CN108255062B - Power positioning energy-saving thrust distribution method based on improved differential evolution mechanism - Google Patents
Power positioning energy-saving thrust distribution method based on improved differential evolution mechanism Download PDFInfo
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Abstract
The invention provides a dynamic positioning energy-saving thrust distribution method based on an improved differential evolution mechanism, which comprises the following steps of: step S1: determining a dynamic positioning power requirement; step S2: establishing a power distribution mathematical model for dynamic positioning; step S3: initializing a solution to a power distribution problem in dynamic positioning; step S4: selecting a mutation mode according to a mutation constant lambda; step S5: carrying out mutation operation; step S6: performing cross operation; step S7: evaluating the adaptive values of all solutions and recording the optimal solution; step S8: judging whether the termination condition is met, if so, executing the step S9, otherwise, returning to the step S4; step S9: and stopping circulation, outputting an optimal solution, and performing power distribution according to the optimal solution. By the invention, the thrust required by the dynamic positioning ship is reasonably distributed to each propeller, so that the energy consumption of the ship is reduced, the operation cost of the ship is reduced, and the pollution of the ship is reduced on the basis of ensuring the safety of the ship.
Description
Technical Field
The invention relates to the field of ship automation, in particular to a dynamic positioning energy-saving thrust distribution method based on an improved differential evolution mechanism.
Background
The main function of the vessel Dynamic Positioning System (DPS) is to maintain the vessel in a desired position or to drive the vessel along a specified trajectory. The method mainly comprises the steps of calculating the total thrust and moment required by a ship in real time according to the deviation between the current position state and an expected value of the ship and external environment interference, then calculating the thrust required to be generated and the angle of each thruster of ship equipment according to a thrust distribution logic method, transmitting a control command to the thrusters, and finishing ship positioning by the thrusters according to the thrust required by the command. Thus, thrust allocation is an important ring in the DPS, which integrates the controller with the thrust system. The number of propellers is usually not less than 5, but not more is better, and factors such as the interaction between two propellers and between the propeller and the hull must be considered, while the maneuverability necessary for the ship is also taken into account. At the moment, the whole propulsion system has various combinations of thrust size and direction capable of meeting the positioning requirements, and the main function of the thrust distribution logic is to find out a best combination and convert the best combination into a control command to be distributed to each propeller in real time.
The thrust distribution optimization problem is a multi-constraint optimization problem, and requires a propeller to efficiently and reasonably generate thrust required by a ship in real time and meet the requirement of minimizing energy consumption while keeping a certain degree of maneuverability. The excellent distribution method not only can improve the positioning precision of the ship, but also has the functions of reducing energy consumption, mechanical abrasion, noise and the like.
A dynamically positioned vessel is generally equipped with a full-turn thruster, such thrusters and their propulsion systems generally having the following constraints:
(1) the thrust generated by each propeller has a maximum value under the power limit of the driver, and the propellers cannot generate more thrust than the maximum value.
(2) The thrust of the propeller and the change rate of the angle of the propeller are limited and cannot change greatly in a short time.
(3) The full-circle-turning propeller can rotate around the main shaft of the full-circle-turning propeller by 360 degrees, but a thrust forbidden zone exists due to the interaction between adjacent propellers, so that a change range needs to be set for the rotation angle of each propeller.
In addition, the occurrence of singular structures is also considered. For a dynamically positioned vessel, the singular configuration occurs when all of the thrusters it is equipped with have the same azimuth of thrust. At this point, the handling performance of the vessel is greatly reduced or even lost, and due to the limitation of the rotational speed of the propeller, the whole system is recovered for a longer time, which may have serious consequences in the related engineering work. Therefore, in the research and application of the dynamic positioning thrust distribution of the ship, the occurrence of a strange structure should be avoided. In order to maintain the balance between energy consumption and operability, a compromise is proposed, namely, the adjustment coefficient is set according to the actual requirement to balance the requirements of the ship on operability and energy consumption.
In the prior art, the following technical schemes are mainly adopted:
in the 'thrust distribution method of a ship dynamic positioning system adopting a legacy algorithm', application number 201110253236.2, a thrust distribution process is carried out by adopting a genetic algorithm mode.
In the thrust distribution method of the dynamic positioning system, application number 201310003584.3, the azimuth angle and the thrust of the thruster are calculated in a distributed manner by adopting two optimization algorithms of low-pass filtering and sequential quadratic programming.
In the patent of dynamic positioning thrust distribution device using dynamic prohibiting angle and distribution method thereof, application No. 201210356674.6, a quadratic programming algorithm is used to perform the distribution process of thrust.
The main method for distributing the thrust of the ship dynamic positioning at present is to neglect the energy consumption characteristic of the thrust distribution, and an optimal solution of the thrust distribution is difficult to find.
Disclosure of Invention
The invention aims to effectively find the optimal solution for distributing the thrust and the direction instruction of each thruster through an improved differential evolution mechanism according to the constructed dynamic positioning thrust distribution mathematical model, and reduce the energy consumption of the ship thruster on the basis of ensuring that the resultant force of the thrusters meets the control requirement.
In order to achieve the purpose, the invention adopts the following technical scheme: a dynamic positioning energy-saving thrust distribution method based on an improved differential evolution mechanism comprises the following steps: step S1: determining a dynamic positioning power requirement; step S2: establishing a power distribution mathematical model for dynamic positioning; step S3: initializing a solution to a power distribution problem in dynamic positioning; step S4: selecting a mutation mode according to a mutation constant lambda; step S5: carrying out mutation operation; step S6: performing cross operation; step S7: evaluating the adaptive values of all solutions and recording the optimal solution; step S8: judging whether the termination condition is met, if so, executing the step S9, otherwise, returning to the step S4; step S9: and stopping circulation, outputting an optimal solution, and performing power distribution according to the optimal solution.
In an embodiment of the present invention, step S2 includes the following specific steps: step S21: the non-linear optimization mathematical model for the thrust distribution problem is as follows:
the constraints are adjusted as follows:
s＝τ-B(α)F
Fmin≤F≤Fmax
△Fmin≤F-F0≤△Fmax
αmin≤α≤αmax
△αmin≤α-α0≤△αmax
wherein, W in the first term is total energy consumption, P is weight coefficient, FiThrust of the ith propeller, kiTo calculate the parameters; second term sTQs is a penalty term, and s is a generalized thrust error vector; the weight matrix Q is a diagonal positive definite matrix, which should take a large value to ensure that the error s approaches zero; third term (. alpha. -alpha.)0)TΩ(α-α0) Is used for restricting the variation speed of the propulsion angle, wherein alpha is the azimuth angle of the propeller at the moment, and alpha is0The azimuth angle of the propeller at the previous moment, and the weight matrix omega>0 is used to adjust the optimization objective; item four
Is used to avoid singular structures, wherein
lxnAnd lynThe X-direction coordinate and the Y-direction coordinate of the nth propeller are respectively set; the X direction is from the middle of the ship to the bow, and the Y direction is from the middle of the ship to the starboard; if the propulsion system is singular or close to singular, i.e., det (B (α) B' (α)) is equal to zero or close to zero, the value of the fourth term will be large, corresponding to a penalty function; in the formula>0, which is larger than zero, is an adjusting coefficient and is used for balancing the energy consumption and the maneuverability of the ship, the larger the value is, the better the maneuverability is, the corresponding energy consumption is also increased, and the smaller the value is, the opposite is true; step S22: in the constraint, τ ═ (τ)x,τy,τM)TIs the desired force and moment, F is the thrust matrix of the propulsion system, and B (α) F is the sum of the actual generation of the propulsion systemThrust and resultant moment, calculating the generalized thrust error vector between the actual thrust and the expected thrust by a B (alpha) calculation formula; fmaxAnd FminRespectively representing the maximum value and the minimum value of the thrust of the propeller, and limiting the thrust range of the propeller; delta FmaxAnd Δ FminRespectively representing the upper limit and the lower limit of the thrust of the propeller changing in unit time, and the range of the thrust change rate is specified by a B (alpha) calculation formula; accordingly, αmaxAnd alphaminIs the range of the propeller rotation angle, Delta alphamaxAnd Δ αminIs the upper and lower limits of the amplitude of the propeller angle change between two moments.
In an embodiment of the present invention, step S4 includes the following steps: step S41: in the improved differential evolution, a mode of adding an artificial bee colony algorithm into a differential evolution algorithm is used as a local search strategy according to the following formula;
in the formula, xiFor selected individuals performing a neighborhood search, xkIs xiAdjacent individual, x'iIs the resulting particle after neighborhood search, i.e., x'iIs xiBy random individuals x adjacent theretokThe correction solutions after the comparison with each other,
is [ -1,1 [ ]]A randomly generated value of; k ∈ {1,2, 3.,. SN }, where SN is the number of populations; step S42: the social cognition part of the particle swarm optimization is added to optimize the differential evolution algorithm according to the following formula: x'i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) (ii) a Wherein psi is the range [0,1]Of a randomly generated value, xgbestIs a global optimal solution; x is the number ofr1，xr2And xr3Is a randomly selected variable and r1 ≠ r2 ≠ r 3; f is a scaling factor used for controlling the total perturbation amount in the mutation process and improving the convergence rate, and the value range of the scaling factor is [0,1]](ii) a X 'is newly solved'iSynthesized by three partsGenerating: first part of selected target individuals x'i(ii) a The second part is a vector generated by the difference of randomly selected parent individuals; the last part is a solution vector generated by carrying out difference operation according to the difference value of the selected target individual and the global optimal solution in the current whole population; step S43: this step S41 and step S42 are combined in a modified manner as follows: if rand<Lambda then utilizes
Otherwise according to x'i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) Carrying out mutation operation; rand is a random function that generates random numbers; wherein λ is in the range of [0,1]]The control variable of (2).
Further, the lambda value is adjusted to select the optimization strategy according to the following formula:
where T is the current number of cycles and T is the selected maximum number of cycles.
In an embodiment of the present invention, step S5 includes the following steps: respectively using formulas
Carrying out mutation operation by using an ABC improvement strategy or a PSO improvement strategy; wherein the ABC improvement strategy comprises the following steps: 1. leading bee neighborhood search generates a new solution, and calculating the fitness value of the new solution; 2. according to the formula
Generating a solution to be evaluated; 3. obtaining a mutation test population; the PSO improvement strategy comprises the following steps: 1. updating the historical optima Pbest and the global optima Gbest of each individual; 2. according to a formula x'i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) Generating a solution to be evaluated; 3. obtaining a mutation test population.
In an embodiment of the present invention, step S6 includes the following steps: designing the cross parameter of the dynamic increment according to the following formula
CR＝CRmin+(CRmax-CRmin)×(t/T)2
Wherein CRmaxAnd CRminAre the maximum and minimum values of the crossing parameters; t is the current cycle number and T is the selected maximum cycle number.
Compared with the prior art, the method introduces the artificial bee colony algorithm and the particle swarm algorithm into the differential evolution algorithm, and increases the diversity of mutation modes of the differential evolution algorithm; selecting a mutation mode by using a mutation constant lambda, dynamically adjusting the mutation mode by adjusting the value of the lambda, and searching for an ABC improvement strategy which is emphasized in the early stage and a PSO improvement strategy which is emphasized in the later stage so as to improve the convergence speed and accuracy of the algorithm; the cross operation is dynamically adjusted by adjusting the value of the cross constant CR, the cross probability between the mutation individual and the target individual is adjusted, the convergence speed of the algorithm is improved, and the searching precision of the algorithm is enhanced. The method disclosed by the invention carries out thrust distribution according to the dynamic positioning ship thrust distribution model and the optimization result of the improved differential evolution algorithm, so that the thrust distribution of the dynamic positioning ship is more reasonable on the basis of meeting the ship thrust requirement and ensuring the safety of the ship.
Drawings
FIG. 1 is a schematic view of the main process of the present invention.
Detailed Description
The invention is further explained below with reference to the figures and the specific embodiments.
A brief description of the differential evolution algorithm is as follows:
mutation: mutation is a very important link in the reproductive cycle, and it randomly draws three parents from a population to generate experimental individuals. In the mutation operation, the individual variables x 'were tested'iObtained according to the following formula:
x′i＝xr1+F(xr2-xr3) (1)
wherein x isr1，xr2And xr3Is randomSelected variables r1 ≠ r2 ≠ r3, F is a scaling factor for controlling perturbation total amount and improving convergence speed in mutation process, and the value range is [0,1 ≠]。
And (3) crossing: crossover operation is similar to the process in which a gene is crossed and recombined with a certain probability to generate offspring individuals. This procedure was used to increase population diversity. In the operation, the filial generation individuals are generated by the experimental individuals and the parent individuals after being mixed in a crossing way according to the following formula.
Where CR is a cross constant defined by us, RjIs the range [0,1]To a randomly selected real number. j denotes an array corresponding to the jth component.
Selecting: the selection operation is a process of eliminating competition between the target individual and its related filial individuals. The adaptive value is used as the basis for the selection of the advantages and the disadvantages. With the minimum adaptation value as a criterion, the selection operation can be expressed by the following formula:
wherein f (x) represents the fitness value of the individual.
A brief description of the improved differential evolution algorithm is as follows:
in the improved differential evolution, a mode that an artificial bee colony algorithm is added into a differential evolution algorithm is used as a local search strategy according to the following formula.
In formula (II), x'iIs xkBy the modified solution after being compared with the adjacent random values,
is [ -1,1 [ ]]Of the random generated value. k is in the form of {1,2,3N where SN is the number of populations. x is the number ofiFor selected individuals performing a neighborhood search, xkIs xiAdjacent individual, x'iThe resulting particle after the neighborhood search is performed.
Later in the optimization process, since the approximate area of the optimal solution has already been determined, we need to speed up the convergence of the algorithm to facilitate faster optimization. Therefore, the social cognition part of the particle swarm optimization is added to optimize the differential evolution algorithm according to the following formula.
x′i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) (5)
Wherein psi is the range [0,1]Of a randomly generated value, xgbestIs a globally optimal solution. From the formula (5), x 'is newly solved'iProduced synthetically from three parts: first part of selected target individuals x'i(ii) a The second part is a vector generated by the difference of randomly selected parent individuals; the last part is a solution vector generated by carrying out difference operation according to the difference value of the selected target individual and the global optimal solution in the current whole population. These three parts constitute a new way to find a globally optimal solution.
These two modifications are combined as follows.
If(rand<λ)
Carrying out mutation operation by using a formula (4);
Else
carrying out mutation operation by using a formula (5);
End
wherein λ is a control variable in the range of [0,1 ];
since the optimization strategy provided by the formula (4) has strong global search capability, the improved optimization algorithm mainly uses the formula (4) in the first half of the whole optimization process. When the algorithm enters a subsequent optimization process, the optimization strategy provided by the formula (5) has higher convergence speed and precision, and the improved optimization algorithm mainly uses the formula (5) for optimization. The optimization strategy is selected by adjusting the lambda value by the following formula:
where T is the current number of cycles and T is the selected maximum number of cycles.
The crossover constant CR is an important parameter for determining the probability of crossover between a mutant individual and a target individual. If CR is larger, the proportion of mutant individuals in the test individuals is larger, so that the field searching capability of the algorithm can be enhanced and the convergence speed of the algorithm can be improved; and CR is smaller, the proportion of the mutant individuals in the test individuals is smaller, the proportion of the target individuals in the test individuals is larger, and the searching precision of the algorithm can be improved. Therefore, the cross parameters of the dynamic increment are designed according to the following formula, and the searching speed in the early stage and the searching precision in the later stage of the algorithm are improved.
CR＝CRmin+(CRmax-CRmin)×(t/T)2 (7)
Wherein CRmaxAnd CRminAre the maximum and minimum values of the crossing parameter.
As shown in fig. 1, in an embodiment of the present invention, a dynamic positioning energy-saving thrust allocation method based on an improved differential evolution mechanism specifically includes the following steps:
step 1: determining a dynamic positioning thrust requirement;
step 2: establishing a power distribution mathematical model for dynamic positioning;
in one embodiment of the present invention, the non-linear optimization mathematical model for the thrust sharing problem is as follows:
and (3) constraint:
s＝τ-B(α)F (9)
Fmin≤F≤Fmax (10)
△Fmin≤F-F0≤△Fmax (11)
αmin≤α≤αmax (12)
△αmin≤α-α0≤△αmax (13)
in the formula, W in the first term is total energy consumption, P is a weight coefficient and is mainly used for adjusting the proportion of the energy consumption in an optimization target, and the calculation mode of W is given, wherein FiThrust of the ith propeller, kiFor calculating the parameters, the value is generally 0.176.
Second term sTQs is a punishment item, and s is a generalized thrust error vector and is mainly used for ensuring that the thrust and the moment of the propeller can sufficiently offset external interference and finishing the basic positioning task. The weight matrix Q is a diagonal positive definite matrix, which should take a large value to ensure that the error s approaches zero.
Third term (. alpha. -alpha.)0)TΩ(α-α0) Is used to restrict the speed of change of the propulsion angle. Where α is the azimuth angle of the propeller at this time, α0The azimuth angle of the propeller at the previous moment, and the weight matrix omega>0 is used to adjust the optimization objective.
Item four
Is used to avoid singular structures, wherein
lxnAnd lynRespectively, the X-direction coordinate (from midship to bow) and the Y-direction coordinate (from midship to starboard) of the nth propeller. If the propulsion system is singular or close to singular, i.e., det (B (α) B' (α)) is equal to zero or approximately zero, the value of the fourth term will be large, corresponding to a penalty function. In the formula>0, this is to prevent the denominator from being zero. And if the value is smaller, the situation is just opposite.
In addition, in the constraint condition, τ ═ (τ)x,τy,τM)TThe expected force and moment are obtained, F is a thrust matrix of the propulsion system, B (alpha) F is the resultant thrust and the resultant moment which are actually generated by the propulsion system, and the generalized thrust error vector between the actual thrust and the expected thrust is calculated by the formula (15). FmaxAnd FminRespectively representing the maximum value and the minimum value of the thrust of the propeller, and the formula (15) limits the thrust range of the propeller. Delta FmaxAnd Δ FminThe upper and lower limits of the change of the propeller thrust in unit time are respectively expressed, and the range of the thrust change rate is specified by the formula (15). Accordingly, αmaxAnd alphaminIs the range of the propeller rotation angle, Delta alphamaxAnd Δ αminIs the upper and lower limits of the amplitude of the propeller angle change between two moments.
And step 3: initializing a solution to a power distribution problem in dynamic positioning;
and 4, step 4: selecting a mutation mode according to a mutation constant lambda;
the two improvements are combined according to the following steps:
If(rand<λ)
carrying out mutation operation by using a formula (4);
Else
carrying out mutation operation by using a formula (5);
End
and the lambda value is adjusted by equation (6).
And 5: carrying out mutation operation;
mutation operations were performed using equation (1), ABC improvement strategy or PSO improvement strategy, respectively.
The ABC improvement strategy comprises the following steps:
4. leading bee neighborhood search generates a new solution, and calculating the fitness value of the new solution;
5. generating a solution to be evaluated according to a formula (4);
6. obtaining a mutation test population.
The PSO improvement strategy comprises the following steps:
1. updating the historical optima Pbest and the global optima Gbest of each individual;
2. generating a solution to be evaluated according to a formula (5);
3. obtaining a mutation test population.
Step 6: performing cross operation;
the crossover operation is performed according to equation (2), where the value of CR is determined by equation (7).
And 7: evaluating the adaptive values of all solutions and recording the optimal solution;
and 8: judging whether a termination condition is met, if so, executing the step 9, otherwise, returning to the step 4;
the termination condition is the maximum number of iteration steps.
And step 9: and stopping circulation, outputting an optimal solution, and distributing thrust according to the optimal solution.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (1)
1. A dynamic positioning energy-saving thrust distribution method based on an improved differential evolution mechanism is characterized in that: the method comprises the following steps:
step S1: determining a dynamic positioning power requirement;
step S2: establishing a power distribution mathematical model for dynamic positioning;
step S3: initializing a solution to a power distribution problem in dynamic positioning;
step S4: selecting a mutation mode according to a mutation constant lambda;
step S5: carrying out mutation operation;
step S6: performing cross operation;
step S7: evaluating the adaptive values of all solutions and recording the optimal solution;
step S8: judging whether the termination condition is met, if so, executing the step S9, otherwise, returning to the step S4;
step S9: stopping circulation, outputting an optimal solution, and performing power distribution according to the optimal solution;
step S4 includes the following steps:
step S41: in the improved differential evolution, a mode of adding an artificial bee colony algorithm into a differential evolution algorithm is used as a local search strategy according to the following formula;
in the formula, xiFor selected individuals performing a neighborhood search, xkIs xiAdjacent individuals, xi'is the resulting particle after neighborhood search, i.e., x'iIs xiBy random individuals x adjacent theretokThe correction solutions after the comparison with each other,
is [ -1,1 [ ]]A randomly generated value of;
k ∈ {1,2, 3.,. SN }, where SN is the number of populations;
step S42: the social cognition part of the particle swarm optimization is added to optimize the differential evolution algorithm according to the following formula,
x′i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1)
wherein psi is the range [0,1]Of a randomly generated value, xgbestIs a global optimal solution; x is the number ofr1，xr2And xr3Is a randomly selected variable and r1 ≠ r2 ≠ r 3; f is a scaling factor used for controlling the total perturbation amount in the mutation process and improving the convergence rate, and the value range of the scaling factor is [0,1]](ii) a X 'is newly solved'iProduced synthetically from three parts: first part of selected target individuals x'i(ii) a The second part is a vector generated by the difference of randomly selected parent individuals; the last part is a solution vector generated by carrying out difference operation according to the difference value of the selected target individual and the global optimal solution in the current whole population;
step S43: this step S41 and step S42 are combined in a modified manner as follows: if raWhen nd < lambda is used
Otherwise according to x'i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) Carrying out mutation operation; rand is a random function that generates random numbers; wherein λ is in the range of [0,1]]The control variable of (d);
step S2 includes the following specific steps:
step S21: the non-linear optimization mathematical model for the thrust distribution problem is as follows:
the constraints are adjusted as follows:
s＝τ-B(α)F
Fmin≤F≤Fmax
ΔFmin≤F-F0≤ΔFmax
αmin≤α≤αmax
Δαmin≤α-α0≤Δαmax
wherein, W in the first term is total energy consumption, P is weight coefficient, FiThrust of the ith propeller, kiTo calculate the parameters; second term sTQs is a penalty term, and s is a generalized thrust error vector; the weight matrix Q is a diagonal positive definite matrix, which should take a large value to ensure that the error s approaches zero; third term (. alpha. -alpha.)0)TΩ(α-α0) Is used for restricting the variation speed of the propulsion angle, wherein alpha is the azimuth angle of the propeller at the moment, and alpha is0The weight matrix omega is more than 0 and is used for adjusting the optimization target for the azimuth angle of the propeller at the previous moment; item four
Is used to avoid singular structures, wherein
lxnAnd lynThe X-direction coordinate and the Y-direction coordinate of the nth propeller are respectively set; the X direction is from the middle of the ship to the bow, and the Y direction is from the middle of the ship to the starboard; if the propulsion system is singular or close to singular, i.e., det (B (α) B' (α)) is equal to zero or close to zero, the value of the fourth term will be large, corresponding to a penalty function; the adjustment coefficient is used for balancing the energy consumption and the maneuverability of the ship, the larger the value is, the better the maneuverability is, the corresponding energy consumption is increased, and the smaller the value is, the opposite is true;
step S22: in the constraint, τ ═ (τ)x，τy，τM)TThe method comprises the following steps that expected force and moment are obtained, F is a thrust matrix of a propulsion system, B (alpha) F is resultant thrust and resultant moment actually generated by the propulsion system, and a generalized thrust error vector between the actual thrust and the expected thrust is calculated through a B (alpha) calculation formula; fmaxAnd FminRespectively representing the maximum value and the minimum value of the thrust of the propeller, and limiting the thrust range of the propeller; Δ FmaxAnd Δ FminRespectively representing the upper limit and the lower limit of the thrust of the propeller changing in unit time, and the range of the thrust change rate is specified by a B (alpha) calculation formula; accordingly, αmaxAnd alphaminFor the range of rotation angles of the propeller, Δ αmaxAnd Δ αminIs the upper and lower limits of the amplitude of the propeller angle change between two moments;
the optimization strategy is selected by adjusting the lambda value according to the following formula:
wherein T is the current cycle number and T is the selected maximum cycle number;
step S5 includes the following steps: respectively using formulas
Carrying out mutation operation by using an ABC improvement strategy or a PSO improvement strategy;
wherein the ABC improvement strategy comprises the following steps:
1. leading bee neighborhood search generates a new solution, and calculating the fitness value of the new solution;
2. according to the formula
Generating a solution to be evaluated;
3. obtaining a mutation test population;
the PSO improvement strategy comprises the following steps:
1. updating the historical optima Pbest and the global optima Gbest of each individual;
2. according to a formula x'i＝xr1+F(xr2-xr3)+ψ(xgbest-xr1) Generating a solution to be evaluated;
3. obtaining a mutation test population;
step S6 includes the following steps: designing the cross parameter of the dynamic increment according to the following formula
CR＝CRmin+(CRmax-CRmin)×(t/T)2
Wherein CRmaxAnd CRminAre the maximum and minimum values of the crossing parameters; t is the current cycle number and T is the selected maximum cycle number.
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| CN109765910B (en) * | 2019-03-08 | 2021-10-01 | 哈尔滨工程大学 | Ship dynamic positioning thrust distribution method based on improved differential evolution algorithm |
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| CN106875063A (en) * | 2017-02-21 | 2017-06-20 | 集美大学 | A kind of dynamic positioning ship energy management optimization method |
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