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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

本发明公开了一种改进寻优策略的差分搜索算法，主要改变了原差分搜索算法的寻优策略，具体的改进了虚拟个体激活方式和算法寻优范围。首先，本发明根据算法设定好的寻优范围产生一个初始点位置，该位置被称为栖息点，并将栖息点的值替换成全局最优值。然后，算法根据本发明中改进的寻优策略进行不断的迭代与更新操作，将每次迭代后产生的候选值与全局最优值进行比较，选择更好的解作为全局最优值，反复更新直到满足迭代终止条件为止。在此过程中，若迭代后产生的候选值超出了算法设定好的搜索范围，则执行边界限定方法。本发明提高了原算法的寻优精度，同时也加快了算法寻优的速度，能够更加快速、准确的找到待优化参数的最优值。

The invention discloses a differential search algorithm with an improved optimization strategy, which mainly changes the optimization strategy of the original differential search algorithm, and specifically improves the activation mode of virtual individuals and the optimization range of the algorithm. First, the present invention generates an initial point position according to the optimization range set by the algorithm, which is called a perch point, and replaces the value of the perch point with a global optimal value. Then, the algorithm performs continuous iteration and update operations according to the improved optimization strategy in the present invention, compares the candidate value generated after each iteration with the global optimal value, selects a better solution as the global optimal value, and repeatedly updates until the iteration termination condition is met. In this process, if the candidate value generated after iteration exceeds the search range set by the algorithm, the boundary limiting method is performed. The invention improves the optimization precision of the original algorithm, and also speeds up the algorithm optimization speed, and can find the optimal value of the parameter to be optimized more quickly and accurately.

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)

1.一种改进寻优策略的差分搜索算法，其特征在于，包括以下步骤：1. a differential search algorithm for improving the optimization strategy, is characterized in that, comprises the following steps: 步骤1 设置初始参数：设定搜索范围，设定种群中个体的数量以及寻优问题的维度，设定迭代次数或终止条件，设定寻优模式，并设定计时程序；Step 1 Set initial parameters: set the search range, set the number of individuals in the population and the dimension of the optimization problem, set the number of iterations or termination conditions, set the optimization mode, and set the timing program; 步骤2 根据搜索范围随机产生一个初始位置即栖息点，并将栖息点的值替换成全局最优值；Step 2 Randomly generate an initial position or habitat point according to the search range, and replace the value of the habitat point with the global optimal value; 步骤3 判断此时的优化过程是否达到预设的迭代最大值或迭代值等于目标函数值，若不满足则进行下一轮迭代；Step 3: Determine whether the optimization process at this time has reached the preset maximum iteration value or the iteration value is equal to the objective function value, if not, proceed to the next iteration; 步骤4 根据布朗运动随机进化种群位置，下一个进化的种群位置被称为停留点，由此停留点可以得到一个此轮迭代产生的候选值；Step 4 Randomly evolve the population position according to Brownian motion, and the next evolutionary population position is called the stay point, from which a candidate value generated by this round of iterations can be obtained; 步骤5 判断由步骤4产生的候选值是否超出了预先设定好的搜索范围，若是则执行边界限定方法，并将此边界限定产生的值替换成为此轮迭代产生的候选值；若否，则继续执行步骤6；Step 5 Determine whether the candidate value generated by step 4 exceeds the preset search range, if so, execute the boundary limit method, and replace the value generated by this boundary limit with the candidate value generated by this round of iteration; if not, then Continue to step 6; 步骤6 判断此轮迭代产生的候选值是否优于现有的全局最优值即候选值是否比算法中现有全局最优值更接近测试函数的全局最优值，若是则将此候选值替换成全局最优值，若否则不替换；Step 6 Determine whether the candidate value generated by this round of iteration is better than the existing global optimal value, that is, whether the candidate value is closer to the global optimal value of the test function than the existing global optimal value in the algorithm, and if so, replace the candidate value. into the global optimal value, otherwise do not replace; 步骤7 重复步骤3-6直至满足步骤3的迭代中止目标，最后输出此时的全局最优值，并终止计时，得到算法运行的时间。Step 7 Repeat steps 3-6 until the iterative termination objective of step 3 is met, and finally output the global optimal value at this time, and stop the timing to obtain the running time of the algorithm. 2.根据权利要求1所述的改进寻优策略的差分搜索算法，其特征在于：所述步骤2中栖息点的随机产生过程为：2. the differential search algorithm of improved optimization strategy according to claim 1, is characterized in that: the random generation process of habitat point in described step 2 is: popmn＝rand·(upn-lown)+lown pop mn =rand·(up n -low n )+low n 其中，栖息点的位置为popmn，m＝{1，2，…，S}，S表示种群中个体的总数，n＝{1，2，…，D}，D表示寻优问题的维度，rand表示函数产生的是介于0到1之间的伪随机数，upn和lown分别表示预先设定的搜索范围的上界和下界。Among them, the location of the habitat point is pop mn , m={1, 2,...,S}, S represents the total number of individuals in the population, n={1, 2,..., D}, D represents the dimension of the optimization problem, rand indicates that the function generates a pseudo-random number between 0 and 1, and up n and low n indicate the upper and lower bounds of the preset search range, respectively. 3.根据权利要求1所述的改进寻优策略的差分搜索算法，其特征在于：所述步骤4的具体过程为：3. the differential search algorithm of improved optimization strategy according to claim 1, is characterized in that: the concrete process of described step 4 is: Stopover＝Pos+R·map·(Dir-Pos)Stopover=Pos+R·map·(Dir-Pos) 其中，Stopover为停留点，表示虚拟超级生物体当前位置；R是运动设定的随机值，用于模拟布朗随机运动，R＝2*rand，其中rand表示函数产生的是介于0到1之间的伪随机数；map是一个由问题维数构成的由0和1组成选择器，0代表该问题方向在此轮迭代中不执行搜索，1反之；Pos表示随机选择个体迁徙的位置；Dir-Pos表示超级生物体迁徙的方向。Among them, Stopover is the stop point, indicating the current position of the virtual super organism; R is the random value set by the motion, which is used to simulate Brownian random motion, R=2*rand, where rand indicates that the function generated is between 0 and 1 Pseudo-random number between; map is a selector composed of 0 and 1 composed of problem dimensions, 0 means that the problem direction is not searched in this round of iteration, 1 is vice versa; Pos means randomly select the location of individual migration; Dir -Pos indicates the direction of migration of the superorganism. 4.根据权利要求1所述的改进寻优策略的差分搜索算法，其特征在于：所述步骤5中的边界限定方法具体为通过随机赋值的方式来替换掉超出搜索范围的候选值，并将此值替换成为此轮迭代产生的候选值。4. the differential search algorithm of improved optimization strategy according to claim 1, is characterized in that: the boundary limiting method in described step 5 is specifically replaced by the mode of random assignment to replace the candidate value beyond the search range, and This value is replaced with the candidate value produced by this 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
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CN113632105A (en) * 2019-01-31 2021-11-09 摩根士丹利服务集团有限公司 Anomaly response of chaotic system based on artificial intelligence
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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
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CN113722853B (en) * 2021-08-30 2024-03-05 河南大学 Group intelligent evolutionary engineering design constraint optimization method for intelligent computation
CN115130641A (en) * 2022-01-24 2022-09-30 中国人民解放军国防科技大学 A data population optimization method, apparatus, computer equipment and storage medium
CN117970228A (en) * 2024-03-28 2024-05-03 中国人民解放军火箭军工程大学 A multi-target DOA estimation method based on uniform circular array

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