Research And Application Of Differential Evolution Based On Adaptive Population Tuning Scheme

To tackle complex computational problems, researchers have been looking into na-ture for years for inspiration. Optimization is at the heart of many natural processes like Darwinian evolution itself. Through millions of years, every species had to adapt their physical structures to fit to the environments they were in. A keen observation of the underlying relation between optimization and biological evolution led to the development of an important paradigm of computational intelligence-the evolutionary computing techniques for performing very complex search and optimization.Differential Evolution is a reliable and versatile function optimizer. DE, like most popular Evolutionary Algorithms (EAs), is a population-based tool. Over the past decade, the DE algorithm has gained wide-spread popularity among researchers due to its sim-plicity, reliability, high performance and easy implementation. Unlike traditional EAs, DE operates perturbation by adding a weighted moving vector and modifying the values of some randomly selected coordinates. Due to its structure, a DE scheme can be highly explorative in the prophase of the evolution and subsequently become more exploita-tive during the optimization. However, the DE does not guarantee the convergence to the global optimum. It is occasionally trapped into local stagnation or premature convergence resulting in a low optimizing precision or even failure.In this dissertation, firstly, to remedy some of DE’s pitfalls, I propose an adaptive population tuning scheme (APTS) for DE. Secondly, an enhanced adaptive population-handling technique is proposed to solve various types of optimization problems. Thirdly, I study the applications of differential evolution in identification of fractional-order sys-tems, digital IIR filters design and optimum modeling of PEM fuel cells. The main con-tribution of this dissertation are as follows.(1) Adaptive population tuning scheme for differential evolutionAn adaptive population tuning scheme (APTS) for DE is proposed to dynamically adjust the population size. More specifically, an elite-based population-incremental strat- egy is proposed to place several new individuals in appropriate areas to discover new pos-sible solutions. Meanwhile, an inferior-based population-cut strategy is also presented to remove several poor particles according to its ranking method and to reserve a place for a better reproduction. Moreover, both dynamic population strategies are controlled by a status monitor, which is used to keep track of the progress of individuals and improve the sensitivity of the proposed APTS. The experimental studies were carried out on25global numerical optimization problems used in the CEC2005special session on real-parameter optimization. An overall performance comparison between the JADE-APTS variant and other five State-of-the-Art DEs was also carried out. The experimental results illustrated that JADE-APTS achieves a competitive performance in30dimensional problems and exhibits the best performance in100dimensional problems. In addition, the ANOVA results verify that APTS can accelerate the convergence and enhance accuracy.(2) Enhanced differential evolution with entropy-based population adapta-tion and markov chain modelAn enhanced adaptive population-handling technique (CP) is proposed for DE algo-rithm to solve various types of optimization problems. In CPDE, we advocate a stochastic strategy-hopping framework in which the probability of selecting different sub-optimizers to improve the online solution-searching status is completely followed by a Markov chain. One sub-optimizer, called population increasing strategy, adds new individuals into the population to share their up-to-date information when particles are clustered together in a region and trapped into the local basin; the other sub-optimizer, namely population de-creasing strategy, removes redundant particle with its entropy and ranking metrics to save computational load. Extensive experiments have been carried out to compare it with five state-of-the-art DE variants and three other EAs on25commonly used CEC2005con-test test instances. In addition, a scalability study was implemented to show the effect of problem dimension.In the end, runtime complexity analysis and convergence rate com-parison are also validated that CP framework does not impose any serious burden on the time complexity of the existing DE variants.(3) Identification of fractional-order systems via a switching differential evo-lution subject to noise perturbationsA switching differential evolution (SDE) algorithm is employed to identify the or-ders and parameters of incommensurate fractional-order Lorenz, Lii and Chen systems. The main feature of SDE is the switching population utilization strategy which improves the quality of the population and decreases the number of calculations by nonperiodic partial increasing or declining individuals. The results are shown in comparison with five other existing methods. The results obtained by our approach are better than other EAs especially in stochastic environment.(4) Digital IIR filters design using differential evolution with a controllable probabilistic population sizeAn improved differential evolution is proposed for digital ⅡR filter design. The suggested algorithm is a kind of DE variants with a controllable probabilistic (CPDE) population size. It considers the convergence speed and the computational cost simul-taneously by nonperiodic partial increasing or declining individuals according to fitness diversities. Compared with six existing State-of-the-Art algorithms-based digital Ⅱ filter design methods obtained by numerical experiments, CPDE is relatively more promising and competitive. In addition, we discuss as well some important aspects for ⅡR filter design, such as the cost function value, the influence of (noise) perturbations, the conver-gence rate and successful percentage, the parameter measurement, etc. As to the simula-tion result, it shows that the presented algorithm is viable and comparable.(5) Optimum modeling of PEM fuel cells by a hybrid differential evolutionA hybrid differential evolution (HDE) algorithm-based parameter identification ap-proach is proposed in terms of the voltage-current characteristics for the problem of pro-ton exchange membrane (PEM) fuel cell stack modeling. It attempts to utilize an adaptive population tuning scheme, in which the population size can be adjusted dynamically based on the solution-searching status and the desired population distribution. Thus, this active control approach realizes the optimum modeling of the SR-12Modular, the Ballard and the BCS500-W stack. The results indicate that satisfactory identification performance can be achieved by HDE even if the experimental data are corrupted by noise. Simulation results manifest that the proposed HDE reaches both better and more robust results in comparison with three versions of DEs, two versions of EAs, as well as CLPSO.