Towards Improving Self-adaptive Differential Evolution for Numerical Optimization: A Progress Note

Differential evolution improved with self-adaptive control parameters based on simulated annealing

Differential Evolution (DE) is a very simple but powerful Evolutionary Algorithm (EA) for real-world applications. There are two aspects affecting the overall optimization performance significantly, one is parameter control scheme and the other is trial vector generation strategy. As all the control parameters are employed in generating trial vectors, from this perspective of view, the trial vector generation strategy dominates the overall optimization performance. Therefore, trial vector generation strategies are often designed first, and then the corresponding parameter control schemes are well-tuned thereafter. Both of them constitute the main body of a new DE variant. Here in the paper, a novel DE variant with a new designed trial vector generation strategy as well as novel parameter control scheme is proposed to tackle freight trains scheduling problem. By incorporating both a time-stamp mechanism of the external archive and a novel parameter control scheme, the new algorithm can secure better optimization performance not only on man-made benchmarks but also on real-world applications. Both the man-made benchmarks from Congress on Evolutionary Computation (CEC) test suite and the real-world freight train scheduling problem are employed in the validation of the new DE variant. The experiment results show that it is competitive with other state-of-the-art DE techniques for these optimization problems.

Differential evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

Differential evolution with dynamic combination based mutation operator and two-level parameter adaptation strategy

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

Differential Evolution (DE) is a widely used successful evolutionary algorithm (EA) based on a population of individuals, which is especially well suited to solve problems that have non-linear, multimodal cost functions. However, for a given population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitness of the population. This paper presents a novel extension of DE called Randomized and Rank-based Differential Evolution (R2DE) and its self-adaptive version SAR2DE to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the population fitness. In extensive experiments conducted with a wide range of complexity settings, we show that the proposed heuristics lead to an overall improvement in robustness and speed of convergence compared to several global optimization techniques, including DE, Opposition based Differential Evolution (ODE), DE with Random Scale Factor (DERSF) and the self-adaptive Cauchy distribution based DE (NSDE).

Differential Evolution (DE) algorithm generates a population of individuals by encoding with a floating point vector, and it is a simple and effective population-based stochastic optimization algorithm for global optimization of continuous space. Because of its excellent performance, DE variants can be applied in a wide range of applications in science and engineering. However, the performance of DE is sensitive to the choice of trial vector generation strategy and the associated control parameters. Therefore, it is necessary to choose appropriate mutation strategy and control parameters when tackling optimization applications. In this paper, an adaptive update mechanism is proposed to update control parameters F and Cr . The experimental results are verified on the CEC 2013 test suite which contains 28 benchmark functions for the evaluation of single objective real parameter optimization. The proposed algorithm is compared with jDE, iwPSO and ccPSO, and experiment results show its good performance.

Differential Evolution with exponential crossover can be also competitive on numerical optimization

Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.

Differential evolution (DE) is a simple yet powerful smart computing technique for numerical optimization. However, the performance of DE significantly relies on its parameters (scale factor F and crossover rate CR) of trial vector generating strategy. To address this issue, we propose a new DE variant by introducing a new parameter self-adaptation method into DE, called ADEDE. In ADEDE, a parameter population is established for the solution population, which is also updated from generation to generation based on the differential evolution under the basic principle that the good parameter individuals will go into the next generation at a high probability, while the bad parameter individuals will be updated by learning from the good parameter individuals at a large probability. To validate the efficiency of the proposed parameter self-adaptation method, the comparison experiments are tested on 22 benchmark functions. The experimental results show that the performance of classical DE can be significantly improved by our parameter self-adaptation method, and our method is better than or at least comparable to some other parameter control techniques.

Enhancing the search ability of differential evolution through orthogonal crossover

Differential evolution with orthogonal array‐based initialization and a novel selection strategy

Identification of homogeneous regions in a satellite image is essentially the clustering of pixels in intensity space. Importantly remote sensing image like satellite images contain varieties of land cover types. Some of the covers are significantly large areas whereas some are relatively smaller regions. Therefore, automatically detecting such wide varying areas is a challenging task. Hence, this fact motivated us to propose an improved clustering technique viz. Ensemble based Differential Evolution for Fuzzy Clustering (EDEFC). For this purpose, very recently developed three variants of differential evolution (DE) are used in order to perform the clustering with different set of solutions. As a result, better clustering solution yields from the ensemble of DEs by exhaustive exploration of search space. The proposed EDEFC technique is applied on two numeric remote sensing datasets and Indian Remote Sensing (IRS) satellite image of Kolkata. The results of the EDEFC are shown quantitatively and visually by comparing with eight other clustering techniques. Moreover, the statistical significance test has also been performed in order to judge the superiority of EDEFC.

Differential evolution (DE), as a class of biologically inspired and meta-heuristic techniques, has attained increasing popularity in solving many real world optimization problems. However, DE is not always successful. It can easily get stuck in a local optimum or an undesired stagnation condition. This paper proposes a new DE algorithm Differential Evolution with Alopex-Based Local Search (DEALS), for enhancing DE performance. Alopex uses local correlations between changes in individual parameters and changes in function values to estimate the gradient of the landscape. It also contains the idea of simulated annealing that uses temperature to control the probability of move directions during the search process. The results from experiments demonstrate that the use of Alopex as local search in DE brings substantial performance improvement over the standard DE algorithm. The proposed DEALS algorithm has also been shown to be strongly competitive (best rank) against several other DE variants with local search.

The differential evolution (DE) algorithm relies mainly on mutation strategy and control parameters' selection. To take full advantage of top elite individuals in terms of fitness and success rates, a new mutation operator is proposed. The control parameters such as scale factor and crossover rate are tuned based on their success rates recorded over past evolutionary stages. The proposed DE variant, MIDE, performs the evolution in a piecewise manner, i.e., after every predefined evolutionary stages, MIDE adjusts its settings to enrich its diversity skills. The performance of the MIDE is validated on two different sets of benchmarks: CEC 2014 and CEC 2017 (special sessions & competitions on real-parameter single objective optimization) using different performance measures. In the end, MIDE is also applied to solve constrained engineering problems. The efficiency and effectiveness of the MIDE are further confirmed by a set of experiments.