Comparing Genetic Algorithm and Simulated

National Conference on Emerging Trends in Mechanical Engineering in Education & Professional Practices (ETMEPP-2015), Jaipur, India, February 28- March -1, 2015.

Comparing Genetic Algorithm and Simulated Annealing for optimization of machining parameters in wet machining of AISI 1040 Steel R.R. Srikant and P. N. Rao Department of Technology University of Northern Iowa Cedar Falls, IA, USA.

Abstract Optimizing the various parameters in machining has ever been of interest to the community. Though, different models for optimization can be found in literature, all of them are used for dry cutting only. Models considering the cost of cutting fluids and their effect on machining are seldom found. The work presented in this paper provides a mathematical model to minimize the machining process cost by choosing optimum machining parameters in wet machining. Experimental data was obtained by machining AISI 1040 steel under different machining conditions, using cutting fluid. An objective function for minimizing the cost was formulated using the data and inputs from literature. The function was optimized using simulated annealing and genetic algorithm. The efficacy of the models and their applicability in real-time implementation were discussed. The results show that the procedure adopted is useful for choosing optimum process parameters for wet machining. Keywords: Machining Parameters, Cutting Fluid, Optimization, Simulated Annealing, Genetic Algorithm, Turning

Nomenclature A, B, C = components of cost, ₹

V = Cutting speed, m/min

d = Depth of cut, mm

TC = Total cost, ₹

f = Feed rate, mm/min

1. Introduction The efficiency of production process is a key component in deciding the total cost of a product. Optimizing the process helps in achieving better economy and thus benefit the manufacturer.


Hence, determination of optimal cutting parameters continues to be one of the most important elements in any process planning of metal parts. Optimization of machining parameters is an important step to minimize the machining time and cutting force, increase productivity and tool life and obtain better surface finish. In machining, many output parameters are used to diagnose machinability. Parameters such as tool wear, tool life, cutting temperature, machining force components, power consumption, surface integrity and chip thickness ratio are regularly employed. Different strategies are found in literature to optimize these parameters and improve the process/economy (Aman, 2005). Though it is well recognized that the application of cutting fluids has a drastic effect on the machining parameters, cutting fluids are looked upon as additiona l expenditure to the tune of 15–25% of total cost of production (Jen, 2002). However, the savings achieved in terms of savings through enhanced tool life and economic consumption of energy generally outweigh

the additional expenditure.

Nevertheless,

optimization

of machining

parameters in wet machining is rarely reported in literature. Khan et al. (1997) utilized benchmark machining models are evaluated for optimal machining conditions from the published literature to evaluate different optimization procedures. They have used the previously published results that utilized gradient based methods, such as, SUMT (Sequential Unconstrained Minimiza tio n Technique), Box's Complex Search, Hill Algorithm (Sequential search technique),

GRG

(Generalized Reduced Gradient), etc. to compare with the evolution methods such as Genetic Algorithms, Simulated Annealing and the Continuous Simulated Annealing. They conclude that Genetic Algorithms, Simulated Annealing and the Continuous Simulated Annealing which are non-gradient based optimization techniques are reliable and accurate for solving machining optimization problems and offer certain advantages over gradient based methods. All three methods converge to global minima and do not require any gradient information. This property makes these methods suitable for discontinuous functions. The disadvantage of these methods is the number of function evaluations required per run (i.e., the time required to converge) may be long. However, the total number of function and constraints evaluations for GA, CSA, and SA are much higher than any gradient based methods. This results in longer convergence times and make these methods not very attractive for real-time parameter optimization. Saravanan et al. (2001) utilized various optimisation procedures for solving the CNC turning problem to find the optimum operating parameters such as cutting speed and feed rate. Utilizing the total production time as the objective function, with constraints such as cutting force, power,


tool–chip interface temperature and surface roughness of the product, they applied conventio na l optimisation techniques such as the Nelder Mead simplex method and the boundary search procedure, and non-conventional techniques such as genetic algorithms and simulated annealing. They found that the results obtained by simulated annealing are comparable with the boundary search procedure. The genetic Algorithm method deviates from boundary search method, but by adopting a suitable coding system, this can be used to solve any type of machining optimisa tio n problem such as milling, cylindrical grinding, surface grinding, etc., by including any number of variables.

1.1 Genetic Algorithm (GA) GA (Deb, 2002) is generally preferred for large and complex cutting process parameter optimization problems which is based on three basic operators, reproduction, crossover, and mutation to provide a population of solutions. The algorithm iteratively produces new population from an initial random population (obtained from different feasible combination of process decision variables) by reproduction, crossover, and mutation. The new generation of population is evaluated with pre-defined termination criteria. The procedure successively reproduces population 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 probabilis tic, 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 multimodal function, multiple objectives and nonlinear response function problems, and it may be applied to both discrete and continuo us objective functions.

Some of the disadvantages of GA-based optimization techniques are: (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.

Onwubolu and Kumalo (2001) utilized an optimization technique based on genetic algorithms for the determination of the cutting parameters in multi-pass machining operations. They formulated a cutting model that is a non-linear-constrained programming (NCP) problem with 20 machining parameter constraints for rough and finish machining. The results from the proposed algorithm are compared with results of simulated annealing, fuzzy possibilistic-genetic algorithm, linearprogramming (LP) approaches. Since the genetic algorithm-based approach can obtain nearoptimal solution, it can be used for machining parameter selection of complex machined parts that require many machining constraints. They show that the proposed genetic algorithm-based procedure for solving the NCP problem is both effective and efficient, and can be integrated into an intelligent manufacturing system for solving complex machining optimization problems. Integration of the proposed approach with an intelligent manufacturing system will lead to reduction in production cost, reduction in production time, flexibility in machining parameter selection, and improvement of product quality. Cus, F. and Balic, J. (2003) proposes a new optimization technique based on genetic algorithms (GA) for the determination of the cutting parameters in machining operations in milling. Instead of a one shot optimization, they use a multipronged attack on the problem. First the modifica tio n of recommended cutting conditions is obtained from a machining data, through learning of obtained cutting conditions using neural networks and the substitution of better cutting conditions for those learned previously by a proposed GA. Experimental results show that the proposed genetic algorithm-based procedure for solving the optimization problem is both effective and efficient, and can be integrated into an intelligent manufacturing system for solving complex machining optimization problems. Quiza Sardiñas et al. (2006) presented a multi-objec tive optimization technique, based on genetic algorithms, to optimize the cutting parameters in turning processes: cutting depth, feed and speed. They used two conflicting objectives, tool life and


machining time. They consider that a multi-objective optimization offers greatest amount of information in order to make a decision on selecting cutting parameters in turning. The proposed model uses a microgenetic algorithm in order to obtain the non-dominated points and build the Pareto front graph. An application sample is developed and its results are analysed for several different production conditions. Palanisamy et al. (2007) developed a mathematical model based on the material behavior and the machine dynamics to determine cutting force for milling operations. The objective function is minimization of the machining time with constraints tool life, limits of feed rate, depth of cut, cutting speed, surface roughness, cutting force and amplitude of vibrations while maintaining a constant material removal rate. Genetic algorithms (GA) is used to solve the problem which converged very quickly. They also proved experimentally the optimized results give good accuracy of prediction of the cutting forces and surface finish. The obtained results indicate that the optimized parameters are capable of machining the work piece more efficiently with better surface finish. Santos Jr et al. (2014) minimized the machining force (Fu), and chip thickness ratio (CTR), under various cutting conditions (cutting speed: Vc, feed rate: f, and depth of cut: doc) for a ductile material. The minimization was done using genetic algorithm. The genetic algorithm multiobjective optimization method was able to determine the cutting conditions that generate the lower machining force and the smaller CTR for the materials studied in this work. Mu-Chen Chen and 1.2 Simulated Annealing Simulated Annealing introduced in early 1980’s (Khan et al. 1997) is used extensively in optimization of complex engineering systems. SA technique (Kirkpatrick et al., 1983), based on the concept of modelling and simulation of a thermodynamic system. The analogy with a physical system is achieved by assuming 

Solution to the optimization problem is equivalent to the states of a physical system.



Cost of the solution is equivalent to the energy of the state.



Temperature is analogous to the control parameter.

This technique starts with selection of an initial random process decision vector, and moves to new neighborhood 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. Simulated Annealing can be considered as a generalization of the local search. The effort required to program Simulated Annealing is small while the computational effort required is very large for the convergence to a near-optimum problem. Asokan, et al. (2003) optimized the machining parameters for turning cylindrical stock into continuous finished profiles minimizing the machining cost with a set of practical constraints. The model includes rough and finish machining. The constraints considered in this problem are cutting force, power constraint and tool tip temperature. Because of the high complexity of this problem, a simulated annealing (SA) and genetic algorithm (GA) are applied to solve. They found that out of the two algorithms, SA produces marginally better results than GA. Ma et al. (2000) used simulated annealing to plan processes in a concurrent environment. It is able to generate the entire solution space by considering multiple planning tasks, i.e. operations (machine, tool and tool approach direction), selection and operations sequencing simultaneous ly. An algorithm based on simulated annealing (SA) has been developed to search for the optimal solution. Several cost factors including machine cost, tool cost, machine change cost, tool change cost and set-up change cost can be used flexibly as the objective function. Wang et al. (2004) applied genetic simulated annealing (GSA), which is a hybrid of GA and SA, to determine optimal machining parameters for milling operations. The proposed GSA algorithm uses a population of solutions and crossover and mutation operations among population members (as in GA) and a selection mechanism based on a temperature cooling schedule (as in SA). They used a plain milling operation (feed rate and speed) subject to a set of constraints. To compare the efficacy of the proposed method they utilized already solved machining problem. This has been compared with basic GA as well as geometric programming (GP) method. The results indicate that GSA is more efficient than GA and GP in the application of optimization. Saravanan et al. (2005) compared a number of optimization techniques by measuring the machining performance by the production cost to optimize the machining parameters in multipass turning are depth of cut, cutting speed and feed. Because the machining optimization is highly


complex, they used six non-traditional algorithms, the genetic algorithm (GA), simulated annealing algorithm (SA), Tabu search algorithm (TS), memetic algorithm (MA), ant colony algorithm (ACO) and the particle swarm optimization (PSO). Kai-Ying Chen (2003) utilizing the algorithm of Onwubolu and Kumalo (2001) show that genetic algorithms significantly outperform simulated annealing. Different mathematical models are available in literature to optimize machining parameters and achieve an objective function like minimizing tool wear, surface roughness or cost of machining. However, the models are generally formulated for dry machining and the effect of cutting fluids on the machining parameters is often neglected. The present work aims to develop an optimization model to minimize the total cost of machining including cutting fluid costs and then solve it using simulated annealing and genetic algorithm.

2. Experimentation AISI 1040 steel (C-0.36-0.44%, Si- 0.10-0.40%, Mn-0.60-1.00%, S-0.050%, P-0.050%, Hardness30+ 2 HRC) of size Ø35×350 mm on a 10 HP lathe (Make: PSG-124) was machined in order to build a suitable mathematical that could be used for optimization. The cutting conditions used for experimentation are two cutting speeds 220 m/min, and 275 m/min, three Feed rates 0.45 mm/rev, 0.75 mm/rev and 1 mm/rev, and two depths of cuts 0.5 mm and 1 mm. Uncoated Carbide, SNMG 120408 H13A (Make: Sandvik) and corresponding tool holder PSRNR 12125F09 were used for turning. Tool wear was measured using a tool maker’s microscope (Make: Olympus GX51).

3. Costs associated with cutting fluids The total expenditure in wet machining was categorized into three different parts. While the first part (A) consisted of cost involved in procurement and disposal of cutting fluid and water, second part (B) consisted of cost involved due to power consumption and the third part (C) was the amount spent on cutting tools. The data pertaining to the costs of various components are taken from literature (Amrita, 2013).

3.1 Components of A: Assuming the machine sump of 120 litres, with 12.5% makeup per day and complete replacement of the cutting fluid every month, the following costs were calculated for a year. Total cost of cutting fluid: ₹ 51,300.00


Total Cost of water: ₹ 1,115.00 Labor Cost for cleaning: ₹ 1,380.00 Hazardous material disposal cost: ₹ 55,200.00 Hence total cost of A = ₹ 1,08,995.00

3.2 Components of B: Considering a 10 HP lathe and 0.02 HP pump for supply of coolant, the following costs were calculated for a year. Average working time 8 hours per day was considered, 5 days a week. Cost of running the lathe: ₹ 5,92,000.00 Cost of running the pump: ₹ 520.00 Total cost of B = ₹ 5,92,520.00

3.3 Components of C: Since carbide tools are used, there is no need for regrinding. Each insert has four edges. Tool life was calculated using the data and considering 0.6 mm of flank wear as the limiting value. The tool life was considered as a function of the machining parameters to be incorporated in the objective function. Extended Taylor’s tool life equation derived from the previous experimental data is T = 100.505 0.62.426 V0.811  f -0.361 d0.164

(1)

Total cost of tools per year with a square insert costing ₹ 541, C=

4 10

8 5 52  541  0.62.426 V 0.811  f -0.361 d 0.164

(2)

0.505

4. Optimization The objective function for minimizing the total cost, i.e. the sum of components of A, B and C, was framed as: Minimize, TC = 108,995  592,520 

4 10

8 5 52  541  0.62.426 V0.811  f -0.361 d 0.164

0.505

(3)

Simulated Annealing and Genetic Algorithm models were built in MATLAB using the Global Optimization Tool Box.


In the present work, the formulated objective function was optimized using the two algorithms , considering different levels for the design variables. At each level, one of the variables was kept constant and the optimal values for the two other variables was obtained from the algorithms. Both the algorithms yielded same values (Table 1). For simulated annealing, the initial search point was taken as (0, 0, 0), initial temperature was set as 100°C, while for genetic algorithm random initia l state and population size of 50 were taken. The best function (total cost) returned for each case (Fig. 1 & 2) is shown in the table. Total cost per unit material removal rate was calculated to understand the effect of each variable on productivity of the process. Genetic algorithm produced the result in less iterations compared to simulated annealing (Fig. 1 and 2). On estimation of processor time using the stopping time criteria in the tool box, it was found that genetic algorithm took an average computation time of 1.655 seconds while simulated annealing took 9.146 seconds. 5

7.0385

Best Function Value: 703428

x 10

7.038 7.0375

Function value

7.037 7.0365 7.036 7.0355 7.035 7.0345 7.034 0 10

1

10

2

10 Iteration

3

10

4

10

Fig. 1 Variation of function value in Simulated Annealing Figs. 3 to 5 reveal that increase in any of the cutting parameters decreases cost/MRR. However, it can be seen that change in feed or depth of cut has higher impact than the cutting speed. Effect of the depth of cut is almost stabilized at 2 mm depth of cut indicating that any further increase in depth of cut may not affect the result. However, this needs to be endorsed through further experimentation.


It may be noted that higher feed and depths of cut are always economical in terms of higher material removal rates but are not preferred due to high tool wear, cutting temperatures and other associated problems in dry machining. However, when cutting fluids are used, tool wear and other responses are in control and hence higher feeds/depths of cut may be used.

5

7.041

Best: 703428 Mean: 703428

x 10

7.04

7.038

7.037

7.036

7.035

7.034

0

10

20

30 Generation

40

50

60

Fig. 2 Variation of function value in Genetic Algorithm

6 5

Cost/MRR

Fitness value

7.039

4 3 2 1 0

100

150

200

250

300

350

Speed, m/min

Fig. 3 Effect of cutting speed on Cost/MRR

400


Table 1Optimization results using GA and SA Annual Speed,

Feed,

Doc,

Total cost,

Cost/MRR

m/min

mm/rev

mm

₹

₹/mm3 /min

1

175

0.5

1.5

704870.5

5.37

2

200

0.5

1.5

704526.1

4.70

3

250

0.5

1.5

704027.6

3.75

4

275

0.5

1.5

703840.7

3.41

5

300

0.5

1.5

703682.3

3.13

6

350

0.5

1.5

703427.6

2.68

7

350

0.5

1.5

703427.6

2.68

8

350

0.75

1.5

703729.0

1.79

9

350

1

1.5

703971.3

1.34

10

350

1.25

1.5

704177.4

1.07

11

350

1.5

1.5

704358.5

0.89

12

350

2

1.5

704669.7

0.67

13

350

0.5

0.5

703805.1

8.04

14

350

0.5

0.75

703657.8

5.36

15

350

0.5

1

703559.1

4.02

16

350

0.5

1.25

703485.6

3.22

17

350

0.5

1.5

703427.6

2.68

18

350

0.5

2

703339.4

2.01

S. No.

National Conference on Emerging Trends in Mechanical Engineering in Education & Professional Practices (ETMEPP-2015), Jaipur, India, February 28- March -1, 2015. 3

Cost/MRR

2.5 2 1.5

1 0.5

0 0

0.5

1

1.5

2

2.5

Feed, mm/min

Fig. 4 Effect of feed rate on Cost/MRR 5. Conclusions

1. Total wet machining cost was optimized in the present work using SA and GA. 2. The cost associated with cutting fluids are justified due to the high feeds and depths of cut feasible in wet machining that would increase the material removal rate thereby improving productivity. 3. Though both GA and SA produced same values of final results, GA consumed less computation time and can be a better choice for online implementation in real time. However, this factor needs to further studied in light of different constraints imposed in real-time, namely cutitng forces, surface finish, etc. The work can be extended by considering other optimisation techniques and including more parameters like flowrate of the coolant, composition of cutting fluid, etc. REFERENCES 1. Aman Aggarwal and Hari Singh (2005), Optimization of machining techniques – A retrospective and literature review, Sadhana, 30(6), 699–711. 2. Amrita, M. R.R.Srikant and A.V.Sitaramaraju, (2013) Evaluation of cutting fluid with nanoinclusions, Journal of Nanotechnology in Engineering and Medicine, Transactions of the ASME, 4, 031007-11. 3. Asokan, P., Saravanan, R., & Vijayakumar, K. (2003). Machining parameters optimisation for turning cylindrical stock into a continuous finished profile using genetic algorithm (GA) and simulated annealing (SA). The International Journal of Advanced Manufacturing Technology, 21(1), 1-9.


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