An Improved Fireworks Algorithm with Landscape
Information for Balancing Exploration and
Exploitation
Junfeng Chen
∗†
, Qiwen Yang
∗†
, Jianjun Ni
∗†
, Yingjuan Xie
∗†
, Shi Cheng
‡
∗
College of IOT Engineering, Hohai University, Changzhou China
†
Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Changzhou China
‡
Division of Computer Science, University of Nottingham Ningbo, China
Email: chen-1997@163.com, qwyang2k@126.com, shi.cheng@nottingham.edu.cn
Abstract—Fireworks algorithm is a newly risen and devel-
oping swarm intelligence algorithm, the performance of which
is determined by the tradeoff between exploration and ex-
ploitation. How to develop a satisfactory weight for exploration
and exploitation is an interesting and challenging work. In
this paper, the landscapes of optimization problem are firstly
analyzed, and then a new sparks explosion strategy is designed
to represent and mine the landscape information. Moreover, the
exploration and exploitation coexist in the improved fireworks
algorithm, which can automatically adjust the search strategies
according to landscape structure. Finally, numerical experiments
are performed for the algorithms investigations, performance
analysis, and comparisons. The simulation results indicate that
the proposed algorithm has a significant performance on all the
test functions and can achieve the global minimum for most test
functions.
Index Terms—Fireworks algorithm, landscape information,
exploration, exploitation
I. INTRODUCTION
Fireworks Algorithm (FWA) [1], [2] is a newly risen and
developing swarm intelligence algorithm, which is inspired by
the explosion and illumination of fireworks in the night sky.
It is originally attributed to Tan and Zhu, and was modified
for solving practical problems, such as nonnegative matrix
factorization [3], digital filters [4], spam detection [5], and
oil crop fertilization [6]. Similar to most swarm algorithms,
FWA makes few or no assumptions about the problem being
optimized and takes an advantage of swarm searching with
a population (called a swarm) of candidate solutions (called
sparks) to seek high quality solutions of complicated optimiza-
tion problems efficiently and effectively.
Many researchers believe that the behavior of a swarm algo-
rithm is determined by two forces: exploration and exploitation
[7]. Excessive exploitation will be high-efficiency, but easy
to induce premature convergence. Excessive exploration will
increase accuracy, but consume too much computation time.
Thus, how to get a tradeoff between the exploration and
exploitation is really a key to the global performance of
swarm intelligence algorithms. Many strategies for balancing
exploration and exploitation were proposed in the past decade.
For instance, Blum and Roli pointed out that the mechanisms
of metaheuristics to efficiently explore a search space are all
based on intensification and diversification, although they are
inspired by different philosophies [7]. Liu et al. introduced an
entropy-driven exploration and exploitation approach for evo-
lutionary algorithms [8]. Olorunda and Engelbrecht developed
a diversity rate for a particle swarm optimization to quantify
the rate of change from exploration to exploitation [9]. Zhao et
al. designed fitness function, crossover operator and mutation
operator for the genetic algorithms to improve the explorative
capabilities and the exploitation effects [10]. Epitropakis et al.
proposed a hybrid differential mutation method, which was a
linear combination of the explorative and exploitive operators
[11]. Lin and Gen introduced fuzzy logic control into genetic
algorithm for balancing between exploration and exploitation
[12]. Li et al. presented a well-designed density estimator for a
dynamic neighborhood evolutionary algorithm, which achieves
auto-tuning between proximity and diversity [13]. Pei et al.
employed elite individuals sampling, the elite neighborhood
sampling and random sampling strategies into the FWA for
approximating fitness landscape and enhancing search capa-
bility [14]. Liu et al. provided a new parameter for FWA
to control the exploration and exploitation dynamically [15].
Crepinsek et al. discussed what components of evolutionary
algorithms contribute to exploration and exploitation, when
exploration and exploitation are controlled and how balance
between exploration and exploitation is achieved [16].
In view of the above-mentioned facts, FWA is not sophis-
ticated enough and can be further improved by developing a
satisfactory weight for exploration and exploitation. Moreover,
the same search strategies may result in different optimization
effects, when dealing with simple and smooth landscapes,
or dealing with bumpy and rough landscapes. In our view,
the search efficiency of FWA is not only influenced by
search strategies, but also related to the fitness landscape of
optimization problems to be solved. As a result, the main
objective of this paper is to reveal the relationship between
the landscape information of optimization problems and the
interaction mechanisms of exploration and exploitation of
FWA.
The remaining paper is organized as follows. In Section
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