1. Introduction

Since early research work on simulation of forming processes, the finite element method (FEM) has the capability of producing detailed deformation information for hot and cold forging processes, and solves a large variety of problems by changing the model and process parameters. However, design modifications by process simulation using a trial and error procedure may easily become an endless and tedious task.

Nowadays, new procedures became available, which are succeeding as efficient alternative predicting "tools" in the design stage of a component, namely the backward tracing method [PAR 83], [HAN 93], [ZHA 95] and the forward tracing method [GRA 93] and [BER 95]. Other authors developed so-called inverse techniques. The goal of these inverse problems is to determine one or more of the direct problem input data, leading to a prescribed result. Some of the first research work in this area has been concerned with 2D shape inverse problems, which were successfully solved and presented by Fourment et al. [FOU 94, 96, 01], Zabaras et al. [ZAB 93], [BAD 95], Zhao et al. [ZHA 97], and Chung et al. [CHU 98]. More recently, research work on die shape optimal design in three dimensional shape metal extrusion [JOU 98] and 2D microstructure optimization in design of forging [GAO 00] has been presented. Also Rodic et al. [ROD 99] has developed a computer...