A decentralized coordination algorithm for multi-objective linear programming with block angular structure

References

• Abdelaziz, Fouad Ben, and Sameh Mejri. 2013. “Decentralised Bilevel Model for Shared Inventory Management.” Production Planning & Control 24 (8-9): 684–701.
   Web of Science ®Google Scholar
• Alves, Maria João, Stephan Dempe, and Joaquim J. Júdice. 2012. “Computing the Pareto Frontier of a Bi-objective Bi-level Linear Problem Using a Multiobjective Mixed-Integer Programming Algorithm.” Optimization 61 (3): 335–358.
   Web of Science ®Google Scholar
• Boyd, Stephen, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein, 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends${}^{\circledR }$ in Machine learning, 3(1), pp.1–122.
   Google Scholar
• Chen, Caihua, Bingsheng He, Yinyu Ye, and Xiaoming Yuan. 2016. “The Direct Extension of ADMM for Multi-Block Convex Minimization Problems Is Not Necessarily Convergent.” Mathematical Programming 155 (1-2): 57–79.
   Web of Science ®Google Scholar
• Cho, Hang-Min, and In-Jae Jeong. 2012. “Preemptive Goal Programming Based Heuristic Methods for Reentrant Flow Shop Planning with Bi-objective.” Journal of the Society of Korea Industrial and Systems Engineering 35 (3): 240–246.
   Google Scholar
• Dantzig, George B., and Philip Wolfe. “The decomposition algorithm for linear programs.” Econometrica: Journal of the Econometric Society (1961): 767–778.
   Web of Science ®Google Scholar
• Deng, Wei, and Wotao Yin. 2016. “On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers.” Journal of Scientific Computing 66 (3): 889–916.
   Web of Science ®Google Scholar
• Ehtamo, Harri, Markku Verkama, and Raimo P. Hamalainen. 1996. “On Distributed Computation of Pareto Solutions for Two Decision Makers.” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 26 (4): 498–503.
   Web of Science ®Google Scholar
• Evren, Ramazan. 1987. “Interactive Compromise Programming.” Journal of the Operational Research Society 38 (2): 163–172. doi:10.1057/jors.1987.28.
   Web of Science ®Google Scholar
• Han, Deren, and Xiaoming Yuan. 2012. “A Note on the Alternating Direction Method of Multipliers.” Journal of Optimization Theory and Applications 155 (1): 227–238.
   Web of Science ®Google Scholar
• Heiskanen, Pirja. 1999. “Decentralized Method for Computing Pareto Solutions in Multiparty Negotiations.” European Journal of Operational Research 117 (3): 578–590.
   Web of Science ®Google Scholar
• Hong, Mingyi, and Zhi-Quan Luo. 2017. “On the Linear Convergence of the Alternating Direction Method of Multipliers.” Mathematical Programming 162 (1-2): 165–199.
   Web of Science ®Google Scholar
• Inalhan, Gokhan, Dusan M. Stipanovic, and Claire J. Tomlin. 2002. “Decentralized Optimization, with Application to Multiple Aircraft Coordination.” Paper presented at the Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
   Google Scholar
• Kroo, Ilan, Steve Altus, Robert Braun, Peter Gage, and Ian Sobieski. 1994. “Multidisciplinary Optimization Methods for Aircraft Preliminary Design.” Paper presented at the 5th symposium on multidisciplinary analysis and optimization.
   Google Scholar
• Lee, G. M. 2000. “On Relations between Vector Variational Inequality and Vector Optimization Problem.” In: Yang X., Mees A.I., Fisher M., Jennings L. (eds) Progress in Optimization. Applied Optimization, vol 39. 167–179. Springer, Boston, MA.
   Google Scholar
• Li, Fan, Teresa Wu, and Mengqi Hu. 2014. “Design of a Decentralized Framework for Collaborative Product Design Using Memetic Algorithms.” Optimization and Engineering 15 (3): 657–676.
   Web of Science ®Google Scholar
• Löhne, Andreas, and Benjamin Weißing. 2017. “The Vector Linear Program Solver Bensolve–notes on Theoretical Background.” European Journal of Operational Research 260 (3):8077ndash;813.
   Web of Science ®Google Scholar
• Marler, R. Timothy, and Jasbir S. Arora. 2004. “Survey of Multi-objective Optimization Methods for Engineering.” Structural and Multidisciplinary Optimization 26 (6): 369–395.
   Web of Science ®Google Scholar
• Martins, Joaquim R. R. A., and Andrew B. Lambe. 2013. “Multidisciplinary Design Optimization: A Survey of Architectures.” AIAA Journal 51 (9): 2049–2075.
   Web of Science ®Google Scholar
• Roth, Brian Douglas. 2008. Aircraft Family Design Using Enhanced Collaborative Optimization. Stanford: Stanford University.
   Google Scholar
• Roth, Brian D., and Ilan M. Kroo. 2008. “Enhanced Collaborative Optimization: A Decomposition-Based Method for Multidisciplinary Design.” Paper presented at the ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.
   Google Scholar
• Ryberg, Ann-Britt, Rebecka Domeij Bäckryd, and Larsgunnar Nilsson. 2012. Metamodel-Based Multidisciplinary Design Optimization for Automotive Applications. Linköping: Linköping University Electronic Press.
   Google Scholar
• Tao, Siyu, Kohei Shintani, Guang Yang, Herb Meingast, Daniel W. Apley, and Wei Chen. 2018. “Enhanced Collaborative Optimization Using Alternating Direction Method of Multipliers.” Structural and Multidisciplinary Optimization 58: 1571–1588.
   Web of Science ®Google Scholar
• Toksarı, M. Duran, and Yasemin Bilim. 2015. “Interactive Fuzzy Goal Programming Based on Jacobian Matrix to Solve Decentralized Bi-level Multi-objective Fractional Programming Problems.” International Journal of Fuzzy Systems 17 (4): 499–508.
   Web of Science ®Google Scholar
• Zhang, Zhe, and Minghui Chen. 2018. “A Bi-level Multi-agent System Model for Decentralized Multi-project Scheduling of Wind Power Plants.” Journal of Renewable and Sustainable Energy 10 (3): 035502.
   Web of Science ®Google Scholar