Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation. <s> BIB001 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization. <s> BIB002 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> We describe an efficient technique for adapting control parameter settings associated with differential evolution (DE). The DE algorithm has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters, which are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE. We present an algorithm-a new version of the DE algorithm-for obtaining self-adaptive control parameter settings that show good performance on numerical benchmark problems. The results show that our algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained <s> BIB003 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Differential evolution (DE) is a simple evolutionary algorithm that has shown superior performance in the global continuous optimization. It mainly utilizes the differential information to guide its further search. But the differential information also results in instability of performance. Particle swarm optimization (PSO) has been developing rapidly and has been applied widely since it is introduced, as it can converge quickly. But PSO easily got stuck in local optima because it easily loses the diversity of swarm. This paper proposes a combination of DE and PSO (termed DEPSO) that makes up their disadvantages. DEPSO combines the differential information obtained by DE with the memory information extracted by PSO to create the promising solutions. Finally, DEPSO is tested to solve several benchmark optimization problems. The experimental results show the effectiveness of DEPSO algorithm for the multimodal function, and also verify that DEPSO can perform better than other algorithms (DE, CPSO) in solving the benchmark problems. <s> BIB004 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Differential evolution is arguably one of the hottest topics in today's computational intelligence research. This book seeks to present a comprehensive study of the state of the art in this technology and also directions for future research. The fourteen chapters of this book have been written by leading experts in the area. The first seven chapters focus on algorithm design, while the last seven describe real-world applications. Chapter 1 introduces the basic differential evolution (DE) algorithm and presents a broad overview of the field. Chapter 2 presents a new, rotationally invariant DE algorithm. The role of self-adaptive control parameters in DE is investigated in Chapter 3. Chapters 4 and 5 address constrained optimization; the former develops suitable stopping conditions for the DE run, and the latter presents an improved DE algorithm for problems with very small feasible regions. A novel DE algorithm, based on the concept of "opposite" points, is the topic of Chapter 6. Chapter 7 provides a survey of multi-objective differential evolution algorithms. A review of the major application areas of differential evolution is presented in Chapter 8. Chapter 9 discusses the application of differential evolution in two important areas of applied electromagnetics. Chapters 10 and 11 focus on applications of hybrid DE algorithms to problems in power system optimization. Chapter 12 applies the DE algorithm to computer chess. The use of DE to solve a problem in bioprocess engineering is discussed in Chapter 13. Chapter 14 describes the application of hybrid differential evolution to a problem in control engineering. <s> BIB005 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Differential evolution (DE) has emerged as one of the fast, robust, and efficient global search heuristics of current interest. This paper describes an application of DE to the automatic clustering of large unlabeled data sets. In contrast to most of the existing clustering techniques, the proposed algorithm requires no prior knowledge of the data to be classified. Rather, it determines the optimal number of partitions of the data "on the run." Superiority of the new method is demonstrated by comparing it with two recently developed partitional clustering techniques and one popular hierarchical clustering algorithm. The partitional clustering algorithms are based on two powerful well-known optimization algorithms, namely the genetic algorithm and the particle swarm optimization. An interesting real-world application of the proposed method to automatic segmentation of images is also reported. <s> BIB006 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Users of mass rapid transit are often required to make transfers between different train lines to reach their destinations. Timetable synchronization minimizes delays during such transfers. This paper formulates a novel measure for timetable synchronization by means of a total passenger dissatisfaction index (TPDI); and the impact of such synchronization on the original unsynchronized timetable is accounted using a total deviation index (TDV) that assigns penalties when deviations from the original timetable are incurred. Pareto fronts displaying the relationship between TPDI and TDV are generated using the state-of-the-art nondominated sorting genetic algorithm 2 (NSGA 2). To further improve NSGA 2, three schemes-the use of a variant of the NSGA2 with differential evolution, a process we termed "seeding," and finally a hybrid combination with local search techniques like heuristic hill climbing, tabu search, and simulated annealing - are proposed. Simulation results demonstrate that the "seeded" NSGA2-DE combined with the hill climbing heuristic produce the best results for the application. Solutions from the Pareto fronts are chosen for implementation to describe the different operating regions. A discussion section details the advantages and drawbacks of the proposed schemes. <s> BIB007 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> This study presents an adaptive neural fuzzy network (ANFN) controller based on a modified differential evolution (MODE) for solving control problems. The proposed ANFN controller adopts a functional link neural network as the consequent part of the fuzzy rules. Thus, the consequent part of the ANFN controller is a nonlinear combination of input variables. The proposed MODE learning algorithm adopts an evolutionary learning method to optimize the controller parameters. For design optimization, a new criterion is introduced. A hardware-in-the loop control technique is developed and applied to the designed ANFN controller using the MODE learning algorithm. The proposed ANFN controller with the MODE learning algorithm (ANFN-MODE) is used in two practical applications-the planetary-train-type inverted pendulum system and the magnetic levitation system. The experiment is developed in a real-time visual simulation environment. Experimental results of this study have demonstrated the robustness and effectiveness of the proposed ANFN-MODE controller. <s> BIB008 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants. <s> BIB009 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> A. Classical Differential Evolution <s> Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE. <s> BIB010
The DE proposed by Storn and Price BIB001 , BIB002 is a formidable PO, which has been widely applied in practice BIB002 BIB005 BIB010 BIB006 BIB007 BIB008 . It was established on the framework of GAs and inspired by the Nelder-Mead simplex method BIB002 . It has three operatorsmutation, crossover, and selection-which are similar to GAs. However, the mutation in DE is a distinct innovation. It is based on the difference of different individuals, borrowing ideas from the Nelder-Mead simplex method. A general notation for DE is DE/x/y/z, where x specifies the base vector to be mutated, y is the number of difference vectors used, and z denotes the crossover scheme BIB002 . The most classical DE variant is DE/rand/1/bin. In this variant, for the mutation of the ith individual in the DE population{x i |i = 1, 2, . . . , PS}, three different individuals x r 1 , x r 2 , and x r 3 with r1 = r2 = r3 = i will be randomly (rand) chosen from the population to generate a new vector. The new vector can be expressed as follows: indiv.diff . (1) where F is the so-called scaling factor, which is a positive constant. A general setting for this factor is F ∈ [0, 2]. However, Storn and Price suggest F ∈ [0.5, 1] as such a setting may result in good optimization effectiveness BIB001 . In addition, there are many advanced DE variants, which are based on the dynamic tuning of this parameter (e.g., BIB003 and BIB009 , see also the survey BIB010 on DE for more introduction). After mutation, a binominal (bin) crossover operates on the vector z i and the target vector x i to generate the final vector u i in the following way: where , and u i,d are the dth dimensional components of the vectors x i , z i , and u i , respectively; CR is the predefined crossover probability, which is usually set to a fixed value in (0,1) or changes dynamically within (0,1); rn i is a number that is randomly selected from the index set {1, 2, . . . , D} and used to ensure that the trial vector u i is different from the original solution x i . Finally, u i will be compared with x i , and the better one will be selected to be a member of the DE population for the next generation. This replacement scheme is de facto a one-to-one tournament selection. Another typical DE variant is DE/best/2/bin BIB001 . It shares much similarity with DE/rand/1/bin except for the mutation strategy. The DE/best/2 mutation can be described as follows: +F · (x r 1 − x r 2 + x r 3 − x r 4 ) individual difference (3) where x best is the best individual in the current population; x r 1 , x r 2 , x r 3 , and x r 4 are four different individuals that are randomly chosen from the current population. The following two DE mutation strategies are also used in the literature. 1) DE/current-to-best/1(DE/target-to-best/1) BIB002 , BIB009  2) DE/mid-to-better/1  , BIB004  Here, x better is an individual that is randomly selected from the DE population, and its fitness is better than (or equal to) that of x i ; and λ is a scale coefficient with 0 < λ < 1, and it is often set to the same value as F . More DE variants can be found in BIB002 and BIB005 .