Multipass Turning Operation Process Optimization Using Hybrid Genetic Simulated Annealing Algorithm

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Introduction
Metal removal processes such as turning operations involve different variables ranging from input variables (cutting speed, feed rate, depth of cut, and number of passes) to output variables (production cost, production time, tool life, dimensional accuracy, surface roughness, cutting forces, cutting temperature, and power consumption, etc.).Selecting appropriate cutting conditions has a significant impact on machining cost, product quality, and manufacturing cycle-time.These parameters are feed rate (f), speed of cut (V), depth of cut (d), and number of passes (n).Turning operation can be illustrated in Figure 1.
The first paper related to parameter selection problem of multipass turning presented by Shin and Joo [1] initiated a series of studies.Authors from different backgrounds attempted optimization of the same problem using various optimization approaches [2,3].
Chen and Tsai [4] proposed a hybrid technique based on Simulated Annealing Algorithm and the Hooke-Jeeves pattern search (SA-PS) to minimize the unit production cost; Onwubolu and Kumalo [5] presented an optimization based on Genetic Algorithm approach and have shown that GA optimization technique gives better results than [4].However, M.-C.Chen and K.-Y.Chen [6] demonstrated that the result obtained by [5] was invalid, due to incorrect handling of the equality constraint of cutting depth.Vijayakumar et al. [7] have attempted the same problem using the Ant Colony Optimization (ACO) Algorithm.Subsequently, Wang [8] proved that the optimal solution, as found by [7], was also not valid.Srinivas et al. [9] used Particle Swarm Optimization (PSO) to minimize the unit production cost similarly to Chen and Tsai [4].
In the last decade, hybrid optimization techniques continue to attract more researchers by their ability to solve complex combinatorial optimization problems and various combinations approaches have been proposed by several authors.Costa et al. [10] proposed a Hybrid Particle Swarm Optimization (HPSO) technique for solving multipass turning optimization problem as presented by [4]. Lee and Ponnambalam [11] used a hybrid algorithm by combining the GA and the Artificial Immune Algorithm and attempted the same model as [7].Xie and Guo [12] combined Ant Colony Optimizations (ACO) with a Pass Enumerating method to minimize unit production cost as well as [4].
Yildiz implemented several optimization techniques for solving the multipass turning operations problem, such as hybrid approach based on the Differential Evolution algorithm [13], Hybrid Robust Differential Evolution (HRDE) algorithm [14], Hybrid Artificial Bee Colony algorithm [15], and Hybrid Robust Teaching-Learning-Based Optimization (HRTLBO) algorithm [16] and hybrid PSO combined with Receptor Editing property of immune system [17].However, any information about the optimal values of the machining parameters was provided.
Aryanfar and Solimanpur [18] presented an optimization of multipass turning operation based on GA technique which aims to minimize the unit production cost.Jabri et al. [19] proposed GA approach to solve a multiobjective problem where machining cost and tool life cost are simultaneously optimized.Rao and Kalyankar [20] used the Teaching-Learning-Based Optimization algorithm to solve the same problem (multipass turning operation).They concluded that the TLBO can converge to the optimal solution within a lower number of iterations.Belloufi et al. [21] proposed a Firefly Algorithm (FA), but constraint limitation such as cutting force was incorrectly handled.
Mellal and Williams [22] utilized Cuckoo optimization algorithm seeking to minimize production cost and comparing the obtained results with previously published results.In this study, the algorithm obtained the known optimal parameters in one case but failed in another.Chauhan et al. [23] proposed a Totally Disturbed Particle Swarm Optimization (TDSPO) for this problem where the phenomenon of chaos is embedded at PSO in order to disturb the particles at later iterations to prevent stagnation.Compared with the basic PSO the proposed method has given best results.Gayatri and Baskar [24] developed a sequential hybrid approach which is a fusion of GA, SA, and PSO optimization techniques to solve the multipass turning problem.In their work, three different selection methods of GA are studied which are linear ranking, tournament selection, and roulette wheel selection; the former method is the best selection method of GA technique and the hybrid approach has proven effectiveness when compared to each one.Another work related to the multipass turning problem is recently published [25]; it is based on a novel optimization technique called Flower Pollination Algorithm (FPA).The global and local search operators made of this optimization technique a powerful approach and it has given satisfactory results.
As presented in the above literature review, turning process is a complex problem to solve since it involves numerous elements.In fact, various optimization approaches are proposed by authors from different areas hoping to improve quality results in terms of precision and computational time.
Unfortunately, it appears that more efforts are needed to be made to assist the process planner with reliable tool while selecting best machining parameters.In this work, a Hybrid Genetic Simulated Annealing Algorithm is developed to minimize the unit production cost of multipass turning process; the performance of the proposed optimization approach is highlighted by comparing the obtained results with different optimal costs presented by various optimization techniques.
The rest of the paper is organized as follows.In the next section, we present the problem concerned which is an objective function to minimize subject to various operational and practical constraints.In Section 3 the proposed hybrid algorithm optimization for multipass turning operation is presented.Parameters calibration of the proposed algorithm is then studied and obtained results are presented and compared to previously published works in Section 4. Finally, concluding remarks and some possible future works are given.

Multipass Turning Mathematical Model
The mathematical model of multipass turning operation proposed by [1] has remained a topic of interest for researchers; it is adopted in the present paper and the unit production cost subject to constraints will be minimized.Constraints Modelling and Simulation in Engineering 3 including parameter bounds and cutting condition restraints on the tool and the workpiece are taken into account in this study.A detailed presentation of the objective and the constraints is given below.

Objective Function.
The unit production cost, UC, for multipass turning operations can be divided into four basic cost elements.
(i) Cutting cost by actual time: (ii) Machine idle cost due to loading and unloading operations and idling tool motion: (iii) Tool replacement cost: (iv) Tool cost: where Finally, objective function which is the sum of these costs can be expressed as follows: 2.2.Constraints.Constraints are technical and operational limitations that should be taken into consideration during the roughing and finishing operations.These constraints involve parameter bounds, operating constraints, and cutting condition relations.

(i) Parameter Bounds
(ii) Operating Constraints.The cutting force and the power constraints for both roughing and finishing operations are expressed as follows: The chip-tool interface constraint of ( 10) follows the formulation of Hati and Rao (1976) [26]: The stable cutting region constraint of ( 11) and the surface finish constraint of ( 17) follow the formulation of Narang and Fischer (1993) [27]: (iii) Cutting Parameter Relations

Proposed Solution Algorithm
The proposed HSAGA is based on the combination between the GA algorithm and SA-based local search.In this section we present a brief overview on SA and GA techniques.GA is a randomized global search technique that solves problems by imitating processes observed from natural evolution; it has been introduced by Holland in 1960s and further described by Goldberg [28].So far, GA has been successfully adopted in many complex optimization problems and shows its merits over traditional optimization methods.GA starts with a population of candidate solutions that evolves to reach near optimal solution.Each candidate is usually coded as a binary string "chromosome" in order to undergo reproduction; the fitness of each individual is then evaluated after the operation of decoding chromosome.
On the other hand, The SA algorithm mimics the behaviour of a physical system that is heated and then cooled slowly, such as growing crystals or annealing metals.Presented for the first time by Kirkpatrick et al. [29], it can 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 "" called the Boltzmann statistics (see (18)), which helps the algorithm to escape entrapment in local optima and eventually reach the global optima: where Δ represents the difference in the objective value between the generated solution   and the current solution  (see (19))."" is the annealing initial temperature GA optimization technique has strong global search ability, but it also has limitations such as a premature and slow convergence rate, as well as weak local search ability.On the other hand, SA algorithm has strong local search ability and no premature problems.In this paper, a Hybrid Simulated Annealing Genetic Algorithm (HSAGA) is proposed to overcome the limits of each of the two techniques, bringing into play their respective advantages, and improve the solving efficiency.
3.1.Initialization.In this step of Genetic Algorithm a population of individuals (for each variable) is generated using the random uniform distribution in the defined interval, for both roughing and finishing operations.Feed rate (f) is a real number generated between [  ,   ]; cutting speed (V) and depth of cut (d) are integer numbers generated in the ranges [  ,   ], [  ,   ], respectively.In order to take into account the relation between   and   , the depth of cut of roughing is derived, subject to the fact that they lie between the accepted limits of [  ,   ].It should be noted that the population size "Popsize" has a considerable impact on quality solution and computational duration; thus it needs to be fixed at the appropriate value.Each element of the solution space "" has a cost value obtained using the objective function: ().

Evaluation and Constraints
Handling.The purpose of this optimization is to compute the minimal cost of a turning operation.A score function value is associated with each element of solution space (competitiveness).The penalty function is used to penalize the individuals who violate the constraints.The more the constraints are violated, the heavier the penalty will be done.As a result, the fitness of them will be small.In this way, unfeasible solutions have more chance to be eliminated from the solution space.Using the objective function the probability of selection is calculated as follows: where is the value of objective function of the current element "". worst is the worst value of the current solution space (the maximum value of objective function).
The probability   gives to the element the chance to be reproduced based on its competitiveness.

Solution
Encoding.Individuals which represent machining parameters have to undergo some genetic operations such as crossover and mutation.To do so, they should be encoded appropriately.A proper encoding scheme, which is indicative of the characteristics of a solution, has considerable influence on the performance of quality solution.In this step we adopt the same encoding scheme of [4] where individuals represented as string-bit block called (chromosomes) are converted to a binary string and allocated to a 22-bit block.
The operation of converting each individual to a binary string from a real number "" to a binary string { 21 ,  20 , . . .,  0 } is calculated by using the following equation: is then transformed to a binary string.For example, a feed rate value of "0.729" has a string bock as follows: With this representation genetic operators can be applied to individuals and they can be reconverted into integer or real number again, using the binary mapping technique.

Cooling Schedule and Termination Condition.
In this paper, the linear pattern of temperature reduction has been used, where the temperature is obtained from the following equation: The termination condition is when the program makes  iterations without improvement of the best solution.The HSAGA algorithm is shown in Algorithm 1.

Results and Discussion
In this section, minimization of unit production cost as reported in the literature is considered.The hybrid SAGA optimization technique is conducted in order to compute the optimal machining parameters of the metal cutting problem.The example considered is a cylindrical workpiece with 500 mm length and 50 mm diameter and the desired depth to cut is 6mm.Machining data is given in Table 1.
The hybrid SAGA is written in python 3.5 and runs on Intel(R) Core(TM) i5-2430M CPU @2.4 GHz, with 4 GB of RAM.A set of parameters are involved in the proposed algorithm; Table 2 shows this optimization algorithm parameters.As shown in the second column, a range is given for each parameter.Thus, a tuning parameter is needed to select the best values that ensure the program convergence and stability.

Parameters Tuning.
In this stage, Taguchi method is used to select suitable combination of the above-mentioned factors levels.Widely used in robust design, Taguchi technique is a universal approach [30].The robust parameter design is based on the minimization of the sensitivity of noise by determination of factors levels.In such optimization, the response at each setting of parameters is treated as a measure to indicate the mean and the variance of some quality characteristics.These two indicators are combined into a single performance measure so called the signal-to-noise (/) ration.Taguchi proposed different categories of robust parameter design, smaller better, larger better, and so on [31].The category smaller better is the suitable function for our problem, and it is expressed by where ,   , and  denote the trial number, response variable, and the number of replications, respectively.In the proposed algorithm, seven factors should be calibrated, each with three levels.The selected L27 orthogonal array has 27 different combinations of parameter levels, which means that a total of 27 tests are conducted, and each test is replicated five times in order to obtain more reliable results.Table 3 shows the obtained results of each combination of factors proposed by Taguchi method.
To illustrate the performance of Taguchi method, Figure 2 presents evolution of mean S/N ratios of each factor.The levels with the highest values of S/N ratio are selected as the optimal value for each of them; these parameters values are gathered in Table 4.

Comparisons with Other Results.
Using the abovementioned algorithm factors, optimal cutting parameters are obtained and related minimal cost is 2.06$.Table 5 summarizes the optimal machining parameters, constraints values, and limitation; meanwhile it can be seen clearly that all constraints are respected.Moreover, convergence curves of the unit cost using HSAGA are given in Figure 3.It can be observed from this figure that obtained costs solutions are the same for each test, which indicates that the proposed algorithm with selected parameter values based on Taguchi method has good stability.
As presented in the Introduction, there are abundant results in the literature which make it important to compare our results with the others.The hybrid approach, used for the work reported here, is compared with obtained results of some research papers cited previously in the literature.Table 6 shows that our optimization technique gives better solution compared to other optimization approaches.

Conclusion
This work deals with metal removal process and particularly multipass turning operation.A new proposed optimization approach is applied to find minimum unit production cost of this turning operation.This approach is based on combination of SA local search technique with GA global optimization providing a strong possibility to GA of avoiding local minima and having a marked improvement of its performance.Compared to various optimization techniques, obtained results show that HSAGA is an efficient optimization technique and it can be interesting to be implemented in CAPP.Constants pertaining to tool travel and approach/departing time, respectively (min)   and   : Expected tool life for rough and finish machining, respectively (min)   : Tool life of weighted combination of  and  (min) Θ: W e i g h t f o r , 0 <  < 1   ,   : Upper and lower bounds for tool life, respectively (min) , , , and C 0 :  = 1/,  = /,  = /, and  0 =

Figure 2 :
Figure 2: The mean / plot for each level of the HSAGA factors.

Figure 3 :
Figure 3: Trend of unit cost by HSAGA.

Table 4 :
HSAGA optimal parameters values.  and   : Cutting speeds in rough and finish machining, respectively (m/min)   and   : Lower and upper bounds of cutting speed in rough machining, respectively (m/min)   and   : Lower and upper bounds of cutting speed in finish machining, respectively (m/min)   and   : Depths of cut for each pass of rough and finish machining, respectively (mm)   and   : Lower and upper bounds of depth of roughing cut, respectively (mm)   and   : Lower and upper bounds of depth of finishing cut, respectively (mm)

Table 5 :
Obtained optimal unit cost using HSAGA approach.
f r and  s : Feed rates in rough and finish machining, respectively (mm/rev) f rL and f rU : Lower and upper bounds of feed rate in rough machining, respectively (mm/rev)

Table 6 :
Comparison of obtained results of various optimization techniques.  and   : Time required to exchange a tool and tool replacement time, respectively (min) ℎ 1 and ℎ 2 : ], and : Constants of the cutting force equation   and   :  2 , , , and : Constants related to the equation of chip-tool interface temperature  3 ,  4 , and  5 : Constants for roughing and finishing parameter relations SR U : Maximum allowable surface roughness (mm).