Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> This paper introduces a novel scheme of improving the performance of particle swarm optimization (PSO) by a vector differential operator borrowed from differential evolution (DE). Performance comparisons of the proposed method are provided against (a) the original DE, (b) the canonical PSO, and (c) three recent, high-performance PSO-variants. The new algorithm is shown to be statistically significantly better on a seven-function test suite for the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability. <s> BIB001 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> Spatial clustering with obstacles constraints (SCOC) has been a new topic in spatial data mining (SDM).In this paper, we propose an advanced Particle swarm optimization (PSO) and differential evolution (DE) method for SCOC. In the process of doing so,we first developed a novel spatial obstructed distance using PSO-DV(particle swarm optimization with differentially perturbed Velocity) based on grid model to obtain obstructed distance, which is named PDGSOD, and then we presented a new PDKSCOC based on PSO-DV and K-Medoids to cluster spatial data with obstacles constraints. The experimental results show that PDGSOD is effective, and PDKSCOC can not only give attention to higher local constringency speed and stronger global optimum search, but also get down to the obstacles constraints and practicalities of spatial clustering; and it performs better than Improved KMedoids SCOC (IKSCOC) in terms of quantization error and has higher constringency speed than Genetic K-Medoids SCOC (GKSCOC). <s> BIB002 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> Differential evolution (DE) and particle swarm optimization (PSO) are the evolutionary computation paradigms, and both have shown superior performance on complex nonlinear function optimization problems. This paper detects the underlying relationship between them and then qualitatively proves that the two heuristic approaches from different theoretical background are consistent in form. Within the general perspective, the PSO can be regarded as a kind of DE. Inspired by this, a novel variant of DE mixed with particle swarm intelligence (DE-SI) is presented. Comparison experiments involving ten test functions well studied in the evolutionary optimization literature are used to highlight some performance differences between the DE-SI, two versions of DE and two PSO variants. The results from our study show that DE-SI keeps the most rapid convergence rate of all techniques and obtains the global optima for most benchmark problems. <s> BIB003 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> The gear box fault occur can lead to the fatal breakdown of mechanical system. Back propagation neural network (BPNN) have been proved to be of widespread utility for identifying and classifying gear box faults to prevent serious damage in a mechanical system. Some researchers have used particle swarm optimization (PSO) to train BPNN. However, because the PSO algorithm has several parameters to be adjusted by empirical approach, if these parameters are not appropriately set, the search will become very slow near the global optimum and even trap into local minima. In this paper, a novel hybrid intelligent method for classifying gear box faults based on vibration signal using the particle swarm optimization (PSO) algorithm, differential evolution (DE) algorithm and BPNN named PSO-DV based BP is presented. The proposed PSO-DV includes both faster convergence of PSO and capability escape from local optima of DE. Experiments were performed on a gear-box fault simulator. The fault samples are obtained by simulating corresponding fault on experiment gear-box. In presented work, a classical PSO based BP neural network and PSO-DV based BP neural network are used for gear box fault classification, their relative effectiveness in fault diagnosis is compared. The experimental results verified that proposed hybrid PSO-DV intelligent method can escape from local minima, so has better convergence than BP neural network and classical PSO based BP neural network. Meanwhile, it achieves also very high accuracy rate of recognition and thus provides decision support in fault classification. <s> BIB004 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> This paper introduced an almost control parameters free modified differential evolution for global optimization problems. The modifications are derived from the mechanisms of particle swarm optimization viz., topologies, inertial weight, neighborhood best and individual best, with which each individual performed the mutation operator based on its current position, the neighborhood best and its individual best along with the inertial weight. And the crossover operator in traditional differential evolution is removed, while the selection operator was employed. The approach was employed for a tension/compression string design problem and an economic dispatch problem in power system. By comparisons with the other evolutionary algorithms, the proposed approach has shown its feasibility and effectiveness. <s> BIB005 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> A hybrid differential evolution (HDE) approach derived from both the differential evolution (DE) and the particle swarm optimization (PSO) is proposed. In HDE, individuals in a new generation are created, not only by crossover and mutation operation as in DE, but also by PSO operations. The concepts of inertia weight and neighbor topology are adopted in HDE. The former is employed to provide consistency and diversity by adding a weighted velocity to the trial vector. In the latter, instead of the whole population, each individual can only communicate with its neighbors, and each individual creates its trial vector based on the best individual found by its neighbors so far. The proposed approach is employed for four well-known benchmarks, and the simulation results have shown its feasibility and effectiveness. <s> BIB006 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> B. Embedding-Based DEPSOs <s> Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms (EAs) and other search heuristics like the particle swarm optimization (PSO) when tested over both benchmark and real-world problems. DE, however, is not completely free from the problems of slow and/or premature convergence. This paper describes a family of improved variants of the DE/target-to-best/1/bin scheme, which utilizes the concept of the neighborhood of each population member. The idea of small neighborhoods, defined over the index-graph of parameter vectors, draws inspiration from the community of the PSO algorithms. The proposed schemes balance the exploration and exploitation abilities of DE without imposing serious additional burdens in terms of function evaluations. They are shown to be statistically significantly better than or at least comparable to several existing DE variants as well as a few other significant evolutionary computing techniques over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems concerning parameter estimation for frequency modulated sound waves and spread spectrum radar poly-phase code design. <s> BIB007
A typical embedding-based DEPSO is the PSO with differentially perturbed velocity (namely DEPSO-DKC; PSODV in BIB001 ) that is proposed by Das et al. The embedding way in PSODV is shown as follows: where is the dth component of the difference vector of two randomly selected individuals x r 1 and x r 2 with r1 = r2 = i, β is the scaling factor, CR is the predefined crossover probability, and the definitions of v (7). Note that the selection operator that is used in DE/rand/1/bin is also employed in this DEPSO to operate on the trial vector u i and the corresponding individual x i . It was reported that DEPSO-DKC has been successfully applied to spatial clustering with obstacles constraints BIB002 and fault diagnosis of gear-box BIB004 . Li claimed that the parameter-free HDE that he proposed in BIB005 (namely DEPSO-L) is derived from the mechanisms of PSO (viz., topologies, inertia weight, neighborhood best, and personal best). The crossover operation of DE is removed, while its selection operation is retained. The primary operations of DEPSO-L are presented in (16) and (17)  From (16), it seems that DEPSO-L follows the paradigm of differential mutation with nbest being its base vector. However, the difference term in (16) is actually the PSO's individual cognition as shown in (6), not the individual difference that usually exists in diverse DE variants [cf., (1), (3)- (5)]. Besides, the term "velocity" in DEPSO-L turns out to be passive since it is derived from the difference of the same particle's positions at contiguous time instants [cf., (17) ], instead of being modulated by inertia, individual cognition, and social learning [cf., (6) ]. Shu and Li introduced PSO's topology and velocity regulation into DE/best/1/bin to construct an embedding-based DEPSO (namely DEPSO-SL) BIB006 . The primary operations of DEPSO-SL are shown in (18)- (20) , with the base vector of DE/best/1/bin (i.e., gbest) being replaced by nbest i , which is determined by a Ring topology. Velocity, here, is defined as the difference of the same trial vector's positions at contiguous time instants [cf., (20) ]. From (19) , it seems as if there is an inertia part in DEPSO-SL like that in (6); howbeit, the "inertia" here is not used for velocity regulation but for the perturbation of trial vectors: Das et al. proposed a neighborhood-based differential mutation operator, which introduces PSO's population topology into DE (the DEPSO variant, here, is termed as DEPSO-DACK) BIB007 . The primary operations of DEPSO-DACK (i.e., its novel differential mutation operator) are shown as follows: Xu et al. also proposed an embedding-based DEPSO (namely DEPSO-XLFWW) whose primary operation is shown in (24) BIB003 . DEPSO-XLFWW seems very concise, and it inherits the crossover operation and the format of differential mutation in DE. Strictly speaking, however, it does not employ differential mutation. Instead, it applies a PSO version without velocity and individual cognition, which formally shares certain similarity with the differential mutation operator DE/rand/1: where the denotations are the same as those in (1)- (7).