Self-adaptive Differential Evolution Algorithm And Its Applications

In recent years, computational intelligence develops rapidly. In particular, evolutionary computation as an emerging discipline made a great development. Algorithms which is involved in evolutionary computing are called as evolutionary algorithms, evolutionary algorithms mainly includ evolutionary programming, evolution strategies and genetic programming, genetic algorithm, etc. Evolutionary algorithms which are self-adaptive, self-research, parallelism, etc, were widely applied in many engineering fields.Differential evolution algorithm is an effective algorithm for continuous global optimization on the search space, has been proved to be the effective candidate algorithms to solve the optimize problems. Differential evolution algorithm has many advantages such as concise expression, easy to operate, converge to the ideal area of the search space to find the optimal solution of some problems. As a result, the differential evolution algorithm has been widely used, such as engineering design, chemical engineering and biological engineering, control engineering, power system design and the fuzzy control, neural network design, etc.In this paper, the author makes some preliminary researches on self-adaptive differential evolution algorithms and their applications. Firstly, I analyzed the influence of control parameters on the algorithm of differential evolution algorithm,designed the differential evolution algorithm with self-adaptive parameter control.Secondly,in order to solve combinatorial optimization problems,I designed the set-based self-adaptive discrete differential evolution algorithm; Thirdly,in order to solve the problem of fuzzy clustering,I proposed the self-adaptive differential evolution based fuzzy kernel clustering algorithm; Fourthly,the self-adaptive discrete differential evolution was applied to generating secure elliptic curve;Finally,the self-adaptive discrete differential evolution was applied to generating De Bruijn sequences. In this paper,the main contents and the innovative points can be listed as follows:1.The Individual Adaptive Value Based Self-adaptive Differential evolution Algorithm.As we know, the choice of the scaling factor F and cross probability CR is the key to influence the behavior and performance of differential evolution algorithm(DE), which also directly affects the convergence of the DE algorithm. we should consider the scaling factor F and cross probability CR can dynamically adjust according to the fitness of individual. Most of the current parameters adaptive mechanism in the differential evolution algorithm is using random adjustment strategy, the simulation experiments show that random adjustment strategy is a good choice only in the case of improper parameter Settings. At the same time, the random adjustment of parameters which ignores its validity may result in loss of high quality parameter values. Therefore, in this paper, the self-adaptive differential evolution algorithm retains the produce of high quality individual preferences, adjustment can not only produce high quality of the individual parameters. Based on this idea, this paper proposes the self-adaptive differential evolution algorithm based on individual adaptive value. In this paper, the self-adaptive differential evolution algorithm, retained to produce high quality individual preferences, adjustment can not only produce high quality of the individual parameters. When individuals within the population fitness converge or converges to local optimal solution, let the scaling factor F increased; And when dispersed populations within the individual adaptive value, let the scaling factor F decreased. At the same time, to adapt the individual whose fitness is less than the average value of the individuals, to make such an individual corresponding small F value, in order to make the solution be eliminated; Instead, for the individual whose fitness is more than the average fitness of the individuals, or close to the average fitness of the individual, we correspond to the bigger F value in order to ensure the diversity of population. As a result, the self-adaptive scaling factor can provide the best F value relative to each solution. For crossing probability, according to comparing the fitness value of the individual with the average fitness of contemporary individuals. If contemporary individual fitness value is greater than the average individual fitness, we keep the contemporary CR, otherwise, a random number is generated by gaussian random distribution as CR values.From the simulation results, the proposed self-adaptive differential algorithm gets better results in the multiple functions. Individual function gets the same result with the real optimal solution, which means that we really find the best solution. In conclusion, the proposed algorithm has stronger competitiveness, whose results better than or similar to the optimal solution of iterative computation comparing four algorithms in the text.2. A set-based self-adaptive discrete differential evolution algorithm. Differential evolution algorithm is an effective algorithm for continuous global optimization on the search space, it has been proved to be effective to solve the problem of real value to optimize the candidate algorithms. Expression of differential evolution algorithm is concise, easy to operation, it can converge to the expectations of the search space area, and find the optimal solution of some problems. However, the standard differential evolution algorithm is limited to solve the problem of continuous decision variables. So, it is very limited when it is applied to combinatorial optimization problems. Traveling salesman problem is regarded as the classic discrete optimization problems. At the same time, the differential evolution algorithm has been proved to be a powerful evolutionary algorithm, but its variation process contains a series of arithmetic operations are in continuous space. In recent years, researchers began to use differential evolution algorithm to solve combinatorial optimization problem. Many related research mostly focus on improved differential evolution algorithm to solve combinatorial optimization problems based on permutation. To applying self-adaptive differential evolution algorithm to solve combinatorial optimization problems, this paper proposes the set-based self-adaptive discrete differential evolution algorithm (SBSaDDE). In order to make the algorithm can depict discrete search space of the traveling salesman problem, the candidate solution vectors and arithmetic operator is redefined. Through numerical experiments, this method was proved to be effective on the quality and outlook. By comparing the SBSaDDE with the state-of the-art discrete differential evolution algorithm (DDE), discrete differential evolution algorithm with minimum positioning mutation strategy (DDE-SVP). Parameters of these discrete differential evolution algorithms are set in accordance with the parameters in the original. The simulation results show that:my proposed algorithm is better than DDE and DDE-SVP no matter in the average solution and the optimal solution.3.The self-adaptive differential evolution algorithm based fuzzy kernel clustering algorithm.Fuzzy clustering algorithm is based on the number of data points for clustering to classify membership degree matrix. The fuzzy c-means clustering is to use membership to determine each data points belong to a clustering. The standard fuzzy c-means clustering algorithm is poorer for noise robustness, classification result is not very satisfactory. Therefore, it can be mapped to a high dimensional feature space to carry out the fuzzy c-means clustering by introducing Kernel function, which makes the low dimensional space with nonlinear to transform linear inseparable input mode space in the high dimensional feature space, namely Kernel fuzzy clustering algorithm (Kernel FCM, KFCM).Kernel fuzzy clustering algorithm has good robustness for noise interference. But,FCM algorithm and KFCM algorithm are based on the objective function to measure for clustering, and the best clustering results correspond to the objective function extreme value point, because there are many local minimum points, the objective function and the algorithm of each step of iteration is along the direction of objective function decreases, if initialization fall into a local minimum point near, will cause algorithm converge to local minimum, affect the segmentation result. Differential evolution algorithm is a search for the optimal solution by simulating the natural evolution process of the algorithm, the main characteristic is robust, suitable for parallel processing and global searching ability. In this paper, Self-adaptive differential evolution algorithm based Kernel fuzzy clustering algorithm (SaDEBKFCM), in order to get the optimal clustering center by using the value and the membership degree matrix, so as to enhance the global optimization ability of FCM and KFCM algorithm.4.The study of generating secure elliptic curves based on the self-adaptive discrete differential evolution.In recent years,with the advent of cloud computing and quantum computer, internet of things such as the rapid development of new technology and new applications, for the application of cloud computing security, mobile security, especially in the mobile terminal security demand growth has become a new luminescent spot industry.Elliptic curve cryptography system can be well applied to these security applications.For differential evolution algorithm was applied to generate Koblitz secure elliptic curve, this paper proposes a set-based self-adaptive discrete differential evolution algorithm generating secure Koblitz elliptic curve, the security base domain range, the scale and the efficiency of the curves are all more better than the related parameters released by the national institute of standards and technology (NIST).In this paper, the maximum base of the safe elliptic curve searching by the proposed algorithm is 1913 bits, far more than the base released by the NIST which is only 571 bits. This is a better protection effect by the existing attack. At the same time, there are 19 (for a= 0, b= l,there are 9 curves:233,571,1913, etc.; for a= 1, b= 1,there are 10 curves:163,283,701, etc.)elliptic curves searching by my proposed method for the elliptic curve base fields which are more than 163 bits, they can completely cover the five secure elliptic curve recommended by the NIST.5.The study of generating De Bruijn sequences based on self-adaptive discrete differential evolution.Abinary de Bruijn sequence of order n is a cyclic sequence of period 2n,in which each n-bit pattern appears exactly once. De Bruijn sequences is stable, that is to say,the same number of 1s and 0s,and have good randomness. These sequences are commonly used in random number generation and symmetric key cryptography particularly in stream cipher design,mainly due to their good statistical properties.Constructing de Bruijn sequences is of interest and well studied in the literature. In this paper,â…  proposed a new randomized construction method based on self-adaptive discrete differential evolution. The method models de Bruijn sequences as a special type of traveling salesman tours (TSP) and tries to find optimal solutions.In summary,based on the analysis of the standard differential evolution algorithm and the existing self-adaptive differential evolution algorithm,my research is mainly focused on the self-adaptive differential evolution algorithm based on individual fitness,the set-based self-adaptive discrete differential evolution algorithm,the fuzzy kernel clustering algorithm based on self-adaptive differential evolution algorithm,the study of generating secure elliptic curves based on the self-adaptive discrete differential evolution,the study of generating De Bruijn sequences based on self-adaptive discrete differential evolution,etc. In this paper,I proved the effectiveness of the algorithms through the method of experiments.