## 1. Introduction

Turning is one of the essential operations in the lathe. During the turning process, the prominent contributing control variables affecting the process are spindle speed, feed rate, depth of cut, etc. [

1]. These process variables must be optimized to obtain maximum productivity and reduce the costs involved. Traditionally, researchers have relied upon the use of one factor at a time (OFAT) analysis to determine the optimum process parameters. However, OFAT techniques are very inefficient because they require a lot of experiments to be carried out. Thus, the advent of regression-based or machine learning-based, predictive models (or metamodels) has been a boon. These compact, reusable and easily deployable metamodels have in general, excellent generalization power which makes them extremely reliable. However, the effectiveness of such metamodels depends on numerous factors including the quality, integrity and size of data, and the nonlinearity in the physical process.

Polynomial regression (PR) and its variants are by far the most widely used metamodels, especially in machining/manufacturing process optimization. This is perhaps because they are easy to implement (as they do not require high-level programming skills or use of complicated mathematical principles), easily quantifiable (due to their fixed form) and readily deployable. Santhanakrishnan et al. [

2] built a PR model to study the effect of rake angle, nose radius, cutting speed and feed rate on machining of aluminum. Suresh et al. [

3] quantified the material removal rate (MRR) and tool wear rate (TWR) in stainless steels by using PR models. Prabhu and Vinayagam [

4] used a full factorial design (FFD) based electric discharge machining experimental dataset to build a PR model. Apart from PR, symbolic regression [

5], artificial neural network models [

6], adaptive neuro-fuzzy models [

7] are often used in process parameter metamodeling.

On the one hand, the metamodels can be used to find the main or interactive effects of the process variables, carrying out sensitivity analysis or uncertainty quantification of the process itself. On the other hand, they must be deployed in conjunction with optimization algorithms to determine the optimum process variables. The optimization algorithms can range from gradient-based algorithms [

8,

9] to robust topology optimization [

10] to metaheuristic algorithms [

11,

12].

Metaheuristic optimization algorithms are a set of popular optimization algorithms that require no assumptions to be made about the problem to be optimized. Genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), cuckoo search (CS), grey wolf optimization (GWO), etc., are some popular metaheuristics used in process parameter optimization. Kilickap and Huseyinoglu [

11] used a GA with PR metamodel to optimize the burr height during drilling operations. Kilickap et al. [

12] used a similar PR-GA strategy to minimize the material’s surface roughness. Kalita et al. [

13] used both GA and PSO to optimize the laser beam settings in a micro-marking process. In a separate study [

14], the delamination in composites due to drilling was also optimized by GA and PSO. In both the studies, it was found that PSO, in general, had faster convergence compared to traditional GA. Nevertheless, since its advent in the 1960s, GA has been successfully deployed for solving almost all types of optimization problems.

Saidi et al. [

15] used PR metamodels and the concept of desirability function to maximize the MRR and minimize the SR. They found that the depth of cut has the most impact on the MRR, and the DR is adversely affected by increasing feed rate and insert nose radius. Mia et al. [

16] compared the performance of the teaching–learning-based algorithm (TLBO) and bacterial foraging optimization (BFO) to carry out a multiobjective scalar (by using weighted-sum approach) optimization in turning applications. TLBO was found to have a better convergence. Warsi et al. [

17] reported a 5% reduction in specific cutting energy and a simultaneous 33% improvement in MRR by using a multiobjective approach in turning of aluminum alloys. Mia and Dhar [

18] compared the prediction performance of PR and support vector regression (SVR) metamodels in turning of AISI 1060 steel and found that SVR has superior estimation capability. The SVR and PR metamodels were optimized by using GA, and it was reported that a low feed rate, low material hardness and high cutting speed would produce good quality surfaces with less roughness. Laouissi et al. [

19] carried out a similar comparison between PR and ANN metamodels while turning gray cast iron.

Though sufficient work has been done to decide the best parameters in the turning procedure, the scope for further research is adequate. Thus, this research attempts to select the ideal combination for maximizing the MRR during turning of galvanized iron. A novel cuckoo search variant called the coevolutionary host-parasite (CHP) optimization algorithm is used in this study. To the best of authors’ knowledge, this is the first attempt to use a cuckoo search or its variant in the optimization of the turning process.

The rest of the paper is organized as follows. A brief explanation of the approaches such as regression analysis, coevolutionary host-parasite (CHP), material and experimental work is included in

Section 2. The statistical analysis of the experimental data, metamodeling and CHP-based process optimization is presented in

Section 3. Specific inferences established in the study are strained in the last part of the paper.

## 4. Conclusions

The effects of machining variables, namely feed rate (F), spindle speed (N), depth of cut (d) on metal removal rate (MRR) have been analyzed during turning galvanized iron using regression-based second-order mathematical models. Based on the experimentation and statistical analysis of the regression model, it is seen that for attaining maximum MRR, the turning tool should be operated at a low feed rate and low spindle speed, if the depth of cut is high. Similarly, the MRR is minimum when the tool is operated at high spindle speed coupled with a low feed rate for low depth of cut. The confirmation experimental trials run on the optimum parameter setting presented that the CHP was very accurate while predicting the global optima. Only 2.45% variation was seen in the CHP predicted optimal and the corresponding experimental output. By carrying out extensive repeated trials of process parameter optimization as well as a comprehensive robustness test, it was shown that the CHP algorithm is very reliable and efficient in locating the global maxima. Thus, the CHP algorithm may be used in conjunction with regression models for the optimization of various other machining and manufacturing operations as it would lead to significant improvement in productivity. Though the focus of the current study has been to increase the productivity of the turning process, the described approach can be easily tuned to tackle other interesting machining problems like improving dimensional accuracy and obtaining better surface finish. Future work of the researchers will focus on some of these issues, as well as tackling the problem from many objective viewpoints, wherein multiple attributes of the machining process can be simultaneously optimized. Further robustification of the machining process parameter optimization approach by coupling the current memetic cuckoo search with advanced machine learning predictive models like neural networks, symbolic regression, support vectors, etc., can be another interesting avenue.