Advanced Cauchy Mutation for Differential Evolution in Numerical Optimization
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Among many evolutionary algorithms, differential evolution (DE) has received much attention over the last two decades. DE is a simple yet powerful evolutionary algorithm that has been used successfully to optimize various real-world problems. Since it was introduced, many researchers have developed new methods for DE, and one of them makes use of a mutation based on the Cauchy distribution to increase the convergence speed of DE. The method monitors the results of each individual in the selection operator and performs the Cauchy mutation on consecutively failed individuals, which generates mutant vectors by perturbing the best individual with the Cauchy distribution. Therefore, the method can locate the consecutively failed individuals to new positions close to the best individual. Although this approach is interesting, it fails to take into account establishing a balance between exploration and exploitation. In this paper, we propose a sigmoid based parameter control that alters the failure threshold for performing the Cauchy mutation in a time-varying schedule, which can establish a good ratio between exploration and exploitation. Experiments and comparisons have been done with six conventional and six advanced DE variants on a set of 30 benchmark problems, which indicate that the DE variants assisted by the proposed algorithm are highly competitive, especially for multimodal functions.Keywords:
Differential Evolution
Benchmark (surveying)
Sigmoid function
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For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, DE/current/1, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including DE/current/1 and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.
Differential Evolution
Premature convergence
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Differential Evolution
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There are many different operators in evolutionary algorithms.Each operator has been applied successfully in solving some optimization problems,however not efficiently in other problems.A novel improved multi-operator evolutionary algorithm based on communication is proposed.In the algorithm,two subgroups are parallel performed with the different operators:multi-parent crossover operator and Cauchy mutation operator.The individual,together with information,is exchanged while subgroup is reorganized.The new algorithm is tested on 23 benchmark functions.Simulation results have shown that this algorithm can solve all test functions very well and its performance is the same as or even better than the best of pure operator does.
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Differential Evolution(DE) has emerged as a powerful and efficient evolutionary algorithm for solving global optimization problems. It adopts the stochastic searching method to make selection of the parents in the mutation operator, which benefits the search of global optimization value. However, the selection method reveals the convergence in low speed. So for the sake of better convergence performance, in this paper, we propose the Tournament-based mutation operators to accelerate the differential evolution. The proposed algorithm employs the tournament selection for mutation. The process of tournamentbased mutation operators is that the base and differential vectors are replaced by the tournament best vector but other vectors are randomly selected. It is helpful to improve the convergence besides maintain the diversity of DE algorithms. We also integrate the algorithm into jDE to verify the effect on it. Experimental results indicate that our proposed tournamentbased mutation operators are highly competitive to the original DE algorithm and are able to enhance the performance of jDE.
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Differential Evolution
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t-Differential evolution algorithm in solving complex function optimization problems, the problems of convergence rate and precision is not high.At the same time, there is a big difference in the performance of evolutionary algorithms for solving the different types of optimization problems.To solve above two problems, this paper proposes a dynamic multimodal differential evolution algorithm.Firstly, the dynamically population is used to improve the exploration ability of algorithms; In addition, the algorithm uses Four different types of mutation operator to Produce among individuals, choose the best among individuals to enter the next iteration , improved the algorithms's performance of solving different types of optimization problems.Through a variety of BenchMark functions to the algorithm simulation experiment, and comparing and several other classical differential evolution algorithm, show that this algorithm has better optimization performance.
Differential Evolution
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Initialization
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Differential Evolution (DE) has been shown as an effective, efficient and robust evolutionary computing algorithm. The main force to generate promising offspring is the mutation operator. Usually, two randomly selected vectors are used to generate the differential vector, which maintains the large diversity of mutant directions and ensures the possibility to find global optima. However, strong randomness also leads to the ineffective searching and slow convergence speed. A proper degree of certainty in differential vector will help the population evolve efficiently. This paper proposes a novel mutation strategy called Targeted Mutation that takes the determined target vector as the starting point of the differential vector and maintains the randomness of the ending point, which makes a better trade-off between the certainty and randomness in the differential vector. Besides, Targeted Mutation adopts the best vector as the base vector. The extensive experiments of comparison with two popular mutation operators on 20 benchmark functions demonstrate the competitive performance of our proposed targeted mutation scheme. Our method achieves better or equivalent performance over 70% of total benchmarks against the other two methods. 17 out of 20 function results can get further improved when roughly tuning parameters on each function, showing the potential ability to get even better results. In addition, an integrated evaluation scoring scheme is designed to provide a more concrete demonstration of the overall performance of different approaches, and our method gains the highest score.
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Differential Evolution
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Differential Evolution (DE) is well-known as a simple and efficient evolutionary algorithm for global optimization problems. However, the mutation strategies used in DE greatly affect its performance. Although many mutation operators have been proposed in DE, for each operator there are some types of optimization problems that cannot be solved efficiently. In this paper, we propose a novel DE using a mixed mutation strategy (MMSDE), which integrate four different mutation operators, may be able to overcome the shortcomings of a pure strategy. In order to verify the performance of MMSDE, we test it on 8 famous benchmark functions. The simulation results show that MMSDE performs equally well or better than classical DE, modified DE (MoDE) and trigonometric mutation DE (TDE) on all of the test problems.
Differential Evolution
Benchmark (surveying)
Operator (biology)
Adaptive mutation
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