CN103218667A - Container wharf loading plan optimization method based on tabu search - Google Patents
Container wharf loading plan optimization method based on tabu search Download PDFInfo
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Abstract
The invention relates to a container wharf loading plan optimization method based on tabu search. In order to conduct approximation analysis on a container wharf loading plan problem, a tabu search algorithm is designed on the basis of a mathematical model of an existing container wharf loading problem. When the tabu search algorithm is used, the problem is divided into preposition problems and postposition problems which are sequentially solved to finally obtain an initial solution of the whole problem, a mixed search strategy of large-scale search and depth search is provided to be used for improving the algorithm, and a quickening strategy based on calculation of objective function improvement quantity is designed. The container wharf loading plan optimization method can be used for effectively working out optimal container wharf loading, further shortens loading time, improves wharf operation efficiency, reduces cost, and brings huge economic benefits for ports and shipping companies.
Description
Technical field
Main in the world freight transportation has at present all been adopted containerzation and has been responsible for providing the shipping service of container by shipping company.Shipping company is in order to enlarge the economic benefit scale, the tonnage of its container ship also increases day by day, the carrying capacity of container is increased to above 4500TEU by 350TEU and (all adopts two kinds of long containers of 20ft and 40ft in the present international shipping container usually, it is unitized for the container number is calculated, the 20ft container as a unit of account, represent that with TEU the 40ft container is as two unit of accounts, so that the operation amount of unified calculation container).The also corresponding difficulty that has increased the shipment of container of the increase of container ship carrying capacity.For a container ship, depend on ship on the time of whole encased conveying process and the very expensive degree in the loading at harbour and the operation of unload containers, the berthing time of an average container ship at the harbour accounts for about 60% of its whole encased conveying time, thereby the expense and the time of encased conveying ship can be effectively saved in the plan of carrying of rational and effective container handling, the container terminal ship planning optimization method that the present invention sets up can be made optimum plans effectively, for the plenty of time is saved in encased conveying, and then for enterprise saves cost, increasing economic efficiency provides strong technical support.
Background technology
The Loading Plan problem is the problem that the container wharf daily need solves.The loading of container mainly is complete by the captain in the past, and container load plan (CLP) of today is mainly determined the situation of institute's loading container according to the coordinator of shipping company by each harbour.Good and bad directly decision container freighter expense and the time only that container load plan (CLP) is formulated, for this reason, seek a kind of effective container terminal ship planning optimization method, become the technical matters that harbour and shipping company need to be resolved hurrily.
Summary of the invention
Technical matters to be solved by this invention is on existing container terminal ship problem mathematical model basis, to be approximate solution container terminal ship plan problem, the design tabu search algorithm.In the algorithm implementation process, it is decomposed, obtaining the initial solution of contributions problem, and the tabu search algorithm that has is earlier improved, obtain container terminal ship planning optimization method effectively at the problem characteristics.
The technical solution used in the present invention is:
1. the description of existing mathematical model
In order to guarantee the stability of container ship, Proposed Shipping Schedule need satisfy following balance constraint:
(1) lateral balance.Container ship starboard container general assembly (TW) equals (or the weight difference is in certain scope) larboard container general assembly (TW), has comprised the container on the odd-numbered line of the odd-numbered line of cabin and on-deck here.
(2) Bay is to balance.Bow container general assembly (TW) equals (or the weight difference is in certain scope) stern container general assembly (TW).
(3) vertical balance.Each Container Weight is greater than or equals the weight of its underpart Neighbor Set vanning in one deck.
The purpose that studies a question for convenience, the container load plan (CLP) problem has been done following hypothesis:
(1) container ship is in the port of departure, and ship needs to arrive the station, port through a plurality of continuously, and only does unloading operation at each harbour.
(2) but the container quantity in the loading plan is not more than the quantity of " loaded " position on the container ship.
(3) have only port, 1 Taiwan and Hongkong to hang the shipment operation of responsible container.
(4) container quantity that arrives each harbour is known.
In the research of this paper, set up integer programming model based on the feature of Loading Plan problem, its multiple objective function comprises and minimizes total time of shipment and minimize bay weight difference.
(1) parameter
The set of C container.
Location sets on the L container ship.
C c=1 ..., m, m are total container quantity.
L 1=1 ..., n, n are the number of positions on the total container ship.
w
cThe weight of c container.
Bay set on the I container ship.
The quantity of bay on the b container ship.
J
iRow set among i the bay, j=1 ..., g, wherein g is the number of elements in the set.
K
IjI bay, j capable middle level set.
OI container ship odd number bay set,
The set of FC 40ft container,
The maximum loading of Q container ship.
Q
1The maximum magnitude of bow bay and stern bay Weight Loaded difference.
Q
2The maximum magnitude of the capable and right ship side luggage of left side ship side dead weight capacity difference.
D gathers to the station, port, D={1, and 2 ..., q}, wherein d
cFor container c to the station, port.
C
dD gathers to the container at station, port, d=1 ..., q,
t
LcContainer c is loaded into the loading time of 1 position on the ship,
t
LcValue can pass through formula t+ α
1U+ α
2V calculates, and wherein t is a constant, and u is relevant with layer information with the row of position 1 with v, α
1And α
2Be correlation parameter.
(2) decision variable
Here position 1 can be represented with tri-vector, i.e. decision variable x
Lc=x
Ijkc, wherein i represents the bay dimension, j represents the row dimension, k presentation layer dimension.
2.2 mathematical model
Utilize parameter as defined above and decision variable, the integer programming model of Loading Plan problem can be set up as follows:
s.t.
Formula (1) is the objective function of this model, and constraint (2) guarantees that each container can only be placed on the position on the container ship and each container all must be loaded.Each position on constraint (3) the assurance container ship can only be placed a container at most.Constraint (4) is less than the maximum loading of container ship for the general assembly (TW) of container.The container of constraint (5) and (6) assurance 40ft can only be put even number bay, and the container of 20ft can only be put odd number bay.Constraint (7) illustrates that the 20ft container can not be placed in the odd number bay that has placed the 40ft container.Constraint (8) illustrates that the 40ft container can not be placed in the even number bay that has placed the 20ft container.Constraint (9) expression loaded container can not be placed on the light container.Constraint (10) and (11) is that the lateral balance and the bay of container ship retrains to balance, and constraint (12) is decision variable x at last
kSpan.
2. two stage heuritic approaches
Initial solution is separated its quality of separating as the basis of tabu search algorithm and is directly had influence on the operation efficiency of algorithm and the quality of finally separating that is obtained.In this chapter at the characteristics of container load plan (CLP) problem, whole problem branch is found the solution respectively for two subproblems, one is that allocation set vanning subclass is incorporated into each bay, second subproblem is to determine each container particular location aboard ship, and separating as the basis of finding the solution second problem of its previous problem separated.Describe in detail to finding the solution two designed stage heuritic approaches of two subproblems below.
2.1 allocation set vanning subclass is incorporated into each bay
Container set C can be divided into q subclass according to difference to the station, port, what need do in this stage is that the subclass how allocation set is cased is incorporated into each bay.Ship navigation safety factor need be paid attention to as key factor in the process of distributing, and promptly after the container unloading of arriving the station, port midway, container ship also will guarantee the safety problems of navigation of follow-up voyage.Thereby when the design heuritic approach, considered that special appointment rule satisfies above requirement, concrete step is as follows:
Step1. container set C is divided into q subclass C
h, h=1 ..., q, wherein q be in the loading plan container to the quantity at station, port, and q>1.If h=1 represent the container ship voyage first to station, port, C
qThe set expression is last to the unloaded container subclass in port.
Step2. to each container subclass C
h, h=1 ..., q calculates corresponding TEU value, and uses ρ
hRepresent.
Step3. suppose the subclass of bay set
Be used for placing container subclass C
hIn container, the order
In the expression bay set
The TEU quantity of subclass.Bay gives C in the middle of at first assigning container ship
qThe container subclass upgrades
And calculate
If
Then accept this distribution, begin to be next container subclass C
Q-1Distribute bay, otherwise continue to assign
Give container subclass C
q, wherein β is the parameter about the b value, upgrades
With
If ρ
qStill greater than
Then upgrade
With
Be assigned to container subclass C
qBay be followed successively by in proper order
When in the bay assignment order, not having assignable bay, assign from the nearest bay of the middle bay of container ship and give the container subclass that needs appointment, up to satisfying
Definition δ
qFor
The surplus of TEU in the subclass.
Step4. the continuous appointment free time
Give container subclass C
Q-1If
Assign bay to give C with identical method
Q-1, same for remaining container subclass C
h, h=1 ..., q.
By above step, can finally obtain separating of container subclass bay position assignment problem, and try to achieve each container based on this and be assigned to position on the ship, and then obtain finally separating of container load plan (CLP).Just how to determine that the particular location of container on container ship launches to introduce below.
2.2 determine the container particular location
After having found the solution bay appointment subproblem, next target is to determine the particular location of each container on container ship according to the bay information of assigning.After the bay position of each container subclass was determined, the container in each subclass can load under the prerequisite that retrains, thereby the concrete position of Random assignment obtains final separating in fixed bay position.But, what obtained separates initial solution as next step tabu search algorithm, the quality of its quality has influenced the operation efficiency of algorithm and the quality of finally separating to a great extent, thus thereby the better initial solution of acquisition of the character maximum possible below when determining the position of concrete container on boats and ships, having proposed.
The container loading priority of character 1:40ft is greater than the 20ft container.
Proof: the problem that at first needs to consider when allocation set vanning particular location is that all containers all must distribute a position, promptly needs to satisfy constraint condition
Owing to there is constraint (9), and the container of 40ft will account for the position of 2 20ft containers and more be difficult to distribution locations, thereby the container loading priority that can draw 40ft is greater than the 20ft container.
Character 2: set C
h(h=1 ..., q) container in should be assigned to corresponding bay set according to the weight average of each container
In.Concrete method is: suppose
Be subclass C
hThe ordering of the middle non-ascending order of Container Weight, p is the bay set
In bay quantity,
The container that first bay in the set distributes is
The container that second bay in the set distributes is
According to the method with C
hIn container be assigned among the corresponding bay.
Proof: in finding the solution container load plan (CLP) problem process, the balance of container ship is the main safety factor of considering.Objective function has considered to minimize the problem of charging capacity difference between maximum weight bay and the minimum weight bay in the integer programming model of setting up, thus in character 2 to each subclass C
hIn container all assign among the corresponding bay according to its weight, thereby minimize Weight Loaded difference between each bay.Owing to considered the Weight Loaded difference between any two bay on the container ship, so just considered maximum weight bay in the objective function and the charging capacity difference amount between the minimum weight bay, thereby can obtain better to separate by character 2.
2.3 the adjustment of initial solution
After certain rule acquisition initial solution, need to judge whether separating of being obtained is feasible.When separating of being obtained satisfied constraint (10) and (11), need do suitable adjustment to initial solution.Here adopt a simple swap neighborhood search to adjust the position of some container so that satisfy constraint.When carrying out place-exchange, need follow following 2 points:
(1) the arbitrary swap in the neighborhood search moves and does not violate constraint condition involved in the model.
(2) arbitrary swap involved two container c in moving
1And c
2Satisfy condition: c
1, c
2∈ C
h, h=1 ..., q.
3 tabu search algorithms
This trifle is introduced the tabu search algorithm of loading plan problem.Make a feasible solution of S problem of representation, N (S) is for applying the set that certain mobile acquisition is separated on S.Best the separating or still be better than separating as the base of next iteration of historical optimum solution by taboo that tabu search is selected not avoided among the neighborhood N (S) in each iteration separated.
Be incorporated into each bay and determine two subproblems of each container particular location aboard ship because the loading plan problem can be divided into allocation set vanning subclass, designed following tabu search algorithm according to the characteristics of this problem.In the process of tabu search, each iteration is divided into two stages, in the phase one, by changing container subclass C
hThe bay set that is distributed
Produce new separating.For whole container load plan (CLP) problem, bay position allocated phase separate to whole problem to solve influence very big, by changing the bay set
Can enlarge the search volume of separating to a greater extent, thereby the search of phase one is become extensive search.Subordinate phase is given
Determine set C under the prerequisite of set
hThe position of middle container, this stage is called deep search.According to above description, the tabu search algorithm flow process of using among this chapter as shown in Figure 1.S among the figure
*Be the historical optimum solution that is obtained in the tabu search algorithm, and h=1 ..., q.
Extensive search is based on tabu search.Separate and be accepted for one in neighborhood, then the inverse move of moving of its correspondence will be added in the middle of the taboo table.The taboo table is one section internal memory that size is TL, is used for preserving the nearest inverse move of carrying out for TL time of moving, and is absorbed in local optimum to prevent algorithm.The structure of the element in the taboo table is that shape is as (b
u, b
v) so several right.If received moving is with b
uAnd b
vTwo bay exchange, then with element (b
u, b
v) join the end of taboo table, simultaneously first element in the taboo table is therefrom deleted.When moving of avoiding of a quilt can produce a historical optimum solution of ratio and better separates, still accept this and move this moment, the element that will add is Already in the middle of the taboo table in this case, first element in the delete list not then, but the identical therewith element of deletion.
The flow process of extensive search is summarized as follows:
Step 1. obtains the best S that separates in the exchange neighborhood search
1', S is separated in its generation
1' swap operation in move (b
u, b
v) do not avoided or adopt and can separate S
1' the basis on obtain to be better than moving of historical optimum solution.
Step 2. uses heuritic approach and upgrades and b
uAnd b
vThe position of two bay associated container obtains new explanation S '.
If Step 3. new explanation S ' are better than historical optimum solution S
*, S then
*=S '.
Step 4. makes S=S ', will produce new explanation S
1' mobile joining in the taboo table.
S is separated on the basis that can obtain the next stage deep search by above flow process
1'.
3.1 deep search
Deep search is the S that separates with extensive search
1' be the basis, do not changing to separate S
1' be the bay collection on basis
The further search of implementing under the prerequisite, thus obtain whole problem better separate S ".
3.1.1 neighborhood
In deep search, adopted two kinds of move modes to obtain new explanation.
(1) swap moves: exchange two containers distribution locations aboard ship.It should be noted that in the process of exchange separating after must guaranteeing to exchange is feasible solution, i.e. search is only carried out in feasible neighborhood.For container c
1And c
2, establish its position aboard ship and be (i
1, j
1, k
1) and (i
2, j
2, k
2), being respectively of two container correspondences to the station, port
With
Then the place-exchange of two container correspondences need satisfy following condition:
2) if c
1∈ TC, then c
2If ∈ TC is c
1∈ FC, then c
2∈ FC.
3) assumed position (i
1, j
1, k
1+ 1) with (i
1, j
1, k
1-1), (i
2, j
2, k
2+ 1) with (i
2, j
2, k
2-1) all exist and its correspondence position on the weight of the container that distributes be respectively
Then need to satisfy
Do not have container to distribute if above four position parts do not exist or exist, then Xiang Guan weight constraints need not to satisfy.
4) must satisfy constraint (10) and (11) in the model after the exchange.
(2) Shift moves: (i, j k) move to reposition (i ', j ', k ') from initial position a certain container c.Same needs guarantee that the new explanation that is produced is a feasible solution after moving, need satisfy following condition:
2) position (i ', j ', k ') is empty position.
3) if the location (i ', j ', k '+1) and (i ', j ', k '-1), and have the container and the weight of having distributed to be respectively on its position
With
Then need satisfy
Do not have the allocation set vanning if above two position parts do not exist or exist, then related constraint need not to satisfy.
4) if c ∈ FC then need satisfy the constraint (5) in the model, if c ∈ TC then need satisfy the constraint (6) in the model.
5) move the back and satisfy constraint (7), (8), (10) and (11).
3.1.2 acceleration strategy
In order to accelerate the speed of tabu search algorithm, the method for originally researching and proposing by evaluation objective function improvement amount reduces running time of algorithm.In the neighborhood search process, need move through the calculating target function value to each and estimate.When the big and calculating target function of neighborhood space is more time-consuming, need be by designing the computing time that better appraisement system reduces calculating target function.
In this paper research, objective function is mainly by two, minimizes total time of shipment and minimizes weight difference between maximum bay of charging capacity and the minimum bay.If f (x) is the total target function value of this problem, f
1(x) be target function value, f about the time of shipment
2(x) be target function value, then f (x)=ω about the weight difference
1f
1(x)+ω
2f
2(x).Introduce the objective function improvement amount computing method of two kinds of neighborhoods below respectively.
Swap neighborhood target function value change amount
Move for a certain swap, the position of establishing two changes be respectively (i, j, k) and (i ', j ', k ').First in objective function, its change amount Δ f
1(x)=0, only need the objective function change amount of calculating second portion to get final product.When calculating second portion objective function change amount, only need to calculate the variation of the Weight Loaded of i and two bay of i ', need not to recomputate again for the bay that does not relate to, thereby obtain maximum load bay thus and minimum load-carrying bay tries to achieve Δ f
2(x), this variable Δ f (the x)=Δ f of final goal function
1(x)+Δ f
2(x).
Shift neighborhood target function value change amount
In the shift moving process, need move to an empty position to a certain locational container.(i, j k) move to position (i ', j ', k '), then the first change amount Δ f of target function value partly from the position for hypothesis set vanning
1(x) can calculate by following formula:
Δf
1(x)=f
1′(x)-f
1(x)
=t+α
1j′+α
2k′-t-α
1j-α
2k
=α
1(j′-j)+α
2(k′-k)
The change amount computing method of second portion target function value are similar in moving with swap, also only need to calculate i and two bay of i ' Weight Loaded variation and obtain Δ f
2(x), thus finally obtain Δ f (x).
3.2 tabu search algorithm flow process
Tabu search algorithm uses two kinds of general stopping criterions, and algorithm maximum iteration time (MaxIter) and maximum nothing are improved iterations (MaxIterWI), and when any one stopping criterion satisfied, algorithm stopped.
According to two stages of aforementioned tabu search---extensive search and deep search, the algorithm flow of tabu search is as follows:
Step 1. makes that S is an initial solution, and S* is historical optimum solution.Order taboo table
Current iteration number of times Iter=0, current nothing is improved iterations IterWI=0.
Step 2. is that base is separated and carried out extensive search with S, obtains new explanation S '.IterWI=0; Otherwise IterWI=IterWI+1.According to the mobile update taboo table T that accepts in the extensive search.
Step 3. is that base is separated and carried out deep search with S ', obtains new explanation S ", if (S ")<f (S*) makes S*=S ', IterWI=0 to f.Make S=S ".
If Step 4. Iter=MaxIter or IterWI=MaxIterWI, tabu search stops; Otherwise Iter=Iter+1 changes Step 2.
Description of drawings
Fig. 1 tabu search algorithm process flow diagram.
Claims (4)
1. the container terminal ship planning optimization method based on tabu search is characterized in that: on existing container terminal ship problem mathematical model basis, design a kind of improved tabu search algorithm, realize the optimization of container terminal ship plan.
2. the described a kind of container terminal ship planning optimization method based on tabu search of claim 1, its feature also is: in algorithm is implemented, problem is divided into preposition problem and rearmounted problem, and finds the solution successively, finally obtain the initial solution of whole problem.
3. the described a kind of container terminal ship planning optimization method of claim 1 based on tabu search, its feature also is: in design tabu search algorithm process, extensive search and deep search are combined, and use this mixed search strategy that tabu search algorithm is improved.
4. the described a kind of container terminal ship planning optimization method based on tabu search of claim 1, its feature also is: on above-mentioned feature base, designed the acceleration strategy based on calculating target function improvement amount.
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CN112001064A (en) * | 2020-07-29 | 2020-11-27 | 浙江大学 | Full-autonomous water transport scheduling method and system between container terminals |
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Publication number | Priority date | Publication date | Assignee | Title |
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CN105608548A (en) * | 2016-01-20 | 2016-05-25 | 大连海事大学 | Automatic stowage method of bulk carrier stowage meter |
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