle, new particle is replaced into the corresponding optimal grain of individual
Son.Newly-generated population generation replaces current POP, calculates the objective function of POP and current Epa is replaced to gather.Particle swarm algorithm is public
Formula is as follows:
Wherein k refers to that k-th of particle in population, t are current iteration number, and w is tradeoff local search and global search
Parameter, c1、c2For Studying factors, r1、r2It is the random number between 0,1, PkFor the individual desired positions of particle k, grain is led in G guide
The position of son,Refer in the t times iteration, the speed of particle k,Refer to the position of particle k in the t times iteration；
(7) POP and APOP, Epa and Arc are merged respectively, then pick out the optimal grain of Pareto by the update of external archival
Son, the external archival before updating carry out external archival delete operation if the population of external archival is more than nRep, delete
Extra particle；
(8) as t > gmax, Arc, APOP are exported, step (5) is otherwise gone to and carries out circulate operation；
(9) finally by the demand of client, suitable scheme is selected from external archival.
Beneficial effects of the present invention:
(1) present invention introduces the methods of dilatation expands the grid in object space, can will be gone up in original grid,
The borderline point of lower limit is assigned in new small grid, the information of particle corresponding to boundary point is completely saved in this way, thus one
Determine the diversity that optimal solution set is improved in degree.
(2) present invention introduces the methods of dual range decision to screen corresponding particle, firstly for the grain in each small grid
Two distances of sub-definite: one is optimum point that corresponding points of the particle functional value in object space are currently located small grid to it
Distance, which embodies particle and converges on the characteristic of current small grid optimum point, this ensure that whole diversity, allows solution
Collection can be homogeneously dispersed on the forward position Pareto；It, should be away from the other is distance of the corresponding points of the particle functional value to ideal point
From the ability reacted particle and converge on ideal point, convergence is helped to improve.Then using the two distances to external archival
In particle selected, not only can guarantee global diversity, but also convergence can be improved.
(3) present invention is in addition to considering that freight between express delivery point and logistics center and logistics center established takes
With influence of the haulage time factor to entire logistics system outside factor, is also added, a kind of new multitask logistics system is formd
System, relative to the logistics system of other single task targets, the method in the present invention has more practical application value.
Detailed description of the invention
Fig. 1 is the overall flow figure of the method for the present invention.
Fig. 2 is dual range schematic diagram.
Fig. 3 is object space figure.
Fig. 4 is object space grid chart.
Fig. 5 is the object space grid chart after dilatation.
Fig. 6 is that dual range decision dominates schematic diagram.
Fig. 7 is 3- logistics center logistics system figure.
Fig. 8 is 4- logistics center logistics system figure.
Fig. 9 is 5- logistics center logistics system figure.
Specific embodiment
One, theoretical basis introduction
1. multi-objective problem basic conception
X=(x in formula Chinese style1,x2,...,xn) it is decision variable, n is the dimension of decision variable, and m is objective function
Number, Ω are the set of decision variable, and Y is the codomain of decision variable, i.e. object space.In multi-objective problem, Pareto solution
Related definition it is as follows:
Define 1.Pareto to dominate: solution p, q ∈ Ω are denoted as if p dominates qP is to dominate particle, and q is by domination grain
Son, and meet following two condition:
It is optimal to define 2.Pareto: if X is Pareto optimal solution,MakeIt sets up.
Define the set of all Pareto optimal solutions in 3.Pareto optimal solution set PS: Ω.
The definition forward position 4.Pareto: PF=F (x) | X ∈ PS }.
Define 5. ideal point R:R (r1,r2,...,rm) indicate, wherein ri=min { fi(x) | x ∈ Ω }, i=1,2 ...
M, m are the number of objective function.
Define 6. optimum points: after object space is divided into several small grids, each dimension is minimum in each small grid region
Value point is the small grid optimum point, as shown in Fig. 2, shadow region is a certain small grid in object space, in the small grid most
Advantage is point Z.
2. particle swarm optimization algorithm more new formula
Each particle is made of speed and position in particle swarm algorithm, and more new formula is as follows:
Wherein k refers to that k-th of particle in population, t are current iteration number, and w is tradeoff local search and global search
Parameter, c1、c2For Studying factors, r1、r2It is the random number between 0,1, PkFor current particle k individual desired positions, G guide is led
The position of particle,Refer in the t times iteration, the speed of particle k,Refer to the position of particle k in the t times iteration.
Two, the present invention is based on the Logistics System Design methods for improving multi-objective particle swarm algorithm
Referring to Fig.1, specific implementation step of the invention includes as follows.
Step 1. is stored in the position of n express delivery point in [X, Y], wherein X=[x1,x2,…,xi,…,xn], Y=[y1,
y2,…,yi,…,yn], xiIndicate the abscissa of i-th of express delivery point, yiThe ordinate for indicating i-th of express delivery point, is stored with Matrix C
Freight between all express delivery points stores haulage time between each express delivery point with matrix T, is stored with the row vector F of a 1*n
The expense of vertical logistics center, binary column vector H (h are set up in each express delivery point1,h2,…hi,…,hn) in each element table
Show whether each express delivery point is logistics center, if hi=1, then express delivery point i is logistics center, and the number for preparing to establish logistics center is used
P is indicated.Solution (i.e. particle) is the binary matrix of a n*n, and diagonal line upper value is the row (column) where 1 in the matrix
For logistics center, each column refers to an express delivery point in logistics system in matrix, the behavior express delivery point where numerical value is 1 in each column
The number of logistics center subjected.For convenience of use, express delivery point logistics center subjected all in solution is deposited
Enter in array hub, the subscript of array corresponds to express delivery point number, as hub (i) indicates the logistics center that express delivery point i is subordinate to.With following
Solution S for illustrate, express delivery point 2,4 is logistics center in this solution, and express delivery point 1,5 is under the jurisdiction of in logistics
The heart 2, express delivery point 3 are under the jurisdiction of logistics center 4.Then the program is stored in final result hub, hub (1)=2, hub (3)=4,
Hub (5)=2；
Building for step 2. logistics system objective function is as follows:
Wherein i and j is the number of express delivery point, and k and l are respectively express delivery point i and j logistics center subjected, express delivery point and
The corresponding relationship of logistics center is hub.Since the transport between each logistics center is relatively convenient, so the traffic expense between them
With and haulage time all multiplied by a discount factor β (0 < β < 1).f1In first half be entire logistics system traffic expense
With wherein Cik+βCkl+CljIndicate express delivery point i to logistics center k, logistics center k to logistics center l, logistics center l to express delivery
The sum of the freight of point j, f1Latter half F*H be the expense for establishing logistics center；f2For entire logistics system cargo transport
Time；
Location information, that is, the solution of nPOP particle of step 3. random initializtion, the location information set of these particles
It is denoted as POP, nPOP speed of random initializtion, the speed and location information of each particle are the matrixes of same type, these speed
Degree set is denoted as V, initialization maximum number of iterations gmax, external archival capacity nRep, in object space per one-dimensional grid dividing
Number nGrid, the number of objective function is 2, current iteration number is t；
Step 4. calculates the target function value of all particles, is indicated with Epa, enables each particle individual optimal for its own.
Then it filters out in Pareto optimal particle deposit external archival, location information is denoted as APOP, and corresponding target function value is denoted as
Arc；
Step 5. carries out grid using the particle in external archival and builds, the upper limit of all particle functional values in external archival
It is denoted as CU=(fu1,fu2), lower limit is denoted as CL=(fl1,fl2), wherein fu1And fu2The maximum value of respectively two objective functions,
fl1And fl2The minimum value of respectively two objective functions, the span of entire grid are DC=(dc1,dc2), wherein dci=fui-
fli, i=1,2.Bound when traditional method establishes grid using CU and CL as entire grid, Fig. 3, Fig. 4 are illustrated will be outer
Corresponding points of the particle functional value in object space are mapped to the process in grid in portion's archive, and each dimension mesh coordinate is opened from 1
Begin to count, mapping method utilizes following formula:
G (X) is the mesh coordinate of particle, diFor the width of each small grid in i-th dimension in object space, nGrid is mesh
Mark the number of small grid on every dimension in space.It, can not be on grid upper and lower limit boundary but in grid in the mapped
Point distribute reasonable mesh coordinate, which can only be assigned randomly to the small grid where its phase near point, be had in this way
The information contained in particle corresponding to the point is damaged, certain influence is produced to whole diversity, as shown in Figure 4, point p8
It is exactly to be located at the borderline point of lower limit, the reasonable mesh coordinate of point can not be immediately arrived at.
Then, when establishing grid introduce dilatation rate a, a=0.1, in external archival the target function value of particle it is upper
Lower limit carries out dilatation, and obtaining the new upper limit is CU '=(fu '1,fu′2), fu 'i=fui+α*dci, new lower bound is CL '=(fl '1,
fl′2), fl 'i=fli-α*dci, i=1,2, grid is re-established according to new bound, then calculates the net at object space midpoint
Lattice coordinate.After grid dilatation, the borderline point of upper and lower limit in original grid can be assigned in new small grid, rather than
In net boundary, the information of particle corresponding to boundary point is completely saved in this way, to improve optimal solution to a certain extent
The diversity of collection.It is evenly dividing as shown in figure 5, draw by entire object space after dilatation, it can be seen that point p8Positioned at small grid
Interior, very easily finding out its mesh coordinate is (3,1)；
Step 6. guides particle sizing operation by dual range decision-making technique.After establishing grid in object space,
About beam convergence is carried out to particle therein is located at by small grid, uniform grid facilitates optimal solution set and is homogeneously dispersed in
On the forward position Pareto；All particles are drawn close to ideal point as much as possible simultaneously, help to improve convergence.It is right based on this two o'clock
Particle in each small grid defines two distances: one is that corresponding points of the particle functional value in object space are current to it
The distance d of the optimum point of place small grid1, d1The characteristic that particle converges on current small grid optimum point is embodied, this ensure that whole
Disaggregation can be homogeneously dispersed on the forward position Pareto for the diversity of body；The other is the corresponding points of the particle functional value to reason
Think the distance d of point R2, d2The ability that particle converges on ideal point has been reacted, convergence is helped to improve.Using the two apart from right
Particle in external archival carries out optimum selecting, not only can guarantee global diversity, but also can improve convergence.As shown in Fig. 2, certain
The d of particle functional value corresponding points X in object space1And d2Value.
Based on d1And d2Dual range decision-making technique it is as follows: all particle functional values are right in object space in certain small grid
The set that should be put is denoted as P, d1(pi) and d2(pi) respectively indicate particle i functional value corresponding points p in current small gridiD1And d2
Value.The corresponding points p of two particle functional values in certain small grid1,p2∈ P, if p1,p2Meet following two condition:
Then p1Dual range dominates p2, notep1To dominate point, p2For by domination point.
The screening that particle is guided on the basis of based on apart from decision-making technique, after establishing grid in object space,
The concentration of the small grid is judged by the population contained in small grid, the closeness of small grid can be anti-in object space
Answer the dispersibility and diversity of entire disaggregation.
During screening guides particle, the lesser small grid of concentration, intensive journey are selected with wheel disc bet method first
It is more sparse to spend the smaller particle for illustrating this region, facilitates before guiding integral particles into Pareto from this regional choice guidance particle
Along upper sparse region, increase the diversity of disaggregation；After determining small grid, each grain in the small grid is then calculated
The d of subfunction value1、d2Value；Particle is dominated as guidance particle, if there is multiple finally, dominating principle by dual range and filtering out
Particle is dominated, then Pareto optimal particle is selected according to the optimal definition of Pareto, then therefrom selects one at random as guidance
Particle.As shown in fig. 6, by taking three particles contained in certain small grid as an example, correspondence of their functional value in object space
Point is X1、X2、X3, pass through their d1、d2Value can determine whether out X1、X2Dominate X3, but X1And X2That Pareto is optimal again, then from
A point is randomly choosed in the two, and using particle corresponding to the point as guidance particle.
After selecting guidance particle, new particle is generated using particle swarm algorithm more new formula, random number r is then generated, works as r
When > 0.8, differential variation is carried out to the new particle of generation, otherwise without mutation operation.If the new particle generated dominates current grain
New particle is then replaced corresponding individual optimal particle by son.Newly-generated population generation replaces current POP, calculates the objective function of POP
And current Epa is replaced to gather.Particle swarm algorithm formula is as follows:
Wherein k refers to that k-th of particle in population, t are current iteration number, and w is tradeoff local search and global search
Parameter, c1、c2For Studying factors, r1、r2It is the random number between 0,1, PkFor the individual desired positions of particle k, grain is led in G guide
The position of son,Refer in the t times iteration, the speed of particle k,Refer to the position of particle k in the t times iteration；
POP and APOP, Epa and Arc are merged respectively, then pick out Pareto most by the update of step 7. external archival
Excellent particle, the external archival before updating carry out external archival delete operation if the population of external archival is more than nRep,
Extra particle is deleted, specific delete operation is as follows:
When the population in external archival is more than its capacity nRep, then need to carry out delete operation to extra particle.
The biggish small grid of concentration is selected by wheel disc bet method first, deleting particle in the region crowded from this facilitates disaggregation
It is uniformly distributed on the forward position Pareto and multifarious raising；After determining small grid, then calculate in the small grid
The d of each particle target function value point1、d2Value；Finally, filtering out the particle conduct dominated by the two distance properties
Deleted particle inferior, such as X in Fig. 63Corresponding particle is the particle inferior in current small grid.If there is multiple dominated
Particle, then therefrom randomly choose the particle that is dominated as particle inferior, if the particle not dominated, the area Ze Ci
One is randomly choosed in domain to be deleted as particle inferior；
Step 8. exports Arc, APOP as t > gmax, otherwise goes to step 5 and carries out circulate operation；
Step 9. selects suitable scheme finally by the demand of client from external archival.
Effect of the invention can be further illustrated by following emulation experiment.
1. simulated conditions and parameter
For the present invention, designs three kinds of different logistics systems and examine effect of the invention, respectively 3- logistics center object
Streaming system, 4- logistics center logistics system, 5- logistics center logistics system, as shown in Fig. 7, Fig. 8, Fig. 9, small circle is fast in figure
It passs a little, small square is logistics center, and all express delivery points are connected with its logistics center subjected with line, between each logistics center
It is full-mesh.
Basic parameter setting: nPOP=500, nRep=500, nGrid=10, a=0.1, gmax=1000, β=0.7.
Since these three logistics systems are there are two objective function, in freight C Euclidean distance of each element between each point multiplied by
Round, road transport time T are the matrix of n*n, random number of each element between (0,1), C and T again after 10
Diagonal line on numerical value be 0.The design parameter of three kinds of logistics systems is as follows:
The parameter of 3- logistics center logistics system are as follows: n=20, p=3, X=[104.138772039671,
27.9075405335330-1.21376369914406,76.1754858683866,46.8508687849655,
28.5535825270306 70.4117195721234,45.7245181673279,21.7620052223005 ,-
11.7771366479796 105.753521171260,101.300762157825,71.9802867233212,
55.4811941603809-6.84606567541479,99.5910302156580 ,-0.965788166429432,
1.27682695666201 76.2514343865497,96.5404803307022], Y=[24.8797948152149 ,-
0.659516076836153,52.5108291501149,4.37306267615794,4.43709319045759,
21.5453887120451 25.3094363645217,70.1435318255384,45.5459970340529,
99.9726026875866 6.13052123313900,96.9213363449853,76.4855152510402,
99.0976623909150 4.46942455525787,45.6437428197911,25.1302298566599,
77.2101080844489 54.4024408715235,81.1768475820158], F=[2243542,2803144,
2295855,2986372,2322686,2830857,2240386,2341558,2140532,2637093,2746779,
2606777,2483056,2706939,2710189,2742330,2698078,3014778,2261138,2773310].
The parameter of 4- logistics center logistics system are as follows: n=30, p=4, X=[57.1429892037075,
19.4337523198531 79.3611057331790,77.1139493075336,40.6022137786206,
44.2217615852422-0.837230958127928,19.3180998311229 ,-7.33840635345424 ,-
2.58171034920250 35.3557580531495,98.7125511633879,21.7519545003929,
105.077564251302 85.9949815063609,79.6103857767674,38.9326793770479,
62.7250542774574 61.6338639627466,102.550837200052,2.59426348437106,
15.0656494219379 101.801213198699,59.6948699271058,37.4658254101381,
57.6880151895217 104.271525842211, -2.69912536921917,15.8772721572572,
80.7156214937726], Y=[6.70257255844537,20.0851814447077,1.02766478748953,
36.8725092979074 5.58071983926377,60.4166272461501,101.767004188502 ,-
3.17356074467163 2.84680939406826,21.2971524483926,76.1466630501610,
20.1324670899642 98.4980046543081,100.364159805552,99.1648238585128,
19.3669944845044 96.5569549523305,78.9223602619353,42.5550895136848,
45.8155772655635 76.1316002461007,87.9247061746139,85.0869265416903,
100.561691667392 18.9959782355877,17.6711524309826,2.77590191926008,
57.6846491525907 58.4603900228863,62.9453904557361], F=[4213822,3928056,
4341785,5258282,3778073,4394827,5081654,3634645,4787681,5298818,4061322,
3795424,4776394,5175141,4644037,5158294,3901531,4899384,4173370,4302087,
3834449,5014248,4669037,4871166,4989545,3677036,5248667,4442521,4900667,
4878005]。
The parameter of 5- logistics center logistics system are as follows: n=40, p=5, X=[45.8648027495244,
30.5096762099853 36.0458462551390,1.00349707013271,14.1744336018160,
15.5291604623110 84.0660072855024,83.9619774840057,95.1101697641359 ,-
3.44501497449531 61.6011990938269,49.7928810223638,45.0825290075192,
2.00537494121631 80.4605676340377,46.8387805091699,88.4492187717388,
72.8449071123131-2.34079290766359,66.5608106960060,38.9419161687396,
98.4563817974956 88.2404870268952,102.342309375751,33.4919642868826,
65.6577371374812 104.837569391561,52.0315725856579,98.1921030381034,
1.12207539245658 47.4915383824927,100.425558369170,4.37679455845659,
18.1862316986661-2.17047747374656,100.994240402014,81.3396113332616,
22.4361374476554 28.2084775217169,14.7823593740661], Y=[85.5374857274981 ,-
2.34383170325013 83.3844424242493,68.5367673052319,36.9267583803276,
14.0178666936811 82.8479685727583,65.3190309878006,83.0069519355311,
51.0556768350552 64.8991944422674,52.2860432112343,101.219131578098,
98.6504835565727 50.7884336584117,36.1454107594655,36.1707831530772,
35.2425022548435-0.185709783642805,48.2282896168603,50.6402979060659,
48.6681823000465-0.948819658249342,19.3089946858684,20.8010252966513,
18.3690441166342 72.5331539702709,12.2973799761750,100.064821643433,
16.9389089812665 71.2795990527605,1.43220906270753,32.4080755873600,
1.58347602884650 85.1688860627622,33.8551193746944,94.2072103567580,
102.923088405729 56.6908329027921,66.9794941957189], F=[6292946,6725708,
5883460,4824577,5448724,6220641,6561518,5390602,5882100,6636986,6111134,
5972895,5488853,5679165,6579461,5517900,5799066,5575866,6309983,6046730,
6244533,5866195,5648005,5834100,4866500,5677607,6991762,6548177,6426424,
6512688,6491330,6695471,6523300,7014295,4971931,5642398,5868425,5317470,
4796746,7004217].
2. emulation content and analysis of experimental results
Test 1:3- logistics center logistics system
3 are picked out from 20 express delivery points as logistics center, then by remaining 17 express deliveries point distribute to this three
A logistics center, each express delivery point are only under the jurisdiction of a logistics center, must just can phase by logistics center between each express delivery point
Mutually connection.
Experimental result: each express delivery point logistics center subjected be hub=[19,9,9,19,9,9,19,8,9,9,19,
19,19,8,9,19,9,9,19,19], logistics center and the distribution of express delivery point are as shown in fig. 7,8,9,19 be wherein logistics center.
Test 2:4- logistics center logistics system
4 are picked out from 30 express delivery points as logistics center, then by remaining 26 express deliveries point distribute to this three
A logistics center, each express delivery point are only under the jurisdiction of a logistics center, must just can phase by logistics center between each express delivery point
Mutually connection.
Experimental result: each express delivery point logistics center subjected are as follows: hub=[25,25,4,4,25,6,17,25,25,25,
6,6,17,6,17,4,17,6,6,4,6,17,4,17,25,4,4,6,6,6], logistics center and express delivery point distribution as shown in figure 8,
Wherein 4,6,17,25 be logistics center.
Test 3:5- logistics center logistics system
5 are picked out from 40 express delivery points as logistics center, then by remaining 35 express deliveries point distribute to this three
A logistics center, each express delivery point are only under the jurisdiction of a logistics center, must just can phase by logistics center between each express delivery point
Mutually connection.
Experimental result: each express delivery point logistics center subjected are as follows: hub=[1,16,1,16,31,12,31,31,31,
12,1,12,1,1,12,16,16,26,12,12,12,1,16,26,16,26,31,12,12,12,31,16,16,16,16,12,
12,31,12,31], logistics center and the distribution of express delivery point are as shown in figure 9,1,12,16,26,31 be wherein logistics center.
From experimental result picture, it is apparent that the method for the present invention can in low cost and in the case where high conevying efficiency, if
The different logistics systems with actual use value is counted out, the demand of different user is able to satisfy, there is good practicability.
Claims (8)
1. a kind of based on the Logistics System Design method for improving multi-objective particle swarm algorithm, which comprises the steps of:
(1) position of n express delivery point is stored in [X, Y], wherein X=[x1,x2,…,xi,…,xn], Y=[y1,y2,…,
yi,…,yn], xiIndicate the abscissa of i-th of express delivery point, yiThe ordinate for indicating i-th of express delivery point is stored all with Matrix C
Freight between express delivery point is stored haulage time between each express delivery point with matrix T, is stored in respectively with the row vector F of a 1*n
A express delivery point sets up the expense of vertical logistics center, binary column vector H (h1,h2,…hi,…,hn) in each element indicate each
Whether express delivery point is logistics center, works as hi=1, then express delivery point i is logistics center, prepares the number p table for establishing logistics center
Show；Solution, i.e. particle, are the binary matrix of a n*n, and the row or column where diagonal line upper value is 1 in the matrix is
Logistics center, each column refers to an express delivery point in logistics system in matrix, the behavior express delivery point institute of numerical value where 1 in each column
The number for the logistics center being subordinate to；By in express delivery point logistics center's deposit array hub subjected all in solution, count
The subscript of group corresponds to express delivery point number, and hub (i) indicates the logistics center that express delivery point i is subordinate to；
(2) logistics system objective function build it is as follows:
Wherein, i and j is the number of express delivery point, and k and l are respectively express delivery point i and j logistics center subjected, express delivery point and logistics
The corresponding relationship at center is hub；Freight and haulage time between each logistics center are all multiplied by discount factor a β, 0 <
β < 1；f1In first half be entire logistics system freight, wherein Cik+βCkl+CljIndicate express delivery point i into logistics
Heart k, logistics center k are to logistics center l, logistics center l to the sum of the freight of express delivery point j, f1Latter half F*H be build
The expense of vertical logistics center；f2For the entire logistics system cargo transport time；
(3) the location information set of the location information, that is, solution of nPOP particle of random initializtion, these particles is denoted as
POP, nPOP speed of random initializtion, these sets of speeds are denoted as V, and initialization maximum number of iterations gmax, external archival hold
Per one-dimensional grid dividing number nGrid in amount nRep, object space, the number of objective function is 2, current iteration number is t；
(4) target function value for calculating all particles, is indicated with Epa, enables each particle individual optimal for its own；Then it screens
Out in Pareto optimal particle deposit external archival, location information is denoted as APOP, and corresponding target function value is denoted as Arc；
(5) grid is carried out using the particle in external archival to build, then calculate the mesh coordinate at object space midpoint；
(6) particle sizing operation is guided by dual range decision-making technique；After selecting guidance particle, more using particle swarm algorithm
New formula generates new particle, then generates random number r, as r > 0.8, carries out differential variation to the new particle of generation, otherwise
Without mutation operation；When the new particle of generation dominates current particle, then new particle is replaced into corresponding individual optimal particle；
Newly-generated population generation replaces current POP, calculates the objective function of POP and current Epa is replaced to gather；Particle swarm algorithm formula is such as
Under:
Wherein, k refers to that k-th of particle in population, t are current iteration number, and w is the ginseng for weighing local search and global search
Number, c1、c2For Studying factors, r1、r2It is the random number between 0,1, PkFor the individual desired positions of particle k, particle is led in G guide
Position,Refer in the t times iteration, the speed of particle k,Refer to the position of particle k in the t times iteration；
(7) POP and APOP, Epa and Arc are merged respectively, then pick out Pareto optimal particle by the update of external archival,
External archival before update carries out external archival delete operation when the population of external archival is more than nRep, and it is extra to delete
Particle；
(8) as t > gmax, Arc, APOP are exported, step (5) is otherwise gone to and carries out circulate operation；
(9) finally by the demand of client, suitable scheme is selected from external archival.
2. Logistics System Design method according to claim 1, which is characterized in that grid described in step (5) is built,
It operates in the steps below:
(2.1) it carries out grid using the particle in external archival to build, the upper limit of all particle functional values is denoted as in external archival
CU=(fu1,fu2), lower limit is denoted as CL=(fl1,fl2), wherein fu1And fu2The maximum value of respectively two objective functions, fl1
And fl2The minimum value of respectively two objective functions, the span of entire grid are DC=(dc1,dc2), wherein dci=fui-fli,
I=1,2；
(2.2) dilatation rate α is utilized, α=0.1 carries out dilatation to the bound of the target function value of particle in external archival, obtains
The new upper limit is CU'=(fu '1,fu′2), fu 'i=fui+α*dci, new lower bound is CL'=(fl '1,fl′2), fl 'i=fli-α*
dci, i=1,2, corresponding points of the particle functional value in object space in external archival are mapped to grid according to the following formula
In:
Wherein, G (X) is the mesh coordinate of particle, diFor the width of each small grid in i-th dimension in object space, nGrid is mesh
The number of small grid on every dimension in space is marked, each dimension mesh coordinate is started counting from 1.
3. the Logistics System Design method according to claims 1 or 2, which is characterized in that dual range described in step (6)
Decision-making technique operates in the steps below:
(3.1) define two distances for the particle in each small grid: one is pair of the particle functional value in object space
The distance d of its optimum point for being currently located small grid should be put1；The other is the corresponding points of the particle functional value arrive ideal point
Distance d2；
(3.2) it is based on d1And d2Dual range decision: the collection of all particle functional value corresponding points in object space in certain small grid
Conjunction is denoted as P, d1(pi) and d2(pi) respectively indicate particle i functional value corresponding points p in current small gridiD1And d2Value；Certain small net
The corresponding points p of two particle functional values in lattice1,p2∈ P, works as p1,p2When meeting following two condition:
Then p1Dual range dominates p2, notep1To dominate point, p2For by domination point.
4. the Logistics System Design method according to claims 1 or 2, which is characterized in that guidance grain described in step (6)
Son screening, operates in the steps below:
(4.1) the small small grid of concentration is selected with wheel disc bet method；
(4.2) after determining small grid, the d of each particle functional value in the small grid is then calculated1And d2Value；
(4.3) particle is dominated as guidance particle, when there are multiple domination particles finally, filtering out by dual range administration method
When, then Pareto optimal particle is selected according to the optimal definition of Pareto, then therefrom select one at random as guidance particle.
5. Logistics System Design method according to claim 3, which is characterized in that guidance particle described in step (6)
Screening operates in the steps below:
(4.1) the small small grid of concentration is selected with wheel disc bet method；
(4.2) after determining small grid, the d of each particle functional value in the small grid is then calculated1And d2Value；
(4.3) particle is dominated as guidance particle, when there are multiple domination particles finally, filtering out by dual range administration method
When, then Pareto optimal particle is selected according to the optimal definition of Pareto, then therefrom select one at random as guidance particle.
6. according to Logistics System Design method described in claims 1,2 or 5, which is characterized in that outside described in step (7)
Delete operation is achieved, is operated in the steps below:
(5.1) the big small grid of concentration is selected by wheel disc bet method；
(5.2) after determining small grid, the d of each particle target function value point in the small grid is then calculated1、d2Value；
(5.3) finally, filtering out the particle dominated as deleted particle inferior by the two distance properties；It is more when having
When a particle dominated, then therefrom randomly chooses the particle that one is dominated and be used as particle inferior, when the grain not dominated
The period of the day from 11 p.m. to 1 a.m then randomly chooses one in the region and is deleted as particle inferior.
7. Logistics System Design method according to claim 3, which is characterized in that external archival described in step (7)
Delete operation operates in the steps below:
(5.1) the big small grid of concentration is selected by wheel disc bet method；
(5.2) after determining small grid, the d of each particle target function value point in the small grid is then calculated1、d2Value；
(5.3) finally, filtering out the particle dominated as deleted particle inferior by the two distance properties；It is more when having
When a particle dominated, then therefrom randomly chooses the particle that one is dominated and be used as particle inferior, when the grain not dominated
The period of the day from 11 p.m. to 1 a.m then randomly chooses one in the region and is deleted as particle inferior.
8. Logistics System Design method according to claim 4, which is characterized in that external archival described in step (7)
Delete operation operates in the steps below:
(5.1) the big small grid of concentration is selected by wheel disc bet method；
(5.2) after determining small grid, the d of each particle target function value point in the small grid is then calculated1、d2Value；
(5.3) finally, filtering out the particle dominated as deleted particle inferior by the two distance properties；It is more when having
When a particle dominated, then therefrom randomly chooses the particle that one is dominated and be used as particle inferior, when the grain not dominated
The period of the day from 11 p.m. to 1 a.m then randomly chooses one in the region and is deleted as particle inferior.
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| CN107992051A (en) * | 2017-12-26 | 2018-05-04 | 江南大学 | Unmanned vehicle paths planning method based on improved multi-objective particle swarm algorithm |
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| CN107992051A (en) * | 2017-12-26 | 2018-05-04 | 江南大学 | Unmanned vehicle paths planning method based on improved multi-objective particle swarm algorithm |
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