Fitness Proportionate Random Vector Selection based DE Algorithm (FPRVDE)

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

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.

Orthogonal frequency division multiple access (OFDMA) is a promising technique, which can provide high downlink capacity for the future wireless systems. The total capacity of OFDMA can be maximized by adaptively assigning subchannels to the user with the best gain for that subchannel, with power subsequently distributed by water-filling. In this paper, we propose the use of composite differential evolution (CoDE) algorithm to allocate the subchannels. The CoDE algorithm is population-based where a set of potential solutions evolves to approach a near-optimal solution for the problem under study. CoDE uses three trial vector generation strategies and three control parameter settings. It randomly combines them to generate trial vectors. In CoDE, three trial vectors are generated for each target vector unlike other differential evolution (DE) techniques where only a single trial vector is generated. Then the best one enters the next generation if it is better than its target vector. It is shown that the proposed method obtains higher sum capacities as compared to that obtained by previous works, with comparable computational complexity.

Differential evolution (DE) is a simple and efficient technique for real parameter optimization over continuous spaces. Its success is highly dependent on the choice of correct trial vector generation strategies and control parameters. Choosing appropriate trial vector generation strategies and control parameters for new problems by trial and error method can be computationally costly and inefficient. This paper proposes a hybrid approach, incorporating genetic programming (GP) with DE, where GP generates trial vector generation strategies based on the problem specification and the state of the population using a simple learning method. Trial vector generation strategies are chosen from this pool of strategies generated by GP. The choice of a particular strategy depends on the type of the problem, initialization values and state of evolution. Consequently, the strategies chosen for different run of the same problem are different. However, it allows self-adaptation to be completely problem dependent and as a result for a unknown problem domain the method is expected to perform better than other state-of-the-art self-adaptive evolutionary techniques. In this method, the control parameter F is eliminated and crossover ratio Cr is evolved with the population and population size NP is still fixed empirically. The performance of this method is extensively evaluated using the CEC2005 contest test instances. Experimental results show that, self-adaptive genetically programmed differential evolution (SaGPDE) leads to quick convergence and produce very competitive results.

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.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Regulation-based formulas and improved Differential Evolution(DE) algorithm is used to optimize PID parameters. In order to improve the global search ability and the convergence rate of the common DE algorithm, self-adaptive method is introduced to obtain DE parameters. On the other hand, initial population quality of DE algorithm has important influence on convergence of the algorithm. So the regulation-based formulas are used to guide the production of initial population, which is good to improve the convergence rate and realize obtaining of PID parameters completely adaptive without any personal experience. The simulation is developed on steam temperature system of cycle fluidized bed boiler with serious parameter uncertainties and many disturbance and long-time delay. The results show that the improved DE algorithm has higher optimal speed, small amount of calculation and effective optimization of parameters. The proposed method has better control quality and system robustness.

A self-competitive mutation strategy for Differential Evolution algorithms with applications to Proportional–Integral–Derivative controllers and Automatic Voltage Regulator systems

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Differential Evolution (DE) is a simple and effective stochastic algorithm for optimization problems, and it became much more popular in recent year because of its easy-implementation and excellent performance. Nevertheless, the performance of DE algorithm is greatly affected by the trial vector generation strategy including mutation strategy and parameter control, both of which still exist some weaknesses, e.g. the premature convergence to some local optima of a mutation strategy and the misleading interaction among control parameters. Therefore in this paper, a novel Di-DE algorithm is proposed to tackle these weaknesses. A depth information based external archive was advanced in our novel mutation strategy, which can get a better perception of the landscape of objective in an optimization. Moreover, a novel grouping strategy was also employed in Di-DE and parameters were updated separately so as to avoid the misleading among parameters. Moreover, a cooperative strategy for information interchange was also advanced aiming at improving the efficiency of the exploration behavior. By absorbing these advancements, the novel Di-DE algorithm can secure better performance in comparison with other famous optimization algorithms. The algorithm validation was conducted on CEC2013 and CEC2017 test suites, and the results revealed the competitiveness of our Di-DE algorithm in comparison with those famous optimization algorithms including Particle Swarm Optimization (PSO) variants, QUasi-Affine TRansformation Evolution (QUATRE) variants and Differential Evolution (DE) variants.

In this paper, we study a problem of the control parameter settings in Differential Evolution algorithm and test novel variant of the algorithm called Co- BiDE. Although Differential Evolution with basic setting (i.e. CR = 0:5; F = 0:5) works quite well, it starts to fail on rotated functions. In general, we want to improve the convergence of algorithm primarily on rotated functions. It is done by adapting crossover parameter CR whereas parameter F is fixed to 0.5. There is a recommendation to set CR = 1 for rotated functions. It means that trial vectors are essentially composed from mutant. However, it is not easy task to set the parameters appropriately for solving optimization problem but it is crucial for obtaining good results. Moreover, the quality of points produced in evolution is highly aected by the coordinate system. In CoBiDE, the authors proposed new coordinate system based on the current distribution of points in the population. We test these two approaches by running both algorithms on six pairs of rotated and non-rotated functions from CEC 2013 benchmark set in two levels of dimension space. This experimental study aims to reveal if such algorithm's setting is invariant under a rotation.

Continuous Adaptive Population Reduction (CAPR) for Differential Evolution Optimization.

Differential Evolution with wavelet basis function based parameter control and dimensional interchange for diversity enhancement

Differential Evolution (DE) proved to be one of the most successful evolutionary algorithms for global optimization purposes in continuous problems. The core operator in DE is a mutation which can provide the algorithm with both exploration and exploitation. In this article, a new notation for DE is proposed which has a formula that can be utilized for generating and extracting novel mutations and by applying this new notation, four novel mutations are proposed. More importantly, by combining these novel trial vector generation strategies and four other well-known ones, we proposed Generalized Differential Evolution (GDE) that takes advantage of two mutation pools that have both explorative and exploitative strategies inside them. Results and experimental analysis are performed on CEC2005 benchmarks and the results stated that GDE is surprisingly competitive and significantly improved the performance of this algorithm.