# Analysis and Improvement of Fireworks Algorithm
## 1 Introduction  
The Fireworks Algorithm (FWA) [1] is a newly developed evolutionary algorithm. Like other evolution algorithms, it also aims to find the vector with the best (usually minimum) fitness in the search space. Inspired by real fireworks, the main idea of the FWA is to use the explosion of the fireworks to search the feasible space of the optimization function, which is a brand new search manner. At present, the fireworks algorithm has been applied to many practical optimization problems [2], the application areas include the factorization of a non-negative matrix [3], the design of digital filters [4], the parameter optimization for the detection of spam [5], the reconfiguration of networks [6], the mass minimization of trusses [7], the parameter estimation of chaotic systems [8], the scheduling of multi-satellite control resources [9], etc.  
However, similar to other intelligent optimization algorithms, fireworks algorithms have some disadvantages such as slow convergence speed and low accuracy, thus, many improved algorithms have been proposed. An enhanced fireworks algorithm (EFWA) was put forward by analyzing the explosion operator, mutation operator, selection strategy and mapping rule of the fireworks algorithm [10]. An adaptive firework algorithm (AFWA) is proposed to carry out the self-tuning for the explosion amplitude [11]. That is to say, the explosion amplitude of the fireworks is determined by the distance between the individual with the best population fitness value and the distance between a specific individual. A dynamic search firework algorithm (dynFWA) is proposed, which divides the fireworks population into optimal firework with the optimal fitness value and non-optimal fireworks. By doing so, the two populations maintained a good balance during the evolution and showed goodperformance [12]. However, the fireworks algorithm is still in the development stage, to be further studied to enhance the performance.  
In this paper, firstly we use the opposition-based learning strategy to initialize population to increase the diversity of the population and improve the probability to search the global optimal solution. Secondly a new explosion amplitude mechanism for the optimal firework is proposed from the aspects of population evolution rate and population aggregation degree, to enhance the ability to search the global optimal solution of the optimal firework. In addition, adaptive \(t\)-distribution for non-optimal fireworks and elite opposition-based learning for optimal firework are applied, in order to improve the global exploration ability and local development ability and make the FWA jump out of the local optimum effectively. Finally, a new selection strategy is proposed to reduce the run-time of the algorithm. Based on this, an improved fireworks optimization algorithm (IFWA) is proposed to improve the convergence speed and precision and reduce the run-time.  
The paper is organized as follows. In Section 2, the fireworks algorithm is introduced. The IFWA algorithm is presented in Section 3. The simulation experiments and results analysis are given in details in Section 4. Finally, the conclusion summarizes in final part.