Wenyin Gong

DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization

Differential evolution (DE) is a fast and robust evolutionary algorithm for global optimization. It has been widely used in many areas. Biogeography-based optimization (BBO) is a new biogeography inspired algorithm. It mainly uses the biogeography-based migration operator to share the information among solutions. In this paper, we propose a hybrid DE with BBO, namely DE/BBO, for the global numerical optimization problem. DE/BBO combines the exploration of DE with the exploitation of BBO effectively, and hence it can generate the promising candidate solutions. To verify the performance of our proposed DE/BBO, 23 benchmark functions with a wide range of dimensions and diverse complexities are employed. Experimental results indicate that our approach is effective and efficient. Compared with other state-of-the-art DE approaches, DE/BBO performs better, or at least comparably, in terms of the quality of the final solutions and the convergence rate. In addition, the influence of the population size, dimensionality, different mutation schemes, and the self-adaptive control parameters of DE are also studied.

Enhanced Differential Evolution With Adaptive Strategies for Numerical Optimization

Differential evolution (DE) is a simple, yet efficient, evolutionary algorithm for global numerical optimization, which has been widely used in many areas. However, the choice of the best mutation strategy is difficult for a specific problem. To alleviate this drawback and enhance the performance of DE, in this paper, we present a family of improved DE that attempts to adaptively choose a more suitable strategy for a problem at hand. In addition, in our proposed strategy adaptation mechanism (SaM), different parameter adaptation methods of DE can be used for different strategies. In order to test the efficiency of our approach, we combine our proposed SaM with JADE, which is a recently proposed DE variant, for numerical optimization. Twenty widely used scalable benchmark problems are chosen from the literature as the test suit. Experimental results verify our expectation that the SaM is able to adaptively determine a more suitable strategy for a specific problem. Compared with other state-of-the-art DE variants, our approach performs better, or at least comparably, in terms of the quality of the final solutions and the convergence rate. Finally, we validate the powerful capability of our approach by solving two real-world optimization problems.

A real-coded biogeography-based optimization with mutation☆

Biogeography-based optimization (BBO) is a new biogeography inspired algorithm for global optimization. There are some open research questions that need to be addressed for BBO. In this paper, we extend the original BBO and present a real-coded BBO approach, referred to as RCBBO, for the global optimization problems in the continuous domain. Furthermore, in order to improve the diversity of the population and enhance the exploration ability of RCBBO, the mutation operator is integrated into RCBBO. Experiments have been conducted on 23 benchmark problems of a wide range of dimensions and diverse complexities. The results indicate the good performance of the proposed RCBBO method. Moreover, experimental results also show that the mutation operator can improve the performance of RCBBO effectively.

Adaptive strategy selection in differential evolution for numerical optimization: An empirical study

Differential evolution (DE) is a versatile and efficient evolutionary algorithm for global numerical optimization, which has been widely used in different application fields. However, different strategies have been proposed for the generation of new solutions, and the selection of which of them should be applied is critical for the DE performance, besides being problem-dependent. In this paper, we present two DE variants with adaptive strategy selection: two different techniques, namely Probability Matching and Adaptive Pursuit, are employed in DE to autonomously select the most suitable strategy while solving the problem, according to their recent impact on the optimization process. For the measurement of this impact, four credit assignment methods are assessed, which update the known performance of each strategy in different ways, based on the relative fitness improvement achieved by its recent applications. The performance of the analyzed approaches is evaluated on 22 benchmark functions. Experimental results confirm that they are able to adaptively choose the most suitable strategy for a specific problem in an efficient way. Compared with other state-of-the-art DE variants, better results are obtained on most of the functions in terms of quality of the final solutions and convergence speed.

A clustering-based differential evolution for global optimization

Hybridization with other different algorithms is an interesting direction for the improvement of differential evolution (DE). In this paper, a hybrid DE based on the one-step k-means clustering, called clustering-based DE (CDE), is presented for the unconstrained global optimization problems. The one-step k-means clustering acts as several multi-parent crossover operators to utilize the information of the population efficiently, and hence it can enhance the performance of DE. To validate the performance of our approach, 30 benchmark functions of a wide range of dimensions and diversity complexities are employed. Experimental results indicate that our approach is effective and efficient. Compared with other state-of-the-art DE approaches, our approach performs better, or at least comparably, in terms of the quality of the final solutions and the reduction of the number of fitness function evaluations (NFFEs).

Enhancing the performance of differential evolution using orthogonal design method

Differential evolution (DE) is a simple and efficient global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problems. However, DE has been shown to have certain weaknesses, especially if the global optimum should be located using a limited number of function evaluations (NFEs). In this paper, we incorporate the orthogonal design method into DE to accelerate its convergence rate. The orthogonal design method is not only to be used to generate the initial population, but also to be applied to design the crossover operator. In addition, two models of DE method are investigated. Moreover, the self-adaptive parameter control is employed to avoid tuning the parameters of DE. Experiments have been conducted on 25 problems of diverse complexities. And the results indicate that our approach is able to find the optimal or close-to-optimal solutions in all cases. Compared with other state-of-the-art evolutionary algorithms (EAs), our approach performs better, or at least comparably, in terms of the quality and stability of the final solutions.

Adaptive Ranking Mutation Operator Based Differential Evolution for Constrained Optimization

Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. Combining with the constraint-handling techniques, recently, DE has been successfully used for the constrained optimization problems (COPs). In this paper, we propose the adaptive ranking mutation operator (ARMOR) for DE when solving the COPs. The ARMOR is expected to make DE converge faster and achieve feasible solutions faster. In ARMOR, the solutions are adaptively ranked according to the situation of the current population. More specifically, the population is classified into three situations, i.e., infeasible situation, semi-feasible situation, and feasible situation. In the infeasible situation, the solutions are ranked only based on their constraint violations; in the semi-feasible situation, they are ranked according to the transformed fitness; while in the feasible situation, the objective function value is used to assign ranks to different solutions. In addition, the selection probability of each solution is calculated differently in different situations. The ARMOR is simple, and it can be easily combined with most of constrained DE (CDE) variants. As illustrations, we integrate our approach into three representative CDE variants to evaluate its performance. The 24 benchmark functions presented in CEC 2006 and 18 benchmark functions presented in CEC 2010 are chosen as the test suite. Experimental results verify our expectation that the ARMOR is able to accelerate the original CDE variants in the majority of test cases. Additionally, ARMOR-based CDE is able to provide highly competitive results compared with other state-of-the-art EAs.

An improved multiobjective differential evolution based on Pareto-adaptive [epsilon]-dominance and orthogonal design

Evolutionary multiobjective optimization has become a very popular topic in the last few years. Since the 1980s, various evolutionary approaches that are capable of searching for multiple solutions simultaneously in a single run have been developed to solve multiobjective optimization problems (MOPs). However, to find a uniformly distributed, near-complete, and near-optimal Pareto front in a small number of fitness function evaluations (NFFEs) is a challenging task for any multiobjective optimization evolutionary algorithm (MOEA). In this paper, we present an improved differential evolution algorithm to MOPs that combines several features of previous evolutionary algorithms in a unique manner. It is characterized by (a) employing the orthogonal design method with quantization technique to generate the initial population, (b) adopting an archive to store the nondominated solutions and employing the new Pareto-adaptive [epsilon]-dominance method to update the archive at each generation, (c) storing the extreme points and inserting them into the final archive in order to remedy one of the limitations of [epsilon]-dominance: the loss of the extreme points in the final archive, and (d) using a hybrid selection mechanism in which a random selection and an elitist selection are alternated in order to allow using the archive solution to guide the search towards the Pareto-optimal front. Experiments have been conducted on a number of unconstrained real-valued artificial functions of two and three objectives. The results prove the efficiency of our approach with respect to the quality of the approximation of the Pareto-optimal front and the considerable reduction of NFFEs in these test problems. By examining the selected performance metrics, our approach is found to be statistically competitive with five state-of-the-art MOEAs in terms of keeping the diversity of the individuals along the tradeoff surface, finding a well-approximated Pareto-optimal front and reducing the computational effort.

Repairing the crossover rate in adaptive differential evolution

Differential evolution (DE) is a simple yet powerful evolutionary algorithm (EA) for global numerical optimization. However, its performance is significantly influenced by its parameters. Parameter adaptation has been proven to be an efficient way for the enhancement of the performance of the DE algorithm. Based on the analysis of the behavior of the crossover in DE, we find that the trial vector is directly related to its binary string, but not directly related to the crossover rate. Based on this inspiration, in this paper, we propose a crossover rate repair technique for the adaptive DE algorithms that are based on successful parameters. The crossover rate in DE is repaired by its corresponding binary string, i.e. by using the average number of components taken from the mutant. The average value of the binary string is used to replace the original crossover rate. To verify the effectiveness of the proposed technique, it is combined with an adaptive DE variant, JADE, which is a highly competitive DE variant. Experiments have been conducted on 25 functions presented in CEC-2005 competition. The results indicate that our proposed crossover rate technique is able to enhance the performance of JADE. In addition, compared with other DE variants and state-of-the-art EAs, the improved JADE method obtains better, or at least comparable, results in terms of the quality of final solutions and the convergence rate.

Adaptive strategy selection in differential evolution

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for global numerical optimization. Different strategies have been proposed for the offspring generation; but the selection of which of them should be applied is critical for the DE performance, besides being problem-dependent. In this paper, the probability matching technique is employed in DE to autonomously select the most suitable strategy while solving the problem. Four credit assignment methods, that update the known performance of each strategy based on the relative fitness improvement achieved by its recent applications, are analyzed. To evaluate the performance of our approach, thirteen widely used benchmark functions are used. Experimental results confirm that our approach is able to adaptively choose the suitable strategy for different problems. Compared to classical DE algorithms and to a recently proposed adaptive scheme (SaDE), it obtains better results in most of the functions, in terms of the quality of the final results and convergence speed.