Differential Evolution (DE) algorithm is known as robust, effective and highly efficient for solving the global optimization problems. In this chapter, a modified variant of Differential Evolution (DE) is proposed, named Cultivated Differential Evolution (CuDE) which is different from basic DE in two ways: 1) the selection of the base vector for mutation operation, 2) population generation for the next generation. The performance of the proposed algorithm is validated on a set of eight benchmark problems taken from literature and a real time molecular potential energy problem. The numerical results show that the proposed approach helps in formulating a better trade-off between convergence rate and efficiency. Also, it can be seen that the performance of DE is improved in terms of number of function evaluations, acceleration rate and mean error.
TopIntroduction
Evolutionary Algorithm (EA) is a stochastic population-based algorithm and has significant rise in the field for solving multi-objective optimization problems because of the fact that EA deals with a set of solutions more efficiently than classical methods. In the mid-90s, Differential Evolution (DE) is initially proposed by Storn and Price (1997) for optimization1 problems over continuous spaces as a new addition to EAs. EA works with three operators named selection, crossover and mutation. DE also uses the same operators, but the difference between DE and other EAs is the working of these operators. DE mainly comprises the characteristics of convergence speed2, robustness and simple in terms of application. Within a short period of approx. 30 years, DE has been successfully applied in a very simple and efficient way for solving single-objective global optimization problems and in many other application fields such as pattern recognition (Wang, Zhang, & Zhang, 2007), medical science (Plagianakos, Tasoulis, & Vrahatis, 2008), integer programming problems (Zaheer & Pant, 2014), chemical engineering and various science and engineering fields (Ilonen, Kamarainen, & Lampinen, 2003). Also DE has been successfully applied to a wide range of problems including Batch Fermentation Process (Wang & Cheng, 1999), Optimal design of heat exchanges (Babu & Munawar, 2007), synthesis and optimization of heat integrated distillation system (Babu & Singh, 2000), optimization of non-linear chemical process (Angira & Babu, 2005), optimization of process synthesis and design problems (Angira & Babu, 2006), optimization of thermal cracker operation (Babu & Angira, 2001), optimization of water pumping system (Babu & Angira, 2003), dynamic optimization of a continuous polymer reactor (Lee, Han, & Chang, 1999), optimization of low pressure chemical vapour deposition reactors (Lu & Wang, 2001), and recentlty used for multi-level image thresholding (Ali, Ahn, & Pant, 2014; Ali, Ahn, Pant, & Siarry, 2015) etc.