Firefly Algorithms for Multimodal Optimization
Xin-She Yang
Department of Engineering, University of Cambridge,
Trumpington Street, Cambridge CB2 1PZ, UK
Abstract. Nature-inspired algorithms are among the most powerful al-
gorithms for optimization. This paper intends to provide a detailed de-
scription of a new Firefly Algorithm (FA) for multimodal optimization
applications. We will compare the proposed firefly algorithm with other
metaheuristic algorithms such as particle swarm optimization (PSO).
Simulations and results indicate that the prop osed firefly algorithm is
superior to existing metaheuristic algorithms. Finally we will discuss its
applications and implications for further research.
1 Introduction
Biologically inspired algorithms are becoming powerful in modern numerical
optimization[1,2,4,6,9,10],especiallyfortheNP-hardproblemssuchas
the travelling salesman problem. Among these biology-derived algorithms, the
multi-agent metaheuristic algorithms such as particle swarm optimization form
hot research topics in the start-of-the-art algorithm development in optimization
and other applications [1, 2, 9].
Particle swarm optimization (PSO) was developed by Kennedy and Eberhart
in 1995 [5], based on the swarm behaviour such as fish and bird schooling in
nature, the so-called swarm intelligence. Though particle swarm optimization
has many similarities with genetic algorithms, but it is much simpler because
it does not use mutation/crossover operators. Instead, it uses the real-number
randomness and the global communication among the swarming particles. In
this sense, it is also easier to implement as it uses mainly real numbers.
This paper aims to introduce the new Firefly Algorithm and to provide the
comparison study of the FA with PSO and other relevant algorithms. We will first
outline the particle swarm optimization, then formulate the firefly algorithms
and finally give the comparison about the performance of these algorithms. The
FA optimization seems more promising than particle swarm optimization in the
sense that FA can deal with multimodal functions more naturally and efficiently.
In addition, particle swarm optimization is just a special class of the firefly
algorithms as we will demonstrate this in this paper.
O. Watanabe and T. Zeugmann (Eds.): SAGA 2009, LNCS 5792, pp. 169–178, 2009.
c
Springer-Verlag Berlin Heidelberg 2009
