In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.

The current study presents an effective framework for automated multi-objective optimization (MOO) of machining processes by using finite element (FE) simulations. The framework is demonstrated by optimizing a metal cutting process in turning AISI-1045, using an uncoated K10 tungsten carbide tool. The aim of the MOO is to minimize tool-chip interface temperature and tool wear depth, that are extracted from FE simulations, while maximizing the material removal rate. The effect of tool geometry parameters, i.e., clearance angle, rake angle, and cutting edge radius, and process parameters, i.e., cutting speed and feed rate on the objective functions are explored. Strength Pareto Evolutionary Algorithm (SPEA2) is adopted for the study. The framework integrates and connects several modules to completely automate the entire MOO process. The capability of performing the MOO in parallel is also enabled by adopting the framework. Basically, automation and parallel computing, accounts for the practicality of MOO by using FE simulations. The trade-off solutions obtained by MOO are presented. A knowledge discovery study is carried out on the trade-off solutions. The non-dominated solutions are analyzed using a recently proposed data mining technique to gain a deeper understanding of the turning process.

Machining process efficiencies can be improved by minimising the non-machining time, thereby resulting in short operation cycles. In automatic-machining centres, this is realised via optimum cutting tool allocation on turret-magazine indices – the “tool-indexing problem”. Extant literature simplifies TIP as a single-objective optimisation problem by considering minimisation of only the tool-indexing time. In contrast, this study aims to address the multi-objective optimisation tool-indexing problem (MOOTIP) by identifying changes that must be made to current industrial settings as an additional objective. Furthermore, tool duplicates and lifespan have been considered. In addition, a novel mathematical model is proposed for solving MOOTIP. Given the complexity of the problem, the authors suggest the use of a modified strength Pareto evolutionary algorithm combined with a customised environment-selection mechanism. The proposed approach attained a uniform distribution of solutions to realise the above objectives. Additionally, a customised solution representation was developed along with corresponding genetic operators to ensure the feasibility of solutions obtained. Results obtained in this study demonstrate the realization of not only a significant (70%) reduction in non-machining time but also a set of tradeoff solutions for decision makers to manage their tools more efficiently compared to current practices.

This study investigates the advantages and potentials of the metamodel-based multi-objective optimization (MOO) of a turning operation through the application of finite element simulations and evolutionary algorithms to a metal cutting process. The objectives are minimizing the interface temperature and tool wear depth obtained from FE simulations using DEFORM-2D software, and maximizing the material removal rate. Tool geometry and process parameters are considered as the input variables. Seven metamodelling methods are employed and evaluated, based on accuracy and suitability. Radial basis functions with a priori bias and Kriging are chosen to model tool–chip interface temperature and tool wear depth, respectively. The non-dominated solutions are found using the strength Pareto evolutionary algorithm SPEA2 and compared with the non-dominated front obtained from pure simulation-based MOO. The metamodel-based MOO method is not only advantageous in terms of reducing the computational time by 70%, but is also able to discover 31 new non-dominated solutions over simulation-based MOO.