WO2018161468A1 - 一种基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法 - Google Patents
一种基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法 Download PDFInfo
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- the invention relates to the technical field of computer programs, including artificial intelligence, in particular to a global optimization, search and machine learning method based on genetic algorithms.
- the common genetic algorithm uses Darwin's "survival of the fittest" natural evolution rule, and repeatedly applies three operators: selection operator, crossover operator and mutation operator.
- the search speed of the algorithm is slow and the search accuracy is relatively low.
- the local search ability of the genetic algorithm is poor, which leads to low efficiency of the algorithm in the late evolutionary stage.
- the genetic algorithm is prone to the problem of premature convergence.
- the selection method not only preserves the good individuals but also maintains the diversity of the group has always been a technical problem that is difficult to solve in genetic algorithms, which limits its greater technical effects in global optimization, search and machine learning.
- the present invention combines the Lamarck acquired genetic principle and the modern “characteristics genetics” with the Darwinian evolutionary theory of "the survival of the fittest”. , constructing the "acquired genetic optimization” technical solution and the "acquired genetic algorithm”.
- an adaptive "genetic operator” and its “rewrite operation” method were invented to directly replace the two operators of the common genetic algorithm (ie “select operator” and “ Crossover operator") simplifies the structure of genetic algorithm, overcomes many technical defects of current genetic algorithm, and enhances the global optimality of genetic algorithm and the sustainability of later evolution.
- the invention of a "use of the retreat operator” can be used to replace the innate mutation operator in the common genetic algorithm, so as to carry out the directional mutation operation in the same generation, so that The mutation operation produces new technical effects, improves the performance of the genetic algorithm, and solves the problems of global optimization, search and machine learning more and better.
- a global optimization, search and machine learning method based on Lamarck's acquired genetic principle including the following steps:
- Step 1 Construct the objective function f(x) according to the problem object of optimization, search and machine learning;
- Step 2 According to the optimization requirement of the problem object, the problem object is encoded into the chromosome of the genetic algorithm, and then the operation parameters of the genetic algorithm are automatically calculated or manually input, and the algorithm is initialized; the genetic algorithm here is a common genetic algorithm;
- Step 3 According to the optimization requirement of the problem object, the k-th generation candidate solution population is G k , and among them Represents the i-th chromosome in the candidate solution population G k , and S is the population size. Then using the iterative optimization method to obtain the k+1 generation population G k+1 , ie among them Represents the i-th chromosome in the population G k+1 , and S is the population size.
- the optimization process is as follows:
- n t L ⁇ p t ;
- L is the length of the gene string, and p t is the genetic percentage of the gene; (if the calculated n t is not an integer, it is rounded up)
- the mutation operator is the mutation operator in the common genetic algorithm
- Step 4 Output the final optimized solution set of the problem object.
- step 2 the initialization method is:
- the operating parameters are determined: the size of the candidate solution population S, the dimension dimension d, the variable value range, the cross genetic probability p c , and the internal parameters in the mutation operator;
- the problem object is encoded to form individual gene strings, chromosomes and candidates. Solve the population and determine the length L of the gene string.
- step 2 (2) the problem object is encoded in such a manner that if d is less than or equal to 2, a binary or decimal encoding method is selected; if d is greater than 2, the real encoding method is selected.
- the objective function value is a fitness function value for the maximization problem or a cost function value for the minimization problem.
- step 3(1) the individual evaluation uses multiple processors or multiple computers.
- step 3 (2) the n t genes selected for rewriting in the Lamarck genetic operator rewriting operation are randomly selected.
- step 3 (3) the mutation operation adopts the non-directional mutation method in the common genetic algorithm, including the uniform variation method with the mutation probability p m , that is, the “use and waste retreat operator” is not used.
- step 3 (3) the mutation operation can also adopt the "use and retreat operator” based on Lamarck's "use and retreat” natural law, that is, implement the directional variation method.
- step 3 (3) the "use waste retreat operator" can use the gradient optimization method if gradient information is available.
- gradient information a method of determining the direction and step size of the variation based on the sign and size of the gradient.
- step 3 (3) the "use of the retreat operator" can adopt the non-gradient optimization method.
- Non-gradient optimization methods include hill climbing algorithm, annealing algorithm, simplex method, pattern search or Powell's method.
- step 3 (2) and step 3 (3) the elite chromosome coding in each generation is not changed by the Lamarckian genetic operator and the mutation operator, that is, the elite is retained, and the rewriting and mutation groups appear to participate in evolution so far.
- the best individual also known as elite individual, elite chromosome coding
- the method of determining the elite is the method of ordinary genetic algorithm.
- step 3 (5) it is evaluated whether the optimal solution satisfies the requirements of the optimization calculation, and if the requirement is met, the operation ends; otherwise, the cross genetic probability p c or the mutation operator in the operating parameter in the operating parameter may be modified.
- step 3 (5) it is evaluated whether the optimal solution satisfies the requirements of the optimization calculation. If the requirement is met, the operation ends; otherwise, the population size and/or the number of iterations in the operation parameter may be increased, and step 3 is repeated. Get the last optimal solution set of the problem object.
- the cross genetic probability p c in the operational parameters determined in step 2, and the internal parameters in the mutation operator, can be automatically adjusted according to the evolution state during the process of step 3.
- the gene coding in the chromosome may represent a numerical parameter of the structure or structure of the problem object.
- the composition of a problem object includes the structure of the problem object, the numerical parameters of each structure, and the combination of structures (some of which are represented by arithmetic operators or logical operators).
- gene coding on a chromosome is generally not an operator; in "genetic programming," a gene encoding on a chromosome can be an operator.
- the genetic coding of the problem object may be an operator, thereby extending the adaptive genetic algorithm of the present invention to "acquired genetic programming" to achieve free optimization that enables qualitative changes in the structure of the problem object.
- the "genetic operator" in acquired genetic programming is similar to the cross-operation of common genetic programming, as shown in Figure 4, but the tree-like "pruning grafting" of chromosomes is done by rewriting operations in the adaptive genetic algorithm. Realized. Similarly, mutation operations and "use and retreat” can replace a small branch with a new branch. Thus, the genetic operators of the present invention and the implementation of the use of the retreat operator in acquired genetic programming have not changed, but have increased the speed and precision of genetic programming. In this way, acquired acquired inheritance can improve free structure optimization, automatic programming attempts, and machine learning functions.
- the invention combines the acquired genetic principle of Lamarck and the modern representational genetics with the natural law of the survival of the Darwinian evolution theory, constructs the technical scheme of acquired genetic optimization, the acquired genetic algorithm and the acquired genetic programming method;
- the genetic operator of the acquired genetic natural law directly replaces the selection operator and the crossover operator of the common genetic algorithm; it also invents the operation of Lamarck to replace the innate in the common genetic algorithm with the use of the retreat of the natural law.
- the mutation operator thus, the acquired directional variation in the same generation is used to make the mutation operation produce new technical effects, so that more problems such as global optimization, search and machine learning are better solved.
- the optimization process has a simple structure, requires less control parameters, has low computational complexity, and is easy to operate;
- Evolutionary computing technology has adaptive, self-learning, self-organizing intelligent behavior, can adapt to environmental changes, reduce fluctuations, ensure high control accuracy, and ensure real-time and rapid control;
- FIG. 3 Schematic diagram of a rewrite operation
- FIG. 4 Schematic diagram of "graft breeding" of acquired genetic programming
- Figure 5 is a comparison of the algorithmic fitness of the present invention and the general genetic algorithm in the global minimum value (f 1 ) optimization and maximum value optimization (f 2 )
- FIG. 7 Schematic diagram of neural network machine learning
- Figure 8 Schematic diagram of the realization of two variables XOR problem in the neural network
- Figure 10 shows the relationship between output and input
- Figure 11 is a schematic diagram showing the comparison of the mean square root error mean value of the method of the present invention and other particle filtering algorithms when the number of particles is 10.
- the cross genetic probability in the present invention is also taken as 0.5
- the mutation probability is taken as 0.2. Run 30 times independently for each test function. The number of function evaluations is 3 ⁇ 10 5 .
- Figures 5 and 6 respectively show the average fitness and average search accuracy of the present invention and the general genetic algorithm as a function of the number of function evaluations.
- the algorithm of the present invention optimizes the test functions f 1 and f 2 , the obtained optimal solution is closer to the theoretical optimal solution, and the search speed of the algorithm of the present invention is also much faster than that of the ordinary genetic algorithm.
- ANNs Artificial Neural Networks
- Ns Neural Networks
- Figure 7 shows a simple neural network with circles representing neurons and input point "-1" called the offset node.
- the leftmost layer of the neural network is the input layer, and the rightmost layer is the output layer. All nodes in the middle form a hidden layer, and we cannot directly observe their values in the training sample set. At the same time, you can see that the god
- there are two input units excluding the offset unit
- two hidden units and one output unit.
- a neural network with a simple network is used to implement the XOR problem of two variables to illustrate the machine learning situation using the adaptive genetic algorithm. It is an important demonstration for finding practical and effective learning algorithms. significance.
- the input training neurons are x 1 and x 2 , and the output is y.
- the four training models of the XOR problem are shown in Table 4.
- connection weights from the input layer neurons to the output layer neurons which are denoted as w n , n ⁇ 1, 2, ..., 9.
- the present invention using a global optimization, and machine learning search solutions XOR problem neural network, training of the network weights values w n, the specific process embodiment shown in FIGS. 1 and 2:
- W is the weight vector
- m is the training model number
- y m represents the output of the training model m
- f is a function of W, the value of which represents the fitness of the understanding, the larger it is, the smaller the training or learning error. Therefore, the goal of this example is to maximize f.
- Step 2 According to the optimization requirements of the problem object, automatically calculate or manually input the running parameters of the common genetic algorithm, encode the W into a chromosome, and initialize it:
- the structure of the problem object and its parameters are coded in decimal, forming individual gene strings, chromosomes and candidate solution populations, and determining the length L of the gene string; here, a two-digit decimal number is used to describe the weight coding scheme.
- variable value range of the problem object is initialized, and a set of initial candidate solutions are randomly generated.
- Step 3 According to the optimization needs, assume that the kth generation is Representing an individual (chromosome) in a population, an iterative method is used to obtain a k+1 generation population by rewriting and mutation operations.
- the optimization process is as follows:
- Step 4 Output the last optimal solution set W 0 of the problem object. As shown in Figure 8, an optimal solution set of weights is also shown.
- 9 and 10 respectively show the 100 optimal and average objective function values and the obtained input-output relationship when the optimization neural network of the present invention implements the problem of 2-variable XOR machine learning.
- the algorithm of the present invention can obtain an output that is close to the desired output when optimizing the weight of the neural network XOR problem.
- the acquired genetic algorithm of the present invention can optimize neural networks, search for optimal weights, and solve machine learning problems.
- network structure as shown in FIG. 7 can also be encoded into a gene string to be optimized simultaneously with weights.
- the network structure of the problem object needs is more complex and adaptive genetic programming can be implemented, the network structure can be more directly and freely optimized.
- Particle filter algorithm is an important technique in nonlinear signal processing. It is not affected by system model characteristics and noise distribution. Limitations and thus wider applicability than other filtering techniques. However, the performance of particle filter algorithms is limited by the problem of self-particle depletion.
- the algorithm of the invention solves the particle shortage problem in the resampling process of the particle filter algorithm, optimizes the particle distribution, and makes the particle sample closer to the real posterior probability density sample, thereby improving the filtering performance.
- the state estimation of a nonlinear dynamic system is realized by particle filtering to illustrate the optimal particle filter processing signal using the adaptive genetic algorithm, which is of great significance for finding a nonlinear filtering algorithm with superior performance.
- the state space model of the system is as follows:
- the process noise is v k to Gamma (3, 2)
- the observed noise is n k to N (0, 0.00001).
- Set the observation time to 70, the number of runs to 200, and the number of particles N to 10.
- the particle optimization algorithm particle optimization algorithm is solved by the global optimization, search and machine learning technical scheme of the invention, and the particle distribution is optimized.
- the specific implementation manner is as follows:
- Step 1 Construct the objective function f(x) according to the state estimation problem of the nonlinear dynamic system, where the weight function of the particle is selected;
- Step 2 Automatically calculate or manually input the running parameters of the common genetic algorithm according to the optimization requirements of the problem object, and initialize it:
- each chromosome represents a particle floating point number format
- the first digit of the floating point value represents the sign bit
- "1" represents a positive number
- "0” represents a negative number
- the string length is the fixed effective number of bits, that is, L ⁇ d ⁇ l x ⁇ 1 ⁇ 7.
- variable value range of the problem object is initialized, and a set of initial candidate solutions are randomly generated. Here, it is randomly generated according to the particle self-initialization step.
- Step 3 Based on the optimization requirements, assume that the current (kth generation) population is Representing an individual (chromosome) in a population, an iterative method is used to obtain a k+1 generation population by rewriting and mutation operations.
- the optimization process is as follows:
- the state values of the two new particles obtained by the two mutations are the same as the original
- the best result is the formation of directional variation. Therefore, the variability is always carried out in a direction that is not worse, and that “use and retreat” is achieved.
- Step 4 Output the last optimal solution set of the problem object, ie the particle set.
- the particle filter algorithm (RPF) performs the comparison of the root mean square error (RMSE) mean and the RMSE variance.
- Figure 11 is a graph showing the RMSE mean as a function of time for the present invention and other particle filtering algorithms.
- the adaptive genetic algorithm of the present invention can well optimize particle filtering, search for optimal particle sets, and solve nonlinear filtering problems.
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- 一种基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,包括如下步骤:步骤1:根据优化、搜索和机器学习的问题对象构造目标函数f(x);步骤2:根据问题对象的优化需求,将问题对象编码成遗传算法的染色体,然后自动计算或手动输入遗传算法的运行参数,并进行算法初始化;步骤3:根据问题对象的优化需求,设第k代候选解种群为Gk,且其中代表候选解种群Gk中第i个染色体编码,S是种群大小,利用迭代优化方法得到k+1代种群Gk+1,即其中代表种群Gk+1中第i个染色体编码,S是种群大小,优化过程如下:(2)执行拉马克获得性遗传算子重写操作,产生临时种群G′k+1,包括如下步骤:(2a)根据交叉遗传概率pc来从候选解种群Gk中随机选择两个染色体编码,比较两个染色体编码的目标函数值fm和fn的大小,并计算基因遗传百分比pt:pt=fm/(fm+fn),fm>fn;(2b)计算遗传给下一代的基因数目nt为:nt=L·pt;L为基因串的长度,pt为基因遗传百分比;(2c)保留目标函数值大的染色体编码,将目标函数值大的染色体编码上的nt个基因对应重写到目标函数值小的染色体编码的相应位置上,形成新的染色体编码;(2d)重复以上(2a)-(2c)过程pcS次,产生重写操作之后的临时种群G′k+1;(3)使用拉马克用进废退算子对临时种群G′k+1执行定向变异操作,获得新候选解种群Gk+1;(4)重复迭代第(1)步到第(3)步,直到满足预先设定的终止条件;(5)评价解码后该最优解是否满足此次优化计算的要求,若满足要求,获取最终优化解集;否则,修改运行参数,重新计算直到获取最终优化解集;步骤4:输出问题对象的最终优化解集。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(1)中:个体评价使用多个处理器或多台计算机。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(2):拉马克遗传算子重写操作时选取重写的nt个基因为随机选取。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(3)中:变异操作采用普通遗传算法中的非定向变异方法,包括变异概率为pm的均匀变异方法。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(3)中:变异操作采用基于拉马克“用进废退”自然法则的“用进废退算子”,即实施定向变异方法,包括梯度优化方法和非梯度优化方法。
- 根据权利要求6所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,定向变异的梯度优化方法包括在可获得梯度信息的情况下,根据梯度的符号和大小确定变异的方向和步长的方法。
- 根据权利要求6所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,定向变异的非梯度优化方法包括爬山算法、退火算法、单纯形方法、模式搜索或鲍尔共轭定向法。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(2)和步骤3(3)中:每一代中的精英染色体编码不受遗传算 子和变异算子改变。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(5)中:最优解不满足此次优化计算的要求时,修改运行参数中的交叉遗传概率pc或变异算子中的内部参数。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤3(5)中:最优解不满足此次优化计算的要求时,增大运行参数中的种群大小和/或迭代次数。
- 根据权利要求1所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤2中确定的交叉遗传概率pc、变异算子中的内部参数,在步骤3的过程中,根据进化状态自动调整。
- 根据权利要求1或2所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤2中,在问题对象编码获得的染色体上,其基因编码代表问题对象的结构或结构的数值参量。
- 根据权利要求13所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤2中,对问题对象进行编码的方式为:如果d小于等于2,则选择二进制或十进制编码方法;如果d大于2,则选择实数编码方法。
- 根据权利要求13所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,在步骤2中,问题对象的基因编码也可以是算数运算符号或逻辑运算符号。
- 根据权利要求15所述的基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法,其特征在于,基于拉马克获得性遗传原理的全局优化、搜索和机器学习方法应用于结构自由化的“获得性遗传编程”。
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