CN103530699A - Multi-time-window vehicle route selection method on basis of improved universal gravitation algorithm - Google Patents

Abstract

The invention discloses a multi-time-window vehicle route selection method on the basis of an improved universal gravitation algorithm and mainly solves the problem that in the prior art, discrete and aggregated multi-time-window vehicle routes cannot be simultaneously selected. The multi-time-window vehicle route selection method comprises the following implementing steps: (1) carrying out clustering processing on input clients, determining a clustering center and numbering vehicles; (2) using a vehicle yard as the center, dividing a client distribution region into a plurality of vehicle areas according to the clustering center and determining a client set of clients served by each vehicle; (3) recording the client set of the clients served by a kth vehicle as a population, initializing the population at the moment that t is equal to 0, and optimizing the population by the universal gravitation algorithm; and (4) executing interlace operation on each individual in the population to obtain a temporary population, then executing boundary constraint checking on each individual in the temporary population and by lower and upper layer termination judgment, obtaining the optimal route of the multi-time-window vehicle route problem. According to the invention, different types of multi-time-window vehicle routes can be simultaneously selected.

Description

Many time windows vehicle route system of selection based on improving universal gravitation algorithm

Technical field

The invention belongs to technical field of traffic transportation, the particularly vehicle route system of selection of many time windows, can be used for many time windows vehicle route of discrete type and accumulation type to dispatch.

Background technology

Many time windows Vehicle Routing Problems refers to that vehicle is from home-delivery center's services client, need to be in user provides several time windows, be chosen in a unique time window and arrive at service, require each client can only by a car service and only service once, routing target is to make cost minimization under the condition such as meet that user time requires and carload is limited.Vehicle Routing Problems based on many time windows is extensively present among the logistics transportation of current actual life, and the domestic research for this problem is also less and generally only can only solve many time windows vehicle dispatching problem of certain specific type.

Many time windows Vehicle Routing Problems is a NP-Hard problem, this means when problem scale increases to some and will be difficult to or cannot try to achieve at all the globally optimal solution of problem.Although adopt exact algorithm to obtain optimum solution to small-scale many time windows vehicle dispatching problem, be not suitable for the large-scale many time windows vehicle dispatching problem solving in reality.Some scholar uses sequence Insertion heuristic algorithm to solve many time windows Vehicle Routing Problems, although obtain good result, but this kind of algorithm can only be selected to work to accumulation type or many time windows of discrete type vehicle route, and can not be applicable to many time windows vehicle route selection of two types simultaneously.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of many time windows vehicle route system of selection based on universal gravitation algorithm, with the many time windows vehicle route to two types simultaneously, select.

Realizing the object of the invention technical thought is that existing universal gravitation algorithm GSA is improved, and effectively to solve the Vehicle Routing Problems of discrete type and the many time windows of accumulation type, improves search capability, and its technical scheme comprises the steps:

(1) input client distributing position situation, the vehicle number M in parking lot, number of times U is adjusted on the iterations D of lower floor and upper strata, and client is carried out to quick clustering processing, selects at random M point as cluster centre, establishes cluster and adjusts number of times I=1;

(2) Clustering: each car is numbered, makes the sequence number k=1 of first car; Centered by parking lot, according to cluster centre, client distributed areas are divided into the several sections of vehicle, determine the client set of each car service;

(3) initialization population: client's collection of remembering k car service is a population, at t=0 constantly, each individual locus in this population of initialization;

(4) utilize the optimizing of universal gravitation algorithm: at t constantly, choose m best individuality of fitness value in population, through universal gravitation effect, make it force in other individualities in population, then upgrade once individual speed and a body position, obtain T=t+1 population initial velocity and position constantly, make t=t+1;

(5) Local Search:

(5a) each individuality in the population after upgrading is carried out to an interlace operation, obtain an interim population, again to each individual exercise boundary constraint checking in interim population, if exist desired value to be better than the individuality of initial individual goal value in this population, with it, replace initial individuality, otherwise each individual invariant position in population;

(5b) compare T and the iterations D of lower floor, if T≤D returns to step (4); Otherwise, record optimal path, path length and the lagged time of k car;

(6) lower floor stops judgement: vehicle sequence number k+1 and vehicle number M are compared, if (k+1)≤M returns to step (3); Otherwise, calculate under current group, seek optimum individual, and this optimum individual is compared with known preferred individuality in population, if under current group, seek the target function value of optimum individual be less than the target function value of known preferred individuality in population, with under current group, seek optimum individual to replace in population known preferred individual; Otherwise known preferred individuality is constant in maintenance population;

(7) upper strata stops judgement: cluster is adjusted to number of times I+1 and adjust number of times U with upper strata and compare, if (I+1)≤U re-starts cluster to the client who inputs, and hard clustering center, and return to step (2); Otherwise, stop cluster, and known preferred path, path length and the lagged time of return recording, this path is the optimal path of selected many time windows vehicle route.

The present invention compared with prior art has the following advantages:

1, the present invention is by cluster and improved universal gravitation algorithm, can realize many time windows vehicle route of discrete type and accumulation type is selected, and the current domestic research for many time windows vehicle route selection problem is less, and general Study can only solve many time windows Vehicle Routing Problems of specific a type.

2, the present invention compares with existing universal gravitation algorithm, shows stronger search capability, and validity and practicality are outstanding.

Accompanying drawing explanation

Fig. 1 is performing step process flow diagram of the present invention.

Specific implementation method:

With reference to Fig. 1, performing step of the present invention is as follows:

Step 1, input client distributing position situation, the vehicle fleet M in parking lot and client's sum C, setting layer iterations is D>=5, it is U>=5 that number of times is adjusted on upper strata, it is I=1 that cluster is adjusted number of times, and client is carried out to quick clustering processing, selects at random M point as cluster centre (X _i, Y _i), i=1,2 ..., M.

Step 2, Clustering

Each car is numbered, makes the sequence number k=1 of first car; Centered by parking lot, according to cluster centre (X _i, Y _i), i=1,2 ..., M, is divided into M section with following formula by client distributed areas, determines the client set of each car service:

$\min \underset{r=1}{\overset{M}{\mathrm{\Σ}}}\underset{i\∈S_r}{\mathrm{\Σ}}\sqrt{{(x_i-X_r)}^2+{(y_i-Y_r)}^2},$

S.t.S _i∩ S _j=φ,

j ∈ 1,2 ..., M}, and i ≠ j,

(x wherein _i, y _i) represent i client's position, S _rthe client set that represents r car service, C represents client's sum of needs service, and s.t. represents to be tied, and ∩ represents intersection of sets,

represent that ∪ represents union of sets arbitrarily.

Step 3, initialization population

Client's collection of remembering k car service is a population, at t=0 constantly, with following formula, each individuality in this population is carried out to initialization:

$p_j^i=(b-a)R+a,p_j^i\∈[a,b],i=\mathrm{1,2},...,L,j=\mathrm{1,2},...,N_k$

Wherein, represent i the individual position coordinates at j dimension space, R represents the random number in [0,1], and L represents population scale, N _krepresent k car services client number, [a, b] representation space scope.

Step 4, utilize the optimizing of universal gravitation algorithm

(4a) at t constantly, defining i individual and j individuality at the universal gravitation of d dimension space is:

$F_{\mathrm{ij}}^d\left(t\right)=G\left(t\right)\frac{M_{\mathrm{pi}}\left(t\right)\×M_{\mathrm{oj}}\left(t\right)}{R_{\mathrm{ij}}\left(t\right)+\mathrm{\ϵ}}(p_j^d\left(t\right)-p_i^d\left(t\right)),$

Wherein, G (t) is t universal gravitation coefficient constantly, R _ij(t) represent the Euclidean distance between t moment i individuality and j individuality, ε is an abundant little constant, M _pi(t) represent constantly stressed i the individual quality of t, M _oj(t) represent t j individual quality of the application of force constantly,

(t) represent i individual position in d dimension space;

(4b), according to above-mentioned Formula of Universal Gravitation, calculate respectively t constantly, i the individual F that makes a concerted effort at d dimension space _i ^dwith i the individual acceleration producing at d dimension space

(t):

${F_i}^d=\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}R\×F_{\mathrm{ij}}^d\left(t\right)$

$a_i^d\left(t\right)=\frac{F_i^d\left(t\right)}{M_{\mathrm{ii}}\left(t\right)},$

Wherein, R is the random number in [0,1], and N is illustrated in d dimension space i individuality applied to gravitational number of individuals, (t) be the universal gravitation between t moment i individuality and j individuality, M _ii(t) represent t i individual quality constantly;

(4c), according to above-mentioned Acceleration Formula, upgrade individual speed and a body position:

At t constantly, choose m best individuality of fitness value in population, through universal gravitation effect, make it force in other individualities in population, then upgrade once individual speed

and body position (t)

(t), obtain each individual speed in T=t+1 moment population

and position

$v_i^d(t+1)=R\×v_i^d\left(t\right)+a_i^d\left(t\right)$

$p_i^d(t+1)=p_i^d\left(t\right)+v_i^d(t+1),$

Wherein

for t moment i individual speed in d dimension space,

for t moment i individual acceleration in d dimension space,

for t moment i individual position in d dimension space, R is the random number in [0,1].

Step 5, Local Search

(5a) make t=t+1, each individuality in population after upgrading is carried out to an interlace operation, obtain an interim population, again to each individual exercise boundary constraint checking in interim population, if exist desired value to be better than the individuality of initial individual goal value in this population, with it, replace initial individuality, otherwise each individual invariant position in population;

(5b) compare T and the iterations D of lower floor, if T≤D returns to step 4; Otherwise, record optimal path, path length and the lagged time of k car.

Step 6, lower floor stop judgement

Vehicle sequence number k+1 and vehicle number M are compared, if (k+1)≤M makes k=k+1 and returns to step 3; Otherwise, calculate under current group, seek optimum individual, and this optimum individual is compared with known preferred individuality in population, if under current group, seek the target function value of optimum individual be less than the target function value of known preferred individuality in population, with under current group, seek optimum individual to replace in population known preferred individual; Otherwise known preferred individuality is constant in maintenance population.

Step 7, upper strata stop judgement

Cluster is adjusted to number of times I+1 and upper strata and adjust number of times U and compare, if (I+1)≤U makes I=I+1 and the client of input is re-started to cluster, hard clustering center (X _i, Y _i), i=1,2 ..., M, and return to step 2; Otherwise, stop cluster, and known preferred path, path length and the lagged time of return recording, this path is the optimal path of selected many time windows vehicle route.

Effect of the present invention can further illustrate by following experiment.

1, experiment condition

(1) experimental data source

Because many time windows Vehicle Routing Problems does not also have the test data set of standard at present, VRPMTW test data set of the present invention is in the VRPTW of single time window Solomon Benchmark test data set, each client node is 1 time window of random increase separately, and generation scale is as follows:

A. from the discrete data collection R1 of VRPTW Solomon Benchmark and focus type data set C1, respectively get 3 groups of data, for each client nodes of every group of data increases by 1 time window not overlapping with the original time window, keep its legacy data constant simultaneously;

If b. original time window length surpasses 100, new generation time window length is the random number between 0 to 100; Otherwise new generation time window equates with former time window length.

(2) experiment parameter

Population scale: p _s=25 client's number: n _c=50 or 100

Cluster number of times: U=5 cluster is adjusted number of times: D=5

Evolution iterations: I _sub=200 service vehicle numbers: 5 < M < 15

Population application of force number of individuals: m is reduced to 1 gradually from population scale.

2, experiment content

(1) test of many time windows of discrete type vehicle dispatching problem

With existing universal gravitation algorithm GSA and the inventive method IGSA, discrete data collection R1 is tested respectively, record optimal path length, worst path length, path length average, path length standard deviation separately and reach time average, result is as shown in table 1:

Table 1R1 data set test result

(2) test of many time windows of accumulation type vehicle dispatching problem

With existing universal gravitation algorithm GSA and the inventive method IGSA, accumulation type data set C1 is tested respectively, record optimal path length, worst path length, path length average, path length standard deviation and lagged time average separately, result is as shown in table 2:

Table 2C1 data set test result

3, experimental analysis

As known from Table 1, the data set R102 that the data set R102, the R103 that are 50 to scale of consumer and scale of consumer are 100, the solving result of R103 show, the result that the inventive method is tried to achieve in 10 left and right, is tried to achieve result customer satisfaction higher without late or lagged time.Scale of consumer is that the solving result of 50 data set R101 and the scale of consumer data set R101 that is 100 shows, because time window is narrower, the lagged time of trying to achieve result is significantly increased, and all in 100 left and right, trying to achieve result customer satisfaction has decline.But relatively optimal path length, worst path length, path average and these data of 4 of path length standard deviation, can obtain, and the result that the inventive method is tried to achieve is all unanimously less than the result that existing universal gravitation algorithm is tried to achieve.Therefore,, when the many time windows Vehicle Routing Problems to discrete type solves, the inventive method is more excellent than existing universal gravitation algorithm performance.

As known from Table 2, the solving result of the data set C103 that the data set C102, the C103 that are 50 to scale of consumer and scale of consumer are 100 shows, the inventive method is tried to achieve result all without late, and the result that existing universal gravitation algorithm is tried to achieve is almost without being late, and tries to achieve result customer satisfaction higher.The data set C101 that the data set C101 that is 50 to scale of consumer and scale of consumer are 100, the solving result of C102 show, the result that the inventive method and existing universal gravitation algorithm are tried to achieve has all occurred 10 ^{+ 2}the order of magnitude is late, and customer satisfaction declines, so the data set narrow to time window, and the higher path of customer satisfaction of requirement also needs to adjust fineness and the iterations that strengthens scanning search.Relatively optimal path length, worst path length, path average and these data of 4 of path standard deviation, can obtain, and the result that the inventive method is tried to achieve is all better than existing universal gravitation algorithm.Therefore,, when the many time windows Vehicle Routing Problems to accumulation type solves, the inventive method is more excellent than existing universal gravitation algorithm performance.

To sum up, when the many time windows Vehicle Routing Problems to discrete type and accumulation type solves, the inventive method has stronger search capability than existing universal gravitation algorithm, and validity and practicality are outstanding.

Claims (3)

1. the many time windows vehicle route system of selection based on improving universal gravitation algorithm, comprises the steps:

(1) input client distributing position situation, the vehicle number M in parking lot, number of times U is adjusted on the iterations D of lower floor and upper strata, and client is carried out to quick clustering processing, selects at random M point as cluster centre, establishes cluster and adjusts number of times I=1;

(2) Clustering: each car is numbered, makes the sequence number k=1 of first car; Centered by parking lot, according to cluster centre, client distributed areas are divided into the several sections of vehicle, determine the client set of each car service;

(3) initialization population: client's collection of remembering k car service is a population, at t=0 constantly, each individual locus in this population of initialization;

(4) utilize the optimizing of universal gravitation algorithm: at t constantly, choose m best individuality of fitness value in population, through universal gravitation effect, make it force in other individualities in population, then upgrade once individual speed and a body position, obtain T=t+1 population initial velocity and position constantly, make t=t+1;

(5) Local Search:

(5a) each individuality in the population after upgrading is carried out to an interlace operation, obtain an interim population, again to each individual exercise boundary constraint checking in interim population, if exist desired value to be better than the individuality of initial individual goal value in this population, with it, replace initial individuality, otherwise each individual invariant position in population;

(5b) compare T and the iterations D of lower floor, if T≤D returns to step (4); Otherwise, record optimal path, path length and the lagged time of k car;

(6) lower floor stops judgement: vehicle sequence number k+1 and vehicle number M are compared, if (k+1)≤M returns to step (3); Otherwise, calculate under current group, seek optimum individual, and this optimum individual is compared with known preferred individuality in population, if under current group, seek the target function value of optimum individual be less than the target function value of known preferred individuality in population, with under current group, seek optimum individual to replace in population known preferred individual; Otherwise known preferred individuality is constant in maintenance population;

(7) upper strata stops judgement: cluster is adjusted to number of times I+1 and adjust number of times U with upper strata and compare, if (I+1)≤U re-starts cluster to the client who inputs, and hard clustering center, and return to step (2); Otherwise, stop cluster, and known preferred path, path length and the lagged time of return recording, this path is the optimal path of selected many time windows vehicle route.

2. the many time windows vehicle route system of selection based on improving universal gravitation algorithm according to claim 1, each individual locus in initialization population in wherein said step (3), by following formula, undertaken:

$p_j^i=(b-a)R+a,p_j^i\&Element;[a,b],i=\mathrm{1,2},...,L,j=\mathrm{1,2},...,N_k$

Wherein,

be i the individual position coordinates at j dimension space, R is the random number in [0,1], and L is population scale, and k represents car number, N _krepresent k car services client number, [a, b] is spatial dimension.

3. the many time windows vehicle route system of selection based on improving universal gravitation algorithm according to claim 1, once individual speed and a body position of the described renewal of step (4) wherein, by following formula, undertaken:

$v_i^d(t+1)=R\&times;v_i^d\left(t\right)+a_i^d\left(t\right),p_i^d(t+1)=p_i^d\left(t\right)+v_i^d(t+1)$

Wherein,

(t) be the t speed of individual i in d dimension space constantly, (t) be the t acceleration of individual i in d dimension space constantly,

(t) be the t position of individual i in d dimension space constantly, R is the random number in [0,1].

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