Cellular direction information based differential evolution for numerical optimization: an empirical study

Abstract

Differential evolution (DE) is a well-known evolutionary algorithm which has been successfully applied in many scientific and engineering fields. In most DE algorithms, the base and difference vectors for mutation are randomly selected from the current population. That is, the useful population information cannot be fully exploited to guide the search of DE through mutation. Furthermore, the selection of parents in mutation has been verified to be critical for the DE performance. Therefore, to alleviate this drawback and improve the performance of DE, a novel DE algorithm with a directional mutation based on cellular topology is proposed in this study. This proposed algorithm is named as Cellular Direction Information based DE (DE-CDI). In DE-CDI, the cellular topology is employed first to define a neighborhood for each individual of population and then the direction information based on the neighborhood is incorporated into the mutation operator. In this way, DE-CDI not only utilizes the neighborhood information to exploit the regions of better individuals and accelerate convergence, but also introduces the direction information to guide the search to the promising area. To evaluate the performance of the proposed method, DE-CDI is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results demonstrate the high performance of DE-CDI for most DE algorithms studied.

Neighborhood guided differential evolution

“…With the panmictic population structure, the original DE algorithms (Storn and Price 1995) are belong to this category, where any individuals can interact with any other one in the whole population. By introducing some structures into population, two main canonical kinds of structured population in DE could be found in literature, i.e., cellular DE (cDE) (Noman and Iba 2011;Noroozi et al 2011;Dorronsoro and Bouvry 2010;Liao et al 2015b) and distributed DE (dDE) (Weber et al 2011(Weber et al , 2010. DE with cellular topology (Noman and Iba 2011;Noroozi et al 2011;Dorronsoro and Bouvry 2010;Liao et al 2015b) Uses the cellular topology to define the configuration of neighborhood and select parents for mutation from the neighbors DE with ring topology-based mutation operators (Liao et al 2015a) Employs the ring topology to define the neighborhood and groups the neighbors to construct direction vector for mutation dDE with scale factor inheritance mechanism (Weber et al 2011) Incorporates the distributed population structure in DE and proposes the employment of multiple scale factor values within dDE structures…”

Neighbor-Induction and Population-Dispersion in Differential Evolution Algorithm

“…Dorronsoro and Bouvry [26] recommended a decentralized population topology and used different decentralized population schemes to propose and analyze several DE variants. Noroozi et al [27], Noman and Iba [28], Dorronsoro and Bouvry [29], and Liao et al [30] introduced a cell topology that defines the range of neighborhoods and selects parents from neighbors. Liao et al [31] used a ring topology to define the neighborhood and grouped the neighbors to construct a direction vector for mutation.…”

A Neighborhood-Assisted Framework for Differential Evolution

“…The original DE algorithms fit into this category, due to that the panmictic population is used in these algorithms and each vector always interacts with all the other vectors [1]. Besides, by introducing the decentralized population, various DE variants are proposed by using the neighborhood relationship defined by the employed population topology, such as, DE with cellular topology [10], [18], DE with distributed topology [11], [11], and DE with ring topology [12], [19]. In these variants, each vector is only allowed to interact with its neighbors with the same indexes during the process of evolution.…”

“…In [25], the hierarchy concept is introduced into cDE to arrange the population based on their fitness values, and thus a hierarchical cDE is proposed to enhance the exploitation ability of algorithm. In [10], the cellular topology is used to define the neighborhood of each vector, and a neighborhood-based directional mutation is proposed by utilizing the neighborhood information from the cellular topology. In addition, the DE variants with the ring topology (e.g., DE with global and local neighborhoods [19], bare-bones DE [20], neighborhood-guided DE [9]) and the DE variants with small-world topology (e.g., small-world DE [25], multitopology-based DE [8]) are proposed by employing the finegrained topology to improve the performance of DE.…”

“…For the second category, the techniques concentrate on the neighborhood structure that affects the neighbors to interact with. Among these techniques, some use the existing population topologies to define the static neighborhood [10]- [12], while others employ the fitness or/and position information to define the dynamic neighborhood [6], [13], [14]. For the third category, the techniques focus on the population model used to extract the relationship between vectors.…”