Applied Soft Computing 12 (2012) 1765–1786 Contents lists available at SciVerse ScienceDirect Applied Soft Computing j ourna l ho mepage: www.elsevier.com/locate/asoc Momentum coefficient for promoting accuracy and convergence speed of evolutionary programming Yousef Alipouri a , Javad Poshtan a , Yagub Alipouri b , Mohammad Reza Alipour c,∗ a Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran b Department of Civil Engineering, Amirkabir University of Technology, Tehran, Iran c Tuberculosis and Lung Research Center, Tabriz University of Medical Sciences, Tabriz, Iran a r t i c l e i n f o Article history: Received 8 August 2010 Received in revised form 11 August 2011 Accepted 10 January 2012 Available online 18 February 2012 Keywords: Evolutionary programming Gathering point Mean value Momentum Coefficient Evolutionary Programming a b s t r a c t Many practical problems culminate with solving optimization problems. Thus, many methods have been introduced for solving these types of problems. The need for algorithms that are fast and more accu- rate at finding global minimums is ever increasing. One of the promising methods is a heuristic and iterative method called Evolutionary Programming (EP). It is one of the computational methods used in optimization that is implemented for many practical applications. Many papers have shown the capa- bility of this algorithm for addressing a variety of optimization problems. These studies have opened a vast new and interesting field of research. Recently, many methods have been proposed for promoting the performance of EP when finding the optimum point of functions or applications; however, EP has some shortcomings that cause slow convergence on some functions, especially multimodal functions. By overcoming these shortcomings, EP could be more effective in the optimization research field. This paper introduces new methods for overcoming these disadvantages and promoting the performance of EP. One of these methods, which has the best results on cost functions, changes the searching procedure by adding a new factor to produce offspring and pulling offspring toward a gathering point (the mean value of the parents). This method was tested on 50 well-known test functions discussed in the literature and was compared with state-of-the-art algorithms on twenty-two new cost functions. Finally, a hybrid method of CEP and MCEP (Momentum Coefficient Evolutionary Programming) called IMCEP (Improved Momentum Coefficient Evolutionary Programming) is introduced. The results of the calculations reported here show the efficiency of MCEP and IMCEP. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Darwinian evolution, proposed in 1859, is intrinsically a robust search and optimization mechanism. Darwin’s principle of the “Sur- vival of the fittest” captured the popular imagination. This principle can be used as a starting point in introducing evolutionary compu- tation. The theory of natural selection proposes that plants and animals that exist today are the result of millions of years of adaptation to the demands of the environment. Evolutionary computation (EC) techniques abstract these evolutionary principles into algorithms that may be used to search for optimal solutions to a problem. In a search algorithm, a number of possible solutions to a problem are ∗ Corresponding author. E-mail addresses: alipouri yousef@elec.iust.ac.ir (Y. Alipouri), jposhtan@iust.ac.ir (J. Poshtan), yagub.alipouri@aut.ac.ir (Y. Alipouri), alipourmr52@gmail.com (M.R. Alipour). available and the task is to find the best solution possible in a fixed amount of time. In the case of evolutionary computation, there are four historical paradigms that have served as the basis for much of the activity of the field: Genetic Algorithms (GA) [1], Genetic Programming (GP) [2], Evolutionary Strategies (ES) [3], and Evolutionary Program- ming (EP) [4]. The basic differences between these paradigms lie in the nature of the representation schemes, the reproduction and mutation operators and the selection methods [5]. These methods have drawn much attention in the research community in conjunction with parallel and/or distributed com- putations. EP especially was studied initially as a method for generating artificial intelligence [6,7]. In the 1960s, Fogel developed EP, which originally resolved problems in weather forecasting. He proposed a finite space evolu- tionary model whose mutations were based on uniform stochastic distributions. In the 1990s, Fogel put the ideas of EP into applica- tions that involve real number spaces, which was the beginning of resolving optimization problems in real number space. After being 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2012.01.010