Model Selecting PSO-FA Hybrid for Complex Function Optimization

Introduction

Optimization is a rational requirement in various fields and there are various kinds of optimization problems in which optimized solutions are aimed to be obtained. Among these optimization problems, black-box function optimization (Jones et al., 1998) is a common one. Black-box means that it expects to get the output with given design variables and the problem knowledge such as the landscape of the objective function is not available when finding optimum solutions. Thus, automatic search methods are usually employed to deal with such kinds of problems. In particular, a metaheuristic (Yang, 2010) approach has been an attractive method since it requires algorithmic knowledge rather than domain-specific knowledge. However, while facing different problems, metaheuristics do not always perform better than other methods. It is important to make a metaheuristic search method work well in different types of problems when facing some complex optimization functions.

Swarm intelligence (Kennedy et al., 2001) is one of the popular metaheuristics for the black-box optimization problem. For example, particle swarm optimization (PSO) (Kennedy & Eberhart, 1995) has been developed in 1995. It is well-known as a swarm intelligence model and has a simple implementation but shows good performance in some typical benchmark problems as unimodal function. Besides, there are a wide variety of swarm models have been proposed, such as the firefly algorithm (FA) (Yang, 2009), Cuckoo search, and so on. These models have their inherent characteristics and different search abilities.

There are some methods commonly used for improving the performance of some swarm intelligence models. Parameter settings for swarm intelligence models have been studied a lot. Parameter tuning is a general method for metaheuristics to effectively handle optimization problems. However, it is difficult to tune the parameters without trial and error. Expensive problems cost a lot, it needs to find ways to well handle such problems without trial and error approaches. On the other hand, the swarm intelligence family has common properties of using interactions among search agents and some kinds of probabilistic factors, and they have inherent properties according to their models. A hybridization of suitable selected swarm models would be another way of handling optimization problems effectively. From this viewpoint, it considers a hybrid swarm model by using the inherent properties in a common particle swarm.

This work focus on particle swarm optimization and firefly algorithm to make a PSO-FA hybrid algorithm. In PSO, the previous knowledge is used for each individual’s learning on the problem. Since the PSO has the weakness of trapping in local optima that would lead to premature convergence, it is important to find ways to improve this issue. Different from that PSO uses previous knowledge for information communication, FA uses current information for communication. FA would not be affected by memory and this helps to avoid premature in some situations. Thus, two different kinds of agents that move according to the PSO model or FA model respectively existing in a common hybrid swarm would be expected to contribute to improving the search performance. There are some related studies about developing PSO-FA hybrid algorithms that have been presented in recent years (Ali & Tawhid, 2017; Aydilek, 2018; Idoumghar et al., 2011; Xia, et al., 2017; Aydilek, 2018). They provide some hybrid strategies as a simple hybridization with fixed numbers of particles and fireflies (Xiao & Hatanaka, 2016a), global best comparing (Aydilek, 2018) and property change (Xiao & Hatanaka, 2016b). Here, the hybrid swarm models are summarized into several categories. One category is that the agent model consists of plural models. This category becomes a homogeneous swarm, but the agent model is more complex than the original one. The other type is that each agent model is selected from plural models, in other words, different type of agents belong to a single swarm. This category is a heterogeneous swarm. Further, the latter type is divided into two classes. One is a simple hybrid model where an agent is not changing its model, and the other is that the agent could be changing its model.