CN109214499A - A kind of difference searching algorithm improving optimizing strategy - Google Patents

A kind of difference searching algorithm improving optimizing strategy Download PDF

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CN109214499A
CN109214499A CN201810842197.1A CN201810842197A CN109214499A CN 109214499 A CN109214499 A CN 109214499A CN 201810842197 A CN201810842197 A CN 201810842197A CN 109214499 A CN109214499 A CN 109214499A
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相艳
桂鹏
王硕
邵党国
马磊
许春荣
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Kunming University of Science and Technology
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Abstract

The invention discloses a kind of difference searching algorithms for improving optimizing strategy, mainly change the optimizing strategy that original error divides searching algorithm, specifically improve virtual individual active mode and algorithm Search Range.Firstly, the Search Range that the present invention is set according to algorithm generates an initial point position, which, which is referred to as, is inhabited a little, and the value for inhabiting a little is substituted for global optimum.Then, algorithm according to the present invention in improved optimizing strategy carry out continuous iteration and update to operate, the candidate value generated after each iteration is compared with global optimum, selects preferably to solve as global optimum, be updated until meeting stopping criterion for iteration repeatedly.In the process, if the candidate value generated after iteration has exceeded the search range that algorithm is set, exercise boundary limits method.The present invention improves the low optimization accuracy of former algorithm, while also accelerating the speed of algorithm optimizing, can more quickly and accurately find out the optimal value of parameter to be optimized.

Description

A kind of difference searching algorithm improving optimizing strategy
Technical field
The present invention relates to a kind of optimization method of improvement difference search, in particular to a kind of difference for improving optimizing strategy is searched Rope algorithm belongs to intelligence computation field.
Background technique
The creation inspiration of difference searching algorithm (Differential Search Algorithm, DSA) derives from nature Different kind organism body migration course.The algorithm has been continued to use it and has been randomly generated initially using differential evolution algorithm as basic structure The method of position and boundary limitation, and Brownian movement has been used to simulate random motion of the organism in migration course, it uses The mode of Random Activation virtual individual carrys out the update of problem of modelling dimension, is a kind of newer, efficient optimizing algorithm.
During evolution, difference searching algorithm easily falls into local extremum, and main cause is the direction mistake that biota is searched In diverging, cause whole fluctuation range very big, is not easy to optimize along optimal path.It is random due to Brownian movement Property, algorithm are easily trapped into local extremum in the iteration later period, are not easy to find peak value, and optimum point often has not yet been reached in searching process It just stopped iteration.The present invention proposes a kind of difference searching algorithm for improving optimizing strategy to solve the above-mentioned problems, solves Former algorithm is easily trapped into the problems such as local extremum and long calculating time.
Summary of the invention
The invention discloses a kind of difference searching algorithms for improving optimizing strategy, mainly change original error and divide searching algorithm Optimizing strategy specially improves virtual individual active mode and algorithm Search Range.Firstly, the present invention is set according to algorithm Search Range generate an initial point position, which, which is referred to as, inhabites a little, and the value for inhabiting a little is substituted for global optimum Value.Then, algorithm according to the present invention in improved method carry out continuous iteration and update to operate, by what is generated after each iteration Candidate value is compared with global optimum, is selected preferably to solve as global optimum, be updated repeatedly until meeting iteration end Only until condition.In the process, if the candidate value generated after iteration has exceeded the search range that algorithm is set, side is executed Boundary determines method.
Specific step is as follows for the difference searching algorithm for improving optimizing strategy:
Step 1: setting initial parameter: setting search range, the global optimum that algorithm generates search for model without departing from this It encloses, sets the dimension of quantity and optimization problem individual in population, set the number of iterations or termination condition, set optimizing mould Formula, and set timing program;
Step 2: the population for improving the difference searching algorithm of optimizing strategy can be randomly generated one initially according to search range Position, which, which is referred to as, inhabites a little, and the value for inhabiting a little is substituted for global optimum.Because optimal value is to produce at random thus It is raw, so it is last solution that optimal value is almost impossible;
Step 3: judging whether optimization process at this time reaches preset iterations max or iterative value equal to objective function Value, carries out next round iteration if being unsatisfactory for;
Step 4: the difference searching algorithm for improving optimizing strategy can be next according to Brownian movement stochastic evolution population position The population position of evolution is referred to as dwell point, the candidate value that thus this wheel iteration of available one of dwell point generates;It is specific:
Stopover=Pos+Rmap (Dir-Pos)
Wherein, Stopover is dwell point, indicates virtual superior biological body current location;R is the random of movement setting Value, for simulating Blang's random motion;Map is one and forms selector by 0 and 1 by what problem dimension was constituted, and 0 represents the problem Direction is taken turns herein does not execute search in iteration, 1 is on the contrary;Pos indicates the position that random selection individual is migrated;Dir-Pos indicates super The direction that grade organism migrates.
The difference searching algorithm for improving optimizing strategy has adjusted using Rmap as the iterative manner of optimizing strategy, specific:
Original error divides the R candidate value of searching algorithm to have 5, is respectively: R1=4*randn;R2=4*randg;R3= Lognrnd (rand, 5*rand);R4=1./gamrnd (1,0.5);R5=1/normrnd (0,5), wherein rand representative function What is generated is the pseudo random number between 0 to 1;Randn indicates that mean value is the normal distribution that 0 variance is 1;Randg indicates ruler Degree parameter and form parameter are 1 Gamma distribution;Lognrnd indicates logarithm normal distribution;Gamrnd indicates Gamma distribution; Normrnd indicates normal distribution.Above-mentioned R1-R5Value all have the characteristics that fluctuation range is larger and unstable.In the present invention It is required that the search range of R becomes smaller and can be more stable.In the present invention, R is assigned R=2*rand.
In difference searching algorithm, map simulates the more new state of problem dimension, and former algorithm is more biased towards in updating a certain ask The dimension of topic, and it is possible to not replacement problem dimension;The present invention is more heavily weighted toward while updating the dimension of multiple problems, and eliminates Not the case where not updating dimension.
Step 5: exercise boundary limits method (inessential), the borders method in difference searching algorithm derived from difference into Change algorithm, because often generating certain candidate values beyond search range in optimization process, for these invalid candidate values, This step replaces the candidate value beyond search range by way of random assignment, and the value that this borders generates is replaced Change the candidate value that wheel iteration generates thus into;If the candidate solution continues to execute step 6 without departing from search range;
Step 6: whether the candidate value for judging that this wheel iteration generates is better than existing global optimum, if YES then this is waited Choosing value is substituted for global optimum, if it is otherwise, not replacing.In the present invention, judge that condition whether candidate value is superior refers to, Candidate value whether than global optimum existing in algorithm closer to the global optimum of test function;
Step 7: repeating step 3-6 until meeting the iteration termination target of step 3, finally export global optimum at this time Value, and timing is terminated, obtain the time of algorithm operation.
Beneficial effects of the present invention: the difference searching algorithm for improving optimizing strategy improves the optimizing that original error divides searching algorithm Precision, while also accelerating the speed of algorithm optimizing compensates for primal algorithm and easily falls into local extremum, Premature Convergence or iteration and stops The defects of stagnant, can more quickly and accurately find out the optimal value of parameter to be optimized.
Detailed description of the invention
Fig. 1 is the overview flow chart for the difference searching algorithm that the present invention improves optimizing strategy;
Fig. 2 is the function curve diagram of the Ackley function that uses in the present invention under two-dimensional problems;
Fig. 3 is the function curve diagram of the Griewank function that uses in the present invention under two-dimensional problems;
Fig. 4 is the function curve diagram of the Rastrigin function that uses in the present invention under two-dimensional problems;
Fig. 5 is the function curve diagram of the Rosenbrock function that uses in the present invention under two-dimensional problems;
Fig. 6 is the function curve diagram of the Sphere function that uses in the present invention under two-dimensional problems;
Fig. 7 is the function curve diagram of the Zakharov function that uses in the present invention under two-dimensional problems.
Specific embodiment
Embodiment 1: as shown in Figure 1, the present invention generates an initial point position according to the Search Range that algorithm is set, it should Position, which is referred to as, to be inhabited a little, and the value for inhabiting a little is substituted for global optimum.Then, algorithm according to the present invention in improved side Method carries out continuous iteration and updates to operate, and the candidate value generated after each iteration is compared with global optimum, is selected Preferably solution is used as global optimum, is updated until meeting stopping criterion for iteration repeatedly.In the process, if being produced after iteration Raw candidate value has exceeded the search range that algorithm is set, then exercise boundary limits method.
Specific step is as follows for the difference searching algorithm for improving optimizing strategy:
Step 1: setting initial parameter: setting search range, the global optimum that algorithm generates search for model without departing from this It encloses.The dimension of quantity and optimization problem individual in population is set, the number of iterations or termination condition are set, sets optimizing mould Formula, and set timing program.In the present invention, for all unconstrained optimization test functions, the difference of optimizing strategy is improved Divide searching algorithm and original error that the search range of searching algorithm (DSA) is divided uniformly to be set as [- 10,10], individual quantity i=50, The dimension d=3 of optimization problem, the number of iterations G=100.Selected test function, such as Sphere function is selected to test letter Number, function curve diagram of the function under two-dimensional problems is as shown in fig. 7, its function expression are as follows:
Wherein, F (x) is required non trivial solution, and d is the dimension of target problem, and i is the number of optimizing particle in algorithm, In this test function, when x=(0,0,0 ..., 0)TWhen, there is globally optimal solution minF (x)=0.
Step 2: the population for improving the difference searching algorithm of optimizing strategy can be randomly generated one initially according to search range Position, which, which is referred to as, inhabites a little, and the value for inhabiting a little is substituted for global optimum.Because optimal value is to produce at random thus It is raw, so it is last solution that optimal value is almost impossible, it is specific:
popmn=rand (upn-lown)+lown
Wherein, the scale pop of populationm, m={ 1,2 ..., S }, wherein S indicates individual sum, total dimension popn, n=1, 2 ..., D }, wherein D indicates the dimension of institute's optimization problem.What rand representative function generated is the pseudo random number between 0 to 1, upnAnd lownRespectively indicate the upper bound and the lower bound of preset search range.
Step 3: judging whether optimization process at this time meets the condition of iteration termination or meet iteration ends target, if not Satisfaction then carries out next round iteration;
Step 4: the difference searching algorithm for improving optimizing strategy can be next according to Brownian movement stochastic evolution population position The population position of evolution is referred to as dwell point, the candidate value that thus this wheel iteration of available one of dwell point generates, specific:
Stopover=Pos+Rmap (Dir-Pos)
Wherein, Stopover is dwell point, indicates virtual superior biological body current location;R is the random of movement setting Value, for simulating Blang's random motion;Map is one and forms selector by 0 and 1 by what problem dimension was constituted, and 0 represents the problem Direction is taken turns herein does not execute search in iteration, 1 is on the contrary;Pos indicates the position that random selection individual is migrated;Dir-Pos indicates super The direction that grade organism migrates.
Step 5: judging whether the candidate value generated by step 4 has exceeded pre-set search range, if then holding Row bound limits method, and the value that this borders generates is substituted for the candidate value that wheel iteration generates thus;If it is not, then continuing Step 6 is executed, specific:
Sitemn=rand (upn-lown)+low n
Wherein, SitemnFor the position of virtual population, m={ 1,2 ..., S }, wherein S indicates that individual is total, n=1, 2 ..., D }, wherein D indicates the dimension of institute's optimization problem.Work as Sitemn<lownOr Sitemn>upnWhen, to SitemnAccording to above formula into The distribution of row random site.That rand representative function generates is the pseudo random number between 0 to 1, upnAnd lownIt respectively indicates pre- The upper bound of the search range first set and lower bound.
Step 6: whether the candidate value for judging that this wheel iteration generates is better than existing global optimum, if then by this candidate Value is substituted for global optimum, if otherwise not replacing;
Step 7: repeating step 3-6 until meeting the iteration termination target of step 3, finally export global optimum at this time Value, and timing is terminated, obtain the time of algorithm operation;
Embodiment 2: as shown in figs. 1-7, present invention incorporates attached drawings and specific implementation case to do to technical solution of the present invention It is described in further detail.The present invention is to improve the difference searching algorithm of optimizing strategy, in unconstrained optimization problem or is had about On beam Global Optimal Problem, optimal solution or feasible solution can be obtained.Several examples in unconstrained optimization problem are given below Son, how to illustrate using the difference searching algorithm of the invention for improving optimizing strategy.Ackley, Griewank are selected, The typical extreme value of a function problem of Rastrigin, Rosenbrock, Sphere, Zakharov, Hartmann this 7, with the present invention The difference searching algorithm and original error for improving optimizing strategy divide searching algorithm (DSA) to carry out test and comparison.
(1) Ackley function:
Ackley function is the experiment function of continuous type obtained from the cosine moderately amplified on index function superposition, and belonging to has The function of many local extremums.It is characterized in that one almost flat region modulated by cosine wave and form hole one by one or peak, from And keep curved surface uneven.Ackley points out that the search of this function is sufficiently complex, because a stringent suboptimization is calculated Method inevitably falls into the trap of local optimum in hill climbing process;And the mountain of interference can be crossed by scanning larger field Paddy progressively reaches preferable optimum point.The function when optimizing, works as x in the region of search of restrictioniWhen=0, most global minima is obtained Value 0.
(2) Griewank function:
The function belongs to the function there are many local extremum.The number of local extremum and the dimension of problem are related, this function It is typical non-linear multi-modal function, there is extensive search space, it is very intractable multiple to be typically considered optimization algorithm Miscellaneous multi-modal problem.The function when optimizing, works as x in the region of search of restrictioniWhen=0, most global minimum 0 is obtained.
(3) Rastrigin function:
The function belongs to the function there are many local extremum, is the function of a multi-peak, there are a large amount of local minimums And maximum of points, it is a kind of typical nonlinear multi-modal function, peak shape is in the appearance of height ups and downs jumping characteristic, to intelligence Energy algorithm has duplicity, and algorithm is made easily to fall into local extremum.The function when optimizing, works as x in the region of search of restrictioniWhen=0, Obtain most global minimum 0.
(4) Rosenbrock function:
The function belongs to the function of valleys, the also known as unimodal function of Banana Type, is a kind of non-convex, pathological function, There are interactional effect between correlated variables, cause what many optimization algorithms can not prepare to find global optimum, it should Function when optimizing, works as x in the region of search of restrictioniWhen=1, most global minimum 0 is obtained.
(5) Sphere function:
This function belongs to bowl-shape type function, is a simple unimodal function, function is interior, and there is no Local Extremums, mainly Intelligent algorithm is investigated for the precise search ability of extreme point.The function when optimizing, works as x in the region of search of restrictioniWhen=0, Obtain most global minimum 0.
(6) Zakharov function:
This function belongs to smooth type function, is a simple unimodal function, which has no other than global minimum Other local minimum points work as x in the region of search of restriction when optimizingiWhen=0, which obtains most global minimum 0.
(7) Hartmann function:
Hartmann function can be used for 3 dimensions or the optimizing of 6 dimensions solves, and what is be used in the present invention is 3 The problem of a dimension, solves, wherein preset The function in the region of search of restriction when optimizing, when x=(0.114614, 0.555649,0.852547) when, most global minimum -3.86278 is obtained.
Test result: according to 1 step of embodiment, test is brought into using 7 functions in embodiment 2, to each function 50 simulation trials are carried out alone, obtained data are counted, and are finally obtained suitable between the method for the present invention and original method Angle value (optimal, worst, average, time) is answered, as shown in table 1:
Table 1: the method for the present invention and original error divide between searching algorithm data compared with fitness
As it can be seen from table 1 inventive algorithm is in 7 kinds of different function tests, the function embodied is adapted to Angle value (optimal, worst, average, time), the original error that compares divides for searching algorithm, and optimizing effect is better, numerically Close to the theoretical extreme of function, in the test of the functions such as Ackley, calculating speed is also superior to former algorithm.By in embodiment 2 to 7 The performance test of functional equation, it was demonstrated that the optimizing performance of the difference searching algorithm of the invention for improving optimizing strategy is compared with original error point For searching algorithm, there is very big raising.
Although above-mentioned experimental section and attached drawing part have carried out certain description to the present invention, the present invention does not limit to In above-mentioned specific embodiment, described above to belong to be illustrative nature, is not belonging to restrictive.The ordinary skill people of this field Member under the inspiration of the present invention, without deviating from the spirit of the invention, can also make many changes to inventive algorithm Shape, these are belonged within present invention protection.

Claims (4)

1. a kind of difference searching algorithm for improving optimizing strategy, which comprises the following steps:
Initial parameter is arranged in step 1: setting search range sets the dimension of quantity and optimization problem individual in population, if Determine the number of iterations or termination condition, sets optimizing mode, and set timing program;
Step 2 is randomly generated an initial position according to search range and inhabites a little, and by the value for inhabiting a little be substituted for it is global most The figure of merit;
The optimization process of step 3 judgement at this time whether reaches preset iterations max or iterative value is equal to target function value, if It is unsatisfactory for, carries out next round iteration;
Step 4 is referred to as dwell point according to Brownian movement stochastic evolution population position, the population position of next evolution, thus The candidate value that this wheel iteration of available one of dwell point generates;
Step 5 judges whether the candidate value generated by step 4 has exceeded pre-set search range, if so then execute side Boundary determines method, and the value that this borders generates is substituted for the candidate value that wheel iteration generates thus;If it is not, then continuing to execute Step 6;
Whether the candidate value that step 6 judges that this wheel iteration generates is better than whether existing global optimum i.e. candidate value compares algorithm In existing global optimum closer to test function global optimum, if this candidate value is then substituted for global optimum, If otherwise not replacing;
Step 7 repeats step 3-6 until meeting the iteration termination target of step 3, finally exports global optimum at this time, and Timing is terminated, the time of algorithm operation is obtained.
2. the difference searching algorithm according to claim 1 for improving optimizing strategy, it is characterised in that: dwell in the step 2 Cease the random generation process of point are as follows:
popmn=rand (upn-lown)+lown
Wherein, the position inhabited a little is popmn, m={ 1,2 ..., S }, S indicate individual sum in population, n=1,2 ..., D }, D indicates the dimension of optimization problem, and that rand representative function generates is the pseudo random number between 0 to 1, upnAnd lownPoint The upper bound and the lower bound of preset search range are not indicated.
3. the difference searching algorithm according to claim 1 for improving optimizing strategy, it is characterised in that: the tool of the step 4 Body process are as follows:
Stopover=Pos+Rmap (Dir-Pos)
Wherein, Stopover is dwell point, indicates virtual superior biological body current location;R is the random value of movement setting, is used for Blang's random motion is simulated, R=2*rand, wherein what rand representative function generated is the pseudo random number between 0 to 1;map It is one and selector is formed by 0 and 1 by what problem dimension was constituted, 0, which represents the problem direction, takes turns do not execute search in iteration herein, 1 is on the contrary;Pos indicates the position that random selection individual is migrated;Dir-Pos indicates the direction that superior biological body is migrated.
4. the difference searching algorithm according to claim 1 for improving optimizing strategy, it is characterised in that: in the step 5 Borders method replaces the candidate value beyond search range specifically by the mode of random assignment, and this value is replaced The candidate value generated as this wheel iteration.
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CN108761282A (en) * 2018-04-18 2018-11-06 国网江苏省电力有限公司电力科学研究院 A kind of ultrasonic wave shelf depreciation auto-check system and its method based on robot
CN111062962A (en) * 2019-12-06 2020-04-24 昆明理工大学 Multi-threshold ultrasonic image segmentation method based on differential search algorithm
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CN112736912A (en) * 2020-12-28 2021-04-30 上海电力大学 Distribution network reconstruction method based on annealing brownian motion and single ring optimization
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CN108761282A (en) * 2018-04-18 2018-11-06 国网江苏省电力有限公司电力科学研究院 A kind of ultrasonic wave shelf depreciation auto-check system and its method based on robot
CN108761282B (en) * 2018-04-18 2024-01-05 国网江苏省电力有限公司电力科学研究院 Ultrasonic partial discharge automatic diagnosis system and method based on robot
CN111062962A (en) * 2019-12-06 2020-04-24 昆明理工大学 Multi-threshold ultrasonic image segmentation method based on differential search algorithm
CN111062962B (en) * 2019-12-06 2022-09-27 昆明理工大学 Multi-threshold ultrasonic image segmentation method based on differential search algorithm
CN112199996A (en) * 2020-09-04 2021-01-08 西安交通大学 Rolling bearing diagnosis method based on parameter self-adaptive VMD and fast Hoyer spectrogram indexes
CN112736912A (en) * 2020-12-28 2021-04-30 上海电力大学 Distribution network reconstruction method based on annealing brownian motion and single ring optimization
CN112736912B (en) * 2020-12-28 2023-09-29 上海电力大学 Distribution network reconstruction method based on desuperheating Brownian motion and single-loop optimization
CN113722853A (en) * 2021-08-30 2021-11-30 河南大学 Intelligent calculation-oriented group intelligent evolutionary optimization method
CN113722853B (en) * 2021-08-30 2024-03-05 河南大学 Group intelligent evolutionary engineering design constraint optimization method for intelligent computation
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Application publication date: 20190115