CN105354612B - A kind of last subdivision method in bulk freighter safe load calculator - Google Patents
A kind of last subdivision method in bulk freighter safe load calculator Download PDFInfo
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Abstract
The invention discloses a kind of last subdivision method in bulk freighter safe load calculator, comprise the following steps：Primary data is input in safe load calculator；The object function, design variable and constraints of last subdivision are determined according to floading condition equation group；Object function is solved using differential evolution algorithm, optimizing；Enter row variation, intersection and selection operation with differential evolution algorithm；Qualified individual collections are traveled through, result is exported.Because the present invention is without using xF, TPC and MTC value calculated, and calculated according to floading condition equilibrium equation group sets target function and constraints, and using differential evolution algorithm, can provide compared with precise results, can effectively reduce error.The present invention not only can adjust the Mean Draught of ship and trim using a small amount of goods, can also be adjusted using lot cargo, and the scope of Mean Draught and trim adjustment is wide.Because the present invention without artificial enquiry related data and is manually entered, manpower can be efficiently reduced, improves convenience.
Description
Technical Field
The invention relates to a bulk carrier stowage instrument, in particular to a final subdivision method in the bulk carrier stowage instrument.
Background
In the process of loading, transporting and unloading the goods of a bulk carrier, ensuring the safety of the ship and the goods is an important work. There are many factors that cause the bulk carrier to be unsafe, with unreasonable stowage being one important reason. To ensure the safety of bulk carrier transportation, the IMO (international maritime organization) stipulates that from 7/1/1998, all newly built and existing bulk carriers with a total length of over 150m and wide open-deck ships that meet the regulations of classification societies must be equipped with a ballast that should provide the shear and bending moment information for the hull as stipulated.
With the development of shipping, bulk freighters tend to be large in size, but the access to some ports is often limited by the depth of berth. Bulk freighters are usually loaded according to a stowage scheme established before loading, and theoretically can meet the requirements of average draft and draft difference. However, in actual loading, the difference between the actual draft and the budget after loading the goods is large, and the draft difference is different. Therefore, when the bulk cargo ship is loaded, a part of cargo is usually reserved for final subdivision, and the average draught and draught difference of the ship are adjusted.
At present, two methods are basically adopted when the last subdivision calculation is carried out on a major pair: the "100 t draft loading method" in documents [1 to 4] and the "pitch moment method" in document [5] are mostly calculated using Excel, as shown in fig. 1.
1. The method is calculated by using a 'loading 100t draft method', and comprises the following specific calculation steps:
(1) Calculating reserved to-be-loaded goods quantity P Ready to be loaded ：
P Ready to be loaded ＝100TPC(T Require that -T Initiation of )
Wherein T is Initial Mean draught, T, for the current initial state of the vessel Require that For the average draught of the desired end state, TPC is according to T Initial Obtaining by inquiring ship's hydrostatic tableTonnage of displacement change caused by the ship floating upwards or sinking 1cm in parallel;
(2) Calculating the load of the last subdivision, P Head Weight of cargo to be loaded in the first compartment, P Tail Weight of cargo to be loaded for the tail tank:
wherein: Δ t Initial The draft difference of the current initial state of the ship; Δ t Require that A draught difference which is the desired final state; Δ d of F head 100 And Δ d A head 100 Respectively obtaining the change quantity of the head draft and the change quantity of the tail draft caused by adding 100t of goods in the head cabin for inquiring a 'loading 100t head-tail draft change table' of the ship; Δ d F tail 100 And Δ d A tail 100 The change of the head draft and the change of the tail draft are caused by adding 100t of cargos in the tail cabin.
2. The calculation is carried out by using a pitch moment method, and the specific calculation steps are as follows:
(1) Calculating reserved to-be-loaded quantity P Ready to be loaded ：
P Ready to be loaded ＝100TPC(T Require to make a request for -T Initial )
(2) Finding the load of the last compartment, P Head Weight of cargo to be loaded in the first compartment, P Tail Weight of cargo to be loaded for the tail tank:
the draft difference change amount formula is calculated by the following pitching moment:
the system of equations can be found:
solve to obtain
Wherein: x is the number of P Is the vertical coordinate of the gravity center of the goods to be loaded; delta t is the change of draught difference; MTC is the pitch moment per centimeter, x F Is the ordinate, x, of the vessel's floating center G head Is the longitudinal coordinate, x, of the center of gravity of the first ship cabin G tail Is the ordinate of the gravity center of the ship tail cabin.
However, the above method has the following disadvantages:
1. the "loading 100t draft method" and the "pitch moment method" have the same calculation principle, and the following assumptions exist: floating center longitudinal coordinate x of ship water line surface during loading F The per cm trim torque MTC and the tonnage TPC of displacement change caused by the vessel floating up or sinking in parallel by 1cm are not changed, so the results are only approximate values, and large errors occur particularly when the draft of the vessel changes greatly.
2. The '100 t draft loading method' and the 'trim moment method' are used for calculation, the method is only suitable for adjusting the average draft and draft difference of the ship by using a small amount of cargoes, and the adjustment range of the average draft and draft difference is relatively small.
3. The 'loading 100t head-to-tail draft change table' and 'ship static water table' of the ship need to be manually inquired and related data needs to be manually input, and the method is very inconvenient.
The present invention relates to the following references:
[1] luan Famin a method of calculating "last load in compartment" for bulk carrier [ J ] navigation in china, 2013,36 (2): 135-137.
[2] Luan Famin. Quick algorithm for adjusting draught difference of bulk ship [ J ]. China water transport, 2007 (02), 52-53.
[3] Luan Famin, liu Jiazhao fast method of bulk ship port draft adjustment [ J ]. World shipping, 2007,30 (2): 1-2.
[4] Xie Funa simplified solution of final draft difference adjustment during bulk ship loading [ J ] navigation technology, 2009 (2), 27-28.
[5] Xing Xianghui study of loading computer mathematical model and application of bulk cargo ship [ D ]. Dalian: maritime college, university of maritime, 2000.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to design a final subdivision method in the bulk carrier stowage instrument, which has small calculation error, large application range and no need of manual inquiry.
In order to achieve the purpose, the technical scheme of the invention is as follows: a final subdivision method in a bulk carrier stowage instrument comprises the following steps:
A. the following data are input into the stowage instrument: under the condition that the first cabin and the tail cabin of the ship are empty, the total displacement M of the ship before final subdivision 0 Longitudinal coordinate of center of gravityTransverse coordinate of center of gravityAnd vertical coordinate of center of gravityThe total displacement M of the ship after final subdivision last Longitudinal coordinate of floating centerTransverse coordinate of floating centerAnd vertical coordinate of center of buoyancy
B. And determining an objective function, design variables and constraint conditions of the final subdivision according to the following floating state equation set:
the floating state equation set determined when the ship is balanced is as follows:
wherein: delta is the displacement of the ship, rho is the density of water, and v is the displacement volume of the ship; x is the number of G 、y G 、z G Respectively a longitudinal coordinate, a transverse coordinate and a vertical coordinate of the gravity center of the ship; x is the number of B 、y B 、z B Respectively a longitudinal coordinate, a transverse coordinate and a vertical coordinate of the ship floating center; theta andrespectively the pitch angle and the roll angle of the vessel.
B1, setting an objective function:
objective function
Wherein: p is a design variable, n is the total number of cargo holds for the last subdivision, P i The weight of the cargo loaded for the ith of the cargo holds for the last subdivision.
B2, determining design variables:
determining the design variable as P = (P) from the objective function 1 ,p 2 ,...p n )。
B3, determining constraint conditions:
according to the buoyancy equation determined when the ship is balanced, the maximum loading weight and the minimum loading weight allowed to be loaded in each cabin, the constraint conditions are obtained as follows:
wherein p is iMax To adjust the maximum cargo weight of the ith of the compartments,andlongitudinal coordinates, transverse coordinates and vertical coordinates of the ship gravity center except for the cabin are adjusted before draft adjustment;andrespectively adjusting the longitudinal coordinate, the transverse coordinate and the vertical coordinate of the gravity center of the ith cargo hold in the cargo hold;andrespectively the longitudinal coordinate, the transverse coordinate and the vertical coordinate of the ship floating center required after adjustment.
C. Solving and optimizing the objective function by using a differential evolution algorithm:
c1, initializing an evolutionary population required by the differential evolution algorithm.
C11, setting the size of the population to be NP, wherein the value range of the NP is 40-60;
c12, randomly generating NP population individuals, namely design variables, and generating each individualThe method for each vitamin of (a) is as follows:
wherein the content of the first and second substances,denotes the jth individual in the tth generation, where t =1;
rand (0,1) represents a random number between 0 and 1 that satisfies uniform distribution;respectively representing the minimum value and the maximum value of the cargo hold loading capacity selected when the weight of the ith cargo hold in the cabin to be adjusted is initialized,for different solution vectors, each dimension element value is independently generated.
And C13, calculating the objective function value of each individual, wherein the longitudinal coordinate, the transverse coordinate and the vertical coordinate value of the corresponding gravity center of the cargo hold under any cargo volume are calculated according to the ship cargo capacity table. The calculation method is as follows:
objective function value:
and recording individuals who meet the following criteria:
whereinTo representViolation of the constraint value.
And calculating the values of the longitudinal coordinate Xg, the transverse coordinate Yg and the vertical coordinate Zg of the center of gravity corresponding to the cargo hold in any cargo volume Vnet according to the cargo capacity table. The data of each cargo hold is stored according to the increasing sequence of Vnet, and the data comprises the following data:
Vnet min ＝Vnet 1 ，Vnet max ＝Vnet last
Vnet min 、Vnet max 、Vnet 1 、Vnet last minimum value, maximum value of net volume, stored first value and stored value respectively representing net volume of cargo loaded in cargo holdThe last value of (c). The values of Xg and Zg were calculated in three cases as follows:
c131, when Vnet min ≤Vnet≤Vnet max When Vnet is between the minimum and maximum of net volume, the adjacent Vnet is selected k-1 And Vnet k Interpolation is performed to obtain Xg, yg and Zg values. The specific method comprises the following steps:
wherein: vnet k-1 ≤Vnet≤Vnet k 2≤k≤last
C132, when Vnet<Vnet min When Vnet is less than the minimum value of net volume, the two smallest volume values Vnet are selected 1 And Vnet 2 Interpolation is performed to obtain Xg, yg, and Zg values. The specific method comprises the following steps:
c133, when Vnet > Vnet max When Vnet is greater than net volume maximum, the two largest volume values Vnet are selected last And Vnet last-1 Interpolation is performed to obtain Xg, yg, and Zg values. The specific method comprises the following steps:
c14, calculating the violation constraint value of each individual, and rewriting the constraint condition into the following form:
respectively representing inequality constraints and equality constraints; q, m-q represent the number of inequality constraints and the number of equality constraints, respectively, where q =2n and m =2n +2.
The value of the individual violating the r-th constraint is expressed as follows:
delta is the allowable error of equality constraint, and the value range of delta is 0.001-0.01.
The individual violates the constraint value as:
c2, calculating the proportion of the individuals in the population, which meet the constraint, in the total individuals, namely the feasible rate, which is expressed by rate, wherein the calculation method is as follows:
c3, setting the values of the scaling factor F and the crossover probability factor CR:
wherein T is the maximum evolution algebra and T is the current algebra.
C4, carrying out mutation, crossing and selection operations by using a differential evolution algorithm, and enabling j =1;
c41, mutation operation, performed as follows:
where r is 1 ,r 2 ,r 3 Is the interval [1, NP]Random integers with different inner values from j, and the random integers are not equal to each other in pairs;represents the j variant individuals of the t generation.
C42, performing crossover operation according to the following modes:
whereinIs shown ast generation j experimental individual; sn is a random integer, and satisfies sn ∈ [1,2](ii) a i represents the ith dimension;
c43, selecting operation:
calculating the corrected objective function values of the experimental individuals and the target individuals, wherein the calculation method comprises the following steps:
c431, normalized objective function value:
wherein:respectively representing the maximum objective function value and the minimum objective function value in the t generation population.
When in useThe normalized objective function value is then:
when in useThe normalized objective function value is then:
when the temperature is higher than the set temperatureThe normalized objective function value is then:
c432, normalize violation constraint values as:
whereinRespectively representing the maximum violation constraint value and the minimum violation constraint value in the population of the t generation.
When in useThe normalized violation constraint value is:
when in useThe normalized violation constraint value is:
when in useThe normalization violation constraint values are:
c433, calculating individual distanceAndthe method is as follows:
c434, calculating a penalty term, wherein the method comprises the following steps:
penalty termAnd withComprises the following steps:
c435, correcting the objective function value, wherein the calculation method is as follows:
c436, the selection method is as follows:
whereinRepresenting selected individuals, replacing in the original populationEligible individuals were recorded.
And is
C44, if j < NP +1, let j = j +1, go to step C41; otherwise, go to step C5.
C5, when T is less than T +1 or the optimal solution is not found, enabling T = T +1, and turning to the step C2; stopping the loop after finding the optimal solution or loop T times, where T =1000; turning to the step D; if no individual is recorded, a feasible scheme cannot be found, a prompt is given, and the step A is returned;
D. and traversing the individual set meeting the conditions, and outputting the result.
Compared with the prior art, the invention has the following beneficial effects:
1. since the invention does not use x F TPC and MTC values are calculated, a target function and constraint conditions are set according to the floating state balance equation set, a differential evolution algorithm is used for calculation, a more accurate result can be given, and errors can be effectively reduced.
2. The invention can not only use a small amount of goods to adjust the average draft and draft difference of the ship, but also use a large amount of goods to adjust, and the adjustment range of the average draft and the draft difference is wide.
3. Because the related data of the 'loading 100t head and tail draft change table' and the 'ship static water table' of the ship do not need to be manually inquired and manually input, the manpower can be effectively reduced, and the convenience is improved.
Drawings
The invention is shown in the attached figure 3, wherein:
FIG. 1 is a schematic diagram of the calculation according to the "load 100t draft method" or the calculation according to the "pitch moment method".
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a flowchart of a differential evolution algorithm of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. A flow chart of a final compartment division method in a bulk carrier stowage instrument is shown in fig. 2-3, and the value of NP in step C11 is 50; the value of δ in step C14 is 0.01.
Taking a 25-ten-thousand-ton grade ore carrier "SHANDONG REN HE" as an example, 1 cabin and 9 cabins are selected for the example calculation of the final subdivision. 25-ten-thousand-ton grade ore carrier 'SHANDONG REN HE' main scale: length between vertical lines L PP =319.5m, form width B =57m, form depth D =25m, and draft T =18m. The whole ship has 9 cargo holds, and 1 hold 2 holds … in sequence from the bow.
Carrying out a first loading condition: the average draft variation Δ T =1.1m is relatively large, as shown in tables 1-4
The cargo distribution amount of the 1 cabin and the 9 cabins are respectively calculated to be 8032.734t and 7393.818t by using a traditional method, the result is input into an Onboar-Napa loading computer to obtain the average draught and the draught difference to be 3.86m and-4.07 m respectively, and the errors of the average draught and the draught difference obtained by calculation are 1.026 percent and 8.33 percent respectively;
the cargo quantities of the 1 cabin and the 9 cabins are respectively calculated to be 7773.98t and 7967.01t by using the invention, the result is input into an Onboard-Napa loading computer to obtain the average draft and the draft difference to be 3.90m and-4.44 m respectively, and the errors of the average draft and the draft difference are respectively 0 percent and 0 percent by calculation.
And a second loading condition: the mean draught change Δ T =0.23m is relatively small, as shown in tables 5-8:
calculating the cargo quantities of the 1 cabin and the 9 cabins respectively to be 2032.02t and 2064.27t by using a traditional method, inputting the result into an Onboard-Napa loading computer to obtain that the average draft and the draft difference are respectively 18.64m and-0.45 m, and calculating that the errors of the average draft and the draft difference are respectively 0% and 2.17%;
the cargo quantities of the 1 cabin and the 9 cabins are respectively calculated to be 1964.2t and 2025t by using the invention, the result is input into an Onboard-Napa loading computer to obtain the average draft and the draft difference to be 18.64m and-0.46 m respectively, and the errors of the average draft and the draft difference are calculated to be 0 percent and 0 percent respectively.
The traditional method has small error when the average draught changes, and the error becomes large when the average draught changes greatly; the invention has small error when the average draught changes small, and has small error when the average draught changes large. The invention is not only suitable for the final subdivision by using a small amount of goods, but also suitable for the final subdivision by using a large amount of goods, can effectively reduce errors and has universality. The invention has more reasonable subdivision results and can ensure that the average draught and draught difference of the ship can reach the expected value.
Carrying out a first loading condition: the variation quantity delta T =1.1m of the average draught is large, RHO =1T/m 3
TABLE 1 initial and expected final states of the ship before and after cargo subdivision
| Average draught (m) | Draught difference (m) | Displacement (t) | Center of gravity/center of buoyancy | |
| Initial state of ship | 2.8 | -4.48 | 34176 | Center of gravity (148.77,0,14.6) |
| Expected end state | 3.90 | -4.44 | 49917 | Floating core (156.02,0,2.07) |
TABLE 2 cargo Loading of the vessels before cargo Subdivision
| 1 cabin | 2 cabin | 3 cabin | 4 cabin | 5 cabin | 6 cabin | 7 cabin | 8 cabin | 9 cabin |
| 0t | 0t | 0t | 0t | 0t | 0t | 0t | 0t | 0t |
TABLE 3 calculation of the Final Subdivision of the conventional method and the present invention
| 1 cabin | 2 cabin | 3 cabin | 4 cabin | 5 cabin | 6 cabin | 7 cabin | 8 cabin | 9 cabin | |
| Conventional methods | 8032.734t | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 7393.818t |
| The invention | 7773.98t | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 7967.01t |
TABLE 4 comparison of results of conventional method and present invention
| Average draft (m) | Mean draft error (%) | Draught difference (m) | Draft difference error (%) | |
| Conventional methods | 3.86 | 1.026 | -4.07 | 8.33 |
| The invention | 3.90m | 0 | -4.44m | 0 |
And a second loading condition: the variation quantity delta T =0.23m of the average draft is smaller, RHO =1.5839T/m 3
TABLE 5 cargo subdivision fore and aft ship states
| Average eating water (m) | Draught difference (m) | Displacement (t) | Center of gravity/center of buoyancy | |
| Initial state of ship | 18.41 | -0.62 | 291346 | Center of gravity (166.72, -0.01,15.39) |
| Expected end state | 18.64 | -0.46 | 295336 | Floating core (166.784,0.013,9.833) |
TABLE 6 cargo Loading of the respective compartments of the vessel before cargo subdivision
| 1 cabin | 2 cabin | 3 cabin | 4 cabin | 5 cabin | 6 cabin | 7 cabin | 8 cabin | 9 cabin |
| 22174.8t | 29359.5t | 29038.3t | 29044.3t | 29044.4t | 29044.4t | 29044.4t | 29044.3t | 22703.5t |
TABLE 7 calculation of the Final Subdivision of the conventional method and the present invention
| 1 cabin | 2 cabin | 3 cabin | 4 cabin | 5 cabin | 6 cabin | 7 cabin | 8 cabin | 9 cabin | |
| Conventional methods | 2032.02t | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2064.27t |
| The invention | 1964.2t | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2025t |
TABLE 8 comparison of results of conventional method and present invention
| Average draught (m) | Mean draught error (%) | Draught difference (m) | Draft difference error (%) | |
| Conventional methods | 18.64 | 0 | -0.45 | 2.17 |
| The invention | 18.64 | 0 | -0.46 | 0 |
Claims (1)
1. A final compartment dividing method in a bulk carrier stowage instrument is characterized in that: the method comprises the following steps:
A. the following data are input into the stowage instrument: under the condition that the first cabin and the tail cabin of the ship are empty, the total displacement M of the ship before final subdivision 0 Longitudinal coordinate of center of gravityTransverse coordinate of center of gravityAnd vertical coordinate of center of gravityThe total displacement M of the ship after final subdivision last Longitudinal coordinate of floating centerTransverse coordinate of floating centerAnd vertical coordinate of center of buoyancy
B. And determining an objective function, design variables and constraint conditions of the final subdivision according to the following floating state equation set:
the floating state equation set determined when the ship is balanced is as follows:
wherein: delta is the displacement of the ship, rho is the density of water,is the displacement volume of the vessel; x is the number of G 、y G 、z G Respectively a longitudinal coordinate, a transverse coordinate and a vertical coordinate of the gravity center of the ship; x is the number of B 、y B 、z B Respectively a longitudinal coordinate, a transverse coordinate and a vertical coordinate of the ship floating center; theta andthe trim angle and the roll angle of the ship are respectively;
b1, setting an objective function:
objective function
Wherein: p is a design variable, n is the total number of cargo holds for the last subdivision, P i The weight of cargo loaded for the ith of the cargo holds for the last subdivision;
b2, determining design variables:
determining the design variable as P = (P) from the objective function 1 ,p 2 ,...p n )；
B3, determining constraint conditions:
according to the floating equation determined when the ship is balanced, the maximum loading weight and the minimum loading weight allowed to be loaded in each cabin, the constraint conditions are obtained as follows:
wherein p is iMax To adjust the maximum cargo weight of the ith of the compartments,andlongitudinal coordinates, transverse coordinates and vertical coordinates of the ship gravity center except for the cabin are adjusted before draft adjustment;andrespectively adjusting the longitudinal coordinate, the transverse coordinate and the vertical coordinate of the gravity center of the ith cargo hold in the cargo hold;andrespectively the longitudinal direction of the floating center of the ship required after adjustmentA directional coordinate, a transverse coordinate and a vertical coordinate;
C. solving and optimizing the objective function by using a differential evolution algorithm:
c1, initializing an evolutionary population required by a differential evolution algorithm;
c11, setting the size of the population to be NP, wherein the value range of NP is 40-60;
c12, randomly generating NP population individuals, namely design variables, and generating each individualThe method for each vitamin of (a) is as follows:
wherein the content of the first and second substances,denotes the jth individual in the tth generation, where t =1;
rand (0,1) represents a random number between 0 and 1 that satisfies uniform distribution;respectively representing the minimum value and the maximum value of the cargo hold loading capacity selected when the weight of the ith cargo hold in the cabin to be adjusted is initialized,for different solution vectors, each dimension element value is independently generated;
c13, calculating the objective function value of each individual, wherein the longitudinal coordinate, the transverse coordinate and the vertical coordinate value of the center of gravity corresponding to the cargo hold under any cargo volume are calculated according to a ship cargo capacity table; the calculation method is as follows:
objective function value:
and recording individuals who meet the following criteria:
and is
WhereinTo representViolation constraint value of;
calculating the values of a longitudinal coordinate Xg, a transverse coordinate Yg and a vertical coordinate Zg of the center of gravity corresponding to the cargo hold in any cargo volume Vnet according to the cargo capacity table; the data of each cargo hold are stored according to the increasing order of Vnet, and the data comprise the following data:
Vnet min ＝Vnet 1 ，Vnet max ＝Vnet last
Vnet min 、Vnet max 、Vnet 1 、Vnet last respectively representing the minimum value, the maximum value, the stored first value and the stored last value of the net volume of the cargo loaded in the cargo hold; the values of Xg and Zg were calculated in three cases as follows:
c131, when Vnet min ≤Vnet≤Vnet max When Vnet is between the minimum and maximum of net volume, selecting Vnet adjacent to it k-1 And Vnet k Interpolating to obtain Xg, yg and Zg values; the specific method comprises the following steps:
wherein: vnet k-1 ≤Vnet≤Vnet k 2≤k≤last
C132, when Vnet<Vnet min When Vnet is smaller than the minimum value of net volume, selecting two volume values Vnet with minimum value 1 And Vnet 2 Interpolating to obtain Xg, yg and Zg values; the specific method comprises the following steps:
c133, when Vnet > Vnet max When Vnet is greater than net volume maximum, the two largest volume values Vnet are selected last And Vnet last-1 Interpolating to obtain Xg, yg and Zg values; the specific method comprises the following steps:
c14, calculating the violation constraint value of each individual, and rewriting the constraint condition into the following form:
respectively representing inequality constraint and equality constraint; q, m-q represent the number of inequality constraints and the number of equality constraints, respectively, where q =2n, m =2n +2;
the value of the individual violating the r-th constraint is expressed as follows:
delta is the allowable error of equality constraint, and the value range of delta is 0.001-0.01;
the individual violates the constraint value as:
c2, calculating the proportion of the individuals in the population, which meet the constraint, in the total individuals, namely the feasible rate, which is expressed by rate, wherein the calculation method is as follows:
c3, setting the values of the scaling factor F and the crossover probability factor CR:
wherein T is the maximum evolution algebra, and T is the current algebra;
c4, carrying out mutation, crossing and selection operations by using a differential evolution algorithm, and enabling j =1;
c41, mutation operation, performed as follows:
where r is 1 ,r 2 ,r 3 Is the interval [1, NP]Random integers with different inner values from j, and the random integers are not equal to each other in pairs;representing the jth variant individual of the generated generation t;
c42, performing crossover operation according to the following modes:
whereinRepresents the jth experimental individual of the tth generation; sn is a random integer, and satisfies sn ∈ [1,2](ii) a i represents the ith dimension;
c43, selecting operation:
calculating the corrected objective function values of the experimental individuals and the target individuals, wherein the calculation method comprises the following steps:
c431, normalized objective function value:
wherein:respectively representing the maximum objective function value and the minimum objective function value in the t generation population;
when in useThe normalized objective function value is then:
when in useThe normalized objective function value is then:
when in useThe normalized objective function value is then:
c432, normalized violation constraint values are:
whereinRespectively representing the maximum violation constraint value and the minimum violation constraint value in the population of the t generation;
when in useThe normalized violation constraint value is:
when in useThe normalized violation constraint value is:
when in useThe normalized violation constraint value is:
c433, calculating individual distanceAndthe method is as follows:
c434, calculating a penalty item, wherein the method comprises the following steps:
penalty termAndcomprises the following steps:
c435, correcting the objective function value, wherein the calculation method is as follows:
c436, the selection method is as follows:
whereinRepresenting selected individuals, replacing in the original populationRecording the individuals meeting the conditions;
and is
C44, if j < NP +1, let j = j +1, go to step C41; otherwise, turning to the step C5;
c5, when T is less than T +1 or the optimal solution is not found, enabling T = T +1, and turning to the step C2; stopping the loop after finding the optimal solution or loop T times, where T =1000; turning to the step D; if no individual is recorded, a feasible scheme cannot be found, a prompt is given, and the step A is returned;
D. and traversing the individual set meeting the conditions, and outputting the result.
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