CN104021431A - Robust optimization method based on average gradient value and improved multi-objective particle swarm optimization - Google Patents
Robust optimization method based on average gradient value and improved multi-objective particle swarm optimization Download PDFInfo
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Abstract
The invention relates to a robust optimization method based on an average gradient value and improved multi-objective particle swarm optimization. The robust optimization method comprises the following steps: (1) determining technological parameters to be optimized according to actual engineering situations and an optimization objective, (2) determining constraint conditions of the technological parameters to be optimized according to the actual engineering situations, (3) establishing an objective function model of the optimization objective and the technological parameters to be optimized, (4) obtaining the discrete relation between the optimization objective and welding technological parameters through a finite test, (5) calculating an objective function according to the discrete relation, (6) setting an uncertain region and calculating the robustness through the average gradient value of sample points of the uncertain region, (7) carrying out bi-objective optimization solution with the objective function and the robustness as two optimization sub-objectives. According to the robust optimization method, evaluation of the robustness and calculation of the original objective function are taken as the two optimization sub-objectives at the same time, and therefore a designer can select a reasonable compromise solution between a performance index and the amplitude of variation of the uncertain region according to actual needs.
Description
Technical field
The present invention relates to field of computer data processing, relate in particular to a kind of robust Optimal methods based on average gradient value and improvement multi-objective particle swarm optimization.
Background technology
Robust optimization is a kind of new optimization method solving under inner structure (as parameter) and external environment condition (as disturbance) uncertain environment, it is the uncertainty of just considering Optimized model in the time optimizing beginning, by the method for optimizing, make the unification that result is insensitive to uncertain factor and performance index are optimum of optimizing.Classical robust Optimal methods is mainly used in operational research, research be the protruding problems such as linear programming problem, quadratic programming problem and the Semidefinite Programming with multi-form data uncertainty.But the engineering problem of real world often right and wrong are protruding, even there is no mathematic(al) representation, the classical way in operational research is in engineering design and improper.In existing engineering problem, how to solve without the robust optimization solution of analytical expression, nonlinearity, the more high a series of realistic problems of decision space dimension and become robust optimization field urgent problem.
Summary of the invention
The technical problem to be solved in the present invention is for defect of the prior art, and a kind of robust Optimal methods based on average gradient value and improvement multi-objective particle swarm optimization is provided.
The technical solution adopted for the present invention to solve the technical problems is:
Based on the robust Optimal methods of average gradient value and improvement multi-objective particle swarm optimization, comprise the following steps:
1) determine technological parameter to be optimized according to engineering actual conditions and optimization aim;
2) determine the constraint condition of technological parameter to be optimized according to engineering actual conditions;
3) set up the objective function model of optimization aim and technological parameter to be optimized;
4) test by limited number of time the discrete relationship obtaining between optimization aim and welding condition; According to the discrete relationship between objective function model and technological parameter, calculating target function;
5) set uncertain territory, utilize the average gradient value of uncertain territory sample, calculate robustness;
6) optimize sub-goals using objective function and robustness as two, carry out Bi-objective Optimization Solution.
Press such scheme, described step 6) in Bi-objective optimization method comprise the following steps:
6.1) population scale is set, the maximum algebraically of iteration, stochastic variable R1, R2 between maximum Inertia Weight and minimum Inertia Weight and [0,1];
6.2), initialization population, by the position of CVT method initialization particle and the speed of initialization particle;
6.3) calculate the fitness function of each particle, using the position of particle as decision variable, according to the discrete relationship calculating target function between objective function model and technological parameter (decision variable), utilize the average gradient value of sample point in the uncertain territory of particle to calculate the robustness of particle;
6.4) according to Pareto domination principle, the position of the non-domination particle in population is stored in outside files;
Wherein non-domination particle is defined as follows: establishing p and q is two different individualities in population, in the time of p domination q, must meet following two conditions: (1), to all sub-goals, p is poor unlike q; (2) at least there is a sub-goal, make p better than q; Q is called domination particle, and in the time there is no other particle dominations p in population, p is called non-domination particle;
6.5) the memory files of the each particle of initialization, record this particle optimal location up to the present by the memory files of particle;
Wherein, particle optimal location is up to the present defined as follows: if particle is paid out and mixed a generation when evolution, the optimal location of particle is for working as former generation; If former generation is worked as in the previous generation of particle domination, the optimal location of particle is previous generation; If not arranging mutually as former generation and previous generation of particle, the optimal location of particle is for choosing at random one in both;
6.6) optimal location of selected population from outside files;
Be implemented as follows: decision space is divided into multiple hypercubes, the population that the fitness value of each hypercube comprises according to its inside determines, first select hypercube according to this fitness value by roulette method, then from selected hypercube, determine optimum individual randomly;
6.7) calculate the speed of each particle;
Be implemented as follows: the product, the particle optimal location that calculate respectively Inertia Weight and particle previous generation speed arrive the distance of current location and the product of R1 and population optimal location to the distance of particle current location and the product of R2, by speed three products and that be made as particle; Wherein Inertia Weight is along with the increase of evolutionary generation is from maximum Inertia Weight to minimum Inertia Weight linear decrease;
6.8) position of new particle more, adds the position of particle previous generation the speed of this particle, and keeps particle in search volume;
6.9), the fitness function value of new particle more, computing method are with step 6.3);
6.10), upgrade the particle representative in each hypercube of outside files and division; Current non-domination solution is inserted into outside files, and the solution of being arranged will be deleted from outside files; In the time that outside files are full, preferentially preserve the solution in the region that in object space, particle is few;
6.11), the memory files of new particle more;
According to Pareto domination mechanism, in the time that the current position of particle is better than the position in memory files, the desired positions of this particle needs to upgrade; In the time that the current position of particle is worse than memory files, the desired positions of this particle does not need to upgrade; If both do not arrange mutually, choose at random one;
6.12) if iteration reaches the maximum algebraically of iteration, stop output optimum solution; Otherwise, return to step 6.6).
Press such scheme, described step 6.2) in, the position of initialization particle comprises the following steps:
Step 6.2a), a given density function ρ (x), a positive integer q, constant α
1, α
2, β
1and β
2, wherein: α
2>0, β
2>0, α
1+ α
2=1, β
1+ β
2=1;
Point set
expression will initialized population, wherein i=1 ..., N; For i=1 ..., N, arranges j
iinitial value is 1; With Monte Carlo method decision space select an initial point set
Step 6.2b), according to density function ρ (x), decision space select q point
Step 6.2c), for set
in each point, will gather
in from z
inearest point (is put z
ivoronoi region in point) conclude to set w
iin, if set w
ifor sky, z
iremain unchanged; Otherwise, calculate w
ithe mean place u of point in set
i, and upgrade z according to following expression formula
i;
Step 6.2d) if the particle assembly after upgrading meets convergence criterion, renewal stops; Otherwise, forward step 6.2b to).
Press such scheme, described step 6.3) in, the robustness of calculating particle comprises the following steps:
6.3a), establishing the dimension that current particle exists the decision variable of disturbance is c, the dimension in this uncertain territory of particle is also c, every one dimension in uncertain territory is evenly divided into t section, c and t represent respectively because of prime number and number of levels, arrange according to select uniform designs table to carry out factor level data because of prime number, number of levels, in the uncertain territory of current particle, choose sample point set by uniform designs table; The uncertain territory of described particle is artificial default;
6.3b), calculate the target function value of each sample point and the absolute difference of the target function value of current particle and the decision variable of the each sample point Euclidean distance to the decision variable of current particle, the ratio of the absolute difference of record object function and the Euclidean distance of decision variable;
6.3c), calculate the mean value of the ratio of the absolute difference of all sample point objective functions and the Euclidean distance of decision variable, be the robustness evaluation value of this particle.
The beneficial effect that the present invention produces is:
1. the applicable engineering problem wide scope of the present invention;
2. the inventive method, using the calculating of the evaluation of robustness and former objective function simultaneously as the sub-goal of two optimizations, makes deviser between performance index and the amplitude of variation of uncertain territory generation, select rational compromise solution according to actual needs;
3. the inventive method adopts the improvement multi-objective particle based on CVT initialization of population and Dynamic Inertia weights, the ability of finding robust optimization disaggregation is strengthened greatly than the multiple-objection optimization particle cluster algorithm based on random initializtion population and fixing Inertia Weight, and algorithm convergence is faster;
4. the inventive method has proposed a kind of method of evaluation robustness of novelty, and the sample point of choosing in uncertain evaluation point territory arrives the average gradient value of evaluation point as the robustness evaluation value of this evaluation point;
5. the inventive method adopts uniform Design to avoid calculated amount to be exponent increase with the increase of decision space dimension;
6. the inventive method is used relatively less and equally distributed sample point to calculate the object space of evaluation point in uncertain territory and the relative amplitude of variation of decision space, has embodied fully the concept of robustness.
Brief description of the drawings
Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:
Fig. 1 is the method flow diagram of the embodiment of the present invention;
Fig. 2 is the solution procedure process flow diagram of the embodiment of the present invention;
Fig. 3 is the uncertain territory schematic diagram of the embodiment of the present invention;
Fig. 4 is the random initialization of population schematic diagram of the embodiment of the present invention;
Fig. 5 be the embodiment of the present invention based on CVT method initialization of population schematic diagram;
Fig. 6 is the function schematic diagram of the validation verification of the embodiment of the present invention;
Fig. 7 is the optimum results disaggregation schematic diagram of the validation verification of the embodiment of the present invention;
Fig. 8 is the disaggregation schematic diagram of the employing random initializtion of the embodiment of the present invention and the multi-objective particle swarm algorithm of fixing Inertia Weight;
Fig. 9 is the disaggregation schematic diagram of the use CVT method initialization of the embodiment of the present invention and the multi-objective particle swarm algorithm of Dynamic Inertia weights.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.
The engineering problem wide scope that the inventive method is applicable, chooses the design field of mars exploration track in the present embodiment, the inventive method is further elaborated.
In the design of mars exploration track, how both to have ensured to complete detection mission with the least possible fuel, simultaneously again can be in the time there is small disturbance in decision variable the function of keeping system, being one, to have challenge be again urgent problem simultaneously.The earth is realized by conic section splicing method to the design of Mars preliminary orbit, concrete steps are: first determine launch window and shift duration, and can obtain a day heart transfer orbit, next further calculate earth escape orbit and Mars and catch track, finally three sections of tracks that obtain are stitched together, can obtain preliminary orbit.
Be located in the inertial coordinates system of equator, the earth's core, the perigee altitude of escape orbit is r
ep, perigean velocity size is v
ep, orbit inclination is i
e, the argument of perigee is ω
e, right ascension of ascending node is Ω
e.In the inertial coordinates system of fiery heart equator, the periareon height of catching track is r
mp, periareon velocity magnitude is v
mp, orbit inclination is i
m, periareon angular distance is ω
m, right ascension of ascending node is Ω
m.According to 10 variablees above, can calculating detector respectively at perigee, position and the speed of periareon, more given x time t
1with due in t
2, can determine escape orbit and catch orbit parameter, by further calculating, obtain perigee and accelerate size and periareon braking size, both sums can reflect the fuel of required consumption.The Optimized model of old place fire initial orbit design problem is as follows
minf(x)
x＝[r
ep,v
ep,i
e,ω
e,Ω
e,t
1,r
mp,v
mp,i
m,ω
m,Ω
m,t
2]
General i
e, r
ep, i
mand r
mpdetermine t according to the scientific goal of delivery and detection
1, t
2according to engine request given range, other parameters define according to Engineering constraint.
This model cannot provide analytical expression, but in the span of decision variable (established technology parameter), each group decision variable (technological parameter) is a corresponding unique objective function f value all.
We are according to the discrete relationship between objective function model and technological parameter, calculating target function; The method of calculating target function is a lot, can in engineering, obtain by experiment, also can set up mathematical model to original system and obtain.
Next step, we optimize sub-goals using objective function and robustness as two, carry out Bi-objective Optimization Solution.
Bi-objective optimization method comprises the following steps:
6.1) population scale is set, the maximum algebraically of iteration, stochastic variable R1, R2 between maximum Inertia Weight and minimum Inertia Weight and [0,1];
6.2), initialization population, by the position of CVT method initialization particle and the speed of initialization particle;
The position of initialization particle comprises the following steps:
Step 6.2a), a given density function ρ (x), a positive integer q, constant α
1, α
2, β
1and β
2, wherein: α
2>0, β
2>0, α
1+ α
2=1, β
1+ β
2=1;
Point set
expression will initialized population, wherein i=1 ..., N; For i=1 ..., N, arranges j
iinitial value is 1; With Monte Carlo method decision space select an initial point set
Step 6.2b), according to density function ρ (x), decision space select q point
Step 6.2c), for set
in each point, will gather
in from z
inearest point (is put z
ivoronoi region in point) conclude to set w
iin, if set w
ifor sky, z
iremain unchanged; Otherwise, calculate w
ithe mean place u of point in set
i, and upgrade z according to following expression formula
i;
Step 6.2d) if the particle assembly after upgrading meets convergence criterion, renewal stops; Otherwise, forward step 6.2b to).
6.3) calculate the fitness function of each particle, be objective function and robustness, using the position of particle as decision variable, according to the discrete relationship calculating target function between objective function model and technological parameter (decision variable), utilize the average gradient value of sample point in the uncertain territory of particle to calculate the robustness of particle;
The robustness of calculating particle comprises the following steps:
6.3a), establishing the dimension that current particle exists the decision variable of disturbance is c, the dimension in this uncertain territory of particle is also c, every one dimension in uncertain territory is evenly divided into t section, c and t represent respectively because of prime number and number of levels, arrange according to select suitable uniform designs table to carry out factor level data because of prime number, number of levels, in the uncertain territory of current particle, choose sample point set by uniform designs table; The uncertain territory of described particle is artificial default;
6.3b), calculate the target function value of each sample point and the absolute difference of the target function value of current particle and the decision variable of the each sample point Euclidean distance to the decision variable of current particle, the ratio of the absolute difference of record object function and the Euclidean distance of decision variable;
6.3c), calculate the mean value of the ratio of the absolute difference of all sample point objective functions and the Euclidean distance of decision variable, be the robustness evaluation value of this particle.
6.4) according to Pareto domination principle, the position of the non-domination particle in population is stored in outside files;
Wherein non-domination particle is defined as follows: establishing p and q is two different individualities in population, in the time of p domination q, must meet following two conditions: (1), to all sub-goals, p is poor unlike q; (2) at least there is a sub-goal, make p better than q; Q is called domination particle, and in the time there is no other particle dominations p in population, p is called non-domination particle;
6.5) the memory files of the each particle of initialization, record this particle optimal location up to the present by the memory files of particle;
Wherein, particle optimal location is up to the present defined as follows: if particle is paid out and mixed a generation when evolution, the optimal location of particle is for working as former generation; If former generation is worked as in the previous generation of particle domination, the optimal location of particle is previous generation; If not arranging mutually as former generation and previous generation of particle, the optimal location of particle is for choosing at random one in both;
6.6) optimal location of selected population from outside files;
Be implemented as follows: decision space is divided into multiple hypercubes, the population that the fitness value of each hypercube comprises according to its inside determines, first select hypercube according to this fitness value by roulette method, then from selected hypercube, determine optimum individual randomly;
6.7) calculate the speed of each particle;
Be implemented as follows: the product, the particle optimal location that calculate respectively Inertia Weight and particle previous generation speed arrive the distance of current location and the product of R1 and population optimal location to the distance of particle current location and the product of R2, by speed three products and that be made as particle; Wherein Inertia Weight is along with the increase of evolutionary generation is from maximum Inertia Weight to minimum Inertia Weight linear decrease;
6.8) position of new particle more, adds the position of particle previous generation the speed of this particle, and keeps particle in search volume;
6.9), the fitness function of new particle more, computing method are with step 6.3);
6.10), upgrade the particle representative in each hypercube of outside files and division; Current non-domination solution is inserted into outside files, and the solution of being arranged will be deleted from outside files; In the time that outside files are full, preferentially preserve the solution in the region that in object space, particle is few;
6.11), the memory files of new particle more;
According to Pareto domination mechanism, in the time that the current position of particle is better than the position in memory files, the desired positions of this particle needs to upgrade; In the time that the current position of particle is worse than memory files, the desired positions of this particle does not need to upgrade; If both do not arrange mutually, choose at random one;
6.12) if iteration reaches the maximum algebraically of iteration, stop output optimum solution; Otherwise, return to step 6.6).
The inventive method is evaluated the former objective function of design problem and robustness respectively two sub-goals as fitness function, adopt the multi-objective particle based on Pareto principle to optimize this two targets simultaneously, obtain an equally distributed Pareto disaggregation of one-dimensional manifold.As shown in Figure 7.
In the present invention, the type in uncertain territory is cabinet-type.Fig. 3 is that decision variable is the uncertain field type of 2 dimensions.Centered by evaluation point, on every one dimension of decision variable, the value taking evaluation point in this dimension is benchmark, chooses respectively the interval of the positive negative direction Δ of reference point.In the decision space of higher-dimension (decision space dimension is greater than 3), the uncertain territory of evaluation point is a hypercube.
The checking of beneficial effect of the present invention:
1. the evaluation of robustness: the mean value of the ratio of the absolute difference of sample point objective function and the Euclidean distance of decision variable in the employing uncertain territory of evaluation point.In the uncertain territory of evaluation point, sample, the absolute difference of the calculating objective function of sample point and the objective function of evaluation point and sample point be the Euclidean distance to evaluation point at decision space, the gradient of this sample point is: the ratio of the absolute difference of objective function and decision space Euclidean distance, the robustness of evaluation point is the mean value of all sample point gradients in uncertain territory.
As shown in Figure 6, be optimized and solve robustness as objective function, uncertain territory is made as x ± 0.1, the solution that the robustness evaluation method that uses the present invention to propose obtains is 10.0, corresponding robustness evaluation value is 0.004728, has reacted this and has been in neighborhood comparatively smoothly, and robustness is good, the solution obtaining taking robustness as objective function in figure is a c, has confirmed the validity of the method.
2. the present invention adopts uniform Design sampling, the choosing of sample point in uncertain territory: uniform Design sampling.Exist every one dimension of disturbance to be all evenly divided into the equal segments that quantity is equal decision space, be designated as number of levels t, decision space dimension is designated as because of prime number c, arrange according to select suitable uniform designs table to carry out factor level data because of prime number, number of levels, choose corresponding sample point according to uniform designs table at decision space.
Compare existing Grid Sampling method, fiery initial orbit design problem in combination, the decision space that has disturbance is 8 dimensions, in uncertain territory, every one dimension is divided into 50 sections, if adopt Grid Sampling, sampling number is 50
8, and uniform Design sampling only needs 50 times.
3. the thought that adopts multiple-objection optimization, the result of optimization is not single solution, but the disaggregation of an one-dimensional manifold is shown in Fig. 6.
4, the initialization of population of multi-objective particle and Inertia Weight are set: the Dynamic Inertia weights of the initialization of population based on CVT method and linear decrease.Initialization of population based on CVT method: a given density function, first choose an initial point set at decision space according to certain rule (as Monte Carlo method), the voronoi that obtains this point set divides, in decision space, choose again another one point set according to density function, choose for the second time counting of point set according to the voronoi district inclusion of initial point set and adjust the position of initial point set, until initial point set is uniformly distributed at decision space.Fig. 4 is the two-dimentional initial population of choosing at random, and Fig. 5 is the distribution initial population comparatively uniformly obtaining according to CVT method.Dynamic Inertia weights: Inertia Weight is pressed following formula linear change in population search procedure.
Inertia Weight=maximum Inertia Weight-(maximum Inertia Weight-minimum Inertia Weight) × iteration algebraically ÷ greatest iteration algebraically
At the iteration initial stage, Inertia Weight is larger, and algorithm has stronger global optimizing ability; Along with the increase of number of iterations, population is restrained gradually, and Inertia Weight diminishes, and algorithm has stronger local optimal searching ability.
The performance comparison of random initializtion and fixing Inertia Weight and the multi-objective particle swarm algorithm based on the initialization of CVT method and Dynamic Inertia weights.Fig. 8 is the disaggregation that adopts the multi-objective particle swarm algorithm of random initializtion and fixing Inertia Weight, Fig. 9 is the disaggregation that uses the multi-objective particle swarm algorithm of CVT method initialization and Dynamic Inertia weights, both operation algebraically was for 500 generations, can find out and adopt the algorithm optimization disaggregation of CVT method initialization and Dynamic Inertia weights to be more evenly distributed, the optimization solution finding is more, meanwhile, in the situation that iteration algebraically is identical, adopt the algorithm convergence of CVT method initialization and Dynamic Inertia weights faster.
Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improvement and conversion all should belong to the protection domain of claims of the present invention.
Claims (5)
1. the robust Optimal methods based on average gradient value and improvement multi-objective particle swarm optimization, is characterized in that, comprises the following steps:
1) determine technological parameter to be optimized according to engineering actual conditions and optimization aim;
2) determine the constraint condition of technological parameter to be optimized according to engineering actual conditions;
3) set up the objective function model of optimization aim and technological parameter to be optimized;
4) test by limited number of time the discrete relationship obtaining between optimization aim and welding condition; And according to the discrete relationship between objective function model and technological parameter, calculating target function;
5) set uncertain territory, utilize the average gradient value of uncertain territory sample, calculate robustness;
6) optimize sub-goals using objective function and robustness as two, carry out Bi-objective Optimization Solution.
2. robust Optimal methods according to claim 1, is characterized in that, described step 6) in Bi-objective optimization method comprise the following steps:
6.1) population scale is set, the maximum algebraically of iteration, stochastic variable R1, R2 between maximum Inertia Weight and minimum Inertia Weight and [0,1];
6.2) initialization population, by the position of CVT method initialization particle and the speed of initialization particle;
6.3) calculate the fitness function of each particle, using the position of particle as decision variable, described decision variable is used for representing technological parameter; According to the discrete relationship calculating target function between objective function model and decision variable; Utilize the average gradient value of sample point in the uncertain territory of particle to calculate the robustness of particle;
6.4) according to Pareto domination principle, the position of the non-domination particle in population is stored in outside files;
6.5) the memory files of the each particle of initialization, record this particle optimal location up to the present by the memory files of particle;
6.6) optimal location of selected population from outside files;
6.7) calculate the speed of each particle;
6.8) position of new particle more, adds the position of particle previous generation the speed of this particle, and keeps particle in search volume;
6.9) fitness function of new particle more;
6.10) upgrade the particle representative in each hypercube of outside files and division; Current non-domination solution is inserted into outside files, and the solution of being arranged will be deleted from outside files; In the time that outside files are full, preferentially preserve the solution in the region that in object space, particle is few;
6.11) the memory files of new particle more;
6.12) if iteration reaches the maximum algebraically of iteration, stop output optimum solution; Otherwise, return to step 6.6).
3. robust Optimal methods according to claim 1, is characterized in that, described step 6.2) in, the position of initialization particle comprises the following steps:
Step 6.2a), a given density function ρ (x), a positive integer q, constant α
1, α
2, β
1and β
2, wherein: α
2>0, β
2>0, α
1+ α
2=1, β
1+ β
2=1;
Point set
expression will initialized population, wherein i=1 ..., N; For i=1 ..., N, arranges j
iinitial value is 1; With Monte Carlo method decision space select an initial point set
Step 6.2b), according to density function ρ (x), decision space select q point
Step 6.2c), for set
in each point, will gather
in from z
inearest point (is put z
ivoronoi region in point) conclude to set w
iin, if set w
ifor sky, z
iremain unchanged; Otherwise, calculate w
ithe mean place u of point in set
i, and upgrade z according to following expression formula
i;
Step 6.2d) if the particle assembly after upgrading meets convergence criterion, renewal stops; Otherwise, forward step 6.2b to).
4. robust Optimal methods according to claim 1, is characterized in that, described step 6.3) in, the robustness of calculating particle comprises the following steps:
6.3a), establishing the dimension that current particle exists the decision variable of disturbance is c, the dimension in this uncertain territory of particle is also c, every one dimension in uncertain territory is evenly divided into t section, c and t represent respectively because of prime number and number of levels, arrange according to select suitable uniform designs table to carry out factor level data because of prime number, number of levels, in the uncertain territory of current particle, choose sample point set by uniform designs table; The uncertain territory of described particle is artificial default;
6.3b), calculate the target function value of each sample point and the absolute difference of the target function value of current particle and the decision variable of the each sample point Euclidean distance to the decision variable of current particle, the ratio of the absolute difference of record object function and the Euclidean distance of decision variable;
6.3c), calculate the mean value of the ratio of the absolute difference of all sample point objective functions and the Euclidean distance of decision variable, be the robustness evaluation value of this particle.
5. robust Optimal methods according to claim 1, is characterized in that, described step 6.9) in the fitness function of new particle more, the robustness of calculating particle comprises the following steps:
6.9a), establishing the dimension that current particle exists the decision variable of disturbance is c, the dimension in this uncertain territory of particle is also c, every one dimension in uncertain territory is evenly divided into t section, c and t represent respectively because of prime number and number of levels, arrange according to select suitable uniform designs table to carry out factor level data because of prime number, number of levels, in the uncertain territory of current particle, choose sample point set by uniform designs table; The uncertain territory of described particle is artificial default;
6.9b), calculate the target function value of each sample point and the absolute difference of the target function value of current particle and the decision variable of the each sample point Euclidean distance to the decision variable of current particle, the ratio of the absolute difference of record object function and the Euclidean distance of decision variable;
6.9c), calculate the mean value of the ratio of the absolute difference of all sample point objective functions and the Euclidean distance of decision variable, be the robustness evaluation value of this particle.
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| CN108345216A (en) * | 2018-01-12 | 2018-07-31 | 中国科学院理化技术研究所 | A kind of magnetic suspension bearing robust controller building method based on multi-objective particle swarm algorithm |
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| CN111080020B (en) * | 2019-12-23 | 2023-03-31 | 中山大学 | Robustness evaluation method and device for drilling arrangement scheme |
| CN111080020A (en) * | 2019-12-23 | 2020-04-28 | 中山大学 | Robustness evaluation method and device for drilling arrangement scheme |
| CN113420464A (en) * | 2021-07-22 | 2021-09-21 | 西南交通大学 | Aisle arrangement method considering robustness |
| CN113420464B (en) * | 2021-07-22 | 2022-04-19 | 西南交通大学 | Aisle arrangement method considering robustness |
| CN113642220A (en) * | 2021-08-26 | 2021-11-12 | 江苏科技大学 | Ship welding process optimization method based on RBF and MOPSO |
| CN113642220B (en) * | 2021-08-26 | 2023-09-22 | 江苏科技大学 | Ship welding process optimization method based on RBF and MOPSO |
| CN114139459A (en) * | 2021-12-30 | 2022-03-04 | 中国地质大学（武汉） | Wireless sensor configuration optimization method based on constrained multi-objective optimization algorithm |
| CN114139459B (en) * | 2021-12-30 | 2024-04-12 | 中国地质大学（武汉） | Wireless sensor configuration optimization method based on constraint multi-objective optimization algorithm |
| CN114692562A (en) * | 2022-03-16 | 2022-07-01 | 北京理工大学 | High-precision hybrid dynamic priority multi-objective optimization method |
| CN114692562B (en) * | 2022-03-16 | 2024-05-24 | 北京理工大学 | High-precision hybrid dynamic priority multi-objective optimization method |
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