CN108733872A - A kind of immersed tube transportation by driving control optimization method based on multiple target differential evolution algorithm - Google Patents
A kind of immersed tube transportation by driving control optimization method based on multiple target differential evolution algorithm Download PDFInfo
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Abstract
The invention discloses a kind of, and the immersed tube transportation by driving based on multiple target differential evolution algorithm controls optimization method.Its key step is as follows, and (1) utility is measured to evaluate the Mutation Strategy of differential evolution algorithm, and then realizes the adaptive of multiple target differential evolution algorithm Mutation Strategy.(2) immersed tube transportation by driving control Model for Multi-Objective Optimization is established.(3) the actual multi-objective optimization question is solved using the TSP question strategy multiple target differential evolution algorithm based on performance metric of proposition, one group of Pareto disaggregation is provided for policymaker.The present invention has important engineering application value, and a variety of effective control programs can be provided for immersed tube transportation by driving.Can not only cost of implementation saving, and conevying efficiency and safety can also be greatly improved.What is more important, the present invention can in the case of target or environmental change, can similarly be provided for policymaker it is a set of efficiently control scheme, this undoubtedly substantially increases the actual efficiency of decision-making.
Description
Technical field
The invention belongs to a kind of immersed tube transportation by drivings to control optimisation technique, and in particular to heavy based on multiple target differential evolution algorithm
Pipe transportation by driving controls optimization method.
Background technology
Because immersed tube transportation by driving can effectively shorten haulage time, operating efficiency is improved, and small by quality conditionality,
So it has been widely used in underwater large tunnel engineering.Since in most cases, immersed tube itself is that do not have
Power.Thus, in actual operation, a certain number of towboats are generally required to carry out traction control to it to complete to transport
(being realized generally by translation).Under normal conditions, the quantity and control mode of towboat are all by construction personnel by previous
Experience specifically determines.On the one hand, it is contemplated that immersed tube can be influenced during transportation by driving by factors such as flow, wind, times,
It is live generally all to call more towboat, but its result undoubtedly considerably increases transportation by driving cost.On the other hand, when engineering reality
There is uncertain factor appearance when applying, strong influence still will necessarily be brought to channel safe or construction speed using original method.
It is found through looking through a great amount of information, some scholars have also carried out a series of researchs to the control problem of immersed tube before this, but not ugly
Go out, they are only that the problem is solved as a single-object problem.Actually this is not so, because for actual immersed tube
Transportation by driving generally at least can all consider the targets such as the towing tension allowance maximum of the most short and each towboat of haulage time.And these targets it
Between it is often conflicting, need to take measures to can be only achieved relative equilibrium, thus immersed tube transportation by driving control should be mesh more than one
Mark optimization problem.So how effectively to solve multi-objective optimization question then is a difficulty for studying immersed tube control optimization problem
Point.
For Multipurpose Optimal Method, the Multipurpose Optimal Method based on heuritic approach obtains for over ten years recently
Prodigious concern.It is not only because with good optimizing ability, it is often more important that it is not required to substantially it is to be understood that excellent
The mathematical characteristic of change problem.In numerous heuritic approaches, differential evolution algorithm is a typical algorithm, it is excellent in multiple target
The application (i.e. multiple target differential evolution algorithm) in change field, also obtains huge success.Usually, multiple target differential evolution is calculated
The performance of method is closely related with the selection pressure of individual and the performance of differential evolution algorithm.And the performance of differential evolution algorithm by
Its Mutation Strategy is affected, and main cause is that each Mutation Strategy can only be effective to specific multi-objective optimization question.Cause
This, it is an important problem that suitable Mutation Strategy how is automatically selected according to different types of multi-objective optimization question.
For the control optimization problem of immersed tube transportation by driving, the present invention proposes to use the TSP question strategy based on performance metric
Multiple target differential evolution algorithm (Multi-objective differential evolution with performance-
Metric-based self-adaptive mutation operator, MODE-PMSMO) it is solved.Through experimental study
Show that institute's extracting method can not only provide one group of equilibrium disaggregation for policymaker, moreover it is possible to cost-effective, raising conevying efficiency, in addition
The present invention can also be suitable for carrying out control optimization under uncertain environment, have important engineering application value.
Invention content
For the present situation of existing immersed tube transportation by driving control problem studied usually as a single-object problem, originally
Invention proposes that a kind of immersed tube transportation by driving based on multiple target differential evolution algorithm controls optimization method.It is exactly specifically to utilize more mesh
Mark differential evolution algorithm controls optimization problem to solve immersed tube transportation by driving, is selected for policymaker to provide one group of equilibrium disaggregation；With
This is cost-effective at the same time it can also realize, improves conevying efficiency.Technology proposed by the present invention, especially suitable in uncertain ring
Immersed tube transportation by driving control is carried out under border.
To realize that the above target, operating procedure of the invention are as follows：
(1) design of the TSP question strategy multiple target differential evolution algorithm based on performance metric；
Further, the operating procedure of the TSP question strategy multiple target differential evolution algorithm based on performance metric is as follows：
(1.1) initialization operation：Determine the variance control parameter F and cross-over control parameter CR of differential evolution algorithm；Setting
Population scale NP and maximum iterative algebra Gmax；Initial population P is generated in feasible section1 0, each individual is denoted as(=1,
2,…,NP)；And set current algebraically G=0；Meanwhile being set as G using the iterative algebra of single Mutation Strategys=0.2 ×
Gmax.In addition, (i.e. using DE/rand/1) and DE/best/1 is (i.e.) conduct
The Mutation Strategy in algorithm policy library.
(1.2) mutation operation：For each individualIf G<Gs, then using DE/rand/1 Mutation Strategies come to a
Body is updated, and formula is as follows：
In formula (1), F indicates variance control parameter, and range is between [0,1]；r1、r2And r3Expression two is random whole
Number, range is in [1, NP], and r1≠r2≠r3≠i。
If G >=Gs, then the update of individual according to from selected by policy library to Mutation Strategy operated, because
This, for each individual, Mutation Strategy may be formula (1), it is also possible to following Mutation Strategy：
In formula (2),Indicate individual best in current population.
(1.3) crossover operation：For each individualCrossover operation is carried out to it using following Crossover Strategy：
In formula (3), D indicates the dimension of optimization problem；RjAnd jrandA random number in [0,1] range is indicated respectively
With the random integers in [1, D]；CR is the crossing-over rate of differential evolution algorithm.
(1.4) the adaptive operating procedure of Mutation Strategy is as follows in policy library：
The evaluation of Mutation Strategy：Each Mutation Strategy is carried out using an improved IGD (reversed generation distance)
Evaluation, formula are as follows：
In formula (4),Indicate the obtained one group of object vector of this current generation,PFIndicate that previous generation is obtained
Pareto (Pareto) forward position；|PF| it indicatesPFIn individual amount；K is indicatedPFIn object vector；Indicate k andIn object vector minimum euclidean distance.
The adaptive realization of Mutation Strategy：After being evaluated each Mutation Strategy using formula (4), each Mutation Strategy exists
Quantity update in policy library is as follows：
In formula (5), round indicates that bracket function, str_name indicate the Mutation Strategy in policy library；NstrIndicate quilt
Select the individual amount of strategy.
According to formula (4), the individual amount of each Mutation Strategy is updated, formula is as follows：
(1.5) selection operation：
(1.5.1) if(> indicates to dominate), thenIt is saved to P1 G；
(1.5.2) ifSoIt is saved to P1 G；
(1.5.3) ifWithIt is mutually non-dominant, thenIt is saved to P1 G；
(1.6) utilize quick non-dominated ranking and crowding distance sequence both methods from P1 GIn select NP individual, and
Enable P1 G=φ (φ is empty set).Finally, NP individual is stored in P1 G。
(1.7) (1.2)~(1.6) step is repeated, until the iterative algebra of algorithm is Gmax。
(2) immersed tube transportation by driving control Model for Multi-Objective Optimization is established；
One immersed tube transportation by driving Controlling model, the resultant force and resultant moment of main translational velocity and resistance, towboat including immersed tube
Several aspects.
(2.1) rate of translation of immersed tube：It is assumed that immersed tube is v relative to the speed of flow, then immersed tube is in x-axis and y-axis
Speed can be expressed as respectively：
vx=v1cosθ1-v0cosθ0, (7)
vy=v1sinθ1-v0sinθ0, (8)
In formula (7) and (8), v1Indicate speed of the immersed tube relative to bank, v0Indicate the flow velocity of flow；θ1And θ0Table respectively
Show v1With the angle and v of positive direction of the x-axis0With the angle of positive direction of the x-axis.
(2.2) translatory resistance of immersed tube：The residual resistance R of immersed tubebWith frictional resistance RfIt can be obtained respectively by the following formula
Go out：
Rb=0.62 × Cb×Ae,2×v2 (9)
Rf=1.67 × Ae,1×|v|1.83×10-3 (10)
In formula (9) and (10), CbFore body form factor, A are dragged in expressione,2Indicate the underwater cross sectional area of immersed tube, Ae,1
Indicate the underwater surface product of immersed tube.
If immersed tube moving direction is parallel with flow, Ae,1And Ae,2It can be calculated by the following formula：
Ae,1=L (B+2d) (11)
Ae,2=B × d (12)
In formula (11) and (12), L, B and d indicate length, width and the drinking water of immersed tube highly respectively.
If immersed tube moving direction is vertical with flow, Ae,1And Ae,2It can be calculated by the following formula：
Ae,1=B (L+2d) (13)
Ae,2=L × d (14)
The drag overall of convolution (9) and (10), immersed tube towage can be calculated by the following formula：
RT=1.15 (Rf+Rb) (15)
Other than immersed tube tube coupling can be by towage resistance, both sides assist transport floating drum also can by towage resistance, wherein
The towage resistance of single floating drum calculates as follows：
RTp=1.15 × (1.67 × Ap,1×|v|1.83×10-3+0.62×Cb×Ap,2×v2) (16)
In formula (16), Ap,1And Ap,2The underwater surface product of floating drum and underwater cross sectional area are indicated respectively.
So, the total towage resistance of immersed tube is as follows：
R'T=RT+2RTp (17)
(2.3) resultant force and resultant moment of towboat：
The resultant force of towboat can be expressed as：
Representation in components of the F in x-axis and y-axis is as follows：
In formula (19) and (20), R 'TxWith R 'TyR ' is indicated respectivelyTComponent in x-axis and y-axis；FiI-th is indicated to drag
The towing tension of ship, αiIndicate FiThe angle counterclockwise with positive direction of the x-axis；N indicates the quantity of towboat.
(2.4) immersed tube transportation by driving multi-objective optimization question is established：
Transportation by driving control for immersed tube, will meet following three targets：
1) allowance of every towboat towing tension is big as possible；
2) immersed tube haulage time is short as possible；
3) allowance of every towboat towing tension is as equal as possible.
In order to meet three above target, the goal-setting of immersed tube transportation by driving control is as follows：
In formula (21), N indicates towboat quantity, Fi,maxIndicate the maximum towing tension of each towboat,
(3) it solves immersed tube transportation by driving and controls multi-objective optimization question；
According to the object function that formula (21) obtains, using the TSP question strategy multiple target difference based on performance indicator into
Change algorithm to be solved to it, provides one group of Pareto disaggregation.To enable policymaker under different requirements or environment
Immersed tube transportation by driving can be controlled.From the point of view of actual application, this is not only cost-effective, can also greatly improve Transportation Efficiency
Rate.In addition, it is even more important that the solution of multiple-objection optimization may balance each target needed to be considered in practical operation
Between conflict.
Compared with the prior art, the present invention has the following advantages：
First, the present invention realizes automatically selecting for differential evolution algorithm Mutation Strategy using adaptive technique, can
It is enough directed to different types of multi-objective optimization question, selects suitable Mutation Strategy to be solved, which greatly enhances more mesh
Mark the solution efficiency of differential evolution algorithm.Therefore, the present invention can significantly improve multiple target differential evolution algorithm and solve multiple target
The ability of optimization problem.
Second, it is different from single object optimization, the present invention is capable of providing one group of Pareto disaggregation, can allow policymaker being capable of root
The specific embodiment of immersed tube transportation by driving control is chosen according to different targets.Therefore, the present invention can greatly save cost, and improve
Conevying efficiency.
Third, technological means proposed by the present invention can overcome former technological means comprehensive under uncertain environment
Can and safety in terms of deficiency, the control optimization to be immersed tube transportation by driving under uncertain environment provides new technology on the way
Diameter.
Description of the drawings
TSP question strategy multiple target differential evolution algorithm flow charts of the Fig. 1 based on performance indicator.
The vertical view of Fig. 2 immersed tube transportation by drivings.
The front view of Fig. 3 immersed tube transportation by drivings.
The immersed tube transportation by driving control figure of six towboats of Fig. 4.
Fig. 5 obtains four different visual angles figures of Pareto.
Specific implementation mode
With reference to attached drawing, the invention will be further described：
1. the design of the TSP question strategy multiple target differential evolution algorithm based on performance indicator
Although differential evolution algorithm has good optimizing ability, its performance is influenced very big by Mutation Strategy.?
In actual application, each Mutation Strategy can only be effective to certain form of optimization problem, and to the optimization of other type
Problem is then performed poor.If it is possible to suitable Mutation Strategy is automatically selected out according to the characteristic of optimization problem, then
This will greatly improve the ability of algorithm solving-optimizing problem.Based on this, in the present invention, using adaptive technique come to difference into
The Mutation Strategy for changing algorithm is operated so that the algorithm can automatically select suitable variation according to different optimization problems
Strategy, and then the search efficiency of algorithm can be increased substantially.
It is characteristic of the invention that：
The Mutation Strategy of differential evolution algorithm is evaluated using the performance indicator in multiple-objection optimization, is then passed through
Intensified learning uses probability adjust each Mutation Strategy, and phase is selected to allow algorithm according to the property of optimization problem
Matched Mutation Strategy is solved.This undoubtedly greatly improves the energy that differential evolution algorithm solves multi-objective optimization question
Power.
The flow chart of TSP question strategy multiple target differential evolution algorithm based on performance indicator is shown in Fig. 1, specific
Operating procedure is as follows：
(1.1) initialization operation：Determine the variance control parameter F and cross-over control parameter CR of differential evolution algorithm；Setting
Population scale NP and maximum iterative algebra Gmax；Initial population P is generated in feasible section1 0, each individual is denoted asAnd set current algebraically G=0；Meanwhile being set as G using the iterative algebra of single Mutation Strategys
=0.2 × Gmax.In addition, (i.e. using DE/rand/1) and DE/best/1 is (i.e.) Mutation Strategy as algorithm policy library.
(1.2) mutation operation：For each individualIf G<Gs, then using DE/rand/1 Mutation Strategies come to a
Body is updated, and formula is as follows：
In formula (1), F indicates variance control parameter, and range is between [0,1]；r1、r2And r3Expression two is random whole
Number, range is in [1, NP], and r1≠r2≠r3≠i。
If G >=Gs, then the update of individual according to from selected by policy library to Mutation Strategy be updated, because
This, for each individual, Mutation Strategy may be formula (1), it is also possible to following Mutation Strategy：
In formula (2),Indicate individual best in current population.
(1.3) crossover operation：For each individualCrossover operation is carried out to it using following Crossover Strategy：
In formula (3), D indicates the dimension of optimization problem；RjAnd jrandA random number in [0,1] range is indicated respectively
With an integer random number in [1, D]；CR is the crossing-over rate of differential evolution algorithm.
(1.4) the adaptive operating procedure of Mutation Strategy is as follows in policy library：
The evaluation of Mutation Strategy：Each Mutation Strategy is carried out using an improved IGD (reversed generation distance)
Evaluation, formula are as follows：
In formula (4),Indicate the obtained one group of object vector of this current generation,PFIndicate that previous generation is obtained
Pareto (Pareto) forward position；|PF| it indicatesPFIn individual amount；K is indicatedPFIn object vector；Indicate k andIn object vector minimum euclidean distance.
The adaptive realization of Mutation Strategy：After being evaluated each Mutation Strategy using formula (4), each Mutation Strategy exists
Quantity update in policy library is as follows：
In formula (5), round indicates that bracket function, str_name indicate the Mutation Strategy in policy library；NstrIndicate quilt
Select the individual amount of strategy.
According to formula (4), the individual amount of each Mutation Strategy is updated, formula is as follows：
(1.5) selection operation：
(1.5.1) if(> indicates to dominate), thenIt is saved to P1 G；
(1.5.2) ifSoIt is saved to P1 G；
(1.5.3) ifWithIt is mutually non-dominant, thenIt is saved to P1 G；
(1.6) utilize quick non-dominated ranking and crowding distance sequence both methods from P1 GIn select NP individual, and
Enable P1 G=φ (φ is empty set).Finally, NP individual is stored in P1 G。
(1.7) (1.2)~(1.6) step is repeated, until the iterative algebra of algorithm is Gmax。
In order to verify the validity of put forward algorithm, using two multiple target performance indicators (GD and IGD) come to it and seven kinds
Multi-objective Evolutionary Algorithm carries out performance comparison.Wherein, the convergence in the forward positions Pareto obtained by GD primary evaluations, GD is smaller to illustrate institute
It is closer with the true forward positions Pareto to obtain the forward positions Pareto.IGD is the convergence for both having evaluated the forward positions gained Pareto, is also evaluated
Therefore the distributivity in the forward positions gained Pareto is a comprehensive Performance Evaluating Indexes compared to GD, IGD.Seven kinds of ratios simultaneously
Include GDE3, NSGAII-DE, BB-MOPSO, MOEA/D-DE, MODE-RMO, SA-MTLBO, MOMDE-AM compared with algorithm.And it selects
5 biobjective scheduling problems (coming from ZDT test sets) and 5 three objective optimisation problems (coming from DTLZ test sets) are taken to come to them
It is tested.In this experiment, the population scale of all algorithms is set to 100.It is maximum to change for different test functions
Number (G from generation to generationmax) setting is as follows, for 5 biobjective scheduling problem ZDT1~ZDT4 and ZDT6, GmaxIt is set as 250；For three
Objective optimisation problems DTLZ1 and DTLZ2, GmaxIt is set as 300；For three objective optimisation problems DTLZ3, GmaxIt is set as 500；It is right
In three objective optimisation problems DTLZ4 and DTLZ5, GmaxIt is set as 200.For each test function, each multi-objective Evolutionary Algorithm
Number of run be set as 20.In addition, in order to ensure the validity of experiment conclusion, also come pair using 5 nonparametric statistical methods
Each algorithm acquired results are analyzed.This five statistical methods are respectively：Wilcoxon ' s rank sum test, Iman-
Davenport ' s test, Holm ' s procedure, Hochberg ' s procedure and Freidman ' s test.For
Wilcoxon ' s rank sum test, "+", "-", " ≈ " indicate that the performance of carried algorithm will be considerably better than respectively, significance difference
In similar to the performance of institute's comparison algorithm.
For performance indicator GD, result obtained by each algorithm (average value and standard variance) and its statistic analysis result is such as
Under：
As can be seen from the above results, GDE3, NSGAII-DE, MOEA/D-DE, MODE-RMO and MOMDE-AM are arbitrary
It is better than MODE-PMSMO to be failed on one function.Compared to this five kinds of multi-objective Evolutionary Algorithms, what MODE-PMSMO was obtained
The forward positions Pareto have better convergence.Meanwhile BB-MOPSO and SA-MTLBO are asked in 3 and 4 biobjective schedulings respectively
It to be considerably better than MODE-PMSMO in topic.But on three objective optimisation problems, the two multi-objective Evolutionary Algorithms than
The difference of MODE-PMSMO performances.Main cause is, on the one hand, particle cluster algorithm and learning aid algorithm belong to two kinds of local search energy
The very strong heuritic approach of power, in simple biobjective scheduling problem, they can be showed better than MODE-PMSMO.It is another
Aspect, compared to other multiple target differential evolution algorithms, adaptive Mutation Strategy can significantly improve differential evolution algorithm
Performance.Therefore, from the results, it was seen that MODE-PMSMO to be showed in these multi-objective optimization questions it is quite a lot of.It is worth
One is mentioned that, MOMDE-AM and MODE-PMSMO at many aspects there is similitude, the difference between them to be mainly reflected in,
MOMDE-AM uses single Mutation Strategy, and MODE-PMSMO then uses adaptive Mutation Strategy.In the above results,
MODE-PMSMO is better than MOMDE-AM performances in 5 biobjective scheduling problems, this is just because of MODE-PMSMO can be certainly
The suitable Mutation Strategy of selection of adaptation solves corresponding multi-objective optimization question.
In order to further discriminate between performance of each algorithm on performance indicator GD, Holm and Hochberg programs are used
Come for statistical analysis to result, statistical result is as follows：
As can be seen from the above results, the overall performance of NSGAII-DE, MOEA/D-DE and BB-MOPSO will be significantly worse than
MODE-PMSMO.In addition, although the overall performance of MODE-PMSMO cannot be considerably better than GDE3, MODE-RMO, SA-MTLBO and
MOMDE-AM, but from the point of view of average results, MODE-PMSMO can be better than these four multiple targets in most problems
Evolution algorithm.
For performance indicator IGD, result obtained by each algorithm (average value and standard variance) and its statistic analysis result
It is as follows：
Since IGD can evaluate to obtain the convergence and distributivity in the forward positions Pareto simultaneously, it is one comprehensive
Performance indicator.As can be seen from the results, GD3, NSGAII-DE, MOEA/D-DE, MODE-RMO and MOMDE-AM can not
What is showed in any optimization problem is better than MODE-PMSMO.Although tables of the BB-MOPSO and SA-MTLBO in 3 problems
It to be now considerably better than MODE-PMSMO, but the performance of MODE-PMSMO will be considerably better than BB- on 7 and 4 problems respectively
MOPSO and SA-MTLBO.Although MODE-PMSMO is similar with the overall performance of SA-MTLBO, SA-MTLBO is mainly in Bi-objective
It is better than carried algorithm in optimization problem；And on three increasingly complex objective optimisation problems, MODE-PMSMO is then than SA-
MTLBO is showed good.It can also be seen that MODE-PMSMO ratios MOMDE-AM is more suitable for solution multiple-objection optimization and asks from result
Topic.Itself main reason is that, MODE-PMSMO selected using adaptive technique suitable Mutation Strategy go to solve it is corresponding more
Objective optimisation problems.
In order to further discriminate between performance of each algorithm on performance indicator IGD, Holm and Hochberg programs are used
Come for statistical analysis to result, statistical result is as follows：
From the point of view of the above statistic analysis result, the overall performance of MODE-PMSMO to be considerably better than MOEA/D-DE, GDE3 and
BB-MOPSO。
Based on above algorithm comparison, it can be deduced that MODE-PMSMO can take in most of multi-objective optimization question
Obtain the preferable forward positions Pareto.
2. establishing immersed tube transportation by driving control multi-objective Model
In the present embodiment, immersed tube transportation by driving translation Controlling model includes mainly the translational velocity model of immersed tube, immersed tube translation
Resistance model, towboat resultant force and resultant moment model.Its mathematical model is described as follows：
The translational velocity model of 2.1 immersed tube：
In this embodiment it is assumed that immersed tube is v relative to the speed of flow, then its vertical view and front view are shown in figure respectively
2 and Fig. 3.Therefore, speed of the immersed tube in x-axis and y-axis can be expressed as：
vx=v1cosθ1-v0cosθ0, (7)
vy=v1sinθ1-v0sinθ0, (8)
In formula (7) and (8), v1Indicate speed of the immersed tube relative to bank, v0Indicate flow rate of water flow；θ1And θ0V is indicated respectively1
With the angle and v of positive direction of the x-axis0With the angle of positive direction of the x-axis.
The translatory resistance model of 2.2 immersed tube
In the present embodiment, the residual resistance R of immersed tubebWith frictional resistance RfIt can be obtained respectively by the following formula：
Rb=0.62 × Cb×Ae,2×v2 (9)
Rf=1.67 × Ae,1×|v|1.83×10-3 (10)
In formula (9) and (10), CbFore body form factor, A are dragged in expressione,2Indicate the underwater cross sectional area of immersed tube, Ae,1
Indicate the underwater surface product of immersed tube.
If immersed tube moving direction is parallel with flow, Ae,1And Ae,2It can be calculated by the following formula：
Ae,1=L (B+2d) (11)
Ae,2=B × d (12)
In formula (11) and (12), L, B and d indicate length, width and the drinking water of immersed tube highly respectively.
If immersed tube moving direction is vertical with flow, Ae,1And Ae,2It can be calculated by the following formula：
Ae,1=B (L+2d) (13)
Ae,2=L × d (14)
According to formula (9) and (10), the drag overall of immersed tube towage can be calculated by the following formula：
RT=1.15 (Rf+Rb) (15)
Other than immersed tube tube coupling can be by towage resistance, both sides assist transport floating drum also can by towage resistance, wherein
The towage resistance of single floating drum calculates as follows：
RTp=1.15 × (1.67 × Ap,1×|v|1.83×10-3+0.62×Cb×Ap,2×v2) (16)
In formula (16), Ap,1And Ap,2The underwater surface product of floating drum and underwater cross sectional area are indicated respectively.
So, the total towage resistance of immersed tube is as follows：
R'T=RT+2RTp (17)
The resultant force and resultant moment of 2.3 towboats：
In this embodiment, the resultant force of towboat can be expressed as：
Representation in components of the F in x-axis and y-axis is as follows：
In formula (19) and (20), R 'TxWith R 'TyR ' is indicated respectivelyTComponent in x-axis and y-axis；FiI-th is indicated to drag
The towing tension of ship, αiIndicate FiThe angle counterclockwise with positive direction of the x-axis；N indicates the quantity of towboat.It should be noted that utilizing immersed tube
Speed is come to calculate resistance be relatively simple, but in actual calculating process, if being to calculate immersed tube speed with resistance
It is relatively difficult.In order to facilitate calculating, in the present embodiment, with (xi,yi) indicate towing tension point AiCoordinate, enable βi=arctan (xi/
yi), and towboat quantity set is 6.Therefore, FN-2,FN-1, and FNIt can be obtained by the following formula：
In formula (21), (22), (23),
Ti=FiL'i
Wherein, if Δ=0, the positive real number δ of a very little can be assigned to it.
2.4 establish immersed tube transportation by driving multi-objective optimization question：
In the present embodiment, v1,F1,F2,F3,α1~α6As variable, that is, the dimension of the multi-objective optimization question is
10.In addition, in order to meet the control requirement to immersed tube, to meet following three targets as possible：
(1) allowance of every towboat towing tension is big as possible；
(2) immersed tube haulage time is short as possible；
(3) allowance of every towboat towing tension is as equal as possible.
In order to meet three above target, the goal-setting of immersed tube transportation by driving control is as follows：
s.t.
In formula (24), Fi,maxIndicate the maximum towing tension of each towboat,v1,minAnd v1,max
V is indicated respectively1Lower limit and reach the standard grade；F1,minAnd F1,maxThe minimum and maximum towing tension of first towboat is indicated respectively；F2,minWith
F2,maxThe minimum and maximum towing tension of second towboat is indicated respectively；F3,minAnd F3,maxRespectively indicate third towboat minimum and
Maximum towing tension；α1,min~α6,minSix towboat F are indicated respectively1~F6The minimum angles counterclockwise with x-axis；α1,max~α6,maxPoint
It Biao Shi not six towboat F1~F6The maximum angle counterclockwise with x-axis.
3. solving immersed tube transportation by driving controls multi-objective optimization question
Using MODE-PMSMO algorithms multi-objective optimization question is controlled to solve immersed tube transportation by driving.The object function of the problem is shown in
Formula (24).
In the present embodiment, by taking the Zhuhai and Macao bridge project of port as an example, towboat quantity set is 6, therefore, immersed tube transportation by driving such as Fig. 4
It is shown.Meanwhile it is as follows to control parameter setting in Model for Multi-Objective Optimization for immersed tube transportation by driving：
Immersed tube parameter：
Floating drum parameter：
Density of sea water：
Seawater velocity：
First and second towboat parameter：
Third and fourth towboat parameter：
Five, the six towboat parameters：
Angle (the θ of immersed tube and x-axis1)：
Angle (the θ of ocean current and x-axis0)：
In addition, in the present embodiment, each range of variables setting that immersed tube transportation by driving controls multi-objective optimization question is as follows：
The parameter setting of MODE-PMSMO algorithms is as follows：
Population scale is 100；Maximum function evaluation number is 30,000.
Immersed tube transportation by driving control multi-objective optimization question is solved using MODE-PMSMO algorithms, before obtained Pareto
Along as shown in Figure 5.Fig. 5 (a) indicates the forward positions Pareto that three targets obtain in three dimensions；It can from Fig. 5 (b)
Go out, the total towing tension allowance of six towboats is inversely proportional with the speed of immersed tube.Therefore, policymaker needs in haulage time and control
Robustness between obtain balance.What this was mainly determined by environment and construction requirement.It is from Fig. 5 (c) as can be seen that each
The harmonious translational velocity with immersed tube of towboat towing tension allowance is to be inversely proportional.In addition, can be obtained from Fig. 5 (d), big is total abundant
Amount is closely bound up with the allowance of every towboat.Based on the above experimental result, policymaker can be according to construction plan and environment
Variation immersed tube transportation by driving is controlled to select suitable operating condition.In addition, being selected from the obtained forward positions Pareto
Two boundary points (see the S1 and S2 in Fig. 5 (b)), S1 indicate that immersed tube has minimum travelling speed and maximum total allowance；And
S2 indicates that immersed tube has maximum travelling speed and minimum total allowance.That is, for S1, to have to the control of immersed tube
There is stronger robustness；S2 is then that more concern conevying efficiency reaches highest, and the ability of response environment is relatively weak.
The towing tension and angle of six towboats are as follows in S1：
As can be seen from the above results, towboat 2,3,4 do not use big towing tension substantially.Therefore, this group of control program be not only
Cost can be greatlyd save in practical operation, it may also be used for reply adverse circumstances are to ensure transporting safely for immersed tube.
The towing tension and angle of six towboats are as follows in S2：
As can be seen from the above results, it is desirable to conevying efficiency is improved, only by properly increasing the towing tension of towboat 1,2,4,6 just
The transport requirement can be met.
As a whole, immersed tube transportation by driving control problem is solved using multiple target differential evolution algorithm, the present invention can provide
One group of Pareto solution, therefore, the present invention can control for actual immersed tube transportation by driving and provide more effective traffic programs.
Be only the case study on implementation of the present invention in summary, and the practical range of the non-limiting present invention, i.e., it is all according to
Equivalent change or modification made by the content of scope of the present invention patent, all should be in the technology scope of the present invention.
Claims (4)
1. a kind of immersed tube transportation by driving control optimization method based on multiple target differential evolution algorithm includes the following steps：
(1) design of the TSP question strategy multiple target differential evolution algorithm based on performance metric；
(2) by being modeled to immersed tube translational velocity and resistance, the resultant force of towboat and resultant moment, an immersed tube transportation by driving control is established
Model for Multi-Objective Optimization processed；
(3) the actual multiple target is solved using the TSP question strategy multiple target differential evolution algorithm based on performance metric
Optimization problem.
2. the immersed tube transportation by driving based on multiple target differential evolution algorithm controls optimization method as described in claim 1, feature exists
In：The operating procedure of TSP question strategy multiple target differential evolution algorithm based on performance metric is as follows：
(2.1) initialization operation：Determine the variance control parameter F and cross-over control parameter CR of differential evolution algorithm；Set population
Scale NP and maximum iterative algebra Gmax；Initial population P is generated in feasible section1 0, each individual is denoted asAnd set current algebraically G=0；Meanwhile being set as G using the iterative algebra of single Mutation Strategys
=0.2 × Gmax.In addition, (i.e. using DE/rand/1(i.e. with DE/best/1) Mutation Strategy as algorithm policy library.
(2.2) mutation operation：For each individualIf G<Gs, then using DE/rand/1 Mutation Strategies come to individual into
Row update, formula are as follows：
In formula (1), FiIndicate variance control parameter, range is between [0,1]；r1、r2And r3Indicate two random integers,
Range is in [1, NP], and r1≠r2≠r3≠i。
If G >=Gs, then the update of individual according to from selected by policy library to Mutation Strategy be updated, therefore, for
For each individual, Mutation Strategy may be formula (1), it is also possible to following Mutation Strategy：
In formula (2),Indicate individual best in current population.
(2.3) crossover operation：For each individualCrossover operation is carried out to it using following Crossover Strategy：
In formula (3), D indicates the dimension of optimization problem；RjAnd jrandA random number and one in [0,1] range is indicated respectively
A integer random number in [1, D]；CR is the crossing-over rate of differential evolution algorithm.
(2.4) the adaptive operating procedure of Mutation Strategy is as follows in policy library：
The evaluation of Mutation Strategy：Each Mutation Strategy is evaluated using an improved IGD (reversed generation distance),
Its formula is as follows：
In formula (4),Indicate the obtained one group of object vector of this current generation,PFIndicate that previous generation obtains Pareto (pas
Tired support) forward position；|PF| it indicatesPFIn individual amount；K is indicatedPFIn object vector；Indicate k andIn mesh
Mark the minimum euclidean distance of vector.
The adaptive realization of Mutation Strategy：After being evaluated each Mutation Strategy using formula (4), each Mutation Strategy is in strategy
Quantity update in library is as follows：
In formula (5), round indicates that bracket function, str_name indicate the Mutation Strategy in policy library；NstrIt indicates to be chosen plan
Individual amount slightly.
According to formula (4), the individual amount of each Mutation Strategy is updated, formula is as follows：
(2.5) selection operation：
(2.5.1) if(Indicate to dominate), thenIt is saved to P1 G；
(2.5.2) ifSoIt is saved to P1 G；
(2.5.3) ifWithIt is mutually non-dominant, thenIt is saved to P1 G；
(2.6) utilize quick non-dominated ranking and crowding distance sequence both methods from P1 GIn select NP individual, and enable P1 G
=φ (φ is empty set).Finally, NP individual is stored in P1 G。
(2.7) (2.2)~(2.6) step is repeated, until the iterative algebra of algorithm is Gmax。
3. controlling optimization method by the immersed tube transportation by driving described in claim 1 based on multiple target differential evolution algorithm, feature exists
In：The step of establishing immersed tube transportation by driving control Model for Multi-Objective Optimization is as follows：
(3.1) the translational velocity mathematical model of immersed tube is established.
(3.2) the translatory resistance mathematical model of immersed tube is established.
(3.3) resultant force and resultant moment mathematical model of towboat are established.
(3.4) basis requires the control and transport of immersed tube transportation by driving, that is, so that the towing tension allowance of every ship is big as possible, immersed tube fortune
The defeated time is short as possible, the towing tension allowance of every ship is identical as possible.Immersed tube transportation by driving control multi-objective optimization question is established, target is set
It is fixed as follows：
In formula (7), Fi,maxIndicate the maximum towing tension of each towboat,
4. controlling optimization method by the immersed tube transportation by driving based on multiple target differential evolution algorithm described in claim 2, feature exists
In：Performance is measured in step 2.4Carry out the variation to differential evolution algorithm
Strategy carries out performance evaluation.
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