This paper hybridized the Particle Swarm Optimization (PSO) with Signal-to-Noise Ratio (SNR) to solve the numerical optimization problems. PSO has the ability of both global and local searches, where improper parameter settings could cause the algorithm to converge at the local optimum. SNR, on the other hand, has the ability to evaluate “existence possibility of optimal value”. Integration of PSO and SNR thus becomes more robust, statistically sound and efficient than PSO. In this paper, fifteen standard test functions (benchmark problems) with a large number of local optimal solutions and high dimension (30 or 100 dimension) are used for examples and solved by the proposed algorithm. The results show that the proposed algorithm by this study can effectively obtain the global optimal solutions or close-to-optimal solutions.
Global optimization problem has become increasingly important, in fields of science, engineering, trading, management and many natural behaviors. The main challenge in global optimization problems is that the solving process is more likely to fall in the local optimum of problems, especially when the dimension is very high. Most of optimization problems cannot be resolved analytically; therefore, numerical algorithms are used for solution. Evolutional Computation is a common model in solving optimization problems among numerical algorithms.
In fact, some evolutional algorithms have been applied to solving optimization problems. A chaotic bee colony algorithm was presented to solve global numerical optimization (Alatas, 2010). A hybrid genetic algorithm based quantum computing was proposed for numerical optimization and parameter estimation (Wang, Tang, & Wu, 2005). Wang and Huang presented a self-adaptive harmony search algorithm to solve the optimized problems (Wang & Huang, 2010). An improved genetic algorithm based on potential offspring production strategies was proposed for global numerical optimization (Hsieh, Sun, & Liu, 2009). An improved Genetic Algorithms were designed for the global optimization of multi-minima functions (Leung and Wang, 2001, Xing et al., 2006 and Zhang and Leung, 1999). Tsai et al. proposed the hybrid Taguchi-genetic algorithm in the numerical optimization search (Lin and Hsieh, 2009 and Tsai et al., 2004). A few of improved evolutionary algorithms were proposed for numerical optimization (Liu et al., 2007 and Zhao et al., 2008). An Improved immune algorithm was proposed for global numerical optimization and job-shop scheduling problems (Tsai, Ho, Liu, & Chou, 2007). Evolutional Computations simulate the behavioral characteristics of natural organisms, and utilize the solution set of problems to be solved by numerous individuals to carry out the solution search. The solution characteristics of evolutional algorithm are different from the traditional gradient descend, where the individuals of evolution can obtain highly adaptive offspring through evolution mechanism, such as the position updated of individuals to continue on searching, Particle Swarm Optimization (PSO) proposed.
Particle Swarm Optimization (PSO) had been proposed by Dr. Eberhart and Dr. Kennedy in 1995 (Shi & Eberhart, 1999). By observing the foraging behaviors of birds and fish, PSO can apply the activity characteristics of biotic populations to optimization problems. When birds or fish forage, they not only refer to their own experiences, but also learn from the most efficient individual in the group. They learn and exchange their experiences, and pass this experience on until the whole population reaches the optimum condition. The advantage of PSO algorithm is that individuals can converge to the optimal solution rapidly within permissible range through a small number of evolution iterations, and it also has a faster convergence rate. PSO has been successfully applied to problems in optimal search and in engineering problems. Ali and Kaelo proposed an improved particle swarm algorithm for global optimization (Ali & Kaelo, 2008). Combining particle algorithm and ant colony algorithm was proposed to improve the continuous optimization (Shelokar, Siarry, Jayaraman, & Kulkarni, 2007). Gaussian quantum-behaved Particle Swarm Optimization approaches for constrained engineering design problems was proposed to solve the numerical problems (Coelho, 2010). Xincho presented a perturb swarm algorithm for numerical optimization (Xincho, 2010). Pal and Maiti developed a binary Particle Swarm Optimization for dimensionality reduction (Pal & Maiti, 2010). A binary Particle Swarm Optimization was developed to solve the unit commitment problem (Yuan, Nie, Su, Wang, & Yuan, 2009). PSO had been successfully improved and developed to research more complicated problems.
Although PSO can expedite the solution process, the search space is relatively small, and it is likely to fall into local optimum. Therefore, this study proposed an improved Particle Swarm Optimization (PSO), which is called Particle Swarm Optimization with Signal-to-Noise Ratio (PSO/SNR). This new method integrates PSO and SNR (Phillip, 1988), and applies SNR to the initialization of PSO in order to turn infinite solution problems into finite solution problems. Furthermore, SNR is also used in Local Search in order to refine the quality of solution.
