The use of evolutionary algorithms (EA s) for solving multiobjective optimization problems has been very active in the last few years. The main reasons for this popularity are their ease of use with respect to classical mathematical programming techniques, their scalability, and their suitability for finding trade-off solutions in a single run. However, these algorithms may be computationally expensive because (1) many real-world optimization problems typically involve tasks demanding high computational resources and (2) they are aimed at finding a whole front of optimal solutions instead of searching for a single optimum. Parallelizing EAs emerges as a possible way of reducing the CPU time down to affordable values, but it also allows researchers to use an advanced search engine – the parallel model – that provides the algorithms with an improved population diversity and enable them to cooperate with other (eventually nonevolutionary) techniques. The goal of this chapter is to provide the reader with an up-to-date review of the recent literature on parallel EAs for multiobjective optimization.

Parallel Multiobjective Evolutionary Algorithms

Coupling of evolutionary algorithms (EA) with meta-models (MM) is used to investigate the concept of the optimal die semi-angle in wire drawing. Traditional process design by minimization of the wire drawing force highlights an optimal die angle which increases with friction factor and reduction ratio. When wire drawing optimization is applied on the Latham and Cockcroft damage criterion, an optimal die semi-angle no longer appears: in this mono-objective optimization, the lowest industrially achievable die angle is recommended. Thanks to EA-MM coupling, multi-objective optimizations have been performed and the Pareto optimal front has been precisely plotted so as to find the best compromise. Simultaneous optimization of damage and wire drawing force suggests a refined vision of the optimal die semi-angle concept. Choosing a lower angle than the traditional optimum allows damage to be decreased without a significant increase of the drawing force. However, it is shown that a die semi-angle slightly above the optimum should be selected, for fear of friction drift; this explains the rather high traditional value of the angle.

The optimal die semi-angle concept in wire drawing, examined using automatic optimization techniques

This thesis deals with the numerical simulation of cold forming processes, i.e. wire drawing and rolling. First, high carbon steel mechanical behaviour was measured from experiments throughout this range of steel forming and a progressive mechanical anisotropy has been observed during drawing. Secondly, numerical simulations, with FORGE2005®, have been run to simulate the material behaviour during wire drawing and rolling. The main results show that the widening prediction, with an isotropic behaviour law, is not accurate with an underestimation of 10% on the total width. This underestimation is only 5% when an anisotropic behaviour is used. Then, a microstructural study coupled with an analysis of damage mechanisms was done on high carbon pearlitic steels during wire drawing and rolling. The mechanical anisotropy comes from the orientation of the pearlitic colonies in the drawing, and by the emergence of a preferential crystallographic texture. Three damage mechanisms have been identified during drawing. During rolling, damage expansion kinetics are changed because of heterogeneous strain. Simulation enabled to bring further information and to validate previous experimental observations. Finally, drawing optimization calculations have been performed and enabled to study the sensitivity of the cost functions (damage and drawing force) to optimization parameters (drawing die geometry). Moreover this study highlighted that optimal solution depends on the choice of the cost function and identified an opportunity to reduce damage by reducing the die angle without increasing the axial stresses and the fracture risk.

Study and optimization of high carbon steel flat wires

The aim of this paper is to present a method to perform evolutionary multi-objective optimization of CPU intensive sheet metal forming applications using kriging surrogates. Two main ingredients are employed to achieve this goal. First of all, given a learning dataset, the kriging surrogate is designed to minimize the leave-one-out error. Secondly, during the optimization, new data points are added to the learning set to update the surrogate locally (by well chosen points on the current Pareto front) and globally (by maximum kriging variance points over the entire design landscape). The ability of the method to capture Pareto fronts with accuracy is demonstrated on the well-known ZDT test functions. The method is then tested on a real-life problem, the simultaneous minimization of springback and failure for a three-dimensional CPU intensive high strength steel stamping industrial use case.

Kriging surrogates for evolutionary multi-objective optimization of CPU intensive sheet metal forming applications

In the field of materials forming processes, the use of simulation coupled with optimization is a powerful numerical tool to support design in industry and research. The finite element software Forge®, a reference in the field of the two-dimensional and three-dimensional simulation of forging processes, has been coupled to an automatic optimization engine. The optimization method is based on meta-model assisted evolutionary algorithm. It allows solving complex optimization problems quickly. This paper is dedicated to a specific application of optimization, inverse analysis. In a first stage, a range of reverse analysis applications are considered such as material rheological and tribological characterization, identification of heat transfer coefficients and, finally, the estimation of Time Temperature Transformation curves based on existing Continuous Cooling Transformation diagrams for steel quenching simulation. In a second part, a novel inverse analysis application is presented in the field of cold sheet forming, the identification of the material anisotropic constitutive parameters that allow matching with the final shape of the component after stamping. The advanced numerical methods used in this kind of complex simulations are described along with the obtained optimization results. This article shows that automatic optimization coupled with Forge® can solve many inverse analysis problems and is a valuable tool for supporting development and design of metals forming processes.

Inverse Analysis of Forming Processes Based on FORGE Environment

The use of material processing numerical simulation allows a strategy of trial and error to improve virtual processes without incurring material costs or interrupting production and therefore save a lot of money, but it requires user time to analyze the results, adjust the operating conditions and restart the simulation. Automatic optimization is the perfect complement to simulation. Evolutionary Algorithm coupled with metamodelling makes it possible to obtain industrially relevant results on a very large range of applications within a few tens of simulations and without any specific automatic optimization technique knowledge. Ten industrial partners have been selected to cover the different area of the mechanical forging industry and provide different examples of the forming simulation tools. It aims to demonstrate that it is possible to obtain industrially relevant results on a very large range of applications within a few tens of simulations and without any specific automatic optimization technique knowledge. The large computational time is handled by a metamodel approach. It allows interpolating the objective function on the entire parameter space by only knowing the exact function values at a reduced number of “master points”. Two algorithms are used: an evolution strategy combined with a Kriging metamodel and a genetic algorithm combined with a Meshless Finite Difference Method. The later approach is extended to multi-objective optimization. The set of solutions, which corresponds to the best possible compromises between the different objectives, is then computed in the same way. The population based approach allows using the parallel capabilities of the utilized computer with a high efficiency. An optimization module, fully embedded within the Forge2009 IHM, makes possible to cover all the defined examples, and the use of new multi-core hardware to compute several simulations at the same time reduces the needed time dramatically. The presented examples demonstrate the method versatility. They include billet shape optimization of a common rail, the cogging of a bar and a wire drawing problem.

Mono and multi‐objective optimization techniques applied to a large range of industrial test cases using Metamodel assisted Evolutionary Algorithms

This paper studies efficient techniques to find the optimal set of solutions (Pareto front) for multiobjective optimization problems in the context of time expensive evaluation of functions. These techniques make use of a meta-model based on the Meshless Finite Difference Method (MFDM) coupled with evolutionary Multi-Objective algorithm (here: NSGA-II) in order to minimize the time consuming evaluations and to achieve a faster convergence to the Pareto front. The different studied methods differ in the choice of master points, the evolution of the meta-model, and the updating of elitism. They are studied and compared on several analytical functions, with only 100 exact evaluations of the objective function. The obtained results show the efficiency of these techniques.

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Meta-model assisted multi-objective optimization for non-steady 3D metal forming processes

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Mono and multi‐objective optimization techniques applied to a large range of industrial test cases using Metamodel assisted Evolutionary Algorithms

Meta-model assisted multi-objective optimization for non-steady 3D metal forming processes