Ensemble of niching algorithms
Introduction
In real-world optimization problems, sometimes we are not satisfied with only one optimal solution. The demand for multiple solutions is more prominent when there exist several near optimal answers to a problem. Simple genetic algorithms [1], [9] often lack the ability to locate multiple optima, thus, niching methods are introduced. They are used to solve these problems as they attempt to maintain a diverse population and are not as prone to converge prematurely as simple genetic algorithms.
The concept of niching is inspired by the way organisms evolve in nature. In ecology, a “niche” is a term describing the resources and physical space which a species depends on to exist in the ecosystem; it is an environment in which inhabitants take up their roles, deal with the distribution of resources and competition, and at the same time alter those factors. Within a niche, individuals are forced to share the available resources, whereas among different niches, there will be no conflict for the resources.
In evolutionary computation, niching involves the formation of subgroups within a population where each subgroup targets a specific task such as discovering one peak in a multimodal function. Compared with the simple genetic algorithm, the uniqueness of niching genetic algorithms lies in the fact that they preserve not only the highly-fit individuals, but also weaker individuals so long as they belong to groups without the highly-fit ones. This gives the population an opportunity to pass the genetic information of such individuals to their offspring, and it ensures that this information does not become extinct quickly. By maintaining a reasonably balanced variety of genetic information, niching procedures allow the population to simultaneously focus on more than one region in the search space, which is essential to discover several optima in a single run.
Since the earliest niching approach, preselection, was proposed by Cavicchio [5] in 1970, various niching methods such as crowding [8], [34], [35], [22], [6], [31], sharing [15], [18], [59], [38], [20], [16], [21], [33], [12], and clearing [42], [29], [28] have emerged. However, so far, to solve a certain problem, only one method is used at a time. It is often the case that we have to try out several niching methods and tune their parameters to find the best method and its best set of parameters to solve a given problem. Irrespective of the exhaustiveness of the parameter tuning, no one method can be the best for all problems. The various niching methods divide the population into niches where the same selection and survival criteria are implemented. Instead of that, we can establish several populations, each of which can employ a distinct niching algorithm. The existing niching methods offer us a wide choice of combinations in this scenario.
In this paper, we propose the ensemble of niching algorithms (ENA) which uses several niching methods in a parallel manner in order to preserve diversity of the populations and to benefit from the best method. An instance of ensemble is presented to illustrate the ENA concept. It is tested using a set of 16 multimodal test functions in real and binary domains. Results demonstrate that the performance of ENA is more competitive than that of the constituting individual niching methods.
The rest of the paper is organized as follows. Section 2 discusses the existing niching algorithms. Section 3 presents a description of the proposed ensemble of niching algorithms, including when to use the ENA, the procedures, and some implementation details. The fourth section introduces the test problems. In Section 5, evaluation criteria and parameter settings are given. Section 6 reports the results in terms of searching ability and computation time. Comparisons between ENA and the single methods are also investigated in Section 6. Section 7 presents further comparisons with state-of-the-art niching algorithms. Section 8 concludes the paper.
Section snippets
Crowding and restricted tournament selection
The crowding methods encourage competition for limited resources among similar individuals in the population. They follow the analogy that dissimilar individuals tend to occupy different niches, so that they typically do not compete. The end result is that in a fixed-size population at equilibrium, new members of a particular species replace older members of that species, and the overall number of members of a particular species does not change [34]. They make use of a distance measure (either
Ensemble of niching algorithms
In this section, we will introduce the ensemble of niching algorithms. It combines several existing niching methods into a unified framework for searching for multiple solutions within a multimodal fitness landscape. It is realized by using a separate population for each niching method. The offspring created by every population are considered by all other populations for inclusion in their populations according to the selection rules of the respective populations. The ENA shares similarity with
Test functions
The test suite that we use consists of 16 problems. The first ten test functions of the suite are real-variable functions and the others are binary-variable functions. Many of them have been widely used in previous studies. All the functions are multimodal with 5–32 desired optima. F1–F6 are either 1-dimensional or 2-dimensional, and F7–F10 are higher-dimensional problems. The binary test problems typically have a length of around 30 bits.
F1 is a sine function with decreasing maxima. It is one
Parameterization and evaluation criteria
In our experiments, we aim to show that the conceptual advantages of ENA translate into practical advantages in performance compared with single niching algorithms. For this purpose, we examine the searching ability and the computation cost of both the ensemble methods and their constituting niching methods on the basis of using the same number of function evaluations. For functions F1–F6 and F11–F16, we set the total number of function evaluations to be 50,000. For higher dimensional F7–F10,
Success rate
Table 3 shows the testing results consisting of mean, median and standard deviation values of SR with regard to all 16 functions. By reviewing the tables, we can observe that the performance of a single niching method varies with test problems. For instance, RTS2, with its larger window size, has a high success rate in the 25-peak test problem F3, and it has satisfactory performance in most other low-dimensional real-variable functions, but it cannot maintain its performance in high-dimensional
Comparison with state-of-the-art niching algorithms
From the experimental results, we have demonstrated the advantage of ENA over its composing single methods. Apart from that, we review several other recently proposed niching algorithms, including dynamic fitness sharing (DFS) [12], restricted competition selection (RCS) [29], restricted competition selection with pattern search method (RCS-PSM) [28], the species conserving genetic algorithm (SCGA) [30], the sharing scheme based on niche identification techniques (NIT) [33], a
Conclusion and further discussion
We have proposed an ensemble approach in the field of niching genetic algorithms for solving multimodal optimization problems. The ensemble of niching algorithms possesses several niching algorithms with their own parallel populations. In contrast to most other genetic algorithms with parallel populations, ENA employs different niching schemes and every function evaluation is used by every population. The offspring of every population can be included in other niching populations by going
Acknowledgement
This research was supported by the A∗Star (Agency for Science, Technology and Research) under grant #052 101 0020.
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