Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> An algorithm that is a combination of the particle swarm and differential evolution algorithms is introduced. The results of testing this on a graduated set of trial problems is given. It is shown that the combined algorithm out performs both of the component algorithms under most conditions, in both absolute and computational load weighted terms. <s> BIB001 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Abstract Evolutionary algorithms are promising candidates for obtaining the global optimum. Hybrid differential evolution is one or the evolutionary algorithms, which has been successfully applied to many real-world nonlinear programming problems. This paper proposes a co-evolutionary hybrid differential evolution to solve mixed-integer nonlinear programming (MINLP) problems. The key ingredients of the algorithm consist of an integer-valued variable evolution and a real-valued variable co-evolution, so that the algorithm can be used to solve MINLP problems or pure integer programming problems. Furthermore, the algorithm combines a local search heuristic (called acceleration) and a widespread search heuristic (called migration) to promote the search for a global optimum. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional MINLP optimization methods <s> BIB002 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The Pareto differential evolution (PDE) algorithm was introduced and showed competitive results. The behavior of PDE, as in many other evolutionary multiobjective optimization (EMO) methods, varies according to the crossover and mutation rates. In this paper, we present a new version of PDE with self-adaptive crossover and mutation. We call the new version self-adaptive Pareto differential evolution (SPDE). The emphasis of this paper is to analyze the dynamics and behavior of SPDE. The experiments also show that the algorithm is very competitive with other EMO algorithms. <s> BIB003 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A hybrid particle swarm with differential evolution operator, termed DEPSO, which provide the bell-shaped mutations with consensus on the population diversity along with the evolution, while keeping the self-organized particle swarm dynamics, is proposed. Then it is applied to a set of benchmark functions, and the experimental results illustrate its efficiency. <s> BIB004 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In this paper, we propose an algorithm of hybrid particle swarm with differential evolution (DE) operator, termed DEPSO, to solve the problem of multimodal image registration. This algorithm combines the robustness of entropy based measures and the search power of the DEPSO which provides the bell-shaped mutations with consensus on the population diversity, while keeps the particle swarm dynamics. The main idea is to find the best transformation that superimposes two multimodal images by maximizing the mutual information value through the DEPSO. We show that this algorithm, besides its simplicity, provides a robust and efficient way to rigidly register multimodal images in various situations. <s> BIB005 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Over the last decade, memetic algorithms (MAs) have relied on the use of a variety of different methods as the local improvement procedure. Some recent studies on the choice of local search method employed have shown that this choice significantly affects the efficiency of problem searches. Given the restricted theoretical knowledge available in this area and the limited progress made on mitigating the effects of incorrect local search method choice, we present strategies for MA control that decide, at runtime, which local method is chosen to locally improve the next chromosome. The use of multiple local methods during a MA search in the spirit of Lamarckian learning is here termed Meta-Lamarckian learning. Two adaptive strategies for Meta-Lamarckian learning are proposed in this paper. Experimental studies with Meta-Lamarckian learning strategies on continuous parametric benchmark problems are also presented. Further, the best strategy proposed is applied to a real-world aerodynamic wing design problem and encouraging results are obtained. It is shown that the proposed approaches aid designers working on complex engineering problems by reducing the probability of employing inappropriate local search methods in a MA, while at the same time, yielding robust and improved design search performance. <s> BIB006 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Evolving artificial neural network is an important issue in both evolutionary computation (EC) and neural networks (NN) fields. In this paper, a hybrid particle swarm optimization (PSO) is proposed by incorporating differential evolution (DE) and chaos into the classic PSO. By combining DE operation with PSO, the exploration and exploitation abilities can be well balanced, and the diversity of swarms can be reasonably maintained. Moreover, by hybridizing chaotic local search (CLS), DE operator and PSO operator, searching behavior can be enriched and the ability to avoid being trapped in local optima can be well enhanced. Then, the proposed hybrid PSO (named CPSODE) is applied to design multi-layer feed-forward neural network. Simulation results and comparisons demonstrate the effectiveness and efficiency of the proposed hybrid PSO. <s> BIB007 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In this paper we propose a new Hybrid Particle Swarm Optimizer model based on particle swarm, with breeding concepts from novel evolutionary algorithms. The hybrid PSO combines traditional velocity and position update rules of RANDIW-PSO and ideas from Self Adaptive Pareto Differential Evolution Algorithm (SPDE). The hybrid model is tested and compared with some high quality PSO models like the RANDIW-PSO and TVIW-PSO. The results indicate two good prospects of our proposed hybrid PSO model: potential to achieve faster convergence as well as potential to find a better solution. The hybrid PSO model, with the abovementioned features, is then efficiently utilized to coordinate robot ants in order to help them to probe as much camera coverage area of some planetary surface or working field as possible with minimum common area coverage. <s> BIB008 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The combination of evolutionary algorithms with local search was named "memetic algorithms" (MAs) (Moscato, 1989). These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. Additionally, MAs are inspired by Richard Dawkin's concept of a meme, which represents a unit of cultural evolution that can exhibit local refinement (Dawkins, 1976). In the case of MA's, "memes" refer to the strategies (e.g., local refinement, perturbation, or constructive methods, etc.) that are employed to improve individuals. In this paper, we review some works on the application of MAs to well-known combinatorial optimization problems, and place them in a framework defined by a general syntactic model. This model provides us with a classification scheme based on a computable index D, which facilitates algorithmic comparisons and suggests areas for future research. Also, by having an abstract model for this class of metaheuristics, it is possible to explore their design space and better understand their behavior from a theoretical standpoint. We illustrate the theoretical and practical relevance of this model and taxonomy for MAs in the context of a discussion of important design issues that must be addressed to produce effective and efficient MAs. <s> BIB009 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper presents the evolution of combinational logic circuits by a new hybrid algorithm known as the Differential Evolution Particle Swarm Optimization (DEPSO), formulated from the concepts of a modified particle swarm and differential evolution. The particle swarm in the hybrid algorithm is represented by a discrete 3-integer approach. A hybrid multi-objective fitness function is coined to achieve two goals for the evolution of circuits. The first goal is to evolve combinational logic circuits with 100% functionality, called the feasible circuits. The second goal is to minimize the number of logic gates needed to realize the feasible circuits. In addition, the paper presents modifications to enhance performance and robustness of particle swarm and evolutionary techniques for discrete optimization problems. Comparison of the performance of the hybrid algorithm to the conventional Karnaugh map and evolvable hardware techniques such as genetic algorithm, modified particle swarm, and differential evolution are presented on a number of case studies. Results show that feasible circuits are always achieved by the DEPSO algorithm unlike with other algorithms and the percentage of best solutions (minimal logic gates) is higher. <s> BIB010 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The customer demand and replenishment lead-time can be considered as grey fuzzy variables combining grey and fuzzy twofold uncertain factors. The multistage inventory model under periodical review policy was presented based on the chance measure of grey fuzzy variable. The inventory would be replenished to certain level when the inventory level drops to the re-order point. The optimal re-order point and the inventory replenishment level of every stage can be obtained by minimizing the multistage inventory cost. The grey fuzzy simulation technology can generate input-output data for the uncertain functions. The neural network trained from the input-output data can approximate the uncertain functions. The particle swarm optimization (PSO) algorithm was improved with the differential evolution algorithm. The improved PSO algorithm was combined with neural network to optimize the inventory model. A numerical example was given to illustrate the feasibility of the model and algorithm. <s> BIB011 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Adaptation of parameters and operators represents one of the recent most important and promising areas of research in evolutionary computations; it is a form of designing self-configuring algorithms that acclimatize to suit the problem in hand. Here, our interests are on a recent breed of hybrid evolutionary algorithms typically known as adaptive memetic algorithms (MAs). One unique feature of adaptive MAs is the choice of local search methods or memes and recent studies have shown that this choice significantly affects the performances of problem searches. In this paper, we present a classification of memes adaptation in adaptive MAs on the basis of the mechanism used and the level of historical knowledge on the memes employed. Then the asymptotic convergence properties of the adaptive MAs considered are analyzed according to the classification. Subsequently, empirical studies on representatives of adaptive MAs for different type-level meme adaptations using continuous benchmark problems indicate that global-level adaptive MAs exhibit better search performances. Finally we conclude with some promising research directions in the area. <s> BIB012 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In the last decade, recurrent neural networks (RNNs) have attracted more efforts in inferring genetic regulatory networks (GRNs), using time series gene expression data from microarray experiments. This is critically important for revealing fundamental cellular processes, investigating gene functions, and understanding their relations. However, RNNs are well known for training difficulty. Traditional gradient descent-based methods are easily stuck in local minima and the computation of the derivatives is also not always possible. Here, the performance of three evolutionary-swarm computation technology-based methods, known as differential evolution (DE), particle swarm optimization (PSO), and the hybrid of DE and PSO (DEPSO), in training RNNs is investigated. Furthermore, the gene networks are reconstructed via the identification of the gene interactions, which are explained through corresponding connection weight matrices. The experimental results on two data sets studied in this paper demonstrate that the DEPSO algorithm performs better in RNN training. Also, the RNN-based model can provide meaningful insight in capturing the nonlinear dynamics of genetic networks and revealing genetic regulatory interactions. <s> BIB013 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <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> BIB014 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A new, almost parameter-free optimization algorithm is developed in this paper as a hybrid of the barebones particle swarm optimizer (PSO) and differential evolution (DE). The DE is used to mutate, for each particle, the attractor associated with that particle, defined as a weighted average of its personal and neighborhood best positions. Results of this algorithm are compared to that of the barebones PSO, Von Neumann PSO, a DE PSO, and DE/rand/1/bin. These results show that the new algorithm provides excellent results with the added advantage that no parameter tuning is needed <s> BIB015 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A new hybrid algorithm based on particle swarm optimization (PSO), evolutionary algorithm (EA), and differential evolution (DE) is presented for training a recurrent neural network (RNN) for multiple-input multiple-output (MIMO) channel prediction. The hybrid algorithm is shown to be superior in performance to PSO and differential evolution PSO (DEPSO) for different channel environments. The received signal-to-noise ratio is derived for un-coded and beam-forming MIMO systems to see how the RNN error affects the performance. This error is shown to deteriorate the accuracy of the weak singular modes, making beam-forming more desirable. Bit error rate simulations are performed to validate these results. <s> BIB016 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The non-uniform AC current distribution among the multi-layer conductors in a high-temperature superconducting (HTS) cable reduces the current capacity and increases the AC loss. In this paper, Particle swarm optimization coupled with differential evolution operator (DEPSO) has been applied in structural optimization of HTS cables. While the existence of fluctuation in design variables or operation conditions has a great influence on the cable quality, in order to eliminate the effects of parameter perturbations in design and improve the design efficiency, a robust design method based on design for six sigma (DFSS) is applied in this paper. The optimization solutions show that the proposed optimization procedure can not only achieve a uniform current distribution, but also improve significantly the reliability and robustness of the HTS cable quality. <s> BIB017 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In this paper, swarm and evolutionary algorithms have been applied for the design of digital filters. Particle swarm optimization (PSO) and differential evolution particle swarm optimization (DEPSO) have been used here for the design of linear phase finite impulse response (FIR) filters. Two different fitness functions have been studied and experimented, each having its own significance. The first study considers a fitness function based on the passband and stopband ripple, while the second study considers a fitness function based on the mean squared error between the actual and the ideal filter response. DEPSO seems to be promising tool for FIR filter design especially in a dynamic environment where filter coefficients have to be adapted and fast convergence is of importance. <s> BIB018 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> An improved particle swarm optimizer based on differential evolution theory is proposed. This algorithm introduces differential mutation operator into the basic particle swarm optimizer in order to solve the premature convergence problem. And this new algorithm was used to training weights and thresholds of feedforward neural network, simulation results show that this approach is effective and has an excellent convergence performance. <s> BIB019 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper proposes the super-fit memetic differential evolution (SFMDE). This algorithm employs a differential evolution (DE) framework hybridized with three meta-heuristics, each having different roles and features. Particle Swarm Optimization assists the DE in the beginning of the optimization process by helping to generate a super-fit individual. The two other meta-heuristics are local searchers adaptively coordinated by means of an index measuring quality of the super-fit individual with respect to the rest of the population. The choice of the local searcher and its application is then executed by means of a probabilistic scheme which makes use of the generalized beta distribution. These two local searchers are the Nelder mead algorithm and the Rosenbrock Algorithm. The SFMDE has been tested on two engineering problems; the first application is the optimal control drive design for a direct current (DC) motor, the second is the design of a digital filter for image processing purposes. Numerical results show that the SFMDE is a flexible and promising approach which has a high performance standard in terms of both final solutions detected and convergence speed. <s> BIB020 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper presents a novel fuzzy modeling strategy based on the hybrid of particle swarm optimization (PSO) and differential evolution (DE), and the proposed hybrid algorithm is referred to as PSODE. PSODE is based on a two-population scheme, in which the individuals in one population is enhanced by PSO and the individuals in the other population is evolved by DE. The individuals both in PSO and DE are co-evolved during the algorithm execution by employing an information sharing mechanisms. To further improve the proposed PSODE algorithm a nonlinear inertia weight approach and a mutation mechanism are presented respectively. In the simulation part, the PSODE is used to automatic design of fuzzy identifier for a nonlinear dynamic system. The performance of the suggested method is compared to PSO, DE and some other methods in the fuzzy identifier design to demonstrate its superiority. <s> BIB021 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper presents a simple, hybrid two phase global optimization algorithm called DE-PSO for solving global optimization problems. DE-PSO consists of alternating phases of differential evolution (DE) and Particle Swarm Optimization (PSO). The algorithm is designed so as to preserve the strengths of both the algorithms. Empirical results show that the proposed DE-PSO is quite competent for solving the considered test functions as well as real life problems. <s> BIB022 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The hybridization and composition of different Evolutionary Algorithms to improve the quality of the solutions and to accelerate execution is a common research practice. In this paper we propose a hybrid approach that combines differential evolution mutation operators in an attempt to balance their exploration and exploitation capabilities. Additionally, a self-balancing hybrid mutation operator is presented, which favors the exploration of the search space during the first phase of the optimization, while later opts for the exploitation to aid convergence to the optimum. Extensive experimental results indicate that the proposed approaches effectively enhance DEpsilas ability to accurately locate solutions in the search space. <s> BIB023 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The back-analysis of mechanics parameters needs iterative forward calculating, resulting in low efficiency; meanwhile the Particle Swarm Optimization (PSO) algorithm and other optimization algorithms are exposed to local optimum possibilities. In this paper, DEPSO-ParallelFEM, a system integrated of an algorithm of hybrid particle swarm with Differential Evolution (DE) operator, termed DEPSO, and parallel Finite Element Method (FEM), is proposed to solve these problems. DEPSO guarantees the particle to escape from local minima by enhancing particle’s diversity through the combination of PSO operator and DE operator; and parallel FEM is applied to improve the computing speed and precision by adopting the techniques of Cluster of Workstation (COW), MPI, Domain Decomposition Method (DDM), and Object-Oriented Programming (OOP) and so on. A computational example proves that this system is of excellent parameter exploration capability and high speed; thus it is of great academic value and significant applicable value. <s> BIB024 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Particle swarm optimization (PSO) is population-based heuristic searching algorithm. PSO has excellent ability of global optimization. However, there are some shortcomings of prematurity, low convergence accuracy and speed, similarly to other evolutionary algorithms (EA). To improve its performance, a hybrid particle swarm optimization is proposed in the paper. Firstly, the average position and velocity of particles are incorporated into basic PSO for concerning with the effect of the evolution of the whole swarm. Then a differential evolution (DE) computation, which introduces an extra population for prior crossover, is hybridized with the improved PSO to form a novel optimization algorithm, PSOPDE. The role of prior crossover is to appropriately diversify the population and increase the probability of reaching better solutions. DE component takes into account the stochastic differential variation, and enhances the exploitation in the neighborhoods of current solutions. PSOPDE is implemented on five typical benchmark functions, and compared with six other algorithms. The results indicate that PSOPDE behaves better, and greatly improve the searching efficiency and quality. <s> BIB025 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> in the present study we propose a new hybrid version of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. In the proposed algorithm named as Hybrid Differential Evolution (HDE) a ‘switchover constant’ called α is defined. HDE starts as the basic DE algorithm which switches over to PSO when α is activated. The constant α on the other hand is activated at a point where the DE procedure usually slows down which is usually in the proximity of global optimal i.e. to say when the search domain is contracted around the global optimal. Experimenting with a test bed of 12 benchmark functions, we show the promising nature of the proposed HDE algorithm. <s> BIB026 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper introduces a new vector evaluated multi-objective optimization algorithm. The vector evaluated differential evolution particle swarm optimization (VEDEPSO) algorithm is a hybridization of the classical vector evaluated particle swarm optimization (VEPSO) and vector evaluated differential evolution (VEDE) algorithms of Parsopoulos et. al. [9], [10]. Comparisons of VEDEPSO with respect to VEPSO and VEDE on a well known multi-objective benchmark problem set indicated that significant performance improvements can be attributed to the VEDEPSO algorithm. <s> BIB027 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> To solve the multi-objective problems, a novel hybrid particle swarm optimization algorithm is proposed(called HPSODE). The new algorithm includes three major improvement: (I)Population initialization is constructed by statistical method Uniform Design , (II)Regeneration method has two phases: the first phase is particles updated by adaptive PSO model with constriction factor *** , the second phase is Differential Evolution operator with archive, (III)A new accept rule called Distance/volume fitness is designed to update archive. Experiment on ZDTx and DTLZx problems by jMetal 2.1, the results show that the new hybrid algorithm significant outperforms OMOPSO, SMPSO in terms of additive Epsilon, HyperVolume, Genetic Distance, Inverted Genetic Distance. <s> BIB028 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A chaotic co-evolutionary algorithm based on differential evolution and particle swarm optimization (CCDEPSO) is proposed. CCDEPSO is a two-population co-evolutionary algorithm, in which the individuals of one population are evolved according to differential evolution algorithm (DE) and the other individuals are evolved according to particle swarm optimization algorithm (PSO). In order to realize co-evolving of the two sub-populations, an information sharing scheme by sharing the fitness value and the corresponding position value of the two sub-populations is introduced. Furthermore, in order to improve the searching speed and avoid the results trapping in local optima prematurely, chaotic initialization and chaotic perturbation based on Tent map are introduced in CCDEPSO. The comparative testing experiments are performed by means of CCDEPSO, DE, CPSO and PSO algorithms on six benchmark functions. Experimental results demonstrate that the global optimization ability of CCDEPSO is better than other algorithms above mentioned. <s> BIB029 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A hybrid evolutionary algorithm which synergistically exploits differential evolution, genetic algorithms and particle swarm optimization, has been developed and applied to spacecraft trajectory optimization. The cooperative procedure runs the three basic algorithms in parallel, while letting the best individuals migrate to the other populations at prescribed intervals. Rendezvous problems and round-trip Earth–Mars missions have been considered. The results show that the hybrid algorithm has better performance compared to the basic algorithms that are employed. In particular, for the rendezvous problem, a 100% efficiency can be obtained both by differential evolution and the genetic algorithm only when particular strategies and parameter settings are adopted. On the other hand, the hybrid algorithm always attains the global optimum, even though nonoptimal strategies and parameter settings are adopted. Also the number of function evaluations, which must be performed to attain the optimum, is reduced when the hybrid algorithm is used. In the case of Earth–Mars missions, the hybrid algorithm is successfully employed to determine mission opportunities in a large search space. <s> BIB030 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <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> BIB031 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Reactive power optimization is a mixed integer nonlinear programming problem where metaheuristics techniques have proven suitable for providing optimal solutions. In this paper, swarm and evolutionary algorithm have been applied for reactive power optimization. The objective of this nonlinear optimization is minimization of system losses and improvement of voltage profiles in a power system. A hybrid differential evolution particle swarm optimization algorithm is presented to obtain the global optimum. The proposed algorithm is implemented on the IEEE 14-bus system. To validate the effectiveness of the algorithm, the simulation results are compared with other optimization algorithms'. It is shown that the approach developed is feasible and efficient. <s> BIB032 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A new hybrid PSO-EA-DEPSO algorithm based on particle swarm optimization (PSO), evolutionary algorithm (EA), and differential evolution (DE) is presented for training a recurrent neural network (RNN) for multiple-input multiple-output (MIMO) channel prediction. This algorithm is shown to outperform RNN predictors trained off-line by PSO, EA, and DEPSO as well as a linear predictor trained by the Levinson-Durbin algorithm. To explore the effects of channel prediction error at the receiver, new expressions for the received SNR, array gain, and average probability of error are derived and analyzed. These expressions differ from previous results which assume the prediction error is Gaussian and/or independent of the true CSI. The array gain decays with increasing signal-to-noise ratio and is slightly larger for spatially correlated systems. As the prediction error increases in the non-saturation region, the coding gain decreases and the diversity gain remains unaffected. <s> BIB033 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm's performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions. <s> BIB034 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> The applications of recently developed meta-heuristics in cluster analysis, such as particle swarm optimization (PSO) and differential evolution (DE), have increasingly attracted attention and popularity in a wide variety of communities owing to their effectiveness in solving complicated combinatorial optimization problems. Here, we propose to use a hybrid of PSO and DE, known as differential evolution particle swarm optimization (DEPSO), in order to further improve search capability and achieve higher flexibility in exploring the natural while hidden data structures of data of interest. Empirical results show that the DEPSO-based clustering algorithm achieves better performance in terms of the number of epochs required to reach a pre-specified cutoff value of the fitness function than either of the other approaches used. Further experimental studies on both synthetic and real data sets demonstrate the effectiveness of the proposed method in finding meaningful clustering solutions. <s> BIB035 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In recent years, the Particle Swarm Optimization has rapidly gained increasing popularity and many variants and hybrid approaches have been proposed to improve it. Motivated by the behavior and the proximity characteristics of the social and cognitive experience of each particle in the swarm, we develop a hybrid approach that combines the Particle Swarm Optimization and the Differential Evolution algorithm. Particle Swarm Optimization has the tendency to distribute the best personal positions of the swarm near to the vicinity of problem's optima. In an attempt to efficiently guide the evolution and enhance the convergence, we evolve the personal experience of the swarm with the Differential Evolution algorithm. Extensive experimental results on twelve high dimensional multimodal benchmark functions indicate that the hybrid variants are very promising and improve the original algorithm. <s> BIB036 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Abstract To solve the highly constrained environmental/economic dispatch problem involving conflicting objectives, this paper presents a hybrid multi-objective optimization algorithm based on particle swarm optimization (PSO) and differential evolution (DE). In this algorithm, a PSO with time variant acceleration coefficients is designed to explore the entire search space, while a local version of DE is proposed to exploit the sub-space with sparse solutions. A crowing distance-based approach is introduced to assign the particles’ leaders and to update the external archive. Moreover, a new technique for equality constraints is proposed to hurdle the unfeasible solutions directly. Finally, several optimization trials of the proposed algorithm are carried out on the IEEE 30-bus test system. Results demonstrate superiority of the proposed approach and confirm its potential to solve the multi-objective EED problem. <s> BIB037 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> Regarding the complementarity of particle swarm optimization (PSO) and differential evolution (DE) and the complementarity of different differential evolutionary modes of DE, hybrid PSODE with three populations based on multiple differential evolutionary models is proposed. The algorithm effectively combines PSO and DE of two different evolutionary modes, improving local and global optimization ability dramatically. Hybrid PSODE with three populations, hybrid PSODE with two populations and hybrid DE with two populations are compared by 4 typical test functions, proving that hybrid PSODE with three populations has comprehensive superiority in global convergence properties and local search ability. Besides, among hybrid PSODE with three populations based on different differential evolutionary models, the algorithm with combination of rand and best evolutionary modes performs best and has perfect robustness and stability. <s> BIB038 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A hybrid quantum-behaved particle swarm optimization (QPSO) based on cultural algorithm (CA), which we call cultural QPSO, is proposed. Although QPSO is a promising algorithm for many optimization problems, it is apt to lose the diversity of the swarm in the later period of the search and prematurely converges to the local optimum. Inspired by the structure of human society, this paper uses the CA model to diversify the QPSO population and improve the QPSO's performance. In this model, the swarm is divided into two sub-swarms: the common particle and the elite particle sub-swarm. If a particle comes from a common sub-swarm, it will evolve according to the QPSO method, and during the evolvement, it will be affected not only by the other common particles but also by the elites. For the elites, the differential evolution (DE) method is adopted for evolvement. After each generation, the elites will be re-elected from the whole swarm according to fitness values. The simulation results on benchmark functions demonstrate that cultural QPSO outperforms the original QPSO for many problems. <s> BIB039 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> In this paper, we consider the scenario that a population-based algorithm is applied to a numerical optimization problem and a solution needs to be presented within a given time budget. Although a wide range of population-based algorithms, such as evolutionary algorithms, particle swarm optimizers, and differential evolution, have been developed and studied under this scenario, the performance of an algorithm may vary significantly from problem to problem. This implies that there is an inherent risk associated with the selection of algorithms. We propose that, instead of choosing an existing algorithm and investing the entire time budget in it, it would be less risky to distribute the time among multiple different algorithms. A new approach named population-based algorithm portfolio (PAP), which takes multiple algorithms as its constituent algorithms, is proposed based upon this idea. PAP runs each constituent algorithm with a part of the given time budget and encourages interaction among the constituent algorithms with a migration scheme. As a general framework rather than a specific algorithm, PAP is easy to implement and can accommodate any existing population-based search algorithms. In addition, a metric is also proposed to compare the risks of any two algorithms on a problem set. We have comprehensively evaluated PAP via investigating 11 instantiations of it on 27 benchmark functions. Empirical results have shown that PAP outperforms its constituent algorithms in terms of solution quality, risk, and probability of finding the global optimum. Further analyses have revealed that the advantages of PAP are mostly credited to the synergy between constituent algorithms, which should complement each other either over a set of problems, or during different stages of an optimization process. <s> BIB040 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> To improve the performance of particle swarm optimization and differential evolution, the diploid differential evolution particle swarm optimization was presented according to the genetics rules. The algorithm was applied into the Open Vehicle Routing Problem. In the algorithm, dominant character and recessive character were included in every individual. Particle swarm optimization was implemented by dominant character, and differential evolution was implemented by recessive character. Dominant character was replaced by recessive character if its fitness was smaller than recessive character. A real number encoding method was presented and some heuristics were modified and improved the solution. The parameters of algorithm were analyzed in the experiment. And comparison with other algorithms in the literatures showed the proposed algorithm was effective. <s> BIB041 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> A novel hybrid optimization algorithm, PSOCCA, based on the fusion of the Particle Swarm Optimization (PSO) and Cultural Algorithm (CA), is proposed in this paper to enhance the convergence characteristics of the original PSO. In the PSOCCA, the particle swarm is considered to be a population component of the CA, and three knowledge sources are stored in the belief space to update the population space and establish the relationship between the two CA spaces. A unique mutation operator inspired by the Differential Evolution (DE) is used to mutate those particles with unsatisfactory performances in the population space. A new kind of knowledge, average value knowledge, that is stored in the belief space, is also introduced to regulate the variation ratio in the swarm population. The optimization performance of our PSOCCA is investigated using ten high-dimension and multi-peak functions. Simulation results demonstrate that it can be superior to the regular PSO. <s> BIB042 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called hybrid particle swarm optimization - differential evolution (PSO-DE). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSO-DE. The simulation results of all scenarios of the PSO-DE outperform over the PSO and other existing approaches which appeared in literatures. <s> BIB043 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> III. PREVIOUS DEPSOS <s> This paper presents extensive experiments on a hybrid optimization algorithm (DEPSO) we recently developed by combining the advantages of two powerful population-based metaheuristics—differential evolution (DE) and particle swarm optimization (PSO). The hybrid optimizer achieves on-the-fly adaptation of evolution methods for individuals in a statistical learning way. Two primary parameters for the novel algorithm including its learning period and population size are empirically analyzed. The dynamics of the hybrid optimizer is revealed by tracking and analyzing the relative success ratio of PSO versus DE in the optimization of several typical problems. The comparison between the proposed DEPSO and its competitors involved in our previous research is enriched by using multiple rotated functions. Benchmark tests involving scalability test validate that the DEPSO is competent for the global optimization of numerical functions due to its high optimization quality and wide applicability. <s> BIB044
Following the terminology in GAs, we regard DE and PSO as the parents of DEPSO. As a burgeoning optimizer, DEPSO has shown its prominent advantage and prosperity, which are witnessed by the diversity of DEPSO variants and their applications BIB004 , BIB001 - BIB032 . Besides, DEPSO has been further hybridized with other optimizers, giving birth to more complicated hybrids  BIB016 BIB033 . In the past decade, many scholars have made contributions to DEPSO research. In the sequel, we will review existing DEPSOs by grouping them into three categories according to their basic features: 1) collaboration-based DEPSO; 2) embedding-based DEPSO; and 3) assistance-based DEPSO. The classification criterion here only considers the relationship between parent optimizers for hybridization. Collaboration here means that parent optimizers cooperate with each other in problem space to seek the optimum, they share or exchange accumulated information during their search, and their own operating manners are maintained, respectively. In contrast, the operating manners of parent optimizers in embedding-based hybrids will be changed and cannot be separated explicitly. In this case, it is hard to separate their contribution to fitness improvement since the parents are integrated into a holistic hybrid optimizer. In contrast, assistance leads to a very special hybridization strategy in which one parent will not generate new sampling points in search space but serve as an assistance of another parent. For example, one parent under the assistance relationship may work in the parameter space of another one. It should be noted that a point in search space can be regarded as a sampling point only if it undergoes fitness evaluation. Usually, the assistant will keep its own operating manner, which is a very important feature for distinguishing "assistance" from "embedding." The following is a mathematical formulation of the three kinds of parent relationship: Embedding-Parent A and B where f A and f B represent the mapping of parents A and B, respectively; S s and S ob are the solution space and the objective space, respectively; S BIB002 . Another typical example is the DEPSO that is proposed by Zhang and Xie BIB004 (namely DEPSO-ZX). In this DEPSO, PSO and DE also alternate in a deterministic way, but DE acts on the personal best positions of particles in contrast to the current particle positions in DEPSO-H. DE follows PSO at each generation, and it is expected to further improve the personal best positions of PSO. Note that the DE and PSO in DEPSO-ZX are DE/best/2/bin and the classical PSO with the Gbest model, respectively. The primary operations of DEPSO-ZX can be described, in sequence, by (6) and (7) and the following DE operations: where the denotations are the same as those in (2) and (3). DEPSO-ZX has been successfully applied in multimodal image registration BIB005 , modeling of gene regulatory networks BIB013 , structure optimization of a high-temperature superconducting cable BIB017 , and design of finite-impulse response filters BIB018 . Besides, DEPSO-ZX was even further hybridized with PSO and ES to form a more complicated hybrid BIB016 , BIB033 . In BIB010 , Moore and Venayamoorthy proposed a DEPSO (namely DEPSO-MV), which shares the same idea with DEPSO-ZX, but its DE and PSO parents are DE/rand/2/bin and a modified PSO with "Ring" topology, respectively. DEPSO-MV is used in the multiobjective optimization of combinational logic circuits design. In BIB007 , a DEPSO (namely DEPSO-LWJH) that is similar to DEPSO-ZX is proposed and it is used to train artificial neural networks. Like DEPSO-ZX, the PSO in this hybrid is also based on the Gbest model. Differently, its DE parent is DE/current-tobest/1/bin. In particular, DEPSO-LWJH adopts a chaotic LS to improve its local exploitation ability. Huang et al. also adopted the same hybridization strategy to design their DEPSO (namely DEPSO-HWLR) BIB024 . Besides, DEPSO-HWLR incorporates the technique of the parallel finite-element method (PFEM) to address the back-analysis issue of mechanics parameters in engineering projects. Other analogs of DEPSO-ZX include the DEPSO-LCW proposed by Liu et al. to handle constrained numerical and engineering optimization problems BIB034 , and the DEPSO-XXW proposed by Xu et al. for partitional clustering BIB035 . In BIB036 , a similar scheme of evolution of the personal experience of particles (pbest) by DE is proposed (the resultant DEPSOs are all named DEPSO-EPV); however, DE will only be applied to the personal best positions, which have been improved as compared with previous generation. Liu et al. used DE to perturb the positions of particles with the purpose of keeping population diversity BIB011 . In their DEPSO (namely DEPSO-LHTC), DE follows PSO in each generation to change the current positions of particles. Xu and Gu also proposed a collaboration-based DEPSO, namely DEPSO-XG, in which PSO and DE evolve the whole population alternately BIB025 . In particular, Xu and Gu incorporated the average pbest position and velocity of particles into the velocity regulation of the classical PSO [cf., (10) ]. The DE operations in DEPSO-XG involve two populations: the original DE population and an extra population to record those trial vectors inferior to their target vectors. The "inferior" vectors will be reused in a so-called prior crossover operation to generate intermediate vectors and update particle positions: average velocity attraction (10) where pbest PS . Ning et al. introduced differential mutation operator into a basic PSO in order to alleviate the so-called premature convergence of the classical PSO BIB019 . At each generation of their DEPSO (namely DEPSO-NZL) BIB019 , PSO runs first, and DE/best/2/bin follows to improve the current positions of particles. Caponio et al. designed a DEPSO (namely DEPSO-CNT) by the use of PSO to provide DE a so-called super-fit individual BIB020 . DEPSO-CNT was established on a DE framework that is hybridized with PSO and two local searchers. PSO works only at the beginning of the whole search process, refining a part of the initial population and replacing the worst solution with the refined best one. Local searchers will be adaptively chosen by means of a probabilistic scheme, which relies on an index that measures the quality of the super-fit individual with respect to the rest of the population BIB020 . The performance of DEPSO-CNT was validated in the optimal drive design for a direct current motor and the design of a digital filter. Ali et al. also proposed a two-phase DEPSO (namely DEPSO-APA) in which DE mainly in charge of exploration runs first BIB026 . DEPSO-APA will switch from DE/rand/1/bin to basic PSO (Gbest topology) according to a predefined threshold for the identification of DE's convergence. Once the fitness difference of the best and worst DE individuals reaches the threshold, PSO will act on half of the DE population that consists of elite solutions to achieve the final exploitation of promising regions. Gong et al. hybridized DE/best/2/bin with a PSO variant, which removes traditional velocity terms and adopts timevariant acceleration coefficients BIB037 . Their DEPSO (namely DEPSO-GZQ) was proposed to solve multiobjective environmental/economic power dispatch problems. The motivation behind DEPSO-GZQ is an effective synergy of PSO's exploration ability and the exploitation ability of DE/best/2/bin. The DE and PSO parents of DEPSO-GZQ share and update an external archive, which records nondominated solutions that are found so far. Particularly, the crowding distance, as an index of the solution diversity in multiobjective space, is utilized to differentiate the quality of nondominated solutions. Grobler and Engelbrecht also proposed a DEPSO, namely DEPSO-GE, to solve multiobjective optimization problems BIB027 . Like DEPSO-GZQ, the DE and PSO parents of DEPSO-GE also interact via an external archive. However, they are assigned different objectives to optimize. Another DEPSO for multiobjective optimization is the DEPSO-JC that is proposed by Jiang and Cai BIB028 , employing PSO and DE as regeneration methods. A new acceptance rule that is called distance/volume fitness was proposed to update the external archive of the multiobjective DEPSO. Niu and Li proposed a coevolutionary DEPSO, namely DEPSO-NL, employing DE and PSO to evolve their respective subpopulations. Its DE parent (DE/rand/1/bin) and PSO parent (classical Gbest PSO) interact by sharing the global best solution that is found so far  , BIB021 . The same idea was also adopted by Zhang et al. who created a chaotic coevolutionary DEPSO (namely DEPSO-ZZS) BIB029 . In particular, DEPSO-ZZS employs Tent-map-based chaotic perturbation, which follows both DE (DE/current-to-best/1/bin) and PSO (Gbest) to update DE individuals and particle positions, respectively. Wang et al. also proposed a similar DEPSO (namely DEPSO-WYZ), which maintains three subpopulations that are evolved, respectively, by classical PSO and two DE variants BIB038 . The three subpopulations share the global best solution during their evolution. Another analog is the DEPSO-SC that is proposed by Sentinella and Casalino, incorporating three EAs, which include the GA, PSO, and DE, to solve spacecraft trajectory optimization problems  , BIB030 . The three optimizers work in parallel and, periodically, let their best individuals migrate to other subpopulations. Yang et al. hybridized a quantum-behaved PSO with DE/rand/2/bin to create a coevolutionary DEPSO (namely DEPSO-YMN) in which the DE parent evolves elite individuals and the PSO evolves common individuals BIB039 . The evolution of common individuals is guided by the pbest of elite solutions, while the DE-based evolution of elites contains the perturbation based on the difference of common individuals. Recently, Peng et al. proposed a general coevolutionary framework, namely population-based algorithm portfolio (PAP), to combine different population-based search algorithms BIB040 . Four optimizers, which involve a self-adaptive DE and classical PSO, are chosen as candidate parent optimizers to test the efficiency of PAP. Within the PAP framework, parents exchange the elite solutions that are distributed in different subpopulations by the migration mechanism usually employed in niching GAs. Their findings based on experimental analysis demonstrate that the PAP has obvious superiority over the homogeneous parallel hybridization of any parent optimizer. Peng et al. also pointed out that the complementarity of parents is a key issue to ensure the superior performance of their PAP BIB040 . In BIB041 , a novel coevolutionary DEPSO (namely DEPSO-HW) is proposed based on diploid genetic theory to solve the open vehicle routing problem. In DEPSO-HW, PSO evolves the so-called dominant chromosomes, while DE evolves recessive chromosomes. When a recessive chromosome is better than its corresponding dominant chromosome, they will be exchanged into opposite subpopulations. Wu et al. proposed a distinctive coevolutionary DEPSO (namely DEPSO-WGHZ) by introducing the mutation operator of DE within the framework of the cultural algorithm into PSO BIB042 . The average fitness of all particles is utilized to divide the whole swarm into two subpopulations, which are evolved, respectively, by PSO and DE BIB042 . The DE parent of DEPSO-WGHZ resembles DE/rand/1/bin, but its crossover operator is removed. In addition, the differential mutation that is affected by three kinds of knowledge in belief space is implemented as an influence function to evolve inferior particles whose fitness is lower than average. Recently, Hao et al. constructed a new DEPSO (namely DEPSO-HGH) BIB014 . In this hybrid optimizer, DE and PSO are regarded as two operators to generate candidate solutions, and they act on the level of dimensional components of individuals. Stated another way, each dimensional component of a candidate solution can be generated in either DE or PSO manner. The choice of generation manners depends on a predefined probability (CR) as shown in (11)- (13). In addition, the DE and PSO parents of DEPSO-HGH are DE/mid-to-better/1/bin and the PSO-cf mentioned in Section II: where the denotations are the same as those in (1) is the dth component of the global best position gbest at the kth generation, and it is required that the fitness of x r 1 is not worse than that of x i . The DEPSO that is designed by De et al. (namely DEPSO-DRKC) BIB008 combined the self-adaptive Pareto DE that is proposed by Abbass et al. BIB003 and a basic PSO with random inertia weight. In the evolutionary loop of DEPSO-DRKC, DE operates on some selected dimensions to refine current particle positions, as well as modulate particle velocities, and PSO follows to regulate the current positions of particles. DEPSO-DRKC was employed to maximize camera coverage area in the coordination of robot ants. In BIB015 , two DEPSOs are presented. The first DEPSO (namely DEPSO-OES1) is somewhat similar to DEPSO-HGH. The DE (DE/rand/1/bin) and PSO (PSO-cf) in it also alternate in a stochastic way, but both DE and PSO act on the level of a whole individual, that is to say, each individual at each generation has only one updating method of its current position (DE or PSO). Besides, the probability of selecting an updating method and the scaling factor in DE are dynamic and adaptive. A similar DEPSO (DEPSO-KL) was proposed by Kim and Lee  . At each generation, each individual selects the updating method of its current position, either PSO-cf or DE/best/1/bin, according to a predefined probability. Kim and Lee also employed the reinforcement learning method, i.e., Q-Learning, to adjust three primary parameters of DEPSO-KL  . Another DEPSO akin to DEPSO-OES1 is the one that is proposed by Dhahri et al. (namely DEPSO-DAK)  . Its PSO parent will be selected according to a predefined probability to improve the worst individuals in current population. DEPSO-DAK was applied to the design of beta basis function neural networks. In the DEPSO that is proposed by Pant et al. (namely DEPSO-PTGA) BIB022 , PSO will be activated to evolve an individual only if DE does not bring the improvement of its fitness. Khamsawang et al. proposed four versions of DEPSO (DEPSO-KWJ) with the same goal of the use of DE to improve the exploration ability of PSO BIB043 . It was claimed that the mutation operators of DE will be activated if the velocity values of particles are near zero or violate predefined bounds. According to the formulas that are presented in BIB043 , Khamsawang et al. used the difference of individuals, instead of an entire differential mutation, to regulate the velocity of particles. In other words, the difference-based velocity regulation does not involve base vectors. However, since the velocity that is modulated by DE will be added to the current position as shown in (7), we can also regard the operation as a differential mutation with the current position being its base vector. Takano and Hagiwara proposed an integrated framework to effectively combine the merits of several evolutionary computations that include the GA, PSO, and DE  . The framework holds several individual pools, and each pool corresponds to one EC. Each incorporated EC has its own evaluated value (EV), and it changes according to the best fitness value at each generation. The number of individuals in each EC changes according to the EV. All individuals have their own lifetime to reselect EC, and the probability of each EC to be selected depends on the EV. We term their hybrid, here, as DEPSO-TH for unification though the term GADEPSO seems more suitable to express its hybridization. Xin et al. proposed an adaptive DEPSO, namely DEPSO-XCPP, which achieves on-the-fly adaptation of evolution methods for individuals in a statistical learning way, according to the relative success ratio of PSO versus DE in a previous learning period BIB044 . The idea to employ statistical learning to choose evolution methods can also be applied to the adaptation of control parameters, evolutionary operators (e.g., the differential mutation BIB031 , BIB023 ), and LS techniques BIB009 , BIB006 , BIB012 ,  .