CN105913213A - Reverse logistics recycling vehicle scheduling method under storage commodity collection mode - Google Patents
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Abstract
A reverse logistics recycling vehicle scheduling method under a storage commodity collection mode relates to a logistics vehicle scheduling method. The invention provides a recycling vehicle path design scheme based on path feasibility and storage commodity collection transportation modes. The method is characterized by establishing a VRPRL mathematic model to a reverse logistics recycling vehicle path; exploring two kinds of transportation modes of an infeasible path and storage commodity collection transportation; and finally, through a provided ACO-nso algorithm, carrying out simulation calculating and solving a condition of not considering an infeasible path and a condition of not considering storage commodity collection. Under the condition that a customer demand is low and a demand point position is highly decentralized aiming at a reverse logistics network in an actual life, the mathematic model provided in the invention is used to process so that total cost of the transportation can be effectively reduced, and the method has a certain theory meaning to guide practical application.
Description
Technical field
The present invention relates to vehicles dispatching system method, particularly relate to reverse logistic under storage consolidating the load pattern and reclaim vehicle tune
Degree method.
Background technology
Storage consolidating the load Vehicle Routing Problems (Vehicle Routing Problem, VRP) is by Dantzig and Ramser
Nineteen fifty-nine propose, for study Atlanta oil plant to each gas station's vehicle scheduling transportation route optimization design ask
Topic.As in combinatorial optimization problem typical NP-hard problem, model and traveling salesman problem (Travel Salesman
Problem, TSP) there are many similarities, in decades subsequently, Chinese scholars has carried out deep from different aspect
Study and make VRP problem constantly expand and develop.
Reverse logistic reclaims Vehicle Routing Problems (Vehicle Routing Problem in Reverse
Logistics, VRPRL) it is the important component part in Reverse Logistic Network design problem.Jayar-aman in 2003 etc. build
Found the mathematical model of Reverse Logistic Network design, and introduced heuritic approach and solve.Hong K. Lo etc. have studied cost
Under recovering condition continuous time dimension Logistics Network Design problem, and use the reduced gradient algorithm of broad sense to solve.
In Reverse Logistic Network design process, Location-Routing Problem (Location-Routing Problem, LRP) is as logistics net
Basis in network operation and core, scholar both domestic and external conducts extensive research.Emrah Demir etc. proposes transport
Green multimodal transport service network design problem under time is uncertain, is applied to the algorithm proposed in actual logistics network
And carry out robust analysis.Mazu armies etc. use MILP model solution single product, the Product recycling reverse logistic of restriction of having the ability
Network Optimization Design problem.He Bo etc. propose the garbage under the constraint of multiple target pure integer programming model solution Public Satisfaction
Reverse Logistic Network design problem, according to the modelling heuritic approach set up and prove its effectiveness and feasibility；Bears
Logistics network optimization problem reverse under old for new service purchase pattern is studied by middle patterns etc., and uses particle cluster algorithm to carry out
Solve.Along with the development of third-party logistics industry, enterprise only need to consider position and the demand of each demand point in removal process
Amount information, vehicle is not required to after completing recovery task return former starting point.The transport task of product is contracted out to third-party logistics business
Carrying out, each bar reclaims path and forms open Hamiltonian path.Therefore reclaim path optimization's design and be often also adopted by open car
Routing problem (Open Vehicle Routing Problem, OVRP) model solves.A.D. L ó pez-S á nchez etc.
Have studied the OVRP problem that single the longest distribution time of client minimizes, and solved by multiple spot descent algorithm；Zhangjiang China is right
The OVRP of the most collecting and distributing goods utilizes random frequency conversion neighborhood search method and restarts strategy and solved.
In the situation of many actual lives, Reverse Logistic Network self has the uncertainty of height, network design mistake
In journey, position and the demand of each customer demand point cannot be determined beforehand, and demand is less.Therefore in actual recovery process
In, often transport unifying after the cargo consolidation of several recycle bins to recycle bin to processing center, i.e. create storage collection
Goods Transportation Model.Simultaneously because the extraneous factor such as geographical environment, delivery condition limits, tend not in guarantee logistics network any
All there is feasible path in point-to-point transmission, then needs to complete recovery task by transfer transport between recycle bin, i.e. create infeasible
Path situation.The angle of link is reclaimed, it is considered to both Transportation Models, to reducing logistics cost, promote and client from whole logistics
The market competitiveness have the biggest benefit.Therefore, the research reclaiming Vehicle Routing Problems is important to instructing practical problem to have
Meaning.
Current domestic and international substantial amounts of research is mainly for LRP and OVRP, it is desirable to physics network structure meets any two thing
There is feasible straight line path between stream node, and when there is goods transport transfer situation, each terminal can only receive one
The delivery of individual terminal, its achievement in research cannot directly be applied for the research reclaiming Vehicle Routing Problems with conclusion.
Summary of the invention
It is an object of the invention to provide reverse logistic under a kind of storage consolidating the load pattern and reclaim vehicle dispatching method, the method
Establish the mathematical model of VRPRL, apply mathematical model proposed by the invention to carry out process and always can be effectively reduced transport
Cost, to instructing, reality application is significant.
It is an object of the invention to be achieved through the following technical solutions:
Storage consolidating the load pattern under reverse logistic reclaim vehicle dispatching method, described method include infeasible path situation consideration,
Building LRP model solution and reclaim path, the haulage vehicle in the case of infeasible path is after having serviced last demand point, not
Asking it to return to out departure track, vehicle route is a Hamiltonian path (Hamiltonian path)；The network structure of OVRP；?
In OVRP, multiple demand points are serviced by distribution vehicle successively, service two demand points, in a network time different
It is presented as that transportation route occurs without branched structure；Reverse logistic reclaims network by demand point, recycle bin, processing center three part structure
Become；Figure interior jointFor processing center, node 1 to 28 is the recycle bin set up in logistics network.Recycling logistics networks is in running
During, first garbage is sent to nearest recycle bin by the user of demand point, and recycle bin is receiving the discarded of demand point client
After thing, current recycle bin and garbage quantity and the path viability information closing on logistics node are analyzed, use
Garbage is transported to other recycle bin by transfer transport or storage consolidating the load Transportation Model, or is directly transported to processing center；
VRPRL logistics network is on the basis of VRP model, it is considered to infeasible path and storage consolidating the load two kinds of factors of transport, sets up
Reclaim the mathematical model of the minimum object function of network total Transportation Expenditure with reverse logistic, first provide decision variable:
；
；
Then founding mathematical models is as follows:
In formula:Represent from pointArriveFeasible path length (forIf there is feasible path, then define, whereinRepresent pointArriveEuclidean distance；If there is not feasible path, then define, whereinIt is one
The biggest individual positive number)；For reclaiming the running cost in path；For recycle binMaximum load capability；For recycle binConstruction cost；Represent recycle binGarbage quantity；Represent recycle bin respectivelyReceive other recycle bin to discard
Thing total amount and the garbage amount of sending of this recycle bin；Represent recycle binScrap concrete to processing centerDuring save
PointWhether undertake transhipment；Represent recycle binScrap concrete to processing centerDuring pathWhether undertake and turn
Fortune；The object function of model is made up of two parts, and Part I represents scrap concrete freight, and Part II represents logistics
Facilities Construction expense,Represent the weight of various piece expense.
Under described storage consolidating the load pattern, reverse logistic reclaims vehicle dispatching method, and described expression recycle bin load restraint is
Formula (2), represents garbage that every recycle bin is directly recovered to from demand point client and receives the total of other recycle bin garbage
With may not exceed the maximum load capability transporting recycle bin to.
Under described storage consolidating the load pattern, reverse logistic reclaims vehicle dispatching method, and described access constraints is formula (3), (4),
(5), its Chinese style (3) represent each recycle bin can receive multiple recycle bin delivery but can only to a recycle bin carry out send out
Goods, formula (4) represents that the garbage obtained from customer demand point and other recycle bin must all be sent by each recycle bin, the most all
Garbage can be processed, and formula (5) guarantees that the recycle bin being chosen to receive garbage has built up；Formula (6), (7) are path
Loop eliminates constraint, represents and does not allow to there is loop during scrap concrete.
Under described storage consolidating the load pattern, reverse logistic reclaims vehicle dispatching method, and described variable bound is formula (8), (9).
Advantages of the present invention with effect is:
1. the present invention proposes a kind of recovery vehicle route design based on path viability with storage consolidating the load Transportation Model,
Reverse logistic is reclaimed vehicle route and establishes the mathematical model of VRPRL, and for infeasible path and storage consolidating the load transport
Two kinds of Transportation Models are explored, finally by propose ACO-nso algorithm carried out simulation calculation, solve and respectively with not
Consider infeasible path and do not consider the situation of storage consolidating the load, indicating in real life for visitor in Reverse Logistic Network
In the case of family demand is overall on the low side and demand point position height do not concentrates, mathematical model proposed by the invention is applied to carry out
Process can be effectively reduced transport totle drilling cost, has certain theory significance to instructing reality application.
2. the present invention reclaims vehicle route, infeasible path and storage consolidating the load transport both of which for reverse logistic
The mathematical model set up more conforms to practical situation, and largely decreases the freight in recovery task and thing
Stream Facilities Construction expense so that the total operating cost of logistics system reduces.
The most proposed by the invention reclaims Vehicle Routing Problems for reverse logistic, at mathematical model of the present invention
Reason can be effectively reduced transport totle drilling cost, is suitable for vapour, the freight such as electronic, and reality application is had great importance.
Accompanying drawing explanation
Fig. 1 is LRP physics network structure figure；
Fig. 2 is the transport schematic diagram in the case of infeasible path；
Fig. 3 is the schematic network structure of OVRP；
Fig. 4 is storage consolidating the load Transportation Model schematic diagram；
Fig. 5 is VRPRL physics network structure figure；
Fig. 6 is formal similarity schematic diagram；
Fig. 7 is probability selection operation chart；
Fig. 8 is the 3rd class.path string encoding schematic diagram.
Detailed description of the invention
The present invention is described in detail for illustrated embodiment below in conjunction with the accompanying drawings.
Building LRP model solution and reclaim path, Location-Routing Problem need to assume in logistics network any two when model is set up
There is feasible straight line path between individual logistics node, LRP physics network structure is as shown in Figure 1.
In many situations of real life, generally cannot guarantee can to pass through in the path between any two logistics node,
Then need by the way of transfer transport, find feasible path to transport.
As in figure 2 it is shown, do not have feasible path between recycle bin A and processing center O, then the garbage of recycle bin A is reclaiming
During first have to transport recycle bin B to by path AB, transport processing center O to by path BO afterwards and complete recovery task.Combine
Upper sayed, the consideration of infeasible path situation relative to LRP model closer to practical situation.Location-Routing Problem is built at model
Need to assume logistics network exists feasible straight line path, LRP physics network structure such as Fig. 1 between any two logistics node immediately
Shown in, the transport schematic diagram in the case of infeasible path is as shown in Figure 2.
Open Vehicle Routing Problem be mainly characterized by haulage vehicle after having serviced last demand point, it is not required that
It returns to out departure track, and vehicle route is a Hamiltonian path (Hamiltonian path).The network structure of OVRP such as Fig. 3 institute
Showing, storage consolidating the load Transportation Model schematic diagram is as shown in Figure 4.
In OVRP, multiple demand points are serviced by distribution vehicle successively, but cannot click on two demands simultaneously
Row service, is presented as that transportation route figure not may occur in which branched structure in network.But practical situation is especially existed
In Reverse Logistic Network design, the garbage negligible amounts of most of recycle bins, therefore generally first by multiple in removal process
The garbage consolidated delivery of the less recycle bin of garbage amount, to some recycle bin, carries out reclaiming transport and appoints after focusing on
Business, i.e. storage consolidating the load Transportation Model.Transportation Model is so processed the structure changing logistics network, makes problem more conform to reality
Border situation, reduces vehicle the most significantly and calls expense and freight, reduce the operating cost of logistics network.Its fortune
Defeated schematic diagram is as shown in Figure 4.
Fig. 5 is that a reverse logistic reclaims network structure, and this logistics network is mainly by demand point, recycle bin, process
The heart three part is constituted.Figure interior jointFor processing center, node 1 to 28 is the recycle bin set up in logistics network.Returned logistics
Network is in operation, and first garbage is sent to nearest recycle bin by the user of demand point, and recycle bin is receiving demand point
After the garbage of client, current recycle bin and garbage quantity and the path viability information closing on logistics node are carried out
Analyze, use transfer transport or storage consolidating the load Transportation Model that garbage transports to other recycle bin, or be directly transported to process
Center.
VRPRL physics network structure figure is as it is shown in figure 5, on the basis of VRP model, according to the feature of VRPRL problem, examine
Consider infeasible path and storage consolidating the load two kinds of factors of transport, set up and reclaim the minimum target of network total Transportation Expenditure with reverse logistic
The mathematical model of function, first provides decision variable:
Then can founding mathematical models as follows:
。
In formula:Represent from pointArriveFeasible path length (forIf there is feasible path, then fixed
Justice, whereinRepresent pointArriveEuclidean distance；If there is not feasible path, then define, whereinFor
One abundant big positive number)；For reclaiming the running cost in path；For recycle binMaximum load capability；For reclaiming
StandConstruction cost；Represent recycle binGarbage quantity；Represent recycle bin respectivelyReceive other recycle bin to give up
Gurry total amount and the garbage amount of sending of this recycle bin.Represent recycle binScrap concrete to processing centerProcess
Interior jointWhether undertake transhipment.
Represent recycle binScrap concrete to processing centerDuring pathWhether undertake transhipment.Mould
The object function of type is made up of two parts, and Part I represents scrap concrete freight, and Part II represents logistic facilities
Construction cost,Represent the weight of various piece expense.In constraints, formula (2) represents recycle bin load restraint, represents
Every the recycle bin garbage being directly recovered to from demand point client and the summation receiving other recycle bin garbage may not exceed
Transport the maximum load capability of recycle bin to；Formula (3), (4), (5) are access constraints, and its Chinese style (3) represents that each recycle bin is permissible
Receiving the delivery of multiple recycle bin but can only deliver to a recycle bin, formula (4) represents that each recycle bin palpus will be from client
The garbage that demand point and other recycle bin obtain all sends, i.e. all waste thing can be processed, and formula (5) guarantees selected
The recycle bin selecting reception garbage has built up；Formula (6), (7) are that path loops eliminates constraint, represent in scrap concrete process
In do not allow to there is loop；Formula (8), (9) are variable bound.
Embodiment one:
Randomly generating 1 processing center, 30 recycle bins, the reverse logistic of 120 demand points reclaims network, the seat of processing center
Mark O (37km, 25km), the information of 30 recycle bins is shown in Table 1.Require the addressing reasonably selecting recycle bin and reclaim returning of vehicle
Receive path so that the total transport cost completing recovery task is minimum.
Table 1 recycle bin information
Here, utilize ACO-nso algorithm, to reclaim task total transport cost minimum optimization aim, reverse logistic is reclaimed network
It is optimized and solves, and contrast with the result of calculation not considered under infeasible path and storage consolidating the load Transportation Model, excellent
Change result such as table 2.
The vehicle scheduling of the minimum optimization aim of table 2 total transport cost
By result of calculation in table 2 it is found that reclaim vehicle route, infeasible path and storage consolidating the load for reverse logistic
The mathematical model that transport both of which is set up more conforms to practical situation, and largely decreases in recovery task
Freight and logistics equipment construction expense so that the total operating cost of logistics system reduces.
Embodiment two:
In order to discuss the ACO-nso algorithm proposed by the invention suitability to recovery Vehicle Routing Problems, ask multiple at this
The example of topic scale uses this algorithm to carry out solving analysis, and simulation result is to such as table 3.
Table 3 simulation result relative analysis
By table 3 it can be seen that when problem scale is less than 70, the stability of algorithm is higher, it is possible to draws and preferably optimizes knot
Really；When problem scale continues to increase, the stability of algorithm begins to decline, and mainly shows as under the search success rate to optimal solution
Fall and iterations and calculate the time longer.This is to lead with storage consolidating the load pattern owing to the present invention considers infeasible path
Cause solution space scale fromIt is increased to, the search volume scale exponentially property solved when problem scale increases increases.Therefore
The proposed by the invention ant group algorithm that improves is applicable to solve the Reverse Logistic Network recovery routing problem of medium and following scale,
And the time that calculates is short, ability of searching optimum is strong.
Embodiment three:
As shown in Table 2, ACO-nso algorithm can search for the satisfactory solution obtaining problem.In order to preferably embody ACO-
Nso algorithm solving consider path viability with storage consolidating the load pattern under reclaim Vehicle Routing Problems advantage, by its with piece
The algorithm performance of act method (EM) and genetic algorithm (GA) is analyzed, as shown in table 4.
Table 4 algorithm contrasts with the algorithm performance of enumerative technique and genetic algorithm
Can be seen that ACO-nso algorithm calculates time short and algorithm stability by table 4. higher, the excellent of satisfaction can be obtained
Dissolve.Enumerative technique is solved, although optimal solution can be found accurately, but the calculating time of algorithm is longer.By example two for
The analysis of solution space scale understands, and is the example of 30 with example three problem scale, and solution room scale increases from 2.65e+32
2.05e+44, therefore amount of calculation exponentially property increases, and the calculating time causing enumerative technique is longer；Genetic algorithm is solved,
Although equally searching optimal solution, but the calculating time is poor with search success rate result compared with ACO-nso.Produce above-mentioned
Result is owing to ACO-nso algorithm ensure that the feasibility of initial solution when carrying out probability selection operation, and genetic algorithm is being entered
Randomly generate initial solution during the string encoding of walking along the street footpath, in causing initial solution space, there is substantial amounts of infeasible solution, reduce heredity calculation
The operational efficiency of method and accuracy.
Coded system based on adverse selection operation ant group algorithm.The feature solved for VRPRL, needs to add infeasible path
With the key element of storage consolidating the load transport, then need the coding of intelligent algorithm can give expression to branch path in storage consolidating the load transport accurately
The situation in footpath, and ensure the feasibility in path.The form that the present invention uses path to go here and there encodes, and path is gone here and there by two structures
Constituting, the numbering that each element is a logistics node in structure, the form of solution is represented by:, whereinRepresent recycle binThe recycle bin numbering of service, and forCan be identical, this addresses the problem the expression of the individual path situation stored in a warehouse under consolidating the load Transportation Model.Such asRepresenting recycle bin 1, the garbage at 3,7 is directly transported to processing center,
Recycle bin 2,5 carry out transfer transport, recycle bin 6 by recycle bin 1, and 8 carry out transfer transport by recycle bin 3, and recycle bin 4 is first
Being transported by recycle bin 2 and finally transport processing center to recycle bin 1, the structural representation of this coding homographic solution is as shown in Figure 6.
The probability selection of next node is operated:
The present invention is for Formica fuscaIf,In first point be node to be visited, calculate node to be visited afterwards
Close to set of access nodesIn the transition probability of each element, it is assumed thatIt is chosen node, then
WillJoinEnd, and willFromMiddle deletion joinsIn, probability selection is grasped
Make schematic diagram as shown in Figure 7.When carrying out probability selection operation, if node to be visitedClose to set of access nodesIn the transition probability of each nodeIt is 0, then defines node to be visitedFor can not decision point, can not decision-making
The generation of point is owing to considering that road feasibility causes.Assume node to be visitedOnly and logistics nodeBetween exist can walking along the street
Footpath, andInterior jointPosition at nodeAfter, then nodeWhen carrying out decision-makingDo not exist
In, therefore nodeCannot be carried out decision-making.To decision point carrying out Second Decision behaviour after all nodes all carried out decision-making
Making, if a certain node still cannot be carried out decision-making during Second Decision, then there is not the path with processing center in this point, defines this joint
Point is for can not send with charge free a little.
In sum, for Formica fuscaNon-set of access nodes close in first node,Represent all addressable joints
The set of point, if, then this node be can not decision point, the decision-making defining this point is, and willJoin and visit
Ask in node set；If, then nodeNext nodeTransition probability be:
。
Formula (10) is Formica fuscaFrom nodeArriveTransition probability；For pathTrack intensity, by corresponding
Pheromone concentration represents, initial value is 1, and after Formica fusca completes to circulate several times, track intensity changes,Represent pheromone volatility coefficient,ShowSecondary circulation increases
Pheromone；For pathVisibility, by the expression reciprocal of its distance；RepresentWeight；Table
ShowWeight；In formula (11)Represent fromArriveDistance save ratio.WhereinRepresent theFormica fusca from
NodeIt is directly taken the distance of processing center,Represent nodeTo nodeDistance.
Arthmetic statement:
By the improvement operating coded system and probability selection, the ant group algorithm flow process that can obtain VRPRL problem is as follows:
Step 1. input node parameter, initializes distance matrix, calculates other each logistics node with processing center for initial point
Polar coordinate and according to footpath, pole ascending power arrange, algorithm maximum iteration time is setAnd population scaleAnd decision-making number of times
P, order.According to infeasible path information updating distance matrix, and construct Saving Matrix.
Step 2. initializesCollection, according toCollection determines and accesses setWith do not visit
Ask set, processing center O is joined and has accessed in set.
If the non-set of access nodes of Step 3. is closed, proceed to Step 5, otherwise not access joint
First node in some setFor treating decision point, calculateWithIn each nodeDistance and selectionAfter
Recycle binCar loading, then decision nodeWhether can be by decision-making, i.e.WithBetween exist feasible path and transport after do not surpass
Cross recycle binMaximum load capability.If then can not be searched for by decision-makingMiddle next node, if can be by decision-making, willPut into feasible setIn.After traversal search terminates, obtain nodeCan decision point set.If, then define
NodeFor can not decision point,Middle interpolation node,Middle deletion,Middle addition
,, proceed to Step 3；If,
Then proceed to Step 4.
Step 4. calculates according to formula (10)Each point transition probability, determines node according to transition probabilityDecision-making
Node,Middle interpolation node,Middle interpolation node, and more new nodeGarbage quantity letter
Breath.Middle deletion,, proceed to Step 3.
If Step 5.Concentrate and there is negative decision point, proceed to Step 6；OtherwiseIf,,
Then proceed to Step 2, otherwise proceed to Step 8.
Step 6. is rightThe negative decision point concentrated carries out Second Decision operation, if not existing not after Second Decision
Can decision point, proceed to Step 7；If still suffer from after Second Decision can not decision point, remember these nodes for can not send with charge free a little, order, turn Step 7.
Step7. If,, then proceed to Step 2, otherwise proceed to Step 8.
If Step 8., according toThe travel path of secondary circulation ant colony updates pheromone, thenTurn
Enter Step 2；If, then the optimal result of output last time circulation.
ACO-nso Convergence Properlies:
In algorithm flow, first ACO-nso algorithm has carried out order rearrangement before being iterated searching process and has processed node,
The most non-set of access nodes is closedIn all points rearrange according to footpath, pole ascending power, this operation ensure that and carries out
During probability selection operation, produced solution is feasible solution, reduces the search volume of ACO-nso algorithm solution simultaneously.Therefore we
Need to prove to consider that path viability is in ACO-nso with the optimal solution reclaiming Vehicle Routing Problems under storage consolidating the load pattern and calculates
In the search volume of method, and ACO-nso algorithm can find one in this space when algorithm iteration number of times tends to infinite
The probability of optimal solution is 1.
First set consider path viability with storage consolidating the load pattern under reclaim Vehicle Routing Problems solution space as, then solve
In space, the path string encoding of all solutions can be divided into following three types:
(1) in the string encoding of path, belonging to the coding in the search volume of ACO-nso algorithm, this kind of coding is usedShow.
(2) in the string encoding of path, the coding of an infeasible path is at least created.I.e. path string encoding exists
, selected recycle binWithBetween there is not feasible path, this kind of coding is usedRepresent.
(3) in the string encoding of path, at least there is a coding, under the possibilities of path, have selected footpath, pole more than certainly
The coding of body.As shown in Figure 8, there is feasible path between OA, but A carries out selecting during codes selection the recovery more than self of the footpath, pole
It is serviced by the B that stands, and this kind of coding is usedIt is indicated.
Analytic solution spatial relationship understands, and.In for
Solve, owing to there is infeasible path, therefore in solution be infeasible solution, then optimal solution not in；ForIn solution, always
ExistIn a solution corresponding, and Path selection isIn unselected feasible path.
As a example by Fig. 8, it is clear thatWhen equal (work as the footpath, pole of A, B 2 take equal sign), then forIn any one Xie always existIn one solve value be better than this solve, therefore optimal solution does not exists.To sum up analyze,
If solution spaceOne optimal solution of middle existence, then this optimal solution must be in the search volume of ACO-nso algorithmIn.IfIt is respectively Formica fusca to existWithIn can find the probability of an optimal solution, then:
(12)
Assuming that Formica fusca has carried out altogether T iteration in carrying out optimum path search search procedure, each iteration Formica fusca needs to carry out n time
Probability selection operates, and the corresponding with service node completing n node selects.Formica fusca might as well be set have found in the r time iterative process
Optimal solution, then the path string encoding of optimal solution is:
(13)
Therefore the probability that Formica fusca finds optimal solution when the r time iteration is:
(14)
Wherein,It is state transition probability.Ant group algorithm is existed
Carrying out in searching process, as long as there being the incorrect of a nodes encoding, then can not search optimal solution, therefore Formica fusca is in optimizing
The probability not finding optimal solution in journey is:
(15)
Therefore, in T iteration cycle, Formica fusca does not searches the probability of optimal solution and is.Therefore T iteration week
In phase, Formica fusca can beIn find the probability of optimal solution to be:
(16)
WhereinFor state transition probability,, then can obtain:
(17)
By formula (12), and guarantor's inequality of the limit understands:
(18)
When the iterations of ant group algorithm tends to infinity, ACO-nso algorithm can find the probability of optimal solution to be 1, i.e.
ACO-nso algorithm is convergence.
Claims (4)
1. under storage consolidating the load pattern, reverse logistic reclaims vehicle dispatching method, it is characterised in that described method includes can not walking along the street
The consideration of footpath situation, building LRP model solution and reclaim path, the haulage vehicle in the case of infeasible path is servicing last
After demand point, it is not required that it returns to out departure track, vehicle route is a Hamiltonian path (Hamiltonian path)；OVRP's
Network structure；In OVRP, multiple demand points are serviced by distribution vehicle successively, time different take two demand points
Business, in a network be presented as that transportation route occurs without branched structure；Reverse logistic reclaim network by demand point, recycle bin,
Reason center three part is constituted；Figure interior joint is processing center, and node 1 to 28 is the recycle bin set up in logistics network；
Recycling logistics networks is in operation, and first garbage is sent to nearest recycle bin, recycle bin by the user of demand point
After receiving the garbage of demand point client, can to current recycle bin and garbage quantity and the path closing on logistics node
Row information is analyzed, and uses transfer transport or storage consolidating the load Transportation Model that garbage transports to other recycle bin, or directly
Connect and be transported to processing center；
VRPRL logistics network is on the basis of VRP model, it is considered to infeasible path and storage consolidating the load two kinds of factors of transport, sets up
Reclaim the mathematical model of the minimum object function of network total Transportation Expenditure with reverse logistic, first provide decision variable:
；
；
Then founding mathematical models is as follows:
In formula:Represent from pointArriveFeasible path length (forIf there is feasible path, then define, whereinRepresent pointArriveEuclidean distance；If there is not feasible path, then define, whereinIt is one
The biggest individual positive number)；For reclaiming the running cost in path；For recycle binMaximum load capability；For recycle binConstruction cost；Represent recycle binGarbage quantity；Represent recycle bin respectivelyReceive other recycle bin to discard
Thing total amount and the garbage amount of sending of this recycle bin；Represent recycle binScrap concrete to processing centerDuring save
PointWhether undertake transhipment；Represent recycle binScrap concrete to processing centerDuring pathWhether undertake and turn
Fortune；The object function of model is made up of two parts, and Part I represents scrap concrete freight, and Part II represents logistics
Facilities Construction expense,Represent the weight of various piece expense.
Under storage consolidating the load pattern the most according to claim 1, reverse logistic reclaims vehicle dispatching method, it is characterised in that institute
State formula (2) and represent recycle bin load restraint, represent garbage and reception that every recycle bin is directly recovered to from demand point client
The summation of other recycle bin garbage may not exceed the maximum load capability transporting recycle bin to.
Under storage consolidating the load pattern the most according to claim 1, reverse logistic reclaims vehicle dispatching method, it is characterised in that institute
Stating formula (3), (4), (5) are access constraints, its Chinese style (3) represent each recycle bin can receive multiple recycle bin delivery but only
Can deliver to a recycle bin, formula (4) represents that each recycle bin must will obtain from customer demand point and other recycle bin
Garbage all sends, i.e. all waste thing can be processed, and formula (5) guarantees to be chosen the recycle bin of reception garbage
Set up；Formula (6), (7) are that path loops eliminates constraint, represent and do not allow to there is loop during scrap concrete.
Under storage consolidating the load pattern the most according to claim 1, reverse logistic reclaims vehicle dispatching method, it is characterised in that institute
Stating formula (8), (9) are variable bound.
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