DOI: https://doi.org/10.14710/medstat.17.1.57-68

ANALYSIS OF MULTI-OBJECTIVE LINEAR ROBUST OPTIMIZATION MODEL WITH LEXICOGRAPHICAL METHOD

Chusnul Chatimah Azis  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
*Diah Chaerani  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
Endang Rusyaman  -  Departement of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, Indonesia, Indonesia
Open Access Copyright (c) 2024 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
Problems in robust multi-objective linear optimization are a class of optimization problems with uncertain data parameters which aim in the decision-making process to obtain the best results in certain circumstances by choosing various solution methods for the multi-objective. This research aims to formulate a multi-objective Robust Optimization (RO) model using the Lexicographic Method, then analyzing the existence and uniqueness of the solution. Furthermore, gap analysis on the topic was carried out using a Systematic Literature Review (SLR) approach with the Preferred Reporting Items for Systematic Review and Meta Analysis (PRISMA) method. Results in SLR, the analysis results also shows that the Lexicographic Method is effective in handling data uncertainty with the objective functions sorted by priority. The robust formulation with polyhedral uncertainty sets ensures the flexibility and adaptability of the model. Convexity analysis and application of the Karush-Kuhn-Tucker (KKT) method prove that the resulting solution is exist and unique.
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Keywords: Analysis Convex; Lexicographic Method; Multi-objective Optimization; Polyhedral Uncertainty Set; Robust Optimization.
Funding: Kemendikbudristek under contract 3018/UN6.3.1/PT.00/2023

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Language : EN
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  1. Agarwal, D., Singh, P., and Sayed, M. A. E. (2023). The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems. Mathematics and Computers in Simulation, 205, 861–877. https://doi.org/10.1016/j.matcom.2022.10.024
  2. Bartle, R. G., and Sherbert, D. R. (2010). Introduction to Real Analysis (Fourth). John Wiley and Sons, Inc
  3. Ben-Tal, A., El Ghaoui, L., and Nemirovskiĭ, A. S. (2009). RO. Princeton University Press
  4. Ben-Tal, A., and Nemirovski, A. (2002). Robust Optimization – methodology and applications. Mathematical Programming, 92(3), 453–480. https://doi.org/10.1007/s101070100286
  5. Boyd, S. P., and Vandenberghe, L. (2004). Convex optimization. Cambridge University Press
  6. Brinkhuis, J. (2020). Convex Analysis for Optimization: A Unified Approach. Springer International Publishing. https://doi.org/10.1007/978-3-030-41804-5
  7. Chaerani, D., Irmansyah, A. Z., Perdana, T., and Gusriani, N. (2022). Contribution of Robust Optimization on handling agricultural processed products supply chain problem during Covid-19 pandemic. Uncertain Supply Chain Management, 10(1), 239–254. https://doi.org/10.5267/j.uscm.2021.9.004
  8. Chaerani, D., Ruchjana, B. N., and Romhadhoni, P. (2021). Robust Optimization model using ellipsoidal and polyhedral uncertainty sets for spatial land-use allocation problem. In Engineering Letters (Vol. 29, Issue 3, pp. 1220–1230)
  9. Chaerani, D., Rusyaman, E., and Muslihin, K. R. A. (2021). Comprehensive survey on convex analysis in Robust Optimization. Journal of Physics ldots. https://doi.org/10.1088/1742-6596/1722/1/012075
  10. Chen, X., and Li, M. (2021). Discrete Convex Analysis and Its Applications in Operations: A Survey. Production and Operations Management, 30(6), 1904–1926. https://doi.org/10.1111/poms.13234
  11. Gabrel, V., Murat, C., and Thiele, A. (2014). Recent advances in Robust Optimization: An overview. European Journal of Operational Research, 235(3), 471–483. https://doi.org/10.1016/j.ejor.2013.09.036
  12. Gheouany, S., Ouadi, H., and El Bakali, S. (2023). Hybrid-integer algorithm for a multi-objective optimal home energy management system. Clean Energy, 7(2), 375–388. https://doi.org/10.1093/ce/zkac082
  13. Goberna, M. A., Jeyakumar, V., Li, G., and Vicente-Pérez, J. (2014). Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty. SIAM Journal on Optimization, 24(3), 1402–1419. https://doi.org/10.1137/130939596
  14. Gorissen, B. L., Yanıkoğlu, I., and Hertog, D. den. (2015). A Practical Guide to Robust Optimization. Omega, 53, 124–137. https://doi.org/10.1016/j.omega.2014.12.006
  15. Irmansyah, A., Chaerani, D., and Rusyaman, E. (2022). A Systematic Review on Integer Multi-objective Adjustable Robust Counterpart Optimization Model Using Benders Decomposition. JTAM (Jurnal Teori Dan Aplikasi Matematika), 6, 678. https://doi.org/10.31764/jtam.v6i3.8578
  16. Kecskés, I., and Odry, P. (2021). Robust Optimization of multi-scenario many-objective problems with auto-tuned utility function. Engineering Optimization, 53(7), 1135–1155. https://doi.org/10.1080/0305215X.2020.1775823
  17. Kojima, F., Tamura, A., and Yokoo, M. (2018). Designing matching mechanisms under constraints: An approach from discrete convex analysis. Journal of Economic Theory, 176, 803–833. https://doi.org/10.1016/j.jet.2018.05.004
  18. Li, J., and Mastroeni, G. (2020). Convex Analysis in mathbbZ^n and Applications to Integer Linear Programming. SIAM Journal on Optimization, 30(4), 2809–2840. https://doi.org/10.1137/19M1281678
  19. Moher, D., Liberati, A., Tetzlaff, J., and Altman, D. G. (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. BMJ (Online), 339(7716), 332–336. https://doi.org/10.1136/bmj.b2535
  20. Muslihin, K. R. A., Rusyaman, E., and Chaerani, D. (2022). Conic Duality for Multi-Objective Robust Optimization Problem. Mathematics, 10(21), 3940. https://doi.org/10.3390/math10213940
  21. Panic, N., Leoncini, E., Belvis, G. D., Ricciardi, W., and Boccia, S. (2013). Evaluation of the endorsement of the preferred reporting items for systematic reviews and meta-analysis (PRISMA) statement on the quality of published systematic review and meta-analyses. PLoS ONE, 8(12). https://doi.org/10.1371/journal.pone.0083138
  22. Perdana, T., Chaerani, D., Achmad, A. L. H., and Hermiatin, F. R. (2020). Scenarios for handling the impact of COVID-19 based on food supply network through regional food hubs under uncertainty. Heliyon, 6(10), e05128. https://doi.org/10.1016/j.heliyon.2020.e05128
  23. Rao, S. S. (2009). Engineering optimization: Theory and practice (4th ed). John Wiley and Sons
  24. Rathbone, J., Carter, M., Hoffmann, T., and Glasziou, P. (2015). Better duplicate detection for systematic reviewers: Evaluation of Systematic Review Assistant-Deduplication Module. Systematic Reviews, 4(1), 6. https://doi.org/10.1186/2046-4053-4-6
  25. Sharma, S., and Chahar, V. (2022). A Comprehensive Review on Multi-objective Optimization Techniques: Past, Present and Future. Archives of Computational Methods in Engineering, 29, 3. https://doi.org/10.1007/s11831-022-09778-9
  26. Shi, B., Lookman, T., and Xue, D. (2023). Multi-objective optimization and its application in materials science. Materials Genome Engineering Advances, 1(2), e14. https://doi.org/10.1002/mgea.14
  27. Singh, D., and Singh, J. (2023). Arithmetic Mean-Geometric Mean Inequality for Convex Fuzzy Sets. Journal of Advances in Applied and Computational Mathematics, 10, 71–76. https://doi.org/10.15377/2409-5761.2023.10.7
  28. Siraj, M. M., Van den Hof, P. M. J., and Jansen, J. D. (2015). Handling risk of uncertainty in model-based production optimization: A robust hierarchical approach. IFAC-PapersOnLine, 48(6), 248–253. https://doi.org/10.1016/j.ifacol.2015.08.039
  29. Stovold, E., Beecher, D., Foxlee, R., and Noel-Storr, A. (2014). Study flow diagrams in Cochrane systematic review updates: An adapted PRISMA flow diagram. Systematic Reviews, 3(1), 1–5. https://doi.org/10.1186/2046-4053-3-54
  30. Talatahari, S., and Azizi, M. (2020). Optimization of constrained mathematical and engineering design problems using chaos game optimization. Computers and Industrial Engineering, 145, 106560. https://doi.org/10.1016/j.cie.2020.106560
  31. Tulshyan, R., Arora, R., Deb, K., and Dutta, J. (2010). Investigating EA solutions for approximate KKT conditions in smooth problems. 689–696. https://doi.org/10.1145/1830483.1830609
  32. Utomo, D. S., Onggo, B. S., and Eldridge, S. (2018). Applications of agent-based modelling and simulation in the agri-food supply chains. European Journal of Operational Research, 269(3), 794–805. https://doi.org/10.1016/j.ejor.2017.10.041
  33. Wang, L., and Fang, M. (2018). Robust Optimization model for uncertain multiobjective linear programs. Journal of Inequalities and Applications, 2018(1), 22. https://doi.org/10.1186/s13660-018-1612-3

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