Математика и математическое моделирование. 2019; : 1-18
Выбор рациональной последовательности сборки изделия как задача принятия решений
Аннотация
Автоматизированный синтез процессов сборки сложных технических систем (Computer aided assembly planning, CAAP) – это важная проблема инженерной практики и теории проектирования. Она особенно актуальна для современных роботизированных производств, в которых технологические инструкции на сборку должны быть описаны с предельной глубиной и детализацией. Последовательность сборки представляет собой ключевое проектное решение, от которого зависят многие эксплуатационные свойства изделия и экономические характеристики производства.
Выбор рациональной последовательности сборки (Assembly sequence planning, ASP) – это труднорешаемая задача. Она требует значительных вычислительных ресурсов и учета большого числа технических параметров и экономических характеристик, влияющих на качество проектных альтернатив. Представления о качестве альтернатив заданы не в виде числовых критериев, а в форме предпочтений эксперта.
Перечисленные особенности не позволяют применить для решения ASP классические методы оптимизации или математического программирования. Для этого в большей части современных публикаций предлагаются различные методы поисковой оптимизации, основанные на биологических и поведенческих аналогиях. В данной парадигме считается, что априори известно множество допустимых альтернатив, образующее исходное пространство выбора. Это предположение является нереалистичным в большинстве проектных ситуаций.
В инженерной практике накоплено множество технологических знаний о сборке изделий различного функционального назначения. В своем большинстве, это – неформализованные данные, существующие в виде правил, рекомендаций, рецептов, эвристик, предпочтений эксперта, описаний успешных прецедентов и др. В работе предлагается новый метод выбора рациональный последовательности сборки, основанный на использовании аппарата теории принятия решений. Предложена формализация важных конструкторских и технологических эвристик: согласованность с системой размерных цепей, геометрическая «свобода» при сборке, монотонность по габаритам, весу, точности и др.
Множество функций выбора является открытым. Его можно пополнить дополнительными функциями выбора, описывающими инженерные эвристики и решающие правила, актуальные в данной проектной ситуации. Предложенный подход допускает оценку и выбор альтернатив по нескольким аспектам или критериям. Для этого можно использовать различные методы генерации общей функции выбора по совокупности частных функций.
Список литературы
1. Ghandi S., Masehian El. Review and taxonomies of assembly and disassembly path planning problems and approaches // Computer-Aided Design. 2015. Vol. 67 – 68. Pp. 58 – 86. DOI: 10.1016/j.cad.2015.05.001
2. Wang X., Ong S.K., Nee A.Y.C. A comprehensive survey of augmented reality assembly research // Advances in Manufacturing. 2016. Vol. 4. No. 1. Pp. 1-22. DOI: 10.1007/s40436-015-0131-4
3. Wang L., Keshavarzmanesh S., Hsi-Yung Feng, Buchal R.O. Assembly pro-cess planning and its future in collaborative manufacturing: a review // The Intern. J. of Advanced Manufacturing Technology. 2009. Vol. 41. No. 1 – 2. Pp. 132 – 144. DOI: 10.1007/s00170-008-1458-9
4. Deepak B.B.V.L., Balamurali Gunji, Bahubalendruni M.V.A. Raju, Biswal B.B. Assembly sequence planning using soft computing methods: a review // Proc. of the Institution of Mechanical Engineers. Pt. E: J. of Process Mechanical Engineering. 2019. Vol. 233. No. 3. Pp. 653-683. DOI: 10.1177/0954408918764459
5. Natarajan B.K. On planning assemblies // 4th Annual symp. on computational geometry: SCG’88 (Urbana-Champaign, Ill., USA, June 1988): Proc. N.Y.: ACM, 1988. Pp. 299-308. DOI: 10.1145/73393.73424
6. Goldwasser M.H., Latombe J.-C., Motwani R. Complexity measures for as-sembly sequences // 12th IEEE Intern. conf. on robotics and automation: ICRA 1996 (Minneapolis, MN, USA, April 22-28, 1996): Proc. Vol. 2. N.Y.: IEEE, 1996. Pp. 1851 – 1857. DOI: 10.1109/ROBOT.1996.506981
7. Wilson R.H., Kavraki L., Latombe J.-C., Lozano-Perez T. Two-handed assembly sequencing // Intern. J. of Robotics Research. 1995. Vol. 14. No. 4. Pp. 335 – 350. DOI: 10.1177/027836499501400403
8. Wolter J.D. A combinatorial analysis of enumerative data structures for assembly planning // IEEE Intern. conf. on robotics and automation: ICRA 1991 (Sacramento, CA, USA, April 9-11, 1991): Proc. N.Y.: IEEE, 1991. Pp. 611 – 618. DOI: 10.1109/ROBOT.1991.131649
9. Whitney D.E. Mechanical assemblies: Their design, manufacture and role in product development. N.Y.; Oxf.: Oxf. Univ. Press, 2004. 517 p.
10. Yin Z.-P., Ding H., Xiong Y.-L. A virtual prototyping approach to generation and evaluation of mechanical assembly sequences // Proc. of the Institution of Mechanical Engineers. Pt. B: J. of Engineering Manufacture. 2004. Vol. 218. No. 1. Pp. 87 – 102. DOI: 10.1243/095440504772830237
11. Bahubalendruni M.V.A. Raju, Biswal B.B. A review on assembly sequence generation and its automation // Proc. of the Institution of Mechanical Engineers. Pt. C: J. of Mechanical Engineering Science. 2016. Vol. 230. No. 5. Pp. 824-838. DOI: 10.1177/0954406215584633
12. Bozhko A.N. Math modeling of sequential coherent and linear assembly plans in CAD systems // 2018 Global Smart Industry conf.: GloSIC (Chelyabinsk, Russia, November 13-15, 2018): Proc. N.Y.: IEEE, 2018. Pp. 1-5. DOI: 10.1109/GloSIC.2018.8570090
13. Bozhko A.N. Hypergraph model for assembly sequence problem // IoP conf. ser.: Materials Science and Engineering. 2019. Vol. 560. No. 1. P. 012010. DOI: 10.1088/1757-899x/560/1/012010
14. Карпенко А.П. Современные алгоритмы поисковой оптимизации. Алгоритмы, вдохновленные природой: учеб. пособие. М.: Изд-во МГТУ им. Н.Э. Баумана, 2014. 446 с.
15. Mohd Fadzil Faisae Ab. Rashid. A hybrid ant-wolf algorithm to optimize assembly sequence planning problem // Assembly Automation. 2017. Vol. 37. No. 2. Pp. 238-248. DOI: 10.1108/AA-11-2016-143
16. Muhammad Arif Abdullah, Mohd Fadzil Faisae Ab. Rashid, Zakri Ghazalli. Optimization of assembly sequence planning using soft computing approaches: A review // Archives of Computational Methods in Engineering. 2019. Vol. 26. No. 2. Pp. 461 – 474. DOI: 10.1007/s11831-018-9250-y
17. Balamurali Gunji, Deepak B.B.V.L., Bahubalendruni M.V.A. Raju, Biswal B.B. Optimal assembly sequence planning towards design for assembly using simulated annealing technique // Research into design for communities: 6th intern. conf. on research into design: ICoRD 2017 (Guwahati, India, January 9-11, 2017): Proc. Singapore: Springer, 2017. Pp. 397-407. DOI: 10.1007/978-981-10-3518-0_35
18. Morad Behandish and Horea T. Ilies. Haptic assembly and prototyping: An expository review. 2016. Режим доступа: https://arxiv.org/pdf/1712.00750.pdf (дата обращения 25.01.2020).
19. Bahubalendruni M.V.A. Raju, Biswal B.B., Deepak B.B.V.L. Optimal ro-botic assembly sequence generation using particle swarm optimization // J. of Automation and Control Engineering. 2016. Vol. 4. No. 2. Pp. 89 – 95. DOI: 10.12720/joace.4.2.89-95
20. Lee Dong-Ho, Kang J.-G., Xirouchakis P. Disassembly planning and scheduling: review and further research // Proc. of the Institution of Mechanical Engineers. Pt. B: J. of Engineering Manufacture. 2001. Vol. 215. No. 5. Pp. 695-709. DOI: 10.1243/0954405011518629
21. Cong Lu, Jerry Ying Hsi Fuh, Yoke San Wong. Advanced assembly planning approach using a multi-objective genetic algorithm // Cong Lu, Jerry Ying Hsi Fuh, Yoke San Wong. Collaborative product assembly design and assembly planning: methodologies and applications. Oxf.; Camb.; Phil.: Woodhead Publ., 2011. Pp. 107 – 146. DOI: 10.1533/9780857093882
22. Qin Yong-Fa, Xu Zhi-Gang. Assembly process planning using a mul-ti-objective optimization method // Intern. conf. on mechatronics and automation: ICMA 2007 (Harbin, China, August 5-8, 2007): Proc. N.Y.: IEEE, 2007. Pp. 593 – 598. DOI: 10.1109/ICMA.2007.4303610
23. Mohd Fadzil Faisae Rashid, Windo Hutabarat, Ashutosh Tiwari. A review on assembly sequence planning and assembly line balancing using soft computing approaches // The Intern. J. of Advanced Manufacturing Technology. 2012. Vol. 59. No. 1 – 4. Pp. 335 – 349. DOI: 10.1007/s00170-011-3499-8
24. White D.J. Decision theory. N.Y.: Taylor & Francis, 2006. 196 p. DOI: 10.4324/9780203793695
25. Roman S. Lattices and ordered sets. N.Y.: Springer, 2008. 305 p. DOI: 10.1007/978-0-387-78901-9
26. Bozhko A.N. Theoretic-lattice approach to computer aided generation of assembly units // Intern. Russian automation conf.: RusAutoCon 2018 (Sochi, Russia, September 9-16, 2018): Proc. N.Y.: IEEE, 2018. 5 p. DOI: 10.1109/RUSAUTOCON.2018.8501839
27. Jie Lu, Guangquan Zhang, Da Ruan, Fengjie Wu. Multi-objective group decision making: Methods, software and applications with fuzzy set techniques. Singapore: World Scientific, 2007. 390 p. DOI: 10.1142/p505
Mathematics and Mathematical Modeling. 2019; : 1-18
Choosing a Rational Assembly Sequence of Product as a Decision-making Problem
Abstract
Automated synthesis of computer-aided assembly planning (CAAP) processes is a crucial task for engineering practice and design theory. It is of especial relevance for modern robotic industries, which need in technological assembly instructions to be described in-depth and in-detail as much as possible. The assembly sequence is a key design decision on which many operational properties of the product and economic characteristics of production depend.
Choosing a rational assembly sequence planning (ASP) is a challenge. It requires significant computing resources and taking into consideration a large number of technical parameters and economic characteristics that affect the quality of design alternatives. Insights into the quality of alternatives are given as the expert’s preferences rather than as the numerical criteria.
The abovementioned features do not allow us to apply the classical optimization methods or mathematical programming for making ASP decision. For this, most modern publications offer various search engine optimization methods based on biological and behavioral analogies. In this paradigm, it is believed that a set of acceptable alternatives that form the original choice space is a priori known. In most design situations this presumption is unrealistic.
In engineering practice, considerable technological knowledge about the assembly of products for different function purposes is gained. These are mostly ad hoc data that exist in the form of rules, recommendations, recipes, heuristics, expert preferences, descriptions of successful precedents, etc. The paper suggests a new method for a choice of the rational assembly sequence based on the use of the decision theory apparatus. The proposal contains formalization of important design and technological heuristics, namely consistency with the dimensional chain system, geometric “freedom” during assembly, monotony in size, weight, accuracy, etc.
A set of choice functions is open and can be completed by additional choice functions that describe engineering heuristics and decision rules that are relevant in the given design situation. The proposed approach allows the assessment and choice of alternatives according to several aspects or criteria. To do this, it is possible to use various methods of generating a common choice function from the totality of particular functions.
References
1. Ghandi S., Masehian El. Review and taxonomies of assembly and disassembly path planning problems and approaches // Computer-Aided Design. 2015. Vol. 67 – 68. Pp. 58 – 86. DOI: 10.1016/j.cad.2015.05.001
2. Wang X., Ong S.K., Nee A.Y.C. A comprehensive survey of augmented reality assembly research // Advances in Manufacturing. 2016. Vol. 4. No. 1. Pp. 1-22. DOI: 10.1007/s40436-015-0131-4
3. Wang L., Keshavarzmanesh S., Hsi-Yung Feng, Buchal R.O. Assembly pro-cess planning and its future in collaborative manufacturing: a review // The Intern. J. of Advanced Manufacturing Technology. 2009. Vol. 41. No. 1 – 2. Pp. 132 – 144. DOI: 10.1007/s00170-008-1458-9
4. Deepak B.B.V.L., Balamurali Gunji, Bahubalendruni M.V.A. Raju, Biswal B.B. Assembly sequence planning using soft computing methods: a review // Proc. of the Institution of Mechanical Engineers. Pt. E: J. of Process Mechanical Engineering. 2019. Vol. 233. No. 3. Pp. 653-683. DOI: 10.1177/0954408918764459
5. Natarajan B.K. On planning assemblies // 4th Annual symp. on computational geometry: SCG’88 (Urbana-Champaign, Ill., USA, June 1988): Proc. N.Y.: ACM, 1988. Pp. 299-308. DOI: 10.1145/73393.73424
6. Goldwasser M.H., Latombe J.-C., Motwani R. Complexity measures for as-sembly sequences // 12th IEEE Intern. conf. on robotics and automation: ICRA 1996 (Minneapolis, MN, USA, April 22-28, 1996): Proc. Vol. 2. N.Y.: IEEE, 1996. Pp. 1851 – 1857. DOI: 10.1109/ROBOT.1996.506981
7. Wilson R.H., Kavraki L., Latombe J.-C., Lozano-Perez T. Two-handed assembly sequencing // Intern. J. of Robotics Research. 1995. Vol. 14. No. 4. Pp. 335 – 350. DOI: 10.1177/027836499501400403
8. Wolter J.D. A combinatorial analysis of enumerative data structures for assembly planning // IEEE Intern. conf. on robotics and automation: ICRA 1991 (Sacramento, CA, USA, April 9-11, 1991): Proc. N.Y.: IEEE, 1991. Pp. 611 – 618. DOI: 10.1109/ROBOT.1991.131649
9. Whitney D.E. Mechanical assemblies: Their design, manufacture and role in product development. N.Y.; Oxf.: Oxf. Univ. Press, 2004. 517 p.
10. Yin Z.-P., Ding H., Xiong Y.-L. A virtual prototyping approach to generation and evaluation of mechanical assembly sequences // Proc. of the Institution of Mechanical Engineers. Pt. B: J. of Engineering Manufacture. 2004. Vol. 218. No. 1. Pp. 87 – 102. DOI: 10.1243/095440504772830237
11. Bahubalendruni M.V.A. Raju, Biswal B.B. A review on assembly sequence generation and its automation // Proc. of the Institution of Mechanical Engineers. Pt. C: J. of Mechanical Engineering Science. 2016. Vol. 230. No. 5. Pp. 824-838. DOI: 10.1177/0954406215584633
12. Bozhko A.N. Math modeling of sequential coherent and linear assembly plans in CAD systems // 2018 Global Smart Industry conf.: GloSIC (Chelyabinsk, Russia, November 13-15, 2018): Proc. N.Y.: IEEE, 2018. Pp. 1-5. DOI: 10.1109/GloSIC.2018.8570090
13. Bozhko A.N. Hypergraph model for assembly sequence problem // IoP conf. ser.: Materials Science and Engineering. 2019. Vol. 560. No. 1. P. 012010. DOI: 10.1088/1757-899x/560/1/012010
14. Karpenko A.P. Sovremennye algoritmy poiskovoi optimizatsii. Algoritmy, vdokhnovlennye prirodoi: ucheb. posobie. M.: Izd-vo MGTU im. N.E. Baumana, 2014. 446 s.
15. Mohd Fadzil Faisae Ab. Rashid. A hybrid ant-wolf algorithm to optimize assembly sequence planning problem // Assembly Automation. 2017. Vol. 37. No. 2. Pp. 238-248. DOI: 10.1108/AA-11-2016-143
16. Muhammad Arif Abdullah, Mohd Fadzil Faisae Ab. Rashid, Zakri Ghazalli. Optimization of assembly sequence planning using soft computing approaches: A review // Archives of Computational Methods in Engineering. 2019. Vol. 26. No. 2. Pp. 461 – 474. DOI: 10.1007/s11831-018-9250-y
17. Balamurali Gunji, Deepak B.B.V.L., Bahubalendruni M.V.A. Raju, Biswal B.B. Optimal assembly sequence planning towards design for assembly using simulated annealing technique // Research into design for communities: 6th intern. conf. on research into design: ICoRD 2017 (Guwahati, India, January 9-11, 2017): Proc. Singapore: Springer, 2017. Pp. 397-407. DOI: 10.1007/978-981-10-3518-0_35
18. Morad Behandish and Horea T. Ilies. Haptic assembly and prototyping: An expository review. 2016. Rezhim dostupa: https://arxiv.org/pdf/1712.00750.pdf (data obrashcheniya 25.01.2020).
19. Bahubalendruni M.V.A. Raju, Biswal B.B., Deepak B.B.V.L. Optimal ro-botic assembly sequence generation using particle swarm optimization // J. of Automation and Control Engineering. 2016. Vol. 4. No. 2. Pp. 89 – 95. DOI: 10.12720/joace.4.2.89-95
20. Lee Dong-Ho, Kang J.-G., Xirouchakis P. Disassembly planning and scheduling: review and further research // Proc. of the Institution of Mechanical Engineers. Pt. B: J. of Engineering Manufacture. 2001. Vol. 215. No. 5. Pp. 695-709. DOI: 10.1243/0954405011518629
21. Cong Lu, Jerry Ying Hsi Fuh, Yoke San Wong. Advanced assembly planning approach using a multi-objective genetic algorithm // Cong Lu, Jerry Ying Hsi Fuh, Yoke San Wong. Collaborative product assembly design and assembly planning: methodologies and applications. Oxf.; Camb.; Phil.: Woodhead Publ., 2011. Pp. 107 – 146. DOI: 10.1533/9780857093882
22. Qin Yong-Fa, Xu Zhi-Gang. Assembly process planning using a mul-ti-objective optimization method // Intern. conf. on mechatronics and automation: ICMA 2007 (Harbin, China, August 5-8, 2007): Proc. N.Y.: IEEE, 2007. Pp. 593 – 598. DOI: 10.1109/ICMA.2007.4303610
23. Mohd Fadzil Faisae Rashid, Windo Hutabarat, Ashutosh Tiwari. A review on assembly sequence planning and assembly line balancing using soft computing approaches // The Intern. J. of Advanced Manufacturing Technology. 2012. Vol. 59. No. 1 – 4. Pp. 335 – 349. DOI: 10.1007/s00170-011-3499-8
24. White D.J. Decision theory. N.Y.: Taylor & Francis, 2006. 196 p. DOI: 10.4324/9780203793695
25. Roman S. Lattices and ordered sets. N.Y.: Springer, 2008. 305 p. DOI: 10.1007/978-0-387-78901-9
26. Bozhko A.N. Theoretic-lattice approach to computer aided generation of assembly units // Intern. Russian automation conf.: RusAutoCon 2018 (Sochi, Russia, September 9-16, 2018): Proc. N.Y.: IEEE, 2018. 5 p. DOI: 10.1109/RUSAUTOCON.2018.8501839
27. Jie Lu, Guangquan Zhang, Da Ruan, Fengjie Wu. Multi-objective group decision making: Methods, software and applications with fuzzy set techniques. Singapore: World Scientific, 2007. 390 p. DOI: 10.1142/p505
