Is Algebraic Differential Evolution Really a Differential Evolution Scheme?

In this paper we present an empirical , comparative performance, analysis of fourteen variants of Differential Evolution (DE) and Multiple Trial Vectors Differential Evolution algorithms to solve unconstrained global optimization problems. The aim is (1) to compare Multiple Trial Vectors DE, which allows each parent vector in the population to generate more than one trial vector, against the classical DE and (2) to identify the competitive variants which perform reasonably well on problems with different features. The DE and Multiple Trial Vectors DE variants are benchmarked on 6 test functions grouped by features --- unimodal separable, unimodal nonseparable, multimodal separable and multimodal non-separable. The analysis identifies the competitive variants and shows that Multiple Trial Vectors DE compares well with the classical DE.

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

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.

Differential Evolution (DE) is an algorithm to solve possibly nonlinear and non-differentiable global optimization problems. Classical Differential Evolution (CDE) employs a synchronous generation-based evolution strategy. We propose a modification of the CDE algorithm by incorporating mutation, crossover and selection operations into an asynchronous strategy. A novel Asynchronous Differential Evolution (ADE) is well suited for parallel optimization. Moreover even in the sequential mode its rate of convergence is competitive to CDE. The performance of the Asynchronous Differential Evolution is reported on a set of benchmark functions.

A Differential Evolution Clustering algorithm with weighted validity function is presented in this paper, five validity functions are selected to form the fitness function with weights, and in selection of Differential Evolution, individuals not being selected are put into secondary population. During evolution, individuals in secondary population replace those in main population if their fitness values are less than those in main population. We have carried out experiments on 3 datasets from UCI machine learning repository and compared validity results to those from K-Means and classical Differential Evolution, experimental results show that our approach can improve clustering performance.

Social learning differential evolution

A new mutation concept is proposed to generalize local selection based Differential Evolution algorithm to work in general multi-modal problems. Three variations of the proposed method are compared with classic Differential Evolution algorithm using a set of five well known test functions and their variants. The general idea of the new mutation operation is to divide the mutation into two parts: the local and global mutation. The global mutation works as a migration operator allowing the algorithm perform global search efficiently, while the local mutation improves the efficiency of local search.The results show that the concept of global mutation is able to generalize the good performance of local selection based Differential Evolution from convex uni-modal functions to general non-convex and multi-modal problems. Among the tested functions, the new method was able to outperform the classic Differential Evolution in all butone. A limited analysis of the effects of control parameters to the performance of the algorithm is also done.

A novel optimization method based on a differential evolution (DE) strategy for designing low-weight truss structures is presented for both continuous and discrete variables. Applications of this technique on the optimization of a benchmark-type truss structure with continuous and discrete variables are given to evaluate its effectiveness. Results are compared with various classical and evolutionary optimization methods which show that the proposed procedure based on DE outperforms other methods and can effectively be applied to the optimization problems of truss structures with both continuous and discrete design variables.

New quantum inspired meta-heuristic techniques for multi-level colour image thresholding

Based on differential evolution algorithm and the concept of multi-objective optimization, a differential evolution algorithm for constrained optimization problem based on multi-objective constraint handling is proposed in this paper. This proposed algorithm can achieve global search and local search effectively by using of the differential evolution algorithm. For the constrained optimization problems, this paper presents a new comparison mechanism based on the concept of Pareto optimal solution. The grades of Pareto optimal solutions, feasible solutions and infeasible solutions are prescribed and enable them to be selected at different probabilities during the evolutionary process, which can lead the search towards the direction of the global optimum. In addition, an infeasible solution of replace mechanism is also given. When the algorithm gets into a local optimal, we use infeasible solution, which contains useful information, to replace those redundant and repeat feasible solutions to improve the exploration capabilities of the algorithm in the search space. Compared to Evolutionary Algorithm based on Homomorphous Maps (EAHM), Artificial Immune Response Constrained Evolutionary Strategy (AIRCES), Constraint Handling Differential Evolution (CHDE) and Evolutionary Strategies based on Stochastic Ranking (ESSR), the results of the 13 Standard tests show that the proposed algorithm has certain advantages in the convergence speed and solution accuracy.

This paper presents an analysis of the relationship of particle velocity and convergence of the particle swarm optimization. Its premature convergence is due to the decrease of particle velocity in search space that leads to a total implosion and ultimately fitness stagnation of the swarm. An improved algorithm which introduces a velocity differential evolution (DE) strategy for the hierarchical particle swarm optimization (H-PSO) is proposed to improve its performance. The DE is employed to regulate the particle velocity rather than the traditional particle position in case that the optimal result has not improved after several iterations. The benchmark functions will be illustrated to demonstrate the effectiveness of the proposed method.

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

From a learning perspective, the mutation scheme in differential evolution (DE) can be regarded as a learning strategy. When mutating, three random individuals are selected and placed in a random order. This strategy, however, probably suffers some drawbacks which can slow down the convergence rate. To improve the efficiency of classic DE, this paper proposes a differential evolution based on improved learning strategy (ILSDE). The proposed learning strategy, inspired by the learning theory of Confucius, places the three individuals in a more reasonable order. Experimenting with 23 test functions, we demonstrate that ILSDE performs better than classic DE.

Differential evolution (DE), as a very powerful population-based stochastic optimizer, is one of the most active research topics in the field of evolutionary computation. Self-adaptive differential evolution (SaDE) is a well-known DE variant, which aims to relieve the practical difficulty faced by DE in selecting among many candidates the most effective search strategy and its associated parameters. SaDE operates with multiple candidate strategies and gradually adapts the employed strategy and its accompanying parameter setting via learning the preceding behavior of already applied strategies and their associated parameter settings. Although highly effective, SaDE concentrates more on exploration than exploitation. To enhance SaDE's exploitation capability while maintaining its exploration power, we incorporate local search chains into SaDE following two different paradigms (Lamarckian and Baldwinian) that differ in the ways of utilizing local search results in SaDE. Our experiments are conducted on the CEC-2014 real-parameter single-objective optimization testbed. The statistical comparison results demonstrate that SaDE with Baldwinian local search chains, armed with suitable parameter settings, can significantly outperform original SaDE as well as classic DE at any tested problem dimensionality.