Computers & Industrial Engineering 50 (2006) 15–34 www.elsevier.com/locate/dsw
A review of optimization techniques in metal cutting processes Indrajit Mukherjee, Pradip Kumar Ray * Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur 721 302, India Received 29 June 2004; received in revised form 21 October 2004; accepted 13 October 2005 Available online 3 February 2006
Abstract In today’s rapidly changing scenario in manufacturing industries, applications of optimization techniques in metal cutting processes is essential for a manufacturing unit to respond effectively to severe competitiveness and increasing demand of quality product in the market. Optimization methods in metal cutting processes, considered to be a vital tool for continual improvement of output quality in products and processes include modelling of input–output and in-process parameters relationship and determination of optimal cutting conditions. However, determination of optimal cutting conditions through cost-effective mathematical models is a complex research endeavour, and over the years, the techniques of modelling and optimization have undergone substantial development and expansion. In this paper, the application potential of several modelling and optimization techniques in metal cutting processes, classified under several criteria, has been critically appraised, and a generic framework for parameter optimization in metal cutting processes is suggested for the benefits of selection of an appropriate approach. q 2006 Elsevier Ltd. All rights reserved. Keywords: Process modelling; Parameter optimization; Metal cutting process; Taguchi method; Response surface design; Metaheuristic search
1. Introduction Metal cutting is one of the important and widely used manufacturing processes in engineering industries. The study of metal cutting focuses, among others, on the features of tools, input work materials, and machine parameter settings influencing process efficiency and output quality characteristics (or responses). A significant improvement in process efficiency may be obtained by process parameter optimization that identifies and determines the regions of critical process control factors leading to desired outputs or responses with acceptable variations ensuring a lower cost of manufacturing (Montgomery, 1990). The technology of metal cutting has grown substantially over time owing to the contribution from many branches of engineering with a common goal of achieving higher machining process efficiency. Selection of optimal machining condition(s) is a key factor in achieving this condition (Tan & Creese, 1995). In any multi-stage metal cutting operation, the manufacturer seeks to set the process-related controllable variable(s) at their optimal operating conditions with minimum effect of uncontrollable or noise variables on the levels and variability in the output(s). To design and implement an effective process control for metal cutting operation by parameter optimization, a manufacturer seeks to balance between quality and cost at each stage of operation resulting in improved delivery and reduced warranty or field failure of a product under consideration.
* Corresponding author. Fax: C91 3222 282272. E-mail addresses:
[email protected] (I. Mukherjee),
[email protected] (P.K. Ray).
0360-8352/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2005.10.001
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Out of many types of machining operations, boring, turning, milling, broaching, grinding, honing, and lapping are the key value-adding metal cutting processes required to produce assembly components and final products. Process parameter optimization in these machining operations is required to be undertaken in two stages: (i) modelling of input-output and in-process parameter relationship, and (ii) determination of optimal or near-optimal cutting conditions. Modelling of input–output and in-process parameter relationship is considered as an abstract representation of a process linking causes and effects or transforming process inputs into outputs (Markos Viharos, & Monostori, 1998). The resulting model provides the basic mathematical input required for formulation of the process objective function. An optimization technique provides optimal or near-optimal solution(s) to the overall optimization problem formulated, and subsequently implemented in actual metal cutting process. With time, as complexity in dynamics of cutting processes increased substantially, researchers and practitioners have focused on mathematical modelling techniques to determine optimal or near-optimal cutting condition(s) with respect to various objective criteria (Tan & Creese, 1995). Several modelling techniques proposed and implemented are based on statistical regression (Montgomery & Peck, 1992), artificial neural network (Fu, 2003) and fuzzy set theory (Zadeh, 1973). Optimization tools and techniques proposed are also based on Taguchi method (Ross, 1989), response surface design (Montgomery, 2001), mathematical programming (Hillier & Liebermann, 1999), genetic algorithm (Goldberg, 2002), tabu search (Glover, 1990), and simulated annealing (Kirkpatrick, Gelett, & Vecchi, 1983). Despite numerous studies on process optimization problems, there exists no universal input–output and inprocess parameter relationship model, which is applicable to all kinds of metal cutting processes (Hassan & Suliman, 1990). Luong & Spedding (1995) claim a lack of basic mathematical model that can predict cutting behaviour over a wide range of cutting conditions. Optimization techniques also have certain constraints, assumptions and limitations for implementation in real-life cutting process problems. Some of these limitations and assumptions are discussed in the literature. (Osborne & Armacost, 1996; Dabade & Ray, 1996; Carlyle, Montgomery, & Runger, 2000; Youssef, Sait, & Adiche, 2001). In this paper, an attempt has been made to review critically the existing and frequently used input–output and inprocess parameter relationship modelling and optimization techniques, specific to metal cutting processes. Critical appraisal of these techniques identify key issues, which are required to be addressed while carrying out a metal cutting process parameter optimization. A generic framework for carrying out process optimization study in a metal cutting process is also proposed. 2. Input–output and in-process parameter relationship modelling The first necessary step for process parameter optimization in any metal cutting process is to understand the principles governing the cutting processes by developing an explicit mathematical model, which may be of two types: mechanistic and empirical (Box & Draper, 1987). The functional relationship between input-output and in-process parameters as determined analytically for a cutting process is called mechanistic model. However, as there is a lack of adequate and acceptable mechanistic models for metal cutting processes (Luong & Spedding, 1995), the empirical models are generally used in metal cutting processes. The list of applications of modelling techniques of process input–output and in-process parameter relationship based on statistical regression (Montgomery & Peck, 1992), artificial neural network (Fu, 2003), and fuzzy set theory (Zadeh, 1973a,b; Klir & Yuan, 2002) is endless. Although these types of modelling techniques may be working satisfactorily in different situations, there are constraints, assumptions and shortcomings, limiting the use of a specific technique. The usefulness, applications, and limitations of these techniques are explained below. 2.1. Statistical regression technique Regression is a conceptually simple technique for investigating functional relationship between output and input decision variables of a cutting process and may be useful for cutting process data description, parameter estimation, and control. Several applications of regression equation-based modelling in metal cutting process are reported in literature (Ghoreishi, Low, & Li, 2002; Wasserman, 1996; Tosun & Ozlar, 2002). Hassan & Suliman (1990) use a second order multiple-regression model for medium carbon steel turning operation. Feng (Jack) and Wang (2002) show that for a reasonable large data set, regression analysis generates results comparable to artificial neural network-based
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modelling for surface roughness prediction in finished metal turning process. Lin, Bhattacharyya, and Kecman (2003) show that statistical regression model may make decent tool wear prediction as compared to artificial neural network (ANN) in a typical aluminium metal composite lathe turning operation. Although statistical regression may work well for modelling, this technique may not describe precisely the underlying non-linear complex relationship between the decision variables and responses. A prior assumption regarding functional relationship(s) [such as linear, quadratic, higher-order-polynomial, and exponential] between output(s), and input decision variable(s), is a pre-requisite for regression equation-based modelling. Prediction of output(s) for an unknown set of input(s) based on regression technique is valid only over the region of the regressor variable(s) contained in the observed cutting process data. It is only an aid to confirm cause-effect relationship, and does not imply a cause and effect relationship. Moreover, error components of regression equation need to be mutually independent, normally distributed, and having constant variance (Montgomery & Peck, 1992). 2.2. Artificial neural network (ANN) and fuzzy set theory-based modelling techniques Modelling techniques of input–output and in-process parameter relationship using ANN or fuzzy sets offer a distribution-free alternative, and have attracted attention of practitioners and researchers alike in manufacturing when faced with difficulties in building empirical models in metal cutting process control. These techniques may offer a cost effective alternative in the field of machine tool design and manufacturing approaches, receiving wide attention in recent years. 2.2.1. Artificial neural network (ANN)-based modelling ANN may handle complex input–output and in-process parameter relationship of machining control problems. The learning ability of nonlinear relationship in a cutting operation without going deep into the mathematical complexity, or prior assumptions on the functional form of the relationship between input(s), in-process parameter(s) and output(s) (such as linear, quadratic, higher order polynomial, and exponential) makes ANN an attractive alternative choice for many researchers to model cutting processes (Petri, Billo, & Bidanda, 1998; Zhang & Huang, 1995). Being a multi-variable, dynamic, non-linear estimator, it solves problems by self-learning and selforganization (Fu, 2003). The intelligence of an ANN emerges from the collective behaviour of so-called ‘artificial neuron’, and derives the process knowledge from input and output data set (Petri et al., 1998). Zang & Huang (1995) discuss the process modelling techniques by ANN along with its application potential. Coit, Jackson, and Smith (1998) consider practical aspects of building and validating ANN models, and Viharos Monostori, and Markos (1999) show control and monitoring of a machining process by ANN technique. Several applications of ANN-based input-output relationship modelling for metal cutting processes are reported in the literature. Back propagation neural network, proposed by Rumelhart, Hilton, and Williams (1986), have been successfully applied by Sathyanarayanan, Lin, and Chen (1992) and Jain, Jain, and Kalra (1999), and Feng, Wang, and Yu (2002) for modelling a typical creep feed super alloy-grinding, prediction of material removal rate and surface finish parameter of a typical abrasive flow machining, and a honing operation of engine cylinder liners, respectively. Grzesik & Brol (2003) show the usefulness of ANN modelling for controlling surface finish characteristics in multistage machining processes. There are certain assumptions, constraints, and limitations inherent in these approaches, which may be worth mentioning. ANN techniques are attempted only when regression techniques fail to provide an adequate model. Some of the drawbacks of ANN techniques are: (i) model parameters may be un-interpretable for non-linear relationship, (ii) it is dependent on voluminous data set, as sparse data relative to number of input and output variables may result in over fitting (Coit, Jackson & Smith, 1998) or terminate training before network error reaches optimal or near-optimal point, and (iii) identification of influential observations, outliers, and significance of various predictors may not be possible by this technique. There is always an uncertainty in finite convergence of algorithms used in ANN-based modelling technique, and generally convergence criteria are set based on prior experiences gained from earlier applications. No universal rules exist regarding choice of a particular ANN technique for any typical metal cutting process problem. 2.2.2. Fuzzy set theory-based modelling The fuzzy set also plays an important role in input-output and in-process parameter relationship modelling. The theory on fuzzy set admits the existence of a type of uncertainty (or indecision) in process decision variables due to
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vagueness (referred to as ‘fuzzy uncertainty’) rather than due to randomness alone, and many decisions in process control are in fuzzy environment (Zimmerman, 1976). Fuzzy set theory-based modelling technique is generally preferred when subjective knowledge or opinion(s) of process expert(s) play a key role in defining objective function and decision variables (Zadeh, 1973a,b). Shin & Vishnupad (1996) observe that the fuzzy and ANN-based modelling techniques are an effective means of control in complex grinding process. Kou & Cohen (1998) emphasize the importance of integration between fuzzy and ANN-based technique for effective process control in manufacturing. Several applications of fuzzy set theory-based modelling of metal cutting processes are reported in the literature. Kamatala, Baumgartner, and Moon (1996) develop a fuzzy set theory-based system for predicting surface roughness in a finished turning operation. Chen & Kumara (1998) use a hybrid approach of fuzzy set and ANN-based technique for designing a grinding process and its control. Hashmi, El Baradie, and Ryan (1998) apply fuzzy set theory logic for selection of cutting conditions in machining. Ip (1998) adopts a fuzzy rule based feedrate control strategy in mild steel bar surface milling operation for improvement in cutting efficiency and prolonging the tool life. Lee, Yang, and Moon (1999) use fuzzy set theory-based non-linear model for a turning process as a more effective tool than conventional mathematical modelling techniques if there exists ‘fuzziness’ in the process control variables. Al-Wedyan, Demirli, and Bhat (2001) use fuzzy modelling technique for a down milling cutting operation. Fuzzy set theory-based techniques suffer from a few shortcomings, such as rules developed based on process expert(s) knowledge, and their prior experiences and opinion(s) are not easily amenable to dynamic changes of underlying cutting process. It also does not provide any means of utilizing analytical models of metal cutting processes (Shin & Vishnupad, 1996). 3. Determination of optimal or near-optimal cutting condition(s) With time, complexity in metal cutting process dynamics has increased and as a consequence, problems related to determination of optimal or near-optimal cutting condition(s) are faced with discrete and continuous parameter spaces with multi-modal, differentiable as well as non-differentiable objective function or response(s). Search for optimal or acceptable near-optimal solution(s) by a suitable optimization technique based on input– output and in-process parameter relationship or objective function formulated from model(s) with or without constraint(s), is a critical and difficult task for researchers and practitioners (Chen & Tsai, 1996; Cakir & Gurarda, 2000; Hui, Leung, & Linn, 2001]. A large number of techniques has been developed by researchers to solve these types of parameter optimization problems, and may be classified as conventional and nonconventional optimization techniques. Fig. 1(a) and (b) provides a general classification of different input-output and in-process parameter relationship modelling and optimization techniques in metal cutting processes, respectively. Whereas conventional techniques attempt to provide a local optimal solution, non-conventional techniques based on extrinsic model or objective function developed, is only an approximation, and attempt to provide near-optimal cutting condition(s). Conventional techniques may be broadly classified into two categories: In the first category, experimental techniques that include statistical design of experiment, such as Taguchi method, and response surface design methodology (RSM) are referred to. In the second category, iterative mathematical search techniques, such as linear programming (LP), non-linear programming (NLP), and dynamic programming (DP) algorithms are included. Non-conventional meta-heuristic search-based techniques, which are sufficiently general and extensively used by researchers in recent times are based on genetic algorithm (GA), tabu search (TS), and simulated annealing (SA). A critical appraisal of each of these techniques is given below. 3.1. Conventional optimization techniques 3.1.1. Taguchi method Taguchi’s contribution to quality engineering (Kaker, 1985; Ross, 1989; Phadke, 1989) has been far ranging. The concept of Taguchi’s robust design is based on designing a product or process in such a way so as to make its performance less sensitive to variation due to uncontrolled or noise variables which are not economical to control. Taguchi method is usually appreciated for its distribution-free and orthogonal array design (Ross, 1989), and it provides a considerable reduction of time and resource needed to determine important factors affecting operations with simultaneous improvement of quality and cost of manufacturing (Unal & Dean, 1991).
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Fig. 1. Classification of modelling (a) and optimization (b) techniques in metal cutting process problems.
Taguchi’s two-fold technique of parameter design has been successfully applied in a number of metal cutting problems by researchers and practitioners alike. Youssef, Beauchamp, and Thomas (1994) discuss and compare the economical benefits of Taguchi method and fractional factorial experiments with full factorial design technique in lathe turning operations. Lin (2002) presents an application of Taguchi method for multi-response optimization in face milling operation, and shows the effectiveness of Taguchi method for simultaneous optimization and improvement of milling performance characteristics. Singh, Shan, and Pradeep (2002) illustrate the potential and use of Taguchi method to identify critical process parameters that effect material removal in abrasive flow machining. Shaji & Radhakrisnan (2003) apply Taguchi method in surface grinding process, and show the impact of graphite application to reduce heat generation in grinding zones. Manna and Bhattacharyya (2004) use Taguchi method for determining significant cutting parameter setting to achieve better surface finish during turning operation of aluminium and silicon carbide-based metal matrix composites. The Taguchi method over the years has been criticized by a number of researchers (Box, 1985; Nair, 1992; Carlyle, Montgomery & Runger, 2000). The following criticisms are worth mentioning: (i) The orthogonal array designs suggested by Taguchi are limited in numbers, and may fail to adequately deal with many important interaction effects within the domain of the designs proposed.
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(ii) Taguchi proposes a short term, one-time improvement technique to reduce the number and cost of experimentations, which may eventually lead to sub-optimal solutions. (iii) Taguchi’s method refers to optimization without intrinsic empirical or mechanistic modelling during experimentation. This type of technique closes the possibility for greater in-depth knowledge of the process (Gunter, 1988). (iv) Alternative methods, claimed to be efficient for simultaneous optimization of multiple responses [such as data transformation and using dual-response surface technique (Umland & Smith, 1959; Michaels & Pengilly, 1963), and Lambda plot (Box, 1988)], are available in the literature where basic goals of Taguchi method are achieved by simultaneous optimization of mean and standard deviation without the use of controversial S/N ratio. (v) Universal use of quadratic loss function is unconvincing as true functional relationship in complex cutting process problems may not be quadratic in nature. (vi) Taguchi method for multiple objective optimization problems, as shown by Phadke (1989), is purely based on judgmental and subjective process knowledge.
3.1.2. Response surface design methodology (RSM) The RSM (Box & Wilson, 1951; Montgomery, 2001) is a dynamic and foremost important tool of design of experiment (DOE) wherein the relationship between response(s) of a process with its input decision variables is mapped to achieve the objective of maximization or minimization of the response properties. It is a set of statistical DOE techniques, intrinsic regression modelling, and optimization methods useful for any field of engineering. The first necessary step in RSM is to map response(s), Y as a function of independent decision variables (X1,.,Xn). If the model is adequate, hill climbing or descending technique for maximization or minimization problem is attempted and the same mapping technique is repeated. In the vicinity of optimal point, a second order regression model is generally found adequate. Maximum, minimum, or a saddle point is identified by stationary point approach and canonical analysis of the second order model developed, and ‘ridge analysis’ is attempted if it is a saddle point (Mayers & Carter, 1973). An extension of ridge analysis, called dual-response surface design methodology (Umland & Smith, 1959; Michaels & Pengilly, 1963), is developed where the researchers confront with the need for simultaneous optimization of two or more response variables. Vining and Myers (1990) provide a dual response surface framework to address the primal goal of Taguchi method to obtain a target condition on the mean with minimization of variance by considering standard deviation as primary response and mean as secondary response avoiding S/N ratio approach. Box (1988) and Logothetics (1990) independently provide different ways of data transformation in the application of Taguchi’s philosophy for robust process parameter design, such as lambda plotting technique, and Box and Cox data transformation technique, which is claimed to be statistically valid and meaningful alternative, compared to the use of Taguchi’s S/N ratio scale for performance measure of mean and variability in responses. Many researchers and practitioners use RSM in metal cutting process parameter optimization problems. Taramen (1974) uses a contour plot technique to simultaneously optimize tool wear, surface finish, and tool force for finished turning operation. Lee, Shin, and Yang (1996) provide an interactive algorithm using both RSM and mathematical modelling to solve a parameter optimization problem in turning operation. Fuh and Chang (1997) analyse the effect of change in work piece material and each cutting parameter in various peripheral milling operations, and model the dimensional accuracy by a second order response surface design. El-Axir (2002) concentrates on response surface design methodology to model the effect of machining parameters on residual stresses distribution for five different materials in turning operations. Although RSM works well in many different process optimization problems, there are a few limitations inherent in this approach. Carlyle et al. (2000) emphasize on the application of mathematical iterative search algorithm, and heuristic or meta-heuristic search techniques, in preference to RSM, specific to highly nonlinear, multi-modal, objective functions. They also highlight that these types of problems are extremely difficult to solve by RSM, and problem complexity increases further by the presence of multiple objectives. Del Castillo and Semple (2000) mention that although RSM works well when the number of responses is maximum three, it generally gives indefinite saddle function in quadratic response surface model with more than three responses. RSM techniques are based on series of experimentation, and may not be feasible or cost effective for manufacturers in many manufacturing situations.
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Moreover, objective or response function needs to be continuously differentiable for determination of optimal cutting condition, which may not be the case in many complex physical processes. 3.1.3. Iterative mathematical search technique Linear, non-linear, and dynamic programming techniques (Hillier & Liebermann, 1999) may be described in terms of their structures, computational procedures, and important decision problems formulated as minimization or maximization of a mathematical function of several variables having a number of constraints. In this approaches, there is no need to construct an actual physical model of the metal cutting process under consideration, which is mostly replaced by an empirical mathematical model describing the actual process. In any general LP cutting process problem, both objective function and constraint equation(s) are linear functions, and the most popular search algorithm in LP is simplex. As metal cutting process problems are mostly complex and non-linear in nature, LP techniques does not provide an adequate answer, or may not be appropriate for many such problems. Multi-modal functions and consideration of multiple nonlinear response functions justify the use of NLP solution techniques in this case. In any NLP cutting process optimization problem formulation, either the objective function(s) or at least one of the constraints is non-linear in nature, and a particular combination of cutting conditions is optimal, if and only if, all of Kuhn-Tucker conditions (Hillier & Liebermann, 1999) with other convexity assumptions on response functions are satisfied. Goal programming, introduced by Charner and Cooper (1963), was earlier used to solve many multiobjective NLP process problems. Derringer and Suich (1980) recommend a modified ‘desirability function’-based approach, earlier proposed by Harrington (1965), in multi-response process optimization problem, and use process targets and response deviations to represent a single objective function or scale. Khuri and Conlon (1981) proposed a generalized distance metric, when the responses are correlated in multiple response optimization problems. Carlyle et al. (2000) discuss and critically review a few other useful techniques, such as branch and bound technique (Hillier & Liebermann, 1999), and generalized reduced gradient method (Del Castillo & Montgomery, 1993) developed to solve NLP problems. Determination of optimal cutting process parameter settings is a key factor to achieve machine or process efficiency, and a number of mathematical programming techniques has been proposed and effectively used to achieve this objective. Hayers and Davis (1979) illustrate the application of dynamic programming (DP) approach for attaining optimal machine parameter settings when tool changes occur only between passes in cutting operation. Sekhon (1982) proposes an optimization algorithm, based on DP approach to solve a four-stage machining operation problem when machine variables are considered to be discrete in nature. Hassan and Suliman (1990) illustrate the use of regression analysis with which prediction of surface roughness, tool vibration, cutting time, and power consumption is made prior to obtaining optimal cutting conditions by Powell’s method (Powel, 1964). Agapious (1992a,b & c) suggests DP technique to formulate single and multi-pass machining operations. Tan and Creese (1995) use a sequential method based on LP to attain optimal machine parameter settings in multi-pass turning operation. Gupta, Batra, and Lal (1995) propose a methodology for selection of depth of cut for rough and finished passes in multi-pass turning operation to minimize total manufacturing cost by integer linear programming (ILP). Prasad, Rao and Rao (1997) combine LP and geometric programming to optimize the values of process parameters for a multipass turning operation. Chen, Lee, and Fang (1998) put forward an IP and DP-based two-tier approach for reduction of machining time in NC machining by cutter selection and machining plane. Liang, Mgwatu and Zuo (2001) extend the study of Wang, Zuo, Qi, and Liang (1996) on determination of optimal process parameter settings for multi-pass turning operation. Hui et al. (2001) show how the choice of machining conditions for turning significantly impact on quality cost, by solving a nonlinear continuous constrained optimization problem using a nonlinear optimization search algorithm, based on quasi-Newton method and a finite difference gradient. Many other iterative mathematical search algorithms with their applications are reported in the literature, such as geometric programming approach (GopalaKrisnan & Al-Khayyal, 1991), and Nelson-Mead simplex search approach (Agapious, 1992a,b & c). Although LP, NLP, and DP work well in many situations, a few shortcomings of these techniques may be worth mentioning: (i) mathematical iterative search techniques focus on certain specific aspects of machining (such as cutting force, temperature, and tool wear) and may not handle the overall cutting process complexities due to large number of inter-dependent variables and their stochastic relationships (Markos et al., 1998), (ii) the multi-modal, multi-objective response function need to be continuously differentiable to attain optimal set point by NLP and DP techniques, which may be a restrictive assumption in real life problems. Moreover, heuristic and meta-heuristic
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techniques may provide an alternative near-optimal cutting condition(s), which are cost effective and reasonably acceptable for implementation by manufacturers rather than searching for exact optimal cutting condition(s) based on LP, NLP or DP techniques. 3.2. Non-conventional techniques 3.2.1. Heuristic search technique Heuristics, generally providing simple means of indicating which among several alternative solutions seems to be the most effective one in order to achieve some goal, consist of a rule or a set of rules seeking acceptable solution(s) at a reasonable computational cost (Voß, 2001). Heuristic-based search techniques may be very useful for cases where conventional optimization techniques are not suitable, such as problems with high-dimensional search space with many local optima. Researchers and practitioners prefer alternative cost effective near-optimal (or approximate) solution(s) than exact optimal, as it may be extremely difficult to find exact optimal point in higher dimension, and multimodal search space. In this context, the so-called ‘evolutionary algorithm’ (Zintzler & Theile, 1999, and Deb, 2002) has been extensively used in different types of combinatorial process optimization problems for near-optimal solution(s). Lacksonen (2001) reviews critically the heuristic-based search techniques for discrete event process optimization problems. Lee and Shin (2000) apply an evolutionary algorithm, called ‘modified evolutionary strategy’, for two different kinds of constrained non-linear mixed-discrete optimization problems in grinding processes to find the optimal cutting conditions, highlighting its superiority over quadratic programming technique. 3.2.2. Metaheuristic search technique Although heuristic search may offer near-optimal solution(s), they are mainly problem-specific (De Werra and Hertz, 1983). Researchers suggest several alternatives to problem specific heuristics, also called generalized iterative master strategy or ‘metaheuristic’ (Glover, 1986; Glover & Laguna, 2002), which guide and modify other heuristics to produce solutions that are normally generated in a quest for local optimality. As has been reported in the literature, three types of metaheuristic-based search algorithms viz. genetic algorithm (GA), simulated annealing (SA), and tabu search (TS) are applied in the domain of cutting process parameter optimization. These techniques are derivative-free, and are not based on functional form of relationship existing between response(s) and decision variables for its search direction. Each of these techniques is explained below along with their application and limitation. 3.2.2.1. Genetic algorithm (GA). The working of GA (Holland, 1975; Goldberg, 2002; Deb, 2002) generally preferred for large and complex cutting process parameter optimization problems, is based on three basic operators, viz., reproduction, crossover, and mutation, in order to offer a population of solutions. The algorithm creates new population from an initial random population (obtained from different feasible combination of process decision variables) by reproduction, crossover, and mutation in an iterative process. The selection, crossover and mutation on initial population create a new generation, which is evaluated with pre-defined termination criteria. The procedure continues by considering current population as initial population till the termination criteria are reached. GA is very appealing for single and multi-objective optimization problems (Deb, 2002), and some of its advantages are as follows: (i) as it is not based on gradient-based information, it does not require the continuity or convexity of the design space, (ii) it can explore large search space and its search direction or transition rule is probabilistic, not deterministic, in nature, and hence, the chance of avoiding local optimality is more, (iii) it works with a population of solution points rather than a single solution point as in conventional techniques, and provides multiple near-optimal solutions, (iv) it has the ability to solve convex, and multi-modal function, multiple objectives and non-linear response function problems, and it may be applied to both discrete and continuous objective functions. Fig. 2 explains in detail a typical GA-based optimization technique using extrinsic input-output relationship model or objective function. Several applications of GA-based technique in metal cutting process parameter optimization problems have been reported in the literature. Liu and Wang (1999) claim that by reducing the operating domain of GA, by changing the operating range of decision variables, convergence speed of GA increases along with significant increase in milling process efficiency. Onwubolu and Kumalo (2001) propose a local search GA-based technique in multi-pass turning operation with mathematical formulation in line with work by Chen and Tsai (1996) with simulated annealing-based
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Fig. 2. GA-based optimization technique for metal cutting process problems.
technique. Krimpenis and Vosniakos (2002) use a GA-based optimization tool for sculptured surface CNC milling operation to achieve optimal machining time and maximum material removal. Chowdhury, Pratihar, and Pal (2002) apply a GA-based optimization technique for near optimal cutting conditions selection in a single-pass turning operation, and claim that GA outperform goal programming technique in terms of unit production time at all the solution points. Wang, Da, Balaji and Jawahir (2002) apply GA-based technique for near-optimal cutting conditions for a two-and three-pass turning operation having multiple objectives. Cus and Balic (2003) use GA-based technique to determine the optimal cutting conditions in NC-lathe turning operation on steel blanks that minimize the unit production cost without violating any imposed cutting constraints. Schrader (2003) illustrates the usability of GAbased technique for simultaneous process parameter optimization in multi-pass turning operations.
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Although GA-based optimization technique works well in many situations, a few shortcomings of this technique may be worth mentioning: (i) convergence of the GA is not always assured; (ii) no universal rule exists for appropriate choice of algorithm parameters, such as population size, number of generations to be evaluated, crossover probability, mutation probability, and string length; (iii) GA may require a significant execution time to attain near-optimal solutions, and convergence speed of the algorithm may be slow. Moreover the repeatability of results obtained by GA with same initial decision variable setting conditions is not guaranteed. 3.2.2.2. Tabu search (TS). A local search algorithm-based technique, called ‘Tabu Search’ (TS), developed by Glover (Glover, 1989, 1990) derives its attractiveness due to its greater flexibility and ease of implementation in combinatorial optimization problems. TS algorithm starts with an initial feasible solution point (obtained from random feasible combination of process decision variables), and moves stepwise towards an improved solution point. A sample of decision space vectors in the neighbourhood of the current decision vector is generated, and the best vector within the sample is determined based on a heuristic approach. A move is made from current decision vector to a best decision vector not in tabu list, which provides improved objective function value in a single step by simple modifications of current decision vector. A tabu list contains a certain number of last decision vectors visited. The best decision vector replaces the oldest vector in the tabu list, and the survival vectors in the list are given a tabu active status, which reduces risk of cycling of same decision vector (i.e. modification in current decision vector, which would bring back previously visited vector). In subsequent iteration, uses of tabu active vectors are forbidden (so called ‘tabu moves’) for creating a sample of decision vectors in the neighbourhood of current decision vector space. Tabu active status of a decision vector is overridden only based on certain aspiration level criteria, such as acceptance of the modification on current vector that improves objective function value (De Werra & Hertz, 1989). Fig. 3 explains in detail the TS-based technique for cutting process parameter optimization. TS-based technique has been successfully applied to provide near-optimal and acceptable solution in many combinatorial process optimization problems. Glover and Laguna (2002) provide a probabilistic TS-based technique for discrete process optimization problems. Battiti and Tecchiolli (1994) propose a reactive TS technique, which may be applied for discontinuous or non-differentiable functions, and recommend the use of binary search space where neighbourhood evaluation is based on stochastic sampling. Salhi (2002) advocates a defining functional representation of tabu list size and flexible aspiration level conditions in TS to improve its effectiveness. Cvijovic and Klinowki (1995) claim that the potential of TS technique may be further explored through increased experimentations and applications. Although Kolahan and Liang (1996), while exploring the potentials of TS-based technique for simultaneous decision-making, attempt to minimize drilling cost by setting a number of machining parameters, such as machine cutting speed, tool travel, tool switch, and tool selection for a drilling operation in a plastic injection mould, there is hardly any report indicating an application of this technique for metal cutting process parameter optimization. Although TS may be considered to be a good alternative to GA or SA to solve complex combinatorial optimization problems within a reasonable amount of computational time, there are certain constraints and assumptions inherent in this technique. The convergence of TS algorithm for multi-modal objective function in a finite number of steps is not guaranteed like other metaheuristic. The choice of tabu list size always influences end solution of the problem, as a list of small size may result in wasteful revisit of same cutting condition vectors, and a list of long size may lead to significantly longer computational time to verify tabu status of a candidate cutting condition vector. Selection of aspiration level criteria also plays a key role in randomization of search to unexplored feasible regions. 3.2.2.3. Simulated annealing (SA). SA technique (Kirkpatrick et al., 1983; Cerny, 1985), based on the concept of modelling and simulation of a thermodynamic system, may be used to solve many combinatorial process optimization problems. This technique starts with selection of an initial random process decision vector, and moves to new neighbourhood decision vector that improves objective function value. SA technique may accept inferior decision vector based on certain probabilistic measure to avoid local optimal in a multimodal response function. The probability that there is a move to an inferior decision vector (or the decision vector which provides degraded objective function value) decreases as the value of a ‘temperature parameter’ defined in the algorithm, decreases, which is analogous with slow cooling in an annealing process to attain perfect crystalline state. SA procedure of stochastic search algorithm gradually changes to a traditional gradient descent search method as the temperature parameter value drops.
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Fig. 3. TS-based optimization technique for metal cutting process problems.
Fleischer (1995) highlights several important implementation issues, such as appropriate cooling schedule, suitable objective function, and well-defined neighbourhood structure, which must be addressed before any reasonable SA-based algorithm may be developed for a specific process optimization problem.. Saravanan, Ashokan, and Sachithanandam (2001) make a comparative study of the conventional and non-conventional approaches for CNC-turning process optimization problems, and observe that there is more flexibility incorporated in SA algorithm and GA-based techniques over conventional techniques, such as boundary search procedure and Nelson-Mead simplex search method (Nelson & Mead, 1965). The details of a typical SA algorithm-based technique for metal cutting process parameter optimization problem are briefly described with the help of a flow diagram as shown in Fig. 4. A number of different versions and applications of SA algorithm-based technique in metal cutting process problems is reported in the literature. Chen and Tsai (1996) combine SA and Hooks-Jeeves pattern search technique
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Fig. 4. SA-based optimization technique for metal cutting process problems.
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(Hooks & Jeeves, 1961) for optimizing cutting conditions in complex machining (multi-pass turning operation) to minimize unit operation cost. Chen and Su (1998) determine near optimal machining conditions for a continuous profile turning operation in CNC by using SA algorithm, and claim that the algorithm deliver high quality heuristic solution with reasonable computational requirements. For optimization of CNC turning process, Juan, Yu, and Lee (2003) apply SA-based technique to attain optimal cutting conditions of high sped milling operation. SA techniques may be used to solve continuous or discrete state space cutting process optimization problems. The stochastic nature of the algorithm and guided probabilistic moves are two of its key aspects in case of a multi-modal response function. Although SA is appreciated for its simplicity and effectiveness, the convergence of the algorithm may be strongly affected by the parameters of cooling schedule, and no universally acceptable levels of control parameters in cooling schedule exist for different types of cutting process parameter optimization problem. Moreover, the repeatability of the near-optimal solution obtained by SA with same initial cutting conditions is not guaranteed. Although, each modelling or optimization technique, with its variants, as mentioned have its versatility, no single guideline or clear-cut criterion exists to choose the best one and judge the performance of different alternative techniques in any metal cutting process optimization problem. Table 1 provides a list of typical application areas of different modelling and optimization techniques as mentioned. Table 1 Application of different input-output and in-process parameter relationship modelling and optimization techniques in cutting processes Modelling and optimization approaches
Application areas (as reported in Literature)
Number of objective function(s) considered
Number of operation stage(s) considered
Special consideration in the approach
Statistical regression
(i) Lathe turning (Hassan & Suliman, 1990) (ii) Finished turning (Feng(Jack) and Wang, 2002) (i) Creep feed grinding (Sathyanarayanan et al.,1992)
(i) One (ii) One
(i) One (ii) One
(i) Three
(i) One
(ii) Two
(i) One
(i) None (ii) Fractional factorial design (i) Generalized reduced gradient method (ii) None
(iii) Five
(iii) One
(i) End milling (Ip, 1998) (ii) Down milling (Al-Wedyan et al., 2001) (i) Lathe turning (Youssef et al., 1994) (ii) Face milling (Lin, 2002) (iii) Surface grinding (Shaji and Radhakrisnan, 2003) (i) Finish turning (Taramen, 1974)
(i) Two (ii) One (i) One (ii) Three (iii) Two
(i) One (ii) One (i) One (ii) One (iii) One
(i) Three
(i) One
(ii) Turning (Lee at al., 1996) (i) Multi-stage machining (Sekhon, 1982)
(ii) Two (i) Two
(ii) One (i) Four
(ii) Multi-pass turning (Tan & Creese, 1995)
(ii) One
(iii) Turning (Prasad et al., 1997)
(iii) One
(ii) Maximum 3pass (iii) One
(i) CNC milling (Liu & Wang, 1999) (ii) Multi-pass turning (Onwubolu & Kumalo, 2001) (i) NC multi-pass turning (Chen & Tsai, 1996) (ii) CNC cylinder stock turning (Chen & Su, 1998) (iii) High speed milling (Juan et al., 2003) (i) Drilling (Kolahan, & Liang, 1996)
(i) One (ii) One
(i) One (ii) Two
(i) One
(i) Two
(ii) One
(ii) Four
(ii) Sequential linear programming (iii) Geometric and linear programming (i) None (ii) SA, LP, and fuzzy set (i) Hook-Jeeves pattern search (ii) None
(iii) One (i) One
(iii) One (i) One
(iii) None (i) None
Artificial neural network
(ii) Abrasive flow machining (Petri et al., 1998) (iii) Honing (Feng et al., 2002) Fuzzy set theory Taguchi method
Response surface design methodology Mathematical iterative search algorithm
Genetic algorithm
Simulated annealing
Tabu search
(iii) Paired t-test & Ftest (i) None (ii) Surface plot (i) Full factorial design (ii) None (iii) None (i) Central composite design (ii) Simulation model (i) Lagrange multipliers
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4. A generic framework for process parameter optimization in metal cutting operation As any metal cutting process problem may have some unique characteristics, it may be difficult for researchers and practitioners to select a suitable optimization technique that provides acceptable and improved cutting conditions. A comparative study of the different techniques, based on a suitable measure of quality of solution obtained, may be helpful to select the most appropriate one in this context. Based on the understanding of the input–output and in-process parameter relationship modelling and optimization techniques in metal cutting processes and their merits and potential areas of improvement, a generic framework for process parameter optimization in cutting process problems is considered to be a prime necessity. The details of this framework are explained with the help of a flow chart as shown in Fig. 5. The framework is explained under two broad categories: (i) process input-output and in-process parameter relationship modelling; and (ii) determination of optimal or near optimal solution(s). The steps involved in each category are explained below. 4.1. Process input–output and in-process parameter relationship modelling The objective of any empirical metal cutting process modelling is to reveal the underlying relationship(s) between independent process decision variables and the dependent output response(s). The following steps are required to be incorporated in the modelling approach: Step-1 Define the metal cutting process optimization problem highlighting its criticality in terms of the selected criteria, such as scrap/rework cost, variability in the quality characteristics and/or process performance. Criticality of a problem may be judged based on Pareto analysis (Montgomery, 1990) of scrap/rework cost incurred due to nonconformance to specifications of product quality characteristics. Graphical representations (such as histogram, and control chart) of the data collected on different critical quality characteristics provide an insight into the mean, the variability, and the control state of critical quality characteristics. Initial process performance or capability study also identifies the need for improvement of product/process quality. Step-2 All relevant decision variables and output responses related to the cutting operations considered, their specifications, and actual operating levels and ranges need to be identified at this stage. The response(s) may be related to several aspects, such as functional requirements, productivity, physical characteristics, process efficiency, and other similar factors as identified. An insight into the problems being encountered or reported may lead to an appropriate selection of decision variables. The pertinent and reliable data related to input conditions, in-process parameters, and response variable(s) are to be collected through discussion with the concerned personnel, reference to the relevant documents, standards and performance statistics, and inputs from the feedback sessions for the cutting process. The whole exercise may be planned in an open and interactive mode. Step-3 Preliminary data analysis of multiple responses based on statistically sound data reduction techniques in case data volume is large (e.g. multivariate analysis, (Rencher, 1995)) may be applied. A screening experiment may also facilitate modelling, and may help identify the critical decision variables. Step-4 In this step, an empirical model is to be developed for which statistical regression, or ANN-based, or fuzzy set theory-based modelling techniques to express the complex relationship between input(s), inprocess parameter(s) and output(s) based on prevailing constraints and assumptions need to be applied. It is imperative that the most appropriate, easy-to-implement, and cost-effective model is to be developed. Step-5 The designed process model is tested, and validated in a number of dissimilar situations and circumstances. Validating in dissimilar situations and circumstances evaluates the relevance of the testing methods and also determines if the developed model is a representation of real world. It is also necessary to understand the inherent characteristic features/selection norms indicative of the application potential, and the general condition(s) including constraint(s) under which each modelling techniques are applicable
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Fig. 5. A generic framework for modeling and optimization of a typical metal cutting process problem.
before optimisation techniques are selected. Some of these characteristic features/selection norms of the modelling techniques are provided in Table 2. 4.2. Determination of optimal or near-optimal solution(s) The characteristic features/selection norms of the optimization techniques, indicative of their application potential, and the general condition(s) including constraint(s) in which they are applicable are provided in Table 3.
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Table 2 Inherent characteristic features/selection norms of input–output and in-process parameter relationship modelling techniques Modelling technique
Inherent characteristic features/selection norms
Statistical regression
(i) The form of mathematical function (such as linear, quadratic, higher order polynomial and exponential) is generally presumed for estimation of model parameters, and then the model is tested, verified and validated. (ii) Errors or residuals are assumed to be independent, normally distributed with mean zero, and constant variance s2, and these assumptions are required to be valid for model adequacy. (i) Preferably used for modelling linear or non-linear relationship between process decision variables and responses. (ii) A useful technique when a lower-order polynomial equation seems inappropriate for modelling the cutting process, and effect of noise or missing data seems to influence the model significantly. The physical interpretation of weight parameters is difficult, if not impossible for a multi-layered neural network while modelling a non-linear system. (i) Preferred when objective functions (conflicting), constraints, and decision variables are not completely defined and precisely measured, or linguistically expressed (such as visual inspection of quality characteristics, if not clearly specified in design). (ii) Applicable when conditions indicative of inexact information(s), subjective opinion(s) and vagueness due to personal bias prevail (such as comfort, and beauty of an automobile, if not specified in design). A suitable technique for cutting process problems when multiple quality characteristics exist, and the hierarchy of importance of each objective is not clearly defined by the designer.
Artificial neural network
Fuzzy set theory
Table 3 Inherent characteristic features/selection norms of optimization tools and techniques Optimization tools and techniques
Inherent characteristic features/selection norms
Taguchi method
(i) A useful technique where a series of experimentations may be conducted, and interactions between process decision variables are less significant. (ii) Suitable for both continuous and discrete response(s), and independent of intrinsic modelling approach. (i) Useful intrinsic model-based technique when sequential experimentation is possible in metal cutting processes. (ii) Suitable for process problems where a lower-order-polynomial regression equation exists to establish the relationship between response and decision variables at an early stage of experimentation. (i) Generally preferred when objective function is continuously differentiable, and the functional form (such as linear, non-linear, concave and convex) of the objective function and constraint(s) are well defined and known. (ii) Useful intrinsic model-based technique for cases where an exact optimal solution needs to be achieved, and it is suitable for both single-and multi-stage decision-making problems. (i) Preferred when near-optimal improved cutting condition(s) instead of exact optimal conditions are cost effective and acceptable for implementation by the manufacturers. (ii) A derivative-free approach for near-optimal point(s) search direction, and may be applied to discrete or continuous response function. (i) A generalized, extrinsic model-based, easy-to-implement technique providing near-optimal solution to combinatorial optimization problems, and suitable for multi-modal non-linear response function. (ii) No gradient calculation is required to determine its search direction. It is considered to be less sensitive to the size of a problem, and it attempts to avoid local solutions in multi-modal response function. (i) A generalized, extrinsic model-based, problem independent, easy-to-implement technique that may be applied virtually to any kind of process optimization problems. (ii) A derivative-free approach, and may be applied to multi-minima (or maxima), linear (or non-linear), and discrete (or continuous) response function.
Response surface design methodology
Mathematical iterative search algorithm
Genetic algorithm
Simulated annealing
Tabu search
5. Conclusion A systematic approach of modelling and determination of optimal or near-optimal cutting conditions has shown an interesting potential in both product and process quality improvement of metal cutting operation. The generic framework for process parameter optimization in metal cutting operation attempts to provide a single, unified, and systematic approach to determine optimal or near-optimal cutting conditions in various kinds of metal cutting process
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Indrajit Mukherjee received his B.E. (Mechanical) from Jalpaiguri Government Engineering College, Jalpaiguri, West Bengal, and M. Tech. (Quality, Reliability and Operations Research) form Indian Statistical Institute, Kolkata, West Bengal. He worked as a senior engineer in the department of central quality in Tata Motors Limited during 2001–2002. Presently he has joined as a research scholar in the Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur. His area of interest is quality engineering and applied operations research. He is a student member of several professional bodies, such as ASME, SME, and IIE.
Pradip Kumar Ray is presently a Professor in the Department of Industrial Engineering and Management, Indian Institute of Technology (IIT), Kharagpur, India. He received his Ph. D. (in 1991) and M. Tech (in 1981) degrees from IIT, Kharagpur, and Bachelor of Mechanical Engineering (in 1979) degree from Calcutta University, India. Dr Ray has over 24 years of diversified experience—8 years as Senior Industrial Engineer at General Electric Company of India in Calcutta, 2 years as Associate Professor at Eastern Mediterranean University in Cyprus, and 14 years of teaching and research experience at IIT. He has published a number of papers in international and national journals and conferences in the areas of productivity measurement and evaluation, quality engineering, TQM, operations research, ergonomics, and other related topics. His areas of interest and research include productivity modelling, quality engineering, ergonomics, and JIT-based operations management. Dr Ray is a certified Lead Assessor for ISO9000 registration, and actively involved in a number of industrial consulting in his interest areas. He is a member of several professional bodies such as INFORMS, IIMM, and WAPS.
