A novel adaptive sequential niche technique for multimodal function optimization

doi:10.1016/j.neucom.2006.02.016

Neurocomputing

Volume 69, Issues 16–18, October 2006, Pages 2396-2401

https://doi.org/10.1016/j.neucom.2006.02.016 Get rights and content

Abstract

This paper proposes a novel adaptive sequential niche particle swarm optimization (ASNPSO) algorithm, which uses multiple sub-swarms to detect optimal solutions sequentially. In this algorithm, the hill valley function is used to determine how to change the fitness of a particle in a sub-swarm run currently. This algorithm has strong and adaptive searching ability. The experimental results show that the proposed ASNPSO algorithm is very effective and efficient in searching for multiple optimal solutions for benchmark test functions without any prior knowledge.

Introduction

The stochastic search algorithms are widely used in evolving artificial neural network (ANN) architecture and weights [5], [3]. As a rule, the best weights or architecture of an ANN are not exclusive. In fact, the different architecture of an ANN is very useful in different situations. However, the ordinary stochastic search algorithm only finds one solution. The niche methods for stochastic search algorithms are techniques that can maintain a stable subpopulation for multiple solutions. In practical application, there are two categories of niche techniques, the parallel and sequential niche methods. Since Beasley et al. [1], however first proposed a sequential niche technique, over the years, this method has been ignored by researchers. Thus, there is little progress on it. On the contrary, the parallel techniques have attained more attention in recent years. Mahfound [7] had pointed out that the sequential technique has some disadvantages, while the parallel niche technique is generally faster than the sequential one. Nevertheless, the sequential technique still has its unique advantages. Especially the sequential technique can be integrated with the parallel ones [12]. So a good sequential method can also improve the performance of the entire niche technique.

Currently, most niche techniques need some extra tunable parameters, where the most important parameter is niche radius. An inappropriate radius will generally make a niche algorithm performance worse. In fact, the determination of the niche radius more or less depends on some prior knowledge from a special problem. These situations will often prevent this technique from being widely applied to practical application.

This paper presents a novel adaptive sequential niche technique, which can ensure that most extra niche parameters including niche radius are not needed. In this paper, we combine the particle swarm optimization (PSO) [6], [9] algorithm with our technique to achieve this goal. The proposed algorithm uses multi-sub-swarm to detect multi-optimal solutions sequentially. In addition, the hill valley function proposed in the literature [10] is used in this algorithm to determine how to change the fitness of a particle in the currently running sub-swarm.

This paper is organized as follows. In Section 2, we shall give a brief overview of the hill valley function and PSO algorithm. In Section 3, we present the adaptive sequential niche particle swarm optimization (ASNPSO) algorithm and how it is implemented. Section 4 gives the experimental results for a set of test functions. Section 5 draws some conclusions.

Section snippets

Hill valley function and PSO

The determination of the niche radius is generally a hard work existing in most niche methods. However, if we have a method that can determine whether or not two points of search space belong to a peak of the multimodal function, then the niche radius is not needed in this situation. Ursem's hill valley function is the first method proposed in the literature [10], which can be described in Fig. 1, where i_p and i_q are any two points in search space. Fig. 2 just shows one-dimensional (1D)

Basic principles

The adaptive sequential niche technique is essentially an add-on technique, which can be used together with any stochastic search algorithm. Hereby, we choose the PSO algorithm to implement it. ASNPSO consists of several sub-swarms. Each sub-swarm can detect one optimal solution. Because of the algorithm using multi-sub-swarms to detect different solutions sequentially, in order to avoid all sub-swarms converging to one or several certain optimal solutions, the algorithm must be able to modify

Experimental results

In this section, there are three-benchmark functions with different complexities chosen to test our algorithm. In experiments, the SR is set as 5, and the sample array is defined as [0.02,0.25,0.5,0.75,0.98]. The halt windows are set as 20. Other experimental parameters are similar to the ordinary PSO algorithm. Assume that the inertia weight of every sub-swarm used in an experiment is set to 0.729, C1 and C2 are set to 1.49445, and V_max is set to the maximum range X_max. Shi and Eberhart [4]

Conclusions

In this paper, we proposed a novel adaptive sequential niche algorithm for multimodal function optimization. The algorithm uses hill valley function to determine whether two particles of search space belong to one hill. If a particle and the best solution found before are to locate in the same hill, through changing the particle's fitness, the algorithm will bring the particle that lost its influence into a sub-swarm. By these means, this algorithm does not need the niche radius, and at the

Acknowledgment

This work was supported by the National Science Foundation of China (Nos. 60472111 and 30570368).

Jun Zhang was born in Anhui province, China, in 1971. He received M.Sc. degree in Parttern Recognition & Intelligent System in 2004, from Institute of Intelligent Machines, Chinese Academy of Sciences. He is now in pursuit for Ph.D. degree in Pattern Recognition & Intelligent System in University of Science and Technology of China. His research interests include swarm intelligence, artificial neural networks, intelligent computing, and intelligent information processing.

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LettersA novel adaptive sequential niche technique for multimodal function optimization

Abstract

Introduction

Section snippets

Hill valley function and PSO

Basic principles

Experimental results

Conclusions

Acknowledgment

A sequential niching technique for multimodal function optimization

Evol. Comput.

Combining genetic optimisation with hybrid learning algorithm for radial basis function neural networks

IEE Electron. Lett.

Letters
A novel adaptive sequential niche technique for multimodal function optimization