CN102880798A - Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows - Google Patents
Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows Download PDFInfo
- Publication number
- CN102880798A CN102880798A CN2012103496480A CN201210349648A CN102880798A CN 102880798 A CN102880798 A CN 102880798A CN 2012103496480 A CN2012103496480 A CN 2012103496480A CN 201210349648 A CN201210349648 A CN 201210349648A CN 102880798 A CN102880798 A CN 102880798A
- Authority
- CN
- China
- Prior art keywords
- solution
- algorithm
- vehicle
- expression
- search
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Traffic Control Systems (AREA)
Abstract
The invention provides a variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows. The variable neighborhood search algorithm is characterized in that in a local searching progress, an or-opt and 2-opt mixed operator is utilized for local searching; a Metropolis rule in a simulated annealing algorithm model is introduced into a basic frame of VNS (variable neighborhood search) algorithm for accepting partial poorer solutions under a certain condition, so that the possibility that the algorithm is trapped into local optimization is reduced; in this way, the reliability of the algorithm is improved; and a rear optimization progress is added into the algorithm framework, as a result, both the solving quality is improved and the convergence speed of the algorithm is increased in a way.
Description
Technical field
The present invention relates to the vehicle dispatching problem in the operational research field, be specially a kind of change neighborhood search algorithm or a kind of solving model based on becoming the neighborhood search algorithm of finding the solution many parking lots band time window Vehicle Routing Problems.
Background technology
A large amount of logistics vehicles scheduling problems can be summed up as many parking lots vehicle routing problem with time windows (Multi Depot Vehicle Routing Problem with Time Windows in the reality, MDVRPTW): logistics vehicles is at first respectively at the parking lot on a plurality of different physical location, they need to send to client with the goods of specified quantity with minimum path cost in the time range that requires, and return the parking lot at last.
Although the practical application of MDVRPTW is very extensive, this problem not yet is well solved in theory research." many parking lots " and " time window " make the difficulty that has originally possessed stack with regard to the problem solving with NP complicacy respectively in the double constraints that applies aspect the room and time of problem, are still waiting to improve for the solution efficiency of extensive problem.
MDVRPTW is still one of problems of furtheing investigate that do not obtain few in number in the Vehicle Routing Problems set.Logistics decision maker in the reality to such problem usually adopt " centered by the parking lot to client's subregion and the district in programme path " this empirical way, the science of route planning and validity all be difficult to the guarantee.MDVRPTW comprises the characteristic of many Depot Vehicle Routing Problems (MDVRP) and this two classes subproblem of band time window Vehicle Routing Problems (VRPTW), but since MDVRP and VRPTW institute respectively the constraint of this two aspect of room and time of concern have the conflicting characteristic of finding the solution, so that after being combined as a new problem, being used for solving former problematic heuristic thought, they are difficult to be reused.
The algorithm of current solution MDVRPTW comprises tabu search algorithm, genetic algorithm, change neighborhood search algorithm, particle cluster algorithm and simulated annealing etc. mainly take meta-heuristic as main.And these meta-heuristic algorithms all can run in problem solving process and be absorbed in too early local optimum, i.e. the situation of Premature Convergence, and this also is the large common fault that the meta-heuristic algorithm is being found the solution MDVRPTW.Usually more empirical parameter need to be set in the meta-heuristic algorithm simultaneously, and these parameters often need to arrange according to concrete problem, do not possess stronger versatility.Thereby how reducing possibility and choosing of correlation parameter that algorithm is absorbed in local optimum all is the difficulties of meta-heuristic algorithm research.
Summary of the invention
The purpose of this invention is to provide a kind of change neighborhood search algorithm of finding the solution many parking lots band time window Vehicle Routing Problems.
The objective of the invention is to realize in the following manner, step is as follows:
(1) many parking lots band time window Vehicle Routing Problems has vehicle load, the restriction of long running time of service time window and vehicle, in may the arranging of all customer's locations, what the overwhelming majority was corresponding all is infeasible solution, many algorithms are when the Vehicle Routing Problems of finding the solution with constraint conditions such as load or time windows, usually in solution procedure, all only keep feasible solution, and infeasible solution is given up, but it should be noted that, in these infeasible solutions, the infeasible solution that might have minority, namely through trying to achieve the feasible solution of better quality after the iterative process of certain number of times, Given this, this algorithm model allows the existence of infeasible solution in solution procedure, so that algorithm has more wide search volume, and then increase the possibility that algorithm is tried to achieve more excellent solution;
In this algorithm model, the result appraisal function representation is
f(
x)=
c(
x)+
α q(
x)+
β d(
x)+
γ w(
x), wherein
α,
β,
γBe penalty factor, and
α0,
β0,
γ0.For solution
x, order
c(
x) expression gross vehicle operating range or time, the order
q(
x) expression gross vehicle load-carrying violation amount, the order
d(
x) expression gross vehicle running time violation amount, the order
w(
x) the time window violation amount of expression gross vehicle, calculating vehicle through individual paths
RRunning time violation amount the time, this paper has introduced the concept of the lax Forward Time Slack of forward time that is proposed by Savelsbergh, is used for running time violation amount is optimized accordingly;
(2) this algorithm adopts three standard clustering algorithms at the construction phase of initial solution, is assigned to specific parking lot according to client's geographic position and the large young pathbreaker client of time window, and programme path, and then generates initial solution;
(3) set of the neighbour structure of Shaking process Main Basis predefined is carried out certain adjustment to the structure of separating, search volume with the current solution of abundant expansion, reduce algorithm is absorbed in local optimum in follow-up solution procedure possibility, for the Shaking process, being configured in of neighbour structure set determining the ability that becomes the solution efficiency of neighborhood search algorithm and flee from local optimum to a great extent;
The solution of MDVRPTW is comprised of mulitpath, and every paths is all regarded the oriented sequence of client node as, when finding the solution MDVRPTW, this algorithm is introduced two kinds of commutating operators, is respectively Cross-exchange and iCross-exchange, and utilizes these two kinds of operators that two paths in the current solution are carried out information interaction, and then generation new explanation, during each execution Shaking process, the MVNS algorithm will be selected a kind of for path exchanging from above-mentioned two kinds of operators at random, make parameter
p Icross The probability that is selected of expression iCross-exchange, then the probability that is selected of Cross-exchange be 1-
p Icross , it should be noted that
p Icross Value generally smaller, this mainly is because the solution of MDVRPTW is to have directivity, thereby should keep original direction of subpath to try to achieve the possibility of feasible solution with increase in the path exchanging process as far as possible;
Two initial paths, the reference position of corresponding subpath and the length of subpath that participate in path exchanging all need to determine by the neighbour structure of current solution, generally speaking, what become that the neighborhood search algorithm can adopt all that a plurality of neighbour structures improve algorithm finds the solution quality and stability, this set is comprised of 12 neighbour structures, and each neighbour structure specified the parking lot number that participates in path exchanging and the maximum length of subpath, wherein
C r The path is distributed in expression
rClient's number, because there are a plurality of parking lots in MDVRPTW, two paths that are used for path exchanging were both chosen or were chosen respectively from different parking lots in same parking lot, subpath is one section sequence choosing out at random from selected path, its length can not surpass the maximum length of neighbour structure regulation, in all neighbour structures, the selecteed probability of each sub-sequence length in its specialized range is identical;
(4) in this algorithm model, local search procedure will be to the new explanation that produces in the Shaking process
x s Neighborhood space search in the hope of locally optimal solution
x l , after the Shaking process finishes, because the current solution of MDVRPTW
xIn only have two paths to change, and all the other paths all remain unchanged, therefore Local Search process only need to be carried out respectively Local Search to this two paths, Local Search process is maximum part consuming time in whole VNS algorithm frame, and determining largely the VNS algorithm final find the solution quality, thereby need to fully take into account the solution efficiency of algorithm during local search algorithm in design, 2-op and or-opt in this algorithm model, have been chosen as the Local Search operator, in order to can in short time range, try to achieve preferably locally optimal solution of quality, it should be noted that, each local search procedure all only adopts a kind of operator, two kinds of operators are chosen by mode at random, wherein, the probability that Parametric Representation 2-opt is selected, correspondingly the probability that is selected of Or-opt can be expressed as 1-
p 2-opt , the mode that adopts this hybrid operator is comparatively fully in conjunction with the optimizing ability of 2-opt and two kinds of operators of Or-opt, and the solution room of expandable algorithm to a certain extent;
(5) in order to accelerate to a certain extent convergence of algorithm speed, and improve the quality of finding the solution of algorithm, this algorithm has been introduced rear optimizing process in solution procedure, after Local Search is finished, if the locally optimal solution that obtains
x l Be better than globally optimal solution
x b , that is,
f(
x l )＜
f(
x b ) then continue right
x l Carry out rear Optimum Operation to seek better globally optimal solution, the rear Optimum Operation in this algorithm is selected the US algorithm that is proposed by Gendreau, and this algorithm is applicable to find the solution traveling salesman problem and the Vehicle Routing Problems with time window;
(6) when the result appraisal function of definition MDVRPTW, introduced the load-carrying violation amount of vehicle, running time violation amount and time window violation amount, and these three kinds of violation amounts have been set corresponding penalty factor, and in the experiment solution procedure, these penalty factors are set as larger constant usually, so that so that more trend towards in the algorithm iteration process restraining to feasible solution, but do so simultaneously also so that algorithm is absorbed in local optimum easily, this paper is absorbed in the possibility of local optimum too early by adopting in the solution procedure method of the relatively poor solution in receiving portion to increase disturbance to solution room to reduce algorithm;
This algorithm model comes control algolithm to accept relatively poor solution under certain condition by the Metropolis criterion of introducing in the simulated annealing model, and its reception strategy can be described as following content: order
xRepresent current solution,
x l Expression
xThrough the locally optimal solution that finally obtains after Shaking and the Local Search operation,
f(
x l ) and
f(
x b ) respectively expression solution
xWith
x l The evaluation function value, make Δ f=
f(
x l )-
f(
x), when Δ f≤0, right
x l Optimum Operation obtains separating after doing
x Po , accept solution
x Po And upgrade current solution
x, namely
x=
x Po As Δ f〉0 the time, with certain probability (e
-Δ f/T) accept solution
x l And upgrade current solution
x, namely
x=
x l , this paper adopts the linear method of cooling off to temperature, under original state
T=
T 0 , and every iteration
Iter T Inferior
TJust reduce (
T 0 Iter T )/
Iter Max , wherein,
TThe expression Current Temperatures,
T 0 The expression initial temperature,
Iter Max The total iterations of expression MVNS algorithm;
(7) setting of this algorithm parameters: the iterations that algorithm is total
Iter Max Be set to 10
7, penalty factor
α,
β,
γValue is
α=
β=
γ=100, parameter
p Icross Value is 0.1,
P 2-opt Finally be chosen to be 0.5,
T 0 Value be 5,
Iter T =1000;
(8) by adopting the Cordeau example to assess this algorithm in the performance of finding the solution on the MDVRPTW, the Cordeau example is 20 MDVRPTW examples by Cordeau, Laporte and Mercier design, and obtain from website http://neo.lcc.uma.es/radi-aeb/webvrp/, for each example, the vehicle that is used for dispensing all belongs to same type, and all has identical constraint condition: dead weight
DThe longest running time
T, the distance type in each example all adopts Euclidean distance, i.e. Euclidean distance, and the hypothesis vehicle equals Euclidean distance between the client node at the running time between the client node;
(9) in order to verify the optimizing ability of algorithm model in this paper, respectively with the tabu search algorithm TS that finds the solution the Cordeau example with become neighborhood search algorithm VNS and CAVNS is comparing aspect the optimum solution of trying to achieve and the stability two found the solution.
The invention has the beneficial effects as follows: the construction phase in initial solution adopts clustering algorithm to finish client's distribution, uses hybrid operator to carry out Local Search, strengthening the optimizing effect by rear optimizing process, introduces at last the simulated annealing model new explanation is controlled.
In order to verify the validity of this algorithm model, on the standard testing use-case that Cordeau proposes, this algorithm is tested, and contrast with other optimized algorithms.Experimental result has been upgraded the current optimum solution of most of test case, and embodies stronger advantage in the stability of algorithm.
Description of drawings
Fig. 1 is the basic flow sheet of this algorithm model;
Fig. 2 is the graph-based that MDVRPTW separates;
Fig. 3 is the commutating operator of using in the Shaking process;
Fig. 4 is the neighbour structure set of using in the Shaking process;
Fig. 5 is that the Shaking process is given an example;
Fig. 6 is the hybrid operator that Local Search uses;
Fig. 7 is that the Cordeau example is described;
Fig. 8,9 is the experiment comparing result.
Embodiment
Explain below with reference to Figure of description algorithm of the present invention being done.
The basic flow sheet of this algorithm model, as shown in Figure 1.Below in conjunction with each step in the process flow diagram technical scheme of the present invention is described.
(1) many parking lots band time window Vehicle Routing Problems has vehicle load, service time window and the restriction of long running time of vehicle, and in may the arranging of all customer's locations, what the overwhelming majority was corresponding all is infeasible solution.Many algorithms usually all only keep feasible solution, and infeasible solution are given up when the Vehicle Routing Problems of finding the solution with constraint conditions such as load or time windows in solution procedure.But it should be noted that in these infeasible solutions, might have the such infeasible solution of minority, namely through trying to achieve the feasible solution of better quality after the iterative process of certain number of times.Given this, model allows infeasible solution in solution procedure existence is sent out in this calculation, so that algorithm has more wide search volume, and then increases the possibility that algorithm is tried to achieve more excellent solution;
In this algorithm model, the result appraisal function representation is
f(
x)=
c(
x)+
α q(
x)+
β d(
x)+
γ w(
x), wherein
α,
β,
γBe penalty factor, and
α0,
β0,
γ0.For solution
x, order
c(
x) expression gross vehicle operating range or time, the order
q(
x) expression gross vehicle load-carrying violation amount, the order
d(
x) expression gross vehicle running time violation amount, the order
w(
x) expression gross vehicle time window violation amount.Calculating vehicle through individual paths
RRunning time violation amount the time, this paper has introduced the concept of the forward time lax (Forward Time Slack) that is proposed by Savelsbergh, is used for running time violation amount is optimized accordingly;
(2) this algorithm adopts three standard clustering algorithms at the construction phase of initial solution, is assigned to specific parking lot according to client's geographic position and the large young pathbreaker client of time window, and programme path, and then generates initial solution;
(3) set of the neighbour structure of Shaking process Main Basis predefined is carried out certain adjustment to the structure (as shown in Figure 2) of separating, and with the search volume of the current solution of abundant expansion, reduces algorithm is absorbed in local optimum in follow-up solution procedure possibility.For the Shaking process, being configured in of neighbour structure set determining the ability that becomes the solution efficiency of neighborhood search algorithm and flee from local optimum to a great extent;
The solution of MDVRPTW is comprised of mulitpath, and every paths can be regarded the oriented sequence of client node as.When finding the solution MDVRPTW, this algorithm is introduced two kinds of commutating operators (as shown in Figure 3), is respectively Cross-exchange and iCross-exchange, and utilizes these two kinds of operators that two paths in the current solution are carried out information interaction, and then produce new explanation.During each execution Shaking process, the MVNS algorithm will be selected a kind of for path exchanging from above-mentioned two kinds of operators at random.Make parameter
p Icross The probability that is selected of expression iCross-exchange, then the probability that is selected of Cross-exchange be 1-
p Icross It should be noted that
p Icross Value generally smaller, this mainly is because the solution of MDVRPTW is to have directivity, thereby should keep original direction of subpath to try to achieve the possibility of feasible solution with increase in the path exchanging process as far as possible;
Participating in the reference position of two initial paths of path exchanging, corresponding subpath and the length of subpath all needs the neighbour structure (as shown in Figure 4) by current solution to determine.What generally speaking, become that the neighborhood search algorithm can adopt all that a plurality of neighbour structures improve algorithm finds the solution quality and stability.As shown in the figure, this set is comprised of 12 neighbour structures, and each neighbour structure specified the parking lot number that participates in path exchanging and the maximum length of subpath, wherein
C r The path is distributed in expression
rClient's number.Because there are a plurality of parking lots in MDVRPTW, two paths that are used for path exchanging both can be chosen in same parking lot, also can choose respectively from different parking lots.Subpath is one section sequence choosing out at random from selected path, and its length can not surpass the maximum length of neighbour structure regulation.Can see that in all neighbour structures, the selecteed probability of each sub-sequence length in its specialized range is identical.The Shaking process for example as shown in Figure 5;
(4) in this algorithm model, local search procedure will be to the new explanation that produces in the Shaking process
x s Neighborhood space search in the hope of locally optimal solution
x l After the Shaking process finishes, because the current solution of MDVRPTW
xIn only have two paths to change, and all the other paths all remain unchanged, so Local Search process only need to be carried out respectively Local Search to this two paths.Local Search process is maximum part consuming time in whole VNS algorithm frame, and determining largely the VNS algorithm final find the solution quality, thereby when the design local search algorithm, need to fully take into account the solution efficiency of algorithm.In this algorithm model, chosen 2-op and or-opt(as shown in Figure 6) as the Local Search operator, in order to can in short time range, try to achieve preferably locally optimal solution of quality.It should be noted that each local search procedure all only adopts a kind of operator, two kinds of operators are chosen by mode at random.Wherein, the probability that Parametric Representation 2-opt is selected, correspondingly the probability that is selected of Or-opt can be expressed as 1-
p 2-opt Adopt the mode of this hybrid operator can be comparatively fully in conjunction with the optimizing ability of 2-opt and two kinds of operators of Or-opt, and the solution room of expandable algorithm to a certain extent;
(5) in order to accelerate to a certain extent convergence of algorithm speed, and improve the quality of finding the solution of algorithm, this algorithm has been introduced rear optimizing process in solution procedure.After Local Search is finished, if the locally optimal solution that obtains
x l Be better than globally optimal solution
x b , that is,
f(
x l )＜
f(
x b ) then continue right
x l Carry out rear Optimum Operation to seek better globally optimal solution.Rear Optimum Operation in this algorithm is selected the US algorithm by propositions such as Gendreau, and this algorithm is applicable to find the solution traveling salesman problem and the Vehicle Routing Problems with time window;
(6) when the result appraisal function of definition MDVRPTW, introduced load-carrying violation amount, running time violation amount and the time window violation amount of vehicle, and these three kinds of violation amounts have been set corresponding penalty factor.And in the experiment solution procedure, these penalty factors are set as larger constant usually, so that so that more trend towards in the algorithm iteration process to feasible solution convergence, but do so simultaneously also so that algorithm is absorbed in local optimum easily.This paper is absorbed in the possibility of local optimum too early by adopting in the solution procedure method of the relatively poor solution in receiving portion to increase disturbance to solution room to reduce algorithm.
This algorithm model comes control algolithm to accept relatively poor solution under certain condition by the Metropolis criterion of introducing in the simulated annealing model.Its reception strategy can be described as following content: order
xRepresent current solution,
x l Expression
xThrough the locally optimal solution that finally obtains after Shaking and the Local Search operation,
f(
x l ) and
f(
x b ) respectively expression solution
xWith
x l The evaluation function value.Make Δ f=
f(
x l )-
f(
x), when Δ f≤0, right
x l Optimum Operation obtains separating after doing
x Po , accept solution
x Po And upgrade current solution
x, namely
x=
x Po As Δ f〉0 the time, with certain probability (e
-Δ f/T) accept solution
x l And upgrade current solution
x, namely
x=
x l This paper adopts the linear method of cooling off to temperature, under original state
T=
T 0 , and every iteration
Iter T Inferior
TJust reduce (
T 0 Iter T )/
Iter Max Wherein,
TThe expression Current Temperatures,
T 0 The expression initial temperature,
Iter Max The total iterations of expression MVNS algorithm;
(7) setting of this algorithm parameters: the iterations that algorithm is total
Iter Max Be set to 10
7Penalty factor
α,
β,
γValue is
α=
β=
γ=100.Parameter
p Icross Value is 0.1,
P 2-opt Finally be chosen to be 0.5.
T 0 Value be 5,
Iter T =1000;
(8) by adopting the Cordeau example to assess this algorithm in the performance of finding the solution on the MDVRPTW.The Cordeau example is 20 MDVRPTW examples by Cordeau, Laporte and Mercier design, and can obtain from website http://neo.lcc.uma.es/radi-aeb/webvrp/.As shown in Figure 7,
nExpression client number,
mExpression parking lot number
, tRepresent the vehicle number that each parking lot can be sent.For each example, the vehicle that is used for dispensing all belongs to same type, and all has identical constraint condition: dead weight
DThe longest running time
TDistance type in each example all adopts Euclidean distance, i.e. Euclidean distance, and the hypothesis vehicle equals Euclidean distance between the client node at the running time between the client node;
(9) in order to verify the optimizing ability of algorithm in this paper (being described as MVNS here) model, with the tabu search algorithm of finding the solution the Cordeau example (TS) with become neighborhood search algorithm (VNS and CAVNS) and comparing aspect the optimum solution of trying to achieve and the stability two found the solution, its experimental result is shown in Fig. 8,9 respectively.
Except the described technical characterictic of instructions, be the known technology of those skilled in the art.
Claims (1)
1. change neighborhood search algorithm of finding the solution many parking lots band time window Vehicle Routing Problems is characterized in that step is as follows:
(1) many parking lots band time window Vehicle Routing Problems has vehicle load, the restriction of long running time of service time window and vehicle, in may the arranging of all customer's locations, what the overwhelming majority was corresponding all is infeasible solution, many algorithms are when the Vehicle Routing Problems of finding the solution with constraint conditions such as load or time windows, usually in solution procedure, all only keep feasible solution, and infeasible solution is given up, but it should be noted that, in these infeasible solutions, the infeasible solution that might have minority, namely through trying to achieve the feasible solution of better quality after the iterative process of certain number of times, Given this, this algorithm model allows the existence of infeasible solution in solution procedure, so that algorithm has more wide search volume, and then increase the possibility that algorithm is tried to achieve more excellent solution;
In this algorithm model, the result appraisal function representation is
f(
x)=
c(
x)+
α q(
x)+
β d(
x)+
γ w(
x), wherein
α,
β,
γBe penalty factor, and
α0,
β0,
γ0, for solution
x, order
c(
x) expression gross vehicle operating range or time, the order
q(
x) expression gross vehicle load-carrying violation amount, the order
d(
x) expression gross vehicle running time violation amount, the order
w(
x) the time window violation amount of expression gross vehicle, calculating vehicle through individual paths
RRunning time violation amount the time, this paper has introduced the concept of the lax Forward Time Slack of forward time that is proposed by Savelsbergh, is used for running time violation amount is optimized accordingly;
(2) this algorithm adopts three standard clustering algorithms at the construction phase of initial solution, is assigned to specific parking lot according to client's geographic position and the large young pathbreaker client of time window, and programme path, and then generates initial solution;
(3) set of the neighbour structure of Shaking process Main Basis predefined is carried out certain adjustment to the structure of separating, search volume with the current solution of abundant expansion, reduce algorithm is absorbed in local optimum in follow-up solution procedure possibility, for the Shaking process, being configured in of neighbour structure set determining the ability that becomes the solution efficiency of neighborhood search algorithm and flee from local optimum to a great extent;
The solution of MDVRPTW is comprised of mulitpath, and every paths is all regarded the oriented sequence of client node as, when finding the solution MDVRPTW, this algorithm is introduced two kinds of commutating operators, is respectively Cross-exchange and iCross-exchange, and utilizes these two kinds of operators that two paths in the current solution are carried out information interaction, and then generation new explanation, during each execution Shaking process, the MVNS algorithm will be selected a kind of for path exchanging from above-mentioned two kinds of operators at random, make parameter
p Icross The probability that is selected of expression iCross-exchange, then the probability that is selected of Cross-exchange be 1-
p Icross , it should be noted that
p Icross Value generally smaller, this mainly is because the solution of MDVRPTW is to have directivity, thereby should keep original direction of subpath to try to achieve the possibility of feasible solution with increase in the path exchanging process as far as possible;
Two initial paths, the reference position of corresponding subpath and the length of subpath that participate in path exchanging all need to determine by the neighbour structure of current solution, generally speaking, what become that the neighborhood search algorithm can adopt all that a plurality of neighbour structures improve algorithm finds the solution quality and stability, this set is comprised of 12 neighbour structures, and each neighbour structure specified the parking lot number that participates in path exchanging and the maximum length of subpath, wherein
C r The path is distributed in expression
rClient's number, because there are a plurality of parking lots in MDVRPTW, two paths that are used for path exchanging were both chosen or were chosen respectively from different parking lots in same parking lot, subpath is one section sequence choosing out at random from selected path, its length can not surpass the maximum length of neighbour structure regulation, in all neighbour structures, the selecteed probability of each sub-sequence length in its specialized range is identical;
(4) in this algorithm model, local search procedure will be to the new explanation that produces in the Shaking process
x s Neighborhood space search in the hope of locally optimal solution
x l , after the Shaking process finishes, because the current solution of MDVRPTW
xIn only have two paths to change, and all the other paths all remain unchanged, therefore Local Search process only need to be carried out respectively Local Search to this two paths, Local Search process is maximum part consuming time in whole VNS algorithm frame, and determining largely the VNS algorithm final find the solution quality, thereby need to fully take into account the solution efficiency of algorithm during local search algorithm in design, 2-op and or-opt in this algorithm model, have been chosen as the Local Search operator, in order to can in short time range, try to achieve preferably locally optimal solution of quality, it should be noted that, each local search procedure all only adopts a kind of operator, two kinds of operators are chosen by mode at random, wherein, the probability that Parametric Representation 2-opt is selected, correspondingly the probability that is selected of Or-opt can be expressed as 1-
p 2-opt , the mode that adopts this hybrid operator is comparatively fully in conjunction with the optimizing ability of 2-opt and two kinds of operators of Or-opt, and the solution room of expandable algorithm to a certain extent;
(5) in order to accelerate to a certain extent convergence of algorithm speed, and improve the quality of finding the solution of algorithm, this algorithm has been introduced rear optimizing process in solution procedure, after Local Search is finished, if the locally optimal solution that obtains
x l Be better than globally optimal solution
x b , that is,
f(
x l )＜
f(
x b ) then continue right
x l Carry out rear Optimum Operation to seek better globally optimal solution, the rear Optimum Operation in this algorithm is selected the US algorithm that is proposed by Gendreau, and this algorithm is applicable to find the solution traveling salesman problem and the Vehicle Routing Problems with time window;
(6) when the result appraisal function of definition MDVRPTW, introduced the load-carrying violation amount of vehicle, running time violation amount and time window violation amount, and these three kinds of violation amounts have been set corresponding penalty factor, and in the experiment solution procedure, these penalty factors are set as larger constant usually, so that so that more trend towards in the algorithm iteration process restraining to feasible solution, but do so simultaneously also so that algorithm is absorbed in local optimum easily, this paper is absorbed in the possibility of local optimum too early by adopting in the solution procedure method of the relatively poor solution in receiving portion to increase disturbance to solution room to reduce algorithm;
This algorithm model comes control algolithm to accept relatively poor solution under certain condition by the Metropolis criterion of introducing in the simulated annealing model, and its reception strategy can be described as following content: order
xRepresent current solution,
x l Expression
xThrough the locally optimal solution that finally obtains after Shaking and the Local Search operation,
f(
x l ) and
f(
x b ) respectively expression solution
xWith
x l The evaluation function value, make Δ f=
f(
x l )-
f(
x), when Δ f≤0, right
x l Optimum Operation obtains separating after doing
x Po , accept solution
x Po And upgrade current solution
x, namely
x=
x Po As Δ f〉0 the time, with certain probability (e
-Δ f/T) accept solution
x l And upgrade current solution
x, namely
x=
x l , this paper adopts the linear method of cooling off to temperature, under original state
T=
T 0 , and every iteration
Iter T Inferior
TJust reduce (
T 0 Iter T )/
Iter Max , wherein,
TThe expression Current Temperatures,
T 0 The expression initial temperature,
Iter Max The total iterations of expression MVNS algorithm;
(7) setting of this algorithm parameters: the iterations that algorithm is total
Iter Max Be set to 10
7, penalty factor
α,
β,
γValue is
α=
β=
γ=100, parameter
p Icross Value is 0.1,
P 2-opt Finally be chosen to be 0.5,
T 0 Value be 5,
Iter T =1000;
(8) by adopting the Cordeau example to assess this algorithm in the performance of finding the solution on the MDVRPTW, the Cordeau example is 20 MDVRPTW examples by Cordeau, Laporte and Mercier design, and obtain from website http://neo.lcc.uma.es/radi-aeb/webvrp/, for each example, the vehicle that is used for dispensing all belongs to same type, and all has identical constraint condition: dead weight
DThe longest running time
T, the distance type in each example all adopts Euclidean distance, i.e. Euclidean distance, and the hypothesis vehicle equals Euclidean distance between the client node at the running time between the client node;
(9) in order to verify the optimizing ability of algorithm model in this paper, respectively with the tabu search algorithm TS that finds the solution the Cordeau example with become neighborhood search algorithm VNS and CAVNS is comparing aspect the optimum solution of trying to achieve and the stability two found the solution.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2012103496480A CN102880798A (en) | 2012-09-20 | 2012-09-20 | Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2012103496480A CN102880798A (en) | 2012-09-20 | 2012-09-20 | Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN102880798A true CN102880798A (en) | 2013-01-16 |
Family
ID=47482120
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN2012103496480A Pending CN102880798A (en) | 2012-09-20 | 2012-09-20 | Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN102880798A (en) |
Cited By (29)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103366021A (en) * | 2013-08-07 | 2013-10-23 | 浪潮(北京)电子信息产业有限公司 | Variable neighborhood search method and system on cloud computing platform |
| CN103530699A (en) * | 2013-09-21 | 2014-01-22 | 西安电子科技大学 | Multi-time-window vehicle route selection method on basis of improved universal gravitation algorithm |
| CN104933473A (en) * | 2015-05-22 | 2015-09-23 | 南京邮电大学 | City intelligent traffic dispatching method based on variable neighborhood search ant colony algorithm |
| CN105157712A (en) * | 2015-08-18 | 2015-12-16 | 浙江工商大学 | Vehicle routing planning method and planning system |
| CN106251009A (en) * | 2016-07-27 | 2016-12-21 | 清华大学 | A kind of optimized algorithm of the Vehicle Routing Problems solving time window |
| CN106803136A (en) * | 2017-01-24 | 2017-06-06 | 苏州工业职业技术学院 | A kind of fresh dispatching real-time optimization method based on genetic algorithm |
| CN107194513A (en) * | 2017-05-26 | 2017-09-22 | 中南大学 | A kind of optimization method for solving full channel logistics distribution |
| CN107300927A (en) * | 2017-06-26 | 2017-10-27 | 中国人民解放军国防科学技术大学 | A kind of unmanned plane base station selection and patrol method for optimizing route and device |
| CN107341628A (en) * | 2016-12-30 | 2017-11-10 | 闽江学院 | A kind of axis-spoke logistics network Hub Location and distribution method based on probability Tabu search algorithm |
| CN108280463A (en) * | 2017-12-20 | 2018-07-13 | 中国人民解放军国防科技大学 | Optimization method and device for double-layer path of vehicle-mounted unmanned aerial vehicle |
| CN108389003A (en) * | 2018-03-16 | 2018-08-10 | 广东工业大学 | Service role dispatching method and device under a kind of remote health monitoring line |
| CN108492020A (en) * | 2018-03-16 | 2018-09-04 | 浙江工商大学 | Pollution vehicle dispatching method and system based on simulated annealing and branch's cutting optimization |
| CN108759851A (en) * | 2018-06-01 | 2018-11-06 | 上海西井信息科技有限公司 | More vehicle paths planning methods, system, equipment and storage medium based on time window |
| CN109146163A (en) * | 2018-08-07 | 2019-01-04 | 上海大学 | Optimization method, equipment and the storage medium of Automated Sorting System sorting distance |
| CN109472342A (en) * | 2018-10-25 | 2019-03-15 | 中国人民解放军国防科技大学 | Self-optimized bionic self-repairing hardware fault reconstruction mechanism design |
| CN110110920A (en) * | 2019-04-30 | 2019-08-09 | 浙江财经大学 | A kind of collaborative vehicle method for optimizing route towards coarse localization |
| CN110322066A (en) * | 2019-07-02 | 2019-10-11 | 浙江财经大学 | A kind of collaborative vehicle method for optimizing route based on shared carrier and shared warehouse |
| CN111882099A (en) * | 2020-05-11 | 2020-11-03 | 武汉理工大学 | Logistics distribution path planning method based on variable neighborhood parallel annealing algorithm |
| CN111950761A (en) * | 2020-07-01 | 2020-11-17 | 合肥工业大学 | Development resource integrated scheduling method for high-end equipment complex layered task network |
| CN112001678A (en) * | 2020-08-26 | 2020-11-27 | 莆田烟草物流有限公司 | Method for reducing tobacco distribution mileage |
| CN112067011A (en) * | 2020-08-24 | 2020-12-11 | 安庆师范大学 | Path planning method based on large-scale multi-center problem |
| CN112231984A (en) * | 2020-10-23 | 2021-01-15 | 安庆师范大学 | Effective method for solving large-scale CVRP and electronic equipment |
| CN112257999A (en) * | 2020-10-10 | 2021-01-22 | 东南大学 | Self-adaptive large-scale neighborhood searching method for large-scale pure electric bus scheduling problem |
| CN112801361A (en) * | 2021-01-25 | 2021-05-14 | 西安工业大学 | UAVs and UGVs long-term multi-target path planning problem and solving algorithm |
| CN113313349A (en) * | 2021-04-20 | 2021-08-27 | 合肥工业大学 | Satellite task resource matching optimization method and device, storage medium and electronic equipment |
| CN113393111A (en) * | 2021-06-09 | 2021-09-14 | 东南大学 | Cross-border transportation bilateral connection vehicle scheduling method based on variable neighborhood tabu search algorithm |
| CN113642763A (en) * | 2021-06-30 | 2021-11-12 | 合肥工业大学 | Budget constraint-based high-end equipment development resource allocation and optimal scheduling method |
| CN113935543A (en) * | 2021-10-28 | 2022-01-14 | 北京航空航天大学 | Urban aerial taxi site selection-path optimization method |
| CN114091722A (en) * | 2021-10-09 | 2022-02-25 | 山东师范大学 | Vehicle route optimization method and system based on hybrid tabu search |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2006073759A2 (en) * | 2005-01-04 | 2006-07-13 | Deere & Company | Vision-aided system and method for guiding a vehicle |
| CN101292244A (en) * | 2005-01-04 | 2008-10-22 | 迪尔公司 | Vision-aided system and method for guiding a vehicle |
-
2012
- 2012-09-20 CN CN2012103496480A patent/CN102880798A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2006073759A2 (en) * | 2005-01-04 | 2006-07-13 | Deere & Company | Vision-aided system and method for guiding a vehicle |
| CN101292244A (en) * | 2005-01-04 | 2008-10-22 | 迪尔公司 | Vision-aided system and method for guiding a vehicle |
Non-Patent Citations (1)
| Title |
|---|
| 张俊: "多车场带时间窗车辆路径问题的模型和算法", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (45)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103366021A (en) * | 2013-08-07 | 2013-10-23 | 浪潮(北京)电子信息产业有限公司 | Variable neighborhood search method and system on cloud computing platform |
| CN103530699A (en) * | 2013-09-21 | 2014-01-22 | 西安电子科技大学 | Multi-time-window vehicle route selection method on basis of improved universal gravitation algorithm |
| CN103530699B (en) * | 2013-09-21 | 2016-05-25 | 西安电子科技大学 | Based on the many time windows vehicle route system of selection that improves gravitation algorithm |
| CN104933473A (en) * | 2015-05-22 | 2015-09-23 | 南京邮电大学 | City intelligent traffic dispatching method based on variable neighborhood search ant colony algorithm |
| CN105157712A (en) * | 2015-08-18 | 2015-12-16 | 浙江工商大学 | Vehicle routing planning method and planning system |
| CN106251009A (en) * | 2016-07-27 | 2016-12-21 | 清华大学 | A kind of optimized algorithm of the Vehicle Routing Problems solving time window |
| CN107341628A (en) * | 2016-12-30 | 2017-11-10 | 闽江学院 | A kind of axis-spoke logistics network Hub Location and distribution method based on probability Tabu search algorithm |
| CN107341628B (en) * | 2016-12-30 | 2021-04-27 | 闽江学院 | Hub and spoke type logistics network hub station site selection and distribution method based on probability tabu algorithm |
| CN106803136A (en) * | 2017-01-24 | 2017-06-06 | 苏州工业职业技术学院 | A kind of fresh dispatching real-time optimization method based on genetic algorithm |
| CN107194513B (en) * | 2017-05-26 | 2020-09-29 | 中南大学 | Optimization method for solving problem of whole-channel logistics distribution |
| CN107194513A (en) * | 2017-05-26 | 2017-09-22 | 中南大学 | A kind of optimization method for solving full channel logistics distribution |
| CN107300927A (en) * | 2017-06-26 | 2017-10-27 | 中国人民解放军国防科学技术大学 | A kind of unmanned plane base station selection and patrol method for optimizing route and device |
| CN107300927B (en) * | 2017-06-26 | 2020-02-07 | 中国人民解放军国防科学技术大学 | Unmanned aerial vehicle base station site selection and patrol path optimization method and device |
| CN108280463A (en) * | 2017-12-20 | 2018-07-13 | 中国人民解放军国防科技大学 | Optimization method and device for double-layer path of vehicle-mounted unmanned aerial vehicle |
| CN108280463B (en) * | 2017-12-20 | 2020-08-14 | 中国人民解放军国防科技大学 | Optimization method and device for double-layer path of vehicle-mounted unmanned aerial vehicle |
| CN108389003A (en) * | 2018-03-16 | 2018-08-10 | 广东工业大学 | Service role dispatching method and device under a kind of remote health monitoring line |
| CN108389003B (en) * | 2018-03-16 | 2022-01-11 | 广东工业大学 | Method and device for scheduling service tasks under remote health monitoring line |
| CN108492020B (en) * | 2018-03-16 | 2021-02-02 | 浙江工商大学 | Polluted vehicle scheduling method and system based on simulated annealing and branch cutting optimization |
| CN108492020A (en) * | 2018-03-16 | 2018-09-04 | 浙江工商大学 | Pollution vehicle dispatching method and system based on simulated annealing and branch's cutting optimization |
| CN108759851A (en) * | 2018-06-01 | 2018-11-06 | 上海西井信息科技有限公司 | More vehicle paths planning methods, system, equipment and storage medium based on time window |
| CN109146163A (en) * | 2018-08-07 | 2019-01-04 | 上海大学 | Optimization method, equipment and the storage medium of Automated Sorting System sorting distance |
| CN109146163B (en) * | 2018-08-07 | 2021-12-07 | 上海大学 | Method and equipment for optimizing sorting distance of automatic sorting system and storage medium |
| CN109472342A (en) * | 2018-10-25 | 2019-03-15 | 中国人民解放军国防科技大学 | Self-optimized bionic self-repairing hardware fault reconstruction mechanism design |
| CN109472342B (en) * | 2018-10-25 | 2020-09-11 | 中国人民解放军国防科技大学 | Self-optimized bionic self-repairing hardware fault reconstruction mechanism design |
| CN110110920A (en) * | 2019-04-30 | 2019-08-09 | 浙江财经大学 | A kind of collaborative vehicle method for optimizing route towards coarse localization |
| CN110110920B (en) * | 2019-04-30 | 2021-08-03 | 浙江财经大学 | Cooperative vehicle path optimization method for rough positioning |
| CN110322066A (en) * | 2019-07-02 | 2019-10-11 | 浙江财经大学 | A kind of collaborative vehicle method for optimizing route based on shared carrier and shared warehouse |
| CN110322066B (en) * | 2019-07-02 | 2021-11-30 | 浙江财经大学 | Collaborative vehicle path optimization method based on shared carrier and shared warehouse |
| CN111882099A (en) * | 2020-05-11 | 2020-11-03 | 武汉理工大学 | Logistics distribution path planning method based on variable neighborhood parallel annealing algorithm |
| CN111950761B (en) * | 2020-07-01 | 2022-11-15 | 合肥工业大学 | Development resource integrated scheduling method for high-end equipment complex layered task network |
| CN111950761A (en) * | 2020-07-01 | 2020-11-17 | 合肥工业大学 | Development resource integrated scheduling method for high-end equipment complex layered task network |
| CN112067011A (en) * | 2020-08-24 | 2020-12-11 | 安庆师范大学 | Path planning method based on large-scale multi-center problem |
| CN112067011B (en) * | 2020-08-24 | 2024-04-26 | 安庆师范大学 | Path planning method based on large-scale multi-center problem |
| CN112001678A (en) * | 2020-08-26 | 2020-11-27 | 莆田烟草物流有限公司 | Method for reducing tobacco distribution mileage |
| CN112257999A (en) * | 2020-10-10 | 2021-01-22 | 东南大学 | Self-adaptive large-scale neighborhood searching method for large-scale pure electric bus scheduling problem |
| CN112231984A (en) * | 2020-10-23 | 2021-01-15 | 安庆师范大学 | Effective method for solving large-scale CVRP and electronic equipment |
| CN112231984B (en) * | 2020-10-23 | 2023-09-15 | 安庆师范大学 | Efficient method for solving large-scale CVRP and electronic equipment |
| CN112801361A (en) * | 2021-01-25 | 2021-05-14 | 西安工业大学 | UAVs and UGVs long-term multi-target path planning problem and solving algorithm |
| CN113313349B (en) * | 2021-04-20 | 2022-09-23 | 合肥工业大学 | Satellite task resource matching optimization method and device, storage medium and electronic equipment |
| CN113313349A (en) * | 2021-04-20 | 2021-08-27 | 合肥工业大学 | Satellite task resource matching optimization method and device, storage medium and electronic equipment |
| CN113393111A (en) * | 2021-06-09 | 2021-09-14 | 东南大学 | Cross-border transportation bilateral connection vehicle scheduling method based on variable neighborhood tabu search algorithm |
| CN113642763B (en) * | 2021-06-30 | 2023-06-09 | 合肥工业大学 | High-end equipment development resource allocation and optimal scheduling method based on budget constraint |
| CN113642763A (en) * | 2021-06-30 | 2021-11-12 | 合肥工业大学 | Budget constraint-based high-end equipment development resource allocation and optimal scheduling method |
| CN114091722A (en) * | 2021-10-09 | 2022-02-25 | 山东师范大学 | Vehicle route optimization method and system based on hybrid tabu search |
| CN113935543A (en) * | 2021-10-28 | 2022-01-14 | 北京航空航天大学 | Urban aerial taxi site selection-path optimization method |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN102880798A (en) | Variable neighborhood search algorithm for solving multi depot vehicle routing problem with time windows | |
| CN109034481B (en) | Constraint programming-based vehicle path problem modeling and optimizing method with time window | |
| CN108764777B (en) | Electric logistics vehicle scheduling method and system with time window | |
| Ho et al. | Solving a static repositioning problem in bike-sharing systems using iterated tabu search | |
| Doppstadt et al. | The hybrid electric vehicle–traveling salesman problem | |
| Crainic et al. | Multi-start heuristics for the two-echelon vehicle routing problem | |
| CN110322066B (en) | Collaborative vehicle path optimization method based on shared carrier and shared warehouse | |
| CN110909952B (en) | City two-stage distribution and scheduling method with mobile distribution station | |
| CN112733272A (en) | Method for solving vehicle path problem with soft time window | |
| Ding et al. | Conflict-free electric vehicle routing problem with capacitated charging stations and partial recharge | |
| Ma et al. | Rebalancing stochastic demands for bike-sharing networks with multi-scenario characteristics | |
| CN110098964A (en) | A kind of disposition optimization method based on ant group algorithm | |
| CN113848970A (en) | Multi-target collaborative path planning method for vehicle and unmanned aerial vehicle | |
| CN107341628B (en) | Hub and spoke type logistics network hub station site selection and distribution method based on probability tabu algorithm | |
| CN114462693A (en) | Distribution route optimization method based on vehicle unmanned aerial vehicle cooperation | |
| CN115576343A (en) | Multi-target vehicle path optimization method combining unmanned aerial vehicle distribution | |
| CN113344267A (en) | Logistics network resource allocation optimization method based on cooperation | |
| CN110275535B (en) | Multi-state vehicle path planning method based on improved A star algorithm | |
| Shen et al. | A MultiObjective optimization approach for integrated timetabling and vehicle scheduling with uncertainty | |
| CN113988424A (en) | Circulation drop-and-pull transport scheduling method | |
| Al Theeb et al. | Optimization of logistic plans with adopting the green technology considerations by utilizing electric vehicle routing problem | |
| CN115062868A (en) | Pre-polymerization type vehicle distribution path planning method and device | |
| CN111507662B (en) | Method for planning logistics vehicle path | |
| Leu et al. | A green vehicle routing method for the regional logistics center | |
| CN103530699B (en) | Based on the many time windows vehicle route system of selection that improves gravitation algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C02 | Deemed withdrawal of patent application after publication (patent law 2001) | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20130116 |