ORIGINAL ARTICLE Optimization of die design using metaheuristic methods in cold forward extrusion process Ali Sadollah • Ardeshir Bahreininejad Received: 17 February 2011 / Accepted: 3 May 2011 Ó Springer-Verlag London Limited 2011 Abstract Selection of processing and geometrical parameters is a crucial step in the extrusion process design. Optimized parameters may result in desirable microstruc- ture at minimum load. The purpose of this paper is deter- mination of the optimal cold forward extrusion parameters with the minimization of tool load as the objective function. This paper deals with different optimization approaches in order to determine the optimal values of logarithmic strain, die angle, and friction with the purpose of finding the minimal tool loading obtained by cold forward extrusion process. The obtained extrusion force model as a fitness function was used to carry out the optimization. Based upon the objective function, metaheuristic algorithms such as genetic algorithm and simulated annealing were adopted as optimization methods for finding the optimum values of cold forward extrusion parameters and the obtained results were compared with those in literature. The better results lead to the smallest energy consumption, longer tool life, better formability of the work material, and the quality of the finished product. Keywords Cold forward extrusion  Extrusion force model  Die angle  Simulated annealing  Genetic algorithm 1 Introduction The metal forming process is characterized by various process parameters including the shape of the workpiece and product, forming sequence, shapes of tools or dies, friction, forming speed, temperature, and material property of the workpiece and those of the tools. Therefore, deter- mination of the optimal forming parameters by using optimization techniques is continuous engineering task with main aim to reduce the production cost and achieve desired product quality [1, 2]. The forming technologies that have been applied for many years in a definite conventional form can be inno- vated by applying knowledge from the area of modeling, simulations, optimizations, theory of processes, computer technique, and artificial intelligence [3]. The optimization methods have been improved by development of applied mathematics, statistics, operational researches, design of experiment, simulation, and information computational methods. Today, there are more different optimization methods. The use of the existing methods depend on objects modeling, required degree of model accuracy, type of process, and necessity of optimization. Yanran et al. [4] applied finite element method (FEM) to analyze the steady deformation stage of extrusion and to optimize the semi- code angle of extrusion die based on minimal deformation force and the obtained results compared with result of experimental. Pathak and Ramakrishnan [5] optimized die angle and ram velocity for rod extrusion using genetic algorithm (GA) and dynamic material modeling (DMM). Selection of strain rate was done by DMM and minimi- zation of punch load was carried out using GA. The effect of die profile on the variation of stress and load in the cold forward extrusion of aluminum was studied by Noorani– Azad et al. [6]. The purpose of their research was the reduction in deformation load, improvement in the metal- lurgical properties of the product, and increasing the die life by optimizing die profile. Byon and Hwang [2] based upon an integrated thermo-mechanical finite element A. Sadollah  A. Bahreininejad (&) Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia e-mail: bahreininejad@um.edu.my 123 Neural Comput & Applic DOI 10.1007/s00521-011-0630-6