A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

Chunfeng Liu; Yuanyuan Liu; Jufeng Wang

doi:10.3934/jimo.2021175

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A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

Chunfeng Liu ^1, , Yuanyuan Liu ^1, and Jufeng Wang ^2,,

1.	School of Management, Hangzhou Dianzi University, Hangzhou 310018, China
2.	Department of Mathematics, China Jiliang University, Hangzhou 310018, China

^* Corresponding author: Jufeng Wang

Received February 2021 Revised August 2021 Early access October 2021

Due to the fierce market competition, enterprises try to satisfy customers' requirements for personalized products in order to maximize profit or market share of their products. This not only needs to determine the product variants through product line design, but also needs to pay attention to resource allocation in the manufacturing process. This paper proposes a cellular manufacturing optimization model that considers the market and production. If the company excessively pursues the satisfaction of customers' personalized needs, the manufacturing time and cost may increase accordingly. Of course, with the restriction of production capacity in manufacturing cells and the expectation of reducing cost, managers cannot design attributes' levels of a product line casually, which may result in its unstable marketing share and profit. Therefore, the product demand influenced by customers' preferences could be a key factor to link market and production. The objective of propose model is to maximize product profit which consists of revenue and miscellaneous costs (material, processing, transportation, final assembly and fixed costs). A revised imperialist competitive algorithm (RICA) is developed to optimize the discrete problem. Extensive numerical experiments and t-test are carried out to verify the effect of this method. The results demonstrate the proficiency of RICA over another imperialist competitive algorithm based method and genetic algorithm in terms of solution quality.

Keywords: Cellular manufacturing system, cell formation, product line design, customer preference, imperialist competitive algorithm.

Mathematics Subject Classification: Primary: 90B30, 68W50; Secondary: 90B50.

Citation: Chunfeng Liu, Yuanyuan Liu, Jufeng Wang. A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021175

References:

[1]	M. Abdollahi, A. Isazadeh and D. Abdollahi, Imperialist competitive algorithm for solving systems of nonlinear equations, Comput. Math. Appl., 65 (2013), 1894-1908. doi: 10.1016/j.camwa.2013.04.018.
[2]	M. A. Achabou, S. Dekhili and A. P. Codini, Consumer preferences towards animal-friendly fashion products: An application to the italian market, Journal of Consumer Marketing, 37 (2020), 661-673. doi: 10.1108/JCM-10-2018-2908.
[3]	S. Agnew and P. Dargusch, Consumer preferences for household-level battery energy storage, Renewable and Sustainable Energy Reviews, 75 (2017), 609-617. doi: 10.1016/j.rser.2016.11.030.
[4]	M. A. Ardeh, M. B. Menhaj, E. Esmailian and H. ZandHessami, Explica: An explorative imperialist competitive algorithm based on the notion of Explorers with an expansive retention policy, Applied Soft Computing, 54 (2017), 74-92. doi: 10.1016/j.asoc.2017.01.025.
[5]	A. A. Azami, P. Payvandy and M. M. Jalili, Parameter estimation of viscoelastic model to simulate the compression behavior of artificial grass under dynamic loading using imperialist competitive algorithm, Journal of Textiles and Polymers, 9 (2021), 3-11.
[6]	M. Bagheri and M. Bashiri, A hybrid genetic and imperialist competitive algorithm approach to dynamic cellular manufacturing system, Proceedings of the Institution of Mechanical Engineers, 228 (2014), 458-470. doi: 10.1177/0954405413500662.
[7]	A. Ballakur, An Investigation of Part Family/Machine Group Formation in Designing A Cellular Manufacturing System, Ph. D. Thesis, University of Wisconsin, Madison, WI, 1985.
[8]	B. Bootaki, I. Mahdavi and M. M. Paydar, A hybrid GA-AUGMECON method to solve a cubic cell formation problem considering different worker skills, Computers & Industrial Engineering, 75 (2014), 31-40.
[9]	D. Cao, K. Ramani and Z. Li, Guiding concept generation based on ontology for customer preference modeling, The Eighth International Symposium on Tools and Methods of Competitive Engineering, Italy, (2010), 1–14.
[10]	H. Garg, Handbook of research on artificial intelligence techniques and algorithms, Chapter A Hybrid GA-GSA Algorithm for Optimizing the Performance of An Industrial System by Utilizing Uncertain Data, (2015), 620–654.
[11]	H. Garg, A hybrid PSO-GA algorithm for constrained optimization problems, Appl. Math. Comput., 274 (2016), 292-305. doi: 10.1016/j.amc.2015.11.001.
[12]	H. Garg, A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
[13]	S. Grasso and D. Asioli, Consumer preferences for upcycled ingredients: A case study with biscuits, Food Quality and Preference, 84 (2020), 1-9. doi: 10.1016/j.foodqual.2020.103951.
[14]	Y. Gupta, M. Gupta, A. Kumar and C. Sundaram, A genetic algorithm-based approach to cell composition and layout design problems, International J. Production Research, 34 (1996), 447-482. doi: 10.1080/00207549608904913.
[15]	J. A. Howard and J. N. Sheth, The Theory of Buyer Behavior, John Wiley & Sons, Inc., New York, 1969.
[16]	J. Jouzdani, F. Barzinpour, M. A. Shafia and M. Fathian, Applying simulated annealing to a generalized cell formation problem considering alternative routings and machine reliability, Asia-Pacific Journal of Operational Research, 31 (2014), 1-26. doi: 10.1142/S0217595914500213.
[17]	R. Kamalakannan and R. S. Pandian, A tabu search strategy to solve cell formation problem with ratio level data, International J. Enterprise Network Management, 13 (2018), 209-220. doi: 10.1504/IJBIDM.2018.088431.
[18]	M. Kargar and P. Payvandy, Optimization of fabric layout by using imperialist competitive algorithm, J. Textile and Polymer, 3 (2015), 55-63.
[19]	A. H. Kashan, B. Karimi and A. Noktehdan, A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem, International J. Advanced Manufacturing Technology, 73 (2014), 1543-1556.
[20]	R. Kia, A. Baboli, N. Javadian, R. Tavakkoli-Moghaddam, M. Kazemi and J. Khorrami, Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing, Comput. Oper. Res., 39 (2012), 2642-2658. doi: 10.1016/j.cor.2012.01.012.
[21]	J. R. King and V. Nakornchai, Machine-component group formation in group technology: Review and extension, International J. Production Research, 20 (1982), 117-133. doi: 10.1080/00207548208947754.
[22]	M. Kuzmanovic and M. Martic, An approach to competitive product line design using conjoint data, Expert Systems with Applications, 39 (2012), 7262-7269. doi: 10.1016/j.eswa.2012.01.097.
[23]	M. Kuzmanovic, M. Martic and M. Vujosevic, Designing a profit-maximizing product line for heterogeneous market, Technical Gazette, 26 (2019), 1562-1569.
[24]	Y. Li, X. Li and J. N. D. Gupta, Solving the multi-objective flowline manufacturing cell scheduling problem by hybrid harmony search, Expert Systems with Applications, 42 (2015), 1409-1417. doi: 10.1016/j.eswa.2014.09.007.
[25]	C. Liu, J. Wang, J. Y.-T. Leung and K. Li, Solving cell formation and task scheduling in cellular manufacturing system by discrete bacteria foraging algorithm, International J. Production Research, 54 (2016), 923-944. doi: 10.1080/00207543.2015.1113328.
[26]	C. Liu, J. Wang and M. Zhou, Reconfiguration of virtual cellular manufacturing systems via improved imperialist competitive approach, IEEE Transactions on Automation Science and Engineering, 16 (2019), 1301-1314. doi: 10.1109/TASE.2018.2878653.
[27]	C. Liu and J. Wang, Cell formation and task scheduling considering multi-functional resource and part movement using hybrid simulated annealing, International J. Computational Intelligence Systems, 9 (2016), 765-777. doi: 10.1080/18756891.2016.1204123.
[28]	C. Liu, J. Wang and J. Y.-T. Leung, Worker assignment and production planning with learning and forgetting in manufacturing cells by hybrid bacteria foraging algorithm, Computers & Industrial Engineering, 96 (2016), 162–179. doi: 10.1016/j.cie.2016.03.020.
[29]	C. Liu, J. Wang and J. Y.-T. Leung, Integrated bacteria foraging algorithm for cellular manufacturing in supply chain considering facility transfer and production planning, Applied Soft Computing, 62 (2018), 602-618. doi: 10.1016/j.asoc.2017.10.034.
[30]	E. Mehdizadeh, S. V. D. Niaki and V. Rahimi, A vibration damping optimization algorithm for solving a new multi-objective dynamic cell formation problem with workers training, Computers & Industrial Engineering, 101 (2016), 35–52. doi: 10.1016/j.cie.2016.08.012.
[31]	J. J. Michalek, O. Ceryan, P. Y. Papalambros and Y. Koren, Balancing marketing and manufacturing objectives in product line design, J. Mech. Des., 128 (2006), 1196-1204. doi: 10.1115/1.2336252.
[32]	J. J. Michalek, P. Ebbes, F. Adigzel, F. M. Feinberg and P. Y. Papalambros, Enhancing marketing with engineering: Optimal product line design for heterogeneous markets, International J. Research in Marketing, 28 (2011), 1-12. doi: 10.1016/j.ijresmar.2010.08.001.
[33]	S. M. Mousavi, R. Tavakkoli-Moghaddam, B. Vahdani, H. Hashemi and M. J. Sanjari, A new support vector model-based imperialist competitive algorithm for time estimation in new product development projects, Robotics and Computer-Integrated Manufacturing, 29 (2013), 157-168. doi: 10.1016/j.rcim.2012.04.006.
[34]	K. Nemati, S. M. Shamsuddin and M. S. Kamarposhti, Using imperial competitive algorithm for solving traveling salesman problem and comparing the efficiency of the proposed algorithm with methods in use, Australian J. Basic and Applied Science, 5 (2011), 540-543.
[35]	C. Y. Ng and K. M. Y. Law, Investigating consumer preferences on product designs by analyzing opinions from social networks using evidential reasoning, Computers & Industrial Engineerin, 139 (2020), 1-11. doi: 10.1016/j.cie.2019.106180.
[36]	F. Niakan, A. Baboli, T. Moyaux and V. Botta-Genoulaz, A new multi-objective mathematical model for dynamic cell formation under demand and cost uncertainty considering social criteria, Appl. Math. Model., 40 (2016), 2674-2691. doi: 10.1016/j.apm.2015.09.047.
[37]	S. W. Norton, The coast theorem and suboptimization in marketing channels, Marketing Science, 6 (1987), 268-285.
[38]	R. S. Patwal, N. Narang and H. Garg, A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units, Energy, 142 (2018), 822-837.
[39]	S. J. M. Rad, A. F. Tab and K. Mollazade, Application of imperialist competitive algorithm for feature selection: A case study on bulk rice classification, Inter. J. Computer Appl., 40 (2012), 41-48.
[40]	P. Tarasewich and R. R. McMullen, A pruning heuristic for use with multisource product design, European J. Operational Research, 128 (2001), 58-73. doi: 10.1016/S0377-2217(99)00350-1.
[41]	P. B. Tookanlou and H. Wong, Determining the optimal customization levels, lead times and inventory positioning in vertical product differentiation, Inter. J. Production Economics, 221 (2020), 1-20. doi: 10.1016/j.ijpe.2019.08.014.
[42]	P. B. Tookanlou and H. W. Wong, Product line design with vertical and horizontal consumer heterogeneity: The effect of distribution channel structure on the optimal quality and customization levels, European J. Marketing, 55 (2020), 95-131.
[43]	S. Tsafarakis, C. Saridakis, G. Baltas and N. Matsatsinis, Hybrid particle swarm optimization with mutation for optimizing industrial product lines: An application to a mixed solution space considering both discrete and continuous design variables, Industrial Marketing Management, 42 (2013), 496-506. doi: 10.1016/j.indmarman.2013.03.002.
[44]	S. Tsafarakis, K. Zervoudakis, A. Andronikidis and E. Altsitsiadis, Fuzzy self-tuning differential evolution for optimal product line design, European J. Oper. Res., 287 (2020), 1161-1169. doi: 10.1016/j.ejor.2020.05.018.
[45]	J. Wang, C. Liu and K. Li, A hybrid simulated annealing for scheduling in dual-resource cellular manufacturing system considering worker movement, Automatika, 60 (2019), 172-180. doi: 10.1080/00051144.2019.1603264.
[46]	J. Wang, C. Liu and M. Zhou, Improved bacterial foraging algorithm for cell formation and product scheduling considering learning and forgetting factors in cellular manufacturing systems, IEEE Systems Journal, 14 (2020), 3047-3056. doi: 10.1109/JSYST.2019.2963222.
[47]	M. Zandieh, A. R. Khatami and S. H. A. Rahmati, Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm, Applied Soft Computing, 58 (2017), 449-464.
[48]	S. Zhang, J. Zhang, J. Shen and W. Tang, A joint dynamic pricing and production model with asymmetric reference price effect, J. Ind. Manag. Optim., 15 (2019), 667-688. doi: 10.3934/jimo.2018064.
[49]	Z. Zhao, Study on Multi-Strategy Dynamic Scheduling Optimization Algorithm in Rotating Seru System, Master's Thesis, Dongbei University of Finance and Economics, Dalian, China, 2017.
[50]	A. M. Zohrevand, H. Rafiei and A. H. Zohrevand, Multi-objective dynamic cell formation problem: A stochastic programming approach, Computers & Industrial Engineering, 98 (2016), 323-332.

show all references

References:

[1]	M. Abdollahi, A. Isazadeh and D. Abdollahi, Imperialist competitive algorithm for solving systems of nonlinear equations, Comput. Math. Appl., 65 (2013), 1894-1908. doi: 10.1016/j.camwa.2013.04.018.
[2]	M. A. Achabou, S. Dekhili and A. P. Codini, Consumer preferences towards animal-friendly fashion products: An application to the italian market, Journal of Consumer Marketing, 37 (2020), 661-673. doi: 10.1108/JCM-10-2018-2908.
[3]	S. Agnew and P. Dargusch, Consumer preferences for household-level battery energy storage, Renewable and Sustainable Energy Reviews, 75 (2017), 609-617. doi: 10.1016/j.rser.2016.11.030.
[4]	M. A. Ardeh, M. B. Menhaj, E. Esmailian and H. ZandHessami, Explica: An explorative imperialist competitive algorithm based on the notion of Explorers with an expansive retention policy, Applied Soft Computing, 54 (2017), 74-92. doi: 10.1016/j.asoc.2017.01.025.
[5]	A. A. Azami, P. Payvandy and M. M. Jalili, Parameter estimation of viscoelastic model to simulate the compression behavior of artificial grass under dynamic loading using imperialist competitive algorithm, Journal of Textiles and Polymers, 9 (2021), 3-11.
[6]	M. Bagheri and M. Bashiri, A hybrid genetic and imperialist competitive algorithm approach to dynamic cellular manufacturing system, Proceedings of the Institution of Mechanical Engineers, 228 (2014), 458-470. doi: 10.1177/0954405413500662.
[7]	A. Ballakur, An Investigation of Part Family/Machine Group Formation in Designing A Cellular Manufacturing System, Ph. D. Thesis, University of Wisconsin, Madison, WI, 1985.
[8]	B. Bootaki, I. Mahdavi and M. M. Paydar, A hybrid GA-AUGMECON method to solve a cubic cell formation problem considering different worker skills, Computers & Industrial Engineering, 75 (2014), 31-40.
[9]	D. Cao, K. Ramani and Z. Li, Guiding concept generation based on ontology for customer preference modeling, The Eighth International Symposium on Tools and Methods of Competitive Engineering, Italy, (2010), 1–14.
[10]	H. Garg, Handbook of research on artificial intelligence techniques and algorithms, Chapter A Hybrid GA-GSA Algorithm for Optimizing the Performance of An Industrial System by Utilizing Uncertain Data, (2015), 620–654.
[11]	H. Garg, A hybrid PSO-GA algorithm for constrained optimization problems, Appl. Math. Comput., 274 (2016), 292-305. doi: 10.1016/j.amc.2015.11.001.
[12]	H. Garg, A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
[13]	S. Grasso and D. Asioli, Consumer preferences for upcycled ingredients: A case study with biscuits, Food Quality and Preference, 84 (2020), 1-9. doi: 10.1016/j.foodqual.2020.103951.
[14]	Y. Gupta, M. Gupta, A. Kumar and C. Sundaram, A genetic algorithm-based approach to cell composition and layout design problems, International J. Production Research, 34 (1996), 447-482. doi: 10.1080/00207549608904913.
[15]	J. A. Howard and J. N. Sheth, The Theory of Buyer Behavior, John Wiley & Sons, Inc., New York, 1969.
[16]	J. Jouzdani, F. Barzinpour, M. A. Shafia and M. Fathian, Applying simulated annealing to a generalized cell formation problem considering alternative routings and machine reliability, Asia-Pacific Journal of Operational Research, 31 (2014), 1-26. doi: 10.1142/S0217595914500213.
[17]	R. Kamalakannan and R. S. Pandian, A tabu search strategy to solve cell formation problem with ratio level data, International J. Enterprise Network Management, 13 (2018), 209-220. doi: 10.1504/IJBIDM.2018.088431.
[18]	M. Kargar and P. Payvandy, Optimization of fabric layout by using imperialist competitive algorithm, J. Textile and Polymer, 3 (2015), 55-63.
[19]	A. H. Kashan, B. Karimi and A. Noktehdan, A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem, International J. Advanced Manufacturing Technology, 73 (2014), 1543-1556.
[20]	R. Kia, A. Baboli, N. Javadian, R. Tavakkoli-Moghaddam, M. Kazemi and J. Khorrami, Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing, Comput. Oper. Res., 39 (2012), 2642-2658. doi: 10.1016/j.cor.2012.01.012.
[21]	J. R. King and V. Nakornchai, Machine-component group formation in group technology: Review and extension, International J. Production Research, 20 (1982), 117-133. doi: 10.1080/00207548208947754.
[22]	M. Kuzmanovic and M. Martic, An approach to competitive product line design using conjoint data, Expert Systems with Applications, 39 (2012), 7262-7269. doi: 10.1016/j.eswa.2012.01.097.
[23]	M. Kuzmanovic, M. Martic and M. Vujosevic, Designing a profit-maximizing product line for heterogeneous market, Technical Gazette, 26 (2019), 1562-1569.
[24]	Y. Li, X. Li and J. N. D. Gupta, Solving the multi-objective flowline manufacturing cell scheduling problem by hybrid harmony search, Expert Systems with Applications, 42 (2015), 1409-1417. doi: 10.1016/j.eswa.2014.09.007.
[25]	C. Liu, J. Wang, J. Y.-T. Leung and K. Li, Solving cell formation and task scheduling in cellular manufacturing system by discrete bacteria foraging algorithm, International J. Production Research, 54 (2016), 923-944. doi: 10.1080/00207543.2015.1113328.
[26]	C. Liu, J. Wang and M. Zhou, Reconfiguration of virtual cellular manufacturing systems via improved imperialist competitive approach, IEEE Transactions on Automation Science and Engineering, 16 (2019), 1301-1314. doi: 10.1109/TASE.2018.2878653.
[27]	C. Liu and J. Wang, Cell formation and task scheduling considering multi-functional resource and part movement using hybrid simulated annealing, International J. Computational Intelligence Systems, 9 (2016), 765-777. doi: 10.1080/18756891.2016.1204123.
[28]	C. Liu, J. Wang and J. Y.-T. Leung, Worker assignment and production planning with learning and forgetting in manufacturing cells by hybrid bacteria foraging algorithm, Computers & Industrial Engineering, 96 (2016), 162–179. doi: 10.1016/j.cie.2016.03.020.
[29]	C. Liu, J. Wang and J. Y.-T. Leung, Integrated bacteria foraging algorithm for cellular manufacturing in supply chain considering facility transfer and production planning, Applied Soft Computing, 62 (2018), 602-618. doi: 10.1016/j.asoc.2017.10.034.
[30]	E. Mehdizadeh, S. V. D. Niaki and V. Rahimi, A vibration damping optimization algorithm for solving a new multi-objective dynamic cell formation problem with workers training, Computers & Industrial Engineering, 101 (2016), 35–52. doi: 10.1016/j.cie.2016.08.012.
[31]	J. J. Michalek, O. Ceryan, P. Y. Papalambros and Y. Koren, Balancing marketing and manufacturing objectives in product line design, J. Mech. Des., 128 (2006), 1196-1204. doi: 10.1115/1.2336252.
[32]	J. J. Michalek, P. Ebbes, F. Adigzel, F. M. Feinberg and P. Y. Papalambros, Enhancing marketing with engineering: Optimal product line design for heterogeneous markets, International J. Research in Marketing, 28 (2011), 1-12. doi: 10.1016/j.ijresmar.2010.08.001.
[33]	S. M. Mousavi, R. Tavakkoli-Moghaddam, B. Vahdani, H. Hashemi and M. J. Sanjari, A new support vector model-based imperialist competitive algorithm for time estimation in new product development projects, Robotics and Computer-Integrated Manufacturing, 29 (2013), 157-168. doi: 10.1016/j.rcim.2012.04.006.
[34]	K. Nemati, S. M. Shamsuddin and M. S. Kamarposhti, Using imperial competitive algorithm for solving traveling salesman problem and comparing the efficiency of the proposed algorithm with methods in use, Australian J. Basic and Applied Science, 5 (2011), 540-543.
[35]	C. Y. Ng and K. M. Y. Law, Investigating consumer preferences on product designs by analyzing opinions from social networks using evidential reasoning, Computers & Industrial Engineerin, 139 (2020), 1-11. doi: 10.1016/j.cie.2019.106180.
[36]	F. Niakan, A. Baboli, T. Moyaux and V. Botta-Genoulaz, A new multi-objective mathematical model for dynamic cell formation under demand and cost uncertainty considering social criteria, Appl. Math. Model., 40 (2016), 2674-2691. doi: 10.1016/j.apm.2015.09.047.
[37]	S. W. Norton, The coast theorem and suboptimization in marketing channels, Marketing Science, 6 (1987), 268-285.
[38]	R. S. Patwal, N. Narang and H. Garg, A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units, Energy, 142 (2018), 822-837.
[39]	S. J. M. Rad, A. F. Tab and K. Mollazade, Application of imperialist competitive algorithm for feature selection: A case study on bulk rice classification, Inter. J. Computer Appl., 40 (2012), 41-48.
[40]	P. Tarasewich and R. R. McMullen, A pruning heuristic for use with multisource product design, European J. Operational Research, 128 (2001), 58-73. doi: 10.1016/S0377-2217(99)00350-1.
[41]	P. B. Tookanlou and H. Wong, Determining the optimal customization levels, lead times and inventory positioning in vertical product differentiation, Inter. J. Production Economics, 221 (2020), 1-20. doi: 10.1016/j.ijpe.2019.08.014.
[42]	P. B. Tookanlou and H. W. Wong, Product line design with vertical and horizontal consumer heterogeneity: The effect of distribution channel structure on the optimal quality and customization levels, European J. Marketing, 55 (2020), 95-131.
[43]	S. Tsafarakis, C. Saridakis, G. Baltas and N. Matsatsinis, Hybrid particle swarm optimization with mutation for optimizing industrial product lines: An application to a mixed solution space considering both discrete and continuous design variables, Industrial Marketing Management, 42 (2013), 496-506. doi: 10.1016/j.indmarman.2013.03.002.
[44]	S. Tsafarakis, K. Zervoudakis, A. Andronikidis and E. Altsitsiadis, Fuzzy self-tuning differential evolution for optimal product line design, European J. Oper. Res., 287 (2020), 1161-1169. doi: 10.1016/j.ejor.2020.05.018.
[45]	J. Wang, C. Liu and K. Li, A hybrid simulated annealing for scheduling in dual-resource cellular manufacturing system considering worker movement, Automatika, 60 (2019), 172-180. doi: 10.1080/00051144.2019.1603264.
[46]	J. Wang, C. Liu and M. Zhou, Improved bacterial foraging algorithm for cell formation and product scheduling considering learning and forgetting factors in cellular manufacturing systems, IEEE Systems Journal, 14 (2020), 3047-3056. doi: 10.1109/JSYST.2019.2963222.
[47]	M. Zandieh, A. R. Khatami and S. H. A. Rahmati, Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm, Applied Soft Computing, 58 (2017), 449-464.
[48]	S. Zhang, J. Zhang, J. Shen and W. Tang, A joint dynamic pricing and production model with asymmetric reference price effect, J. Ind. Manag. Optim., 15 (2019), 667-688. doi: 10.3934/jimo.2018064.
[49]	Z. Zhao, Study on Multi-Strategy Dynamic Scheduling Optimization Algorithm in Rotating Seru System, Master's Thesis, Dongbei University of Finance and Economics, Dalian, China, 2017.
[50]	A. M. Zohrevand, H. Rafiei and A. H. Zohrevand, Multi-objective dynamic cell formation problem: A stochastic programming approach, Computers & Industrial Engineering, 98 (2016), 323-332.

Figure 1. The encode scheme for an example solution

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Figure 2. Flowchart of the proposed RICA

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Figure 3. Crossover of country

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Figure 4. Mutation of country

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Figure 5. The diagram of the Taguchi experiment

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Figure 6. Convergence diagram of a typical example

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Table 1. Literature review of research scenario and solution method

Authors	Cell formation	Consumer preference	Product line design	Solution method
Gupta et al. ^[14]	$\surd$	-	-	GAs
Kashan et al. ^[19]	$\surd$	-	-	GBPSO
Kamalakannan and Pandian [17]	$ \surd $	-	-	TS, MGE
Bagheri and Bashiri [6]	$ \surd $	-	-	GICA
Zohrevand et al. [50]	$ \surd $	-	-	TS-GA
Jouzdani et al. [16]	$ \surd $	-	-	SA
Li et al. [24]	$ \surd $	-	-	HHS
Liu et al. [25]	$ \surd $	-	-	DBFA
Zhao [49]	$ \surd $	-	-	Memetic Algorithm
Mehdizadeh et al. [30]	$ \surd $	-	-	MOVDO
Bootaki et al. [8]	$ \surd $	-	-	GA-AUGMECON
Niakan et al. [36]	$ \surd $	-	-	NSGA-II
Liu et al. [26]	$ \surd $	-	-	DICAP
Howard and Sheth [15]	-	$ \surd $	-	Buyer Behavior Theory
Norton [37]	-	$ \surd $	-	Coase Theorem
Cao et al. [9]	-	$ \surd $	-	Ontology-based
Ng and Law [35]	-	$ \surd $	$ \surd $	Fuzzy-ER
Achabou et al. [2]	-	$ \surd $	-	Conjoint Analysis, Cluster Analysis
Agnew and Dargusch [3]	-	$ \surd $	$ \surd $	BWS, DCE
Grasso and Asioli[13]	-	$ \surd $	$ \surd $	DCMs
Michalek et al. [32]	-	$ \surd $	$ \surd $	Conjoint Analysis
Tookanlou and Wong [42]	-	$ \surd $	$ \surd $	Empirical Studies
Tsafarakis et al. [43,44]	-	$ \surd $	$ \surd $	Hybrid PSO, FSTDE
Kuzmanovic et al. [23]	-	$ \surd $	$ \surd $	Conjoint Analysis
This paper	$ \surd $	$ \surd $	$ \surd $	RICA

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Authors	Cell formation	Consumer preference	Product line design	Solution method
Gupta et al. ^[14]	$\surd$	-	-	GAs
Kashan et al. ^[19]	$\surd$	-	-	GBPSO
Kamalakannan and Pandian [17]	$ \surd $	-	-	TS, MGE
Bagheri and Bashiri [6]	$ \surd $	-	-	GICA
Zohrevand et al. [50]	$ \surd $	-	-	TS-GA
Jouzdani et al. [16]	$ \surd $	-	-	SA
Li et al. [24]	$ \surd $	-	-	HHS
Liu et al. [25]	$ \surd $	-	-	DBFA
Zhao [49]	$ \surd $	-	-	Memetic Algorithm
Mehdizadeh et al. [30]	$ \surd $	-	-	MOVDO
Bootaki et al. [8]	$ \surd $	-	-	GA-AUGMECON
Niakan et al. [36]	$ \surd $	-	-	NSGA-II
Liu et al. [26]	$ \surd $	-	-	DICAP
Howard and Sheth [15]	-	$ \surd $	-	Buyer Behavior Theory
Norton [37]	-	$ \surd $	-	Coase Theorem
Cao et al. [9]	-	$ \surd $	-	Ontology-based
Ng and Law [35]	-	$ \surd $	$ \surd $	Fuzzy-ER
Achabou et al. [2]	-	$ \surd $	-	Conjoint Analysis, Cluster Analysis
Agnew and Dargusch [3]	-	$ \surd $	$ \surd $	BWS, DCE
Grasso and Asioli[13]	-	$ \surd $	$ \surd $	DCMs
Michalek et al. [32]	-	$ \surd $	$ \surd $	Conjoint Analysis
Tookanlou and Wong [42]	-	$ \surd $	$ \surd $	Empirical Studies
Tsafarakis et al. [43,44]	-	$ \surd $	$ \surd $	Hybrid PSO, FSTDE
Kuzmanovic et al. [23]	-	$ \surd $	$ \surd $	Conjoint Analysis
This paper	$ \surd $	$ \surd $	$ \surd $	RICA

Table 2. Attributes and levels of vacuum glass

Component	Attribute	Level
Component 1	Thickness	Thin, thick, superthick
	The shape of the support	Cylindrical, spherical, oval
	Glass shape	Square, circular, rhombic
Component 2	Color	Blue, gray, green
	Light transmission	Transparent, translucent, opaque
	Thermal insulation	General, great, excellent
	Edge banding material	Metallic, plastic, rubber
Component 3	Decoration	Retro, fashion, chinoiserie
	Welding of metallic layer	Metal brazing, gastight welding, laser welding

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Component	Attribute	Level
Component 1	Thickness	Thin, thick, superthick
	The shape of the support	Cylindrical, spherical, oval
	Glass shape	Square, circular, rhombic
Component 2	Color	Blue, gray, green
	Light transmission	Transparent, translucent, opaque
	Thermal insulation	General, great, excellent
	Edge banding material	Metallic, plastic, rubber
Component 3	Decoration	Retro, fashion, chinoiserie
	Welding of metallic layer	Metal brazing, gastight welding, laser welding

Table 3. Preference scores of each attribute

	Attribute1 (A1)			Attribute 2 (A2)			Attribute 3(A3)
	Level₁₁ (L11)	Level₁₂ (L12)	Level₁₃ (L13)	Level₂₁ (L21)	Level₂₂ (L22)	Level₂₃ (L23)	Level₃₁ (L31)	Level₃₂ (L32)	Level₃₃ (L33)
Individual 1	2 (0.20)	3 (0.30)	5 (0.50)	1 (0.13)	4 (0.50)	3 (0.38)	2 (0.18)	5 (0.45)	4 (0.36)
Individual 2	2 (0.33)	3 (0.50)	1 (0.17)	3 (0.33)	4 (0.44)	2 (0.22)	3 (0.30)	4 (0.40)	3 (0.30)
Individual 3	4 (0.36)	2 (0.18)	5 (0.45)	4 (0.44)	3 (0.33)	2 (0.22)	5 (0.56)	1 (0.11)	3 (0.33)

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	Attribute1 (A1)			Attribute 2 (A2)			Attribute 3(A3)
	Level₁₁ (L11)	Level₁₂ (L12)	Level₁₃ (L13)	Level₂₁ (L21)	Level₂₂ (L22)	Level₂₃ (L23)	Level₃₁ (L31)	Level₃₂ (L32)	Level₃₃ (L33)
Individual 1	2 (0.20)	3 (0.30)	5 (0.50)	1 (0.13)	4 (0.50)	3 (0.38)	2 (0.18)	5 (0.45)	4 (0.36)
Individual 2	2 (0.33)	3 (0.50)	1 (0.17)	3 (0.33)	4 (0.44)	2 (0.22)	3 (0.30)	4 (0.40)	3 (0.30)
Individual 3	4 (0.36)	2 (0.18)	5 (0.45)	4 (0.44)	3 (0.33)	2 (0.22)	5 (0.56)	1 (0.11)	3 (0.33)

Table 4. Utility of different products

	A1	A2	A3	Individual 1	Individual 2	Individual 3
Product 1	L13	L23	L31	1.06	0.69	1.23
Competitive product 1	L12	L22	L33	1.16	1.24	0.84
Competitive product 2	L11	L23	L32	1.03	0.95	0.69
Competitive product 3	L13	L22	L31	1.18	0.91	1.34
Probability PROB_i1				0.24	0.19	0.30
Demand D₁ (S=300)					73

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	A1	A2	A3	Individual 1	Individual 2	Individual 3
Product 1	L13	L23	L31	1.06	0.69	1.23
Competitive product 1	L12	L22	L33	1.16	1.24	0.84
Competitive product 2	L11	L23	L32	1.03	0.95	0.69
Competitive product 3	L13	L22	L31	1.18	0.91	1.34
Probability PROB_i1				0.24	0.19	0.30
Demand D₁ (S=300)					73

Table 5. Control parameters of RICA

Control parameters	Levels
$ N_{pop} $ (Npop): Number of countries	40, 50, 60
$ N_{imp} $ (Nimp): Number of imperialists	8, 10, 12
$ \xi $ (Xi): Weight coefficient for colony profit	0.1, 0.2, 0.3
$ \rho $ (CORA): Cooling rate	0.6, 0.7, 0.8
$ U $ (UN): The number of times for which the optimal profit remains unchanged	10, 12, 15
$ \varepsilon $ (epsilon): A pre-given threshold	0.0001, 0.0005, 0,001

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Control parameters	Levels
$ N_{pop} $ (Npop): Number of countries	40, 50, 60
$ N_{imp} $ (Nimp): Number of imperialists	8, 10, 12
$ \xi $ (Xi): Weight coefficient for colony profit	0.1, 0.2, 0.3
$ \rho $ (CORA): Cooling rate	0.6, 0.7, 0.8
$ U $ (UN): The number of times for which the optimal profit remains unchanged	10, 12, 15
$ \varepsilon $ (epsilon): A pre-given threshold	0.0001, 0.0005, 0,001

Table 6. Parameters of the proposed problem

Parameter	Value	Min	Max
$ M $ : Number of components of each product type (or number of machines in each cell)	3
$ C $ : Number of cells	3
$ A $ : Number of attributes of each product type	9
$ L $ : Number of levels of each attribute	3
$ J $ : Number of company's product types	8
$ J $$ ^{'} $ : Number of competitive product types for each company's product type	5
$ I $ : Number of sample consumers	100
$ S $ : The size of represented population in the market	1000
$ \phi $ : Fixed cost per unit time	3
$ p $$ _{jsa} $ : Price of an attribute's level		10	20
$ h $$ _{jsa} $ : Material cost of an attribute's level		1	3
$ k $$ _{jsa} $ : Processing cost of an attribute's level		1	2
$ {\theta _j} $ : Material handling cost each time		25	40
$ {\Omega _j} $ : Unit assembly cost of each product type		2	5
$ {\tau _{jsa}} $ : Processing time of an attribute's level		3	8
$ \varphi $ : Preference score for an attribute's level		1	5

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Parameter	Value	Min	Max
$ M $ : Number of components of each product type (or number of machines in each cell)	3
$ C $ : Number of cells	3
$ A $ : Number of attributes of each product type	9
$ L $ : Number of levels of each attribute	3
$ J $ : Number of company's product types	8
$ J $$ ^{'} $ : Number of competitive product types for each company's product type	5
$ I $ : Number of sample consumers	100
$ S $ : The size of represented population in the market	1000
$ \phi $ : Fixed cost per unit time	3
$ p $$ _{jsa} $ : Price of an attribute's level		10	20
$ h $$ _{jsa} $ : Material cost of an attribute's level		1	3
$ k $$ _{jsa} $ : Processing cost of an attribute's level		1	2
$ {\theta _j} $ : Material handling cost each time		25	40
$ {\Omega _j} $ : Unit assembly cost of each product type		2	5
$ {\tau _{jsa}} $ : Processing time of an attribute's level		3	8
$ \varphi $ : Preference score for an attribute's level		1	5

Table 7. Performance comparison between RICA, ICASA and GA for impact parameters

$C=6, A=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$M$	6	398720	335469	322124	19	24	130
	12	607478	517620	489546	17	24	203
	18	797091	673714	657481	18	21	353
	24	1010046	860332	819408	17	23	519

$M=14, C=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$A$	3	1371713	1201124	1156277	14	19	308
	6	1000975	863354	829463	16	21	344
	9	963418	837029	796480	15	21	433
	12	978119	831539	791116	18	24	593

$M=12, C=5, A=10$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$L$	3	459945	402027	388192	14	18	176
	10	916115	788887	741580	16	24	283
	17	1343335	1154694	1104538	16	22	418
	24	1601637	1344834	1285988	19	25	819

$M=17, A=7, L=3$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$C$	3	1304929	1156539	1111787	13	17	294
	18	1427445	1198392	1155033	19	24	541
	13	1403110	1178416	1137835	19	23	813
	18	1421519	1222470	1173408	16	21	801

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$C=6, A=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$M$	6	398720	335469	322124	19	24	130
	12	607478	517620	489546	17	24	203
	18	797091	673714	657481	18	21	353
	24	1010046	860332	819408	17	23	519

$M=14, C=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$A$	3	1371713	1201124	1156277	14	19	308
	6	1000975	863354	829463	16	21	344
	9	963418	837029	796480	15	21	433
	12	978119	831539	791116	18	24	593

$M=12, C=5, A=10$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$L$	3	459945	402027	388192	14	18	176
	10	916115	788887	741580	16	24	283
	17	1343335	1154694	1104538	16	22	418
	24	1601637	1344834	1285988	19	25	819

$M=17, A=7, L=3$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$C$	3	1304929	1156539	1111787	13	17	294
	18	1427445	1198392	1155033	19	24	541
	13	1403110	1178416	1137835	19	23	813
	18	1421519	1222470	1173408	16	21	801

Table 8. Statistical t-test results from SPSS for samples of entries 1-16

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American Institute of Mathematical Sciences

A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

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American Institute of Mathematical Sciences

A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

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