Accelerated cuckoo optimization algorithm for the multiobjective welding process
 191 Downloads
Abstract
Welding is a wellknown process in manufacturing industries due to its importance. Several process parameters should be tuned in order to perform a highquality welding. Usually, the problem is described as an optimization one and the challenge is to reconcile conflicting objectives. This paper deals with a multiobjective welding process namely the submerged arc welding process, involving five objectives. The weighted sum approach is used to handle it. An accelerated cuckoo optimization algorithm is implemented for this process model and applied to a practical instance of it. On this practical example, the superiority of the proposed optimization technique has been demonstrated in terms of better solutions and fewer required generations of the cuckoos relative to the basic COA and four other optimization algorithms.
Keywords
Welding process Process parameters Accelerated cuckoo optimization algorithm (ACCOA)1 Introduction
Manufacturing processes are the baselines for any industrial firm to design and make a product. There is a wide range of processes involved such as turning, grinding, milling, ultrasonic machining, abrasive jet machining, and water jet machining, depending on the target product of the manufacturer. Manufacturers strive to optimize these processes individually or overall as the manufacturing circumstance may dictate. Consequently, in the literature, most of the processes are formulated as optimization problems. These often improve the process performances by providing the best values for the process parameters. Unfortunately, these problems are often intractable meaning that classical approaches are not effective.
In the last decade, it has been observed that soft computing methods (computational intelligence) are powerful enough to solve this kind of problems. In [1], a genetic algorithm has been applied to optimize the fiberreinforced composite injection molding process. The heattreatment process of an alloy of titanium has been optimized in [2] by using the Taguchi method, while the turning of the same alloy has been optimized in [3] by integrating the gray relational analysis with the Taguchi method. The production time of the multipass milling process has been optimized by using the artificial bee colony (ABC) approach, the particle swarm optimization (PSO), and simulated annealing (SA) in [4], whereas the cuckoo optimization algorithm (COA) appears in [5]. The unit production cost of the multipass turning process has been minimized by using the teaching–learningbased optimization algorithm (TLBO) [6] and the COA [7]. The machining parameters of other traditional and nontraditional processes have been investigated in [8, 9]. In engineering optimization, the objectives may vary and conflict at the same time, in which case, the problem becomes multiobjective. It can be converted into a single objective by combining the objectives or solving by a Pareto approach.
Some authors focused on the optimization of the important manufacturing process of welding [10, 11, 12, 13, 14, 15, 16]. The aim of the current work is to deal with the multiobjective optimization problem of the submerged arc welding process (SAW) [11, 16]. Our approach is to convert it into a single objective using the weighted sum method. This allows handling the different objectives by resorting to weights assigned to each objective function [17]. In [11], a regression model has been established by experimental means and the optimization problem has been solved using the teaching–learningbased optimization algorithm, whereas in [16], the Jaya algorithm has been improved for this purpose. An accelerated cuckoo optimization algorithm (ACCOA) is implemented for solving the problem in the current work.
The remainder of the paper is organized as follows: Section 2 defines the multiobjective problem of the SAW process expressed by the weighted sum method. Section 3 describes the steps of the implemented ACCOA. A discussion of the obtained results is given in Sect. 4. Finally, the conclusion summarizes the paper and outlines some further likely developments.
2 Multiobjective model representation of the submerged arc welding
The submerged arc welding process is defined by an arc maintained between a continuously fed bare wire electrode and the workpiece and a blanket of powdered flux which generates a protective gas shield. It is an economical method of metal joining [18].
The multiobjective optimization problem of the submerged arc welding of Cr–Mo–V steel investigated here is based on the empirical formulation developed by Rao and Kalyankar [11, 16]. The problem involves two minimization objectives: bead width (BW) in mm and weld reinforcement (R) in mm, and three maximization objectives: weld penetration (P) in mm, tensile strength (TS) in MPa, and weld hardness (H) in Rc. The control parameters of the considered SAW process are the welding current (I) in Amp, voltage (V) in volts, welding speed (S) in cm/min, and wire feed (F) in cm/min. It should be noted that the weld reinforcement must be greater than zero.
The regression models of the objectives are given as follows:
In the literature, two scenarios are considered for the above objectives, i.e., with and without error terms.
3 Accelerated cuckoo optimization algorithm
The cuckoo optimization algorithm (COA) has been introduced by Rajabioun in [19]. It is a soft computing method inspired by the special lifestyle of the cuckoo. This bird has the trait of laying its eggs in other birds’ nests of different species. The patterns of invaded birds eggshells are mimicked to evade recognition which may result in the destruction of the eggs. However, this is not always successful and some dissimilar eggs are indeed destroyed. It is also the case that, some cuckoo chicks will starve after hatching, as they eat more than the chicks of the invaded species. The algorithm is based on an egg laying radius (ELR) and the migration of mature cuckoos. Its effectiveness has been proved and it has been implemented for solving various engineering optimization problems, such as the PID controller [19, 20], pattern recognition [21], replacement of obsolete components [22, 23], data mining and clustering [24, 25], combined heat and economic power dispatch [26], and machining parameters [5, 7, 9, 27]. The procedure which determines ELR and that which sets the run parameters form crucial steps of COA. They may be the aspects of the algorithm which contribute to the loss of the best solution when dealing with combined objective functions.
In the current work, the ELR is replaced by a binary procedure to improve COA when solving the problem with the combined objective function of the SAW process. This led to the socalled accelerated cuckoo optimization algorithm (ACCOA). It is implemented as follows:
3.1 ACCOA: the accelerated cuckoo optimization algorithm
 Step 1: Generate a random number of solutions which represents a set of candidate habitats.where N is the number of total habitats.$$\begin{array}{*{20}l} {{\text{Habitat}}_{1} = [I,V,S,F]} \hfill \\ {{\text{Habitat}}_{2} = [I,V,S,F]} \hfill \\ \vdots \hfill \\ {{\text{Habitat}}_{N} = [I,V,S,F]} \hfill \\ \end{array}$$(11)

Step 2: Dedicate some eggs to each cuckoo.

Step 3: Binary egg laying.
Some of the dedicated eggs hatch and those remaining are detected and destroyed by the invaded birds. A binary value is randomly generated for each egg.$$Egg = \left\{ {\begin{array}{*{20}l} 0 \hfill & {{\text{if}}\;{\text{the}}\;{\text{egg}}\;{\text{is}}\;{\text{not}}\;{\text{recognized}}} \hfill \\ {\text{else}} \hfill & {} \hfill \\ 1 \hfill & {} \hfill \\ \end{array} } \right.$$(12)Equation (12) is used for the intensification of the algorithm.

Step 4: Limit the total number of surviving cuckoos.

Step 5: Evaluate fitness.

Step 6: Find the best habitat.

Step 7: Migrate the cuckoo to the best habitat.

Step 8: If the number of cuckoo iterations is reached, stop; otherwise, go to Step 2.
End ACCOA
4 Results and discussion
ACCOA has been coded in MATLAB 2015 and run on a personal computer with a processor G620 (2.60 GHz, Sandy Bridge, 4 GB Memory, Windows 7, 32 bits). The algorithm has been applied to the five objectives as singleobjective problems [see Eq. (1)–(5)]. It has then been applied to the problem involving the combination of all five objective functions in a single objective [see Eq. (10)].
Optimal results for a singleobjective problem (without error terms)
Objective  Method  I (Ampere)  V (Volt)  S (cm/min)  F (cm/min)  Optimum result  Required no. of iterations 

BW*  ACCOA  416.357  29.337  20.000  226.852  17.062  8 
COA  416.200  29.328  20.000  227.037  17.062  20  
PPA  415.5685  29.1592  20  229.3993  17.0748  179  
TLBO [11]  412.000  29.000  20.000  228.000  17.110  –  
Jaya [16]  416.200  29.327  20.000  227.043  17.062  25  
QO Jaya [16]  416.500  29.342  20.000  226.940  17.062  17  
R*  ACCOA  426.0490  31.9591  9.3009  191.0474  1.3312E − 05  6 
COA  450.0000  32.0000  4.0000  202.6015  0.0011  14  
PPA  450  32  5.7628  190  9.3467E − 04  23  
TLBO [11]  378.0000  31.0000  18.0000  214.0000  0.0086  –  
Jaya [16]  375.8213  30.9250  7.1382  233.7626  0.00355  15  
QO Jaya [16]  350.0000  30.8981  4.9221  236.2409  0.0027  12  
P*  ACCOA  449.9999  30.0266  12.8725  242.3283  13.1402  7 
COA  450.0000  30.0303  12.9001  242.7443  13.1401  19  
PPA  450.0000  29.8164  12.1109  226.7450  13.0652  15  
TLBO [11]  444.0000  29.0000  5.0000  241.0000  11.16  –  
Jaya [16]  450.0000  30.1887  4.0000  277.1496  11.50  24  
QO Jaya [16]  368.4300  30.3395  11.9418  241.3833  11.50  15  
TS*  ACCOA  450.0000  32.0000  11.7662  259.2621  944.0975  5 
COA  450.0000  32.0000  11.7946  259.3121  944.0971  18  
PPA  450.0000  32.0000  4.0000  259.1989  881.7714  95  
TLBO [11]  448.0000  32.0000  11.0000  253.0000  940.90  –  
Jaya [16]  450.0000  32.0000  11.7660  259.2569  944.12  20  
QO Jaya [16]  450.0000  32.0000  11.7660  259.2569  944.12  9  
H*  ACCOA  350.0000  28.0000  4.0000  310.0000  36.66  2 
COA  350.0000  28.0000  4.0000  310.0000  36.66  3  
PPA  350.0000  28.0000  4.0000  310.0000  36.66  1  
TLBO [11]  350.0000  28.0000  4.0000  307.0000  36.65  –  
Jaya [16]  350.0000  28.0000  4.0000  310.0000  36.66  3  
QO Jaya [16]  350.0000  28.0000  4.0000  310.0000  36.66  2 
Optimal results for combined objective (without error terms)
Method  I (Ampere)  V (Volt)  S (cm/min)  F (cm/min)  BW  R  P  TS  H  Min Z  Required no. of iterations 

ACCOA  382.5168  32.0000  19.6968  214.9693  20.9075  7.5969E − 06  8.1865  812.3678  30.9921  − 0.1065  6 
COA  404.5336  28.0591  17.6312  206.8119  21.8616  0.0010  9.0596  770.4275  30.0361  − 0.0108  15 
PPA  450.0000  32.0000  5.7625  190.0000  26.2462  6.9561E − 04  9.0434  784.4098  34.2587  − 0.0469  78 
TLBO [11]  445.0000  32.0000  7.0000  193.0000  27.05  0.826  9.32  846.6  33.45  19.00  – 
Jaya [16]  423.1719  29.8221  4.0000  267.0907  20.89  0.0152  11.19  856.75  29.69  0.5644  13 
QO Jaya [16]  382.41  29.416  20.0000  190.0000  19.47  0.0062  10.36  717.99  29.02  0.1933  18 
Optimal results for combined objective (with error terms)
Method  I (Ampere)  V (Volt)  S (cm/min)  F (cm/min)  BW  R  P  TS  H  Min Z  Required no. of iterations 

ACCOA  449.6237  30.6568  4.0000  251.0311  22.4001  0.0011  12.0065  900.1521  32.9043  − 0.3215  3 
COA  450.0000  30.7105  4.0000  248.9756  22.3942  7.1693E − 04  11.9645  900.6669  32.9908  − 0.2907  15 
PPA  450.0000  32.0000  5.0089  190.0000  25.9241  3.9623E − 04  9.4577  789.8573  34.3685  − 0.0720  138 
Jaya [16]  350.0000  28.0000  4.0000  190.0000  26.865  5.636  6.9176  672.855  36.077  − 0.0064  11 
QO Jaya [16]  350.0000  28.0000  4.0000  190.0000  26.865  5.636  6.9176  672.855  36.077  − 0.0064  7 
5 Conclusions
The goal of this paper was to evaluate the efficiency and robustness of a number of relatively new heuristics on a wellknown multiobjective problem that arises in manufacturing. One of these algorithms, namely ACCOA which we introduce here for the first time, is a modification (acceleration) of the wellknown cuckoo optimization algorithm. The test problem is the multiobjective optimization model of the submerged arc welding process expressed with the weighed sum method. In the literature, the problem has five objectives: the bead width, the weld reinforcement, the weld penetration, the tensile strength, and the weld hardness. ACCOA implements a binary decision to avoid the disadvantage due to the egg laying radius of the original cuckoo optimization algorithm. The results reveal the effectiveness of the current approach in terms of better results (robustness) and lower numbers of required iterations (efficiency) for reaching the optimum results. The disadvantage of the current work is related to the decision on the number of eggs. Further work on this issue is underway. Moreover, work on an application to a welding process involving more than five objectives and four decision variables will be reported in the future. On the other hand, availability of adequate equipment will experimentally investigate the results.
Notes
Acknowledgements
We are grateful to ESRC for funding this research under grant number ES/L011859/1.
Compliance with ethical standards
Conflict of interest
The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
References
 1.Li K, Yan S, Pan W, Zhao G (2017) Warpage optimization of fiberreinforced composite injection molding by combining back propagation neural network and genetic algorithm. Int J Adv Manuf Technol 90:963–970CrossRefGoogle Scholar
 2.Lee KH, Yang SY, Yang JG (2017) Optimization of heattreatment parameters in hardening of titanium alloy Ti–6Al–4 V by using the Taguchi method. Int J Adv Manuf Technol 90:753–761CrossRefGoogle Scholar
 3.Mia M, Khan MA, Rahman SS, Dhar NR (2017) Monoobjective and multiobjective optimization of performance parameters in high pressure coolant assisted turning of Ti–6Al–4V. Int J Adv Manuf Technol 90:109–118CrossRefGoogle Scholar
 4.Rao RV, Pawar PJ (2010) Parameter optimization of a multipass milling process using nontraditional optimization algorithms. Appl Soft Comput 10:445–456CrossRefGoogle Scholar
 5.Mellal MA, Williams EJ (2016) Total production time minimization of a multipass milling process via cuckoo optimization algorithm. Int J Adv Manuf Technol 87:747–754. https://doi.org/10.1007/s0017001684983 CrossRefGoogle Scholar
 6.Rao RV, Kalyankar VD (2013) Multipass turning process parameter optimization using teachinglearningbased optimization algorithm. Sci Iran 20:967–974. https://doi.org/10.1016/j.scient.2013.01.002 CrossRefGoogle Scholar
 7.Mellal MA, Williams EJ (2015) Cuckoo optimization algorithm for unit production cost in multipass turning operations. Int J Adv Manuf Technol 76:647–656. https://doi.org/10.1007/s0017001463092 CrossRefGoogle Scholar
 8.Pawar PJ, Rao RV (2013) Parameter optimization of machining processes using teaching–learningbased optimization algorithm. Int J Adv Manuf Technol 67:995–1006CrossRefGoogle Scholar
 9.Mellal MA, Williams EJ (2016) Parameter optimization of advanced machining processes using cuckoo optimization algorithm and hoopoe heuristic. J Intell Manuf 27:927–942CrossRefGoogle Scholar
 10.Rambabu G, Balaji Naik D, Venkata Rao CH, Srinivasa Rao K, Madhusudan Reddy G (2015) Optimization of friction stir welding parameters for improved corrosion resistance of AA2219 aluminum alloy joints. Def Technol 11:330–337. https://doi.org/10.1016/j.dt.2015.05.003 CrossRefGoogle Scholar
 11.Rao RV, Kalyankar VD (2013) Experimental investigation on submerged arc welding of Cr–Mo–V steel. Int J Adv Manuf Technol 69:93–106CrossRefGoogle Scholar
 12.Elangovan S, Anand K, Prakasan K (2012) Parametric optimization of ultrasonic metal welding using response surface methodology and genetic algorithm. Int J Adv Manuf Technol 63:561–572. https://doi.org/10.1007/s001700123920y CrossRefGoogle Scholar
 13.Kanigalpula PKC, Pratihar DK, Jha MN, Derose J, Bapat AV, Pal AR (2016) Experimental investigations, input–output modeling and optimization for electron beam welding of Cu–Cr–Zr alloy plates. Int J Adv Manuf Technol 85:711–726. https://doi.org/10.1007/s0017001579647 CrossRefGoogle Scholar
 14.Chen F, Tong GQ, Yue XK, Ma XL, Gao XP (2017) Multiperformance optimization of smallscale resistance spot welding process parameters for joining of Ti–1Al–1Mn thin foils using hybrid approach. Int J Adv Manuf Technol 89:3641–3650CrossRefGoogle Scholar
 15.ResendizFlores EO, LopezQuintero ME (2017) Optimal identification of impact variables in a welding process for automobile seats mechanism by MTSGBPSO approach. Int J Adv Manuf Technol 90:437–443CrossRefGoogle Scholar
 16.Rao RV, Rai DP (2017) Optimisation of welding processes using quasioppositionalbased Jaya algorithm. J Exp Theor Artif Intell. https://doi.org/10.1080/0952813X.2017.1309692 CrossRefGoogle Scholar
 17.Konak A, Coit DW, Smith AE (2006) Multiobjective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91:992–1007. https://doi.org/10.1016/j.ress.2005.11.018 CrossRefGoogle Scholar
 18.Mitra U (1984) Kinetics of slag metal reactions during submerged arc welding of steel. Massachusetts Institute of Technology, USAGoogle Scholar
 19.Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput 11:5508–5518CrossRefGoogle Scholar
 20.Fard AN, Shahbazian M, Hadian M (2016) Adaptive fuzzy controller based on cuckoo optimization algorithm for a distillation column. In: ICCIA international conference computational intelligence and applicationGoogle Scholar
 21.Khormali A, Addeh J (2016) A novel approach for recognition of control chart patterns: type2 fuzzy clustering optimized support vector machine. ISA Trans. https://doi.org/10.1016/j.isatra.2016.03.004 CrossRefGoogle Scholar
 22.Mellal MA, Adjerid S, Williams EJ, Benazzouz D (2012) Optimal replacement policy for obsolete components using cuckoo optimization algorithm basedapproach: dependability context. J Sci Ind Res 71:715–721Google Scholar
 23.Mellal MA, Adjerid S, Williams EJ (2013) Optimal selection of obsolete tools in manufacturing systems using cuckoo optimization algorithm. Chem Eng Trans 33:355–360. https://doi.org/10.3303/CET1333060 CrossRefGoogle Scholar
 24.Afshari MH, Dehkordi MN, Akbari M (2016) Association rule hiding using cuckoo optimization algorithm. Expert Syst Appl 64:340–351. https://doi.org/10.1016/j.eswa.2016.08.005 CrossRefGoogle Scholar
 25.Amiri E, Mahmoudi S (2016) Efficient protocol for data clustering by fuzzy cuckoo optimization algorithm. Appl Soft Comput 41:15–21CrossRefGoogle Scholar
 26.Mellal MA, Williams EJ (2015) Cuckoo optimization algorithm with penalty function for combined heat and power economic dispatch problem. Energy 93:1711–1718. https://doi.org/10.1016/j.energy.2015.10.006 CrossRefGoogle Scholar
 27.Mellal MA, Williams EJ (2017) The cuckoo optimization algorithm and its applications. In: Handbook of neural computation. Elsevier, Amsterdam, pp 269–277CrossRefGoogle Scholar
 28.Salhi A, Fraga ES (2011) Natureinspired optimisation approaches and the new plant propagation algorithm. In: International conference on numerical analysis optimizationGoogle Scholar
 29.Sulaiman M, Salhi A, Selamoglu BI, Kirikchi OB (2014) A plant propagation algorithm for constrained engineering optimisation problems. Math Probl Eng. https://doi.org/10.1155/2014/627416 CrossRefGoogle Scholar
 30.Sulaiman M, Salhi A, Fraga ES, Mashwani WK, Rashidi MM (2015) A novel plant propagation algorithm: modifications and implementation. Sci Int 28:201–209Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.