An Accelerated L-shaped Method for Optimizing Over the Stochastic Efficient Set
By: Ilias Badaoui and Mustapha Moulaï
References
- Abbas, M. & Chaabane, D. Optimizing a linear function over an integer efficient set. European Journal Of Operational Research. 174, 1140-1161 (2006)
- Abbas, M. & Bellahcene, F. Cutting plane method for multiple objective stochastic integer linear programming. European Journal Of Operational Research. 168, 967-984 (2006)
- Amrouche, S. & Moulaï, M. Multi-objective stochastic integer linear programming with fixed recourse. International Journal Of Multicriteria Decision Making 9. 2, 355-378 (2012)
- Badaoui, I., Moulaï, M., Chaiblaine, Y. & Chaabane, D. BIOBJECTIVE INTEGER STOCHASTIC OPTIMIZATION OVER THE INTEGER STOCHASTIC EFFICIENT SET. Pesquisa Operacional. 44 pp. e281853 (2024)
- Belkacem, S. & Abbas, M. New algorithm permitting the construction of an effective spanning tree. Foundations Of Computing And Decision Sciences. 48, 313-329 (2023)
- Belkhiri, H., Chergui, M. & Ouaïl, F. Optimizing a linear function over an efficient set. Operational Research. pp. 1-19 (2022)
- Benson, H. Optimization over the efficient set. Journal Of Mathematical Analysis And Applications. 98, 562-580 (1984)
- Boland, N., Charkhgard, H. & Savelsbergh, M. A criterion space search algorithm for biobjective integer programming: The balanced box method. INFORMS Journal On Computing. 27, 735-754 (2015)
- Boland, N., Charkhgard, H. & Savelsbergh, M. The L-shape search method for triobjective integer programming. Mathematical Programming Computation. 8 pp. 217-251 (2016)
- Boland, N., Charkhgard, H. & Savelsbergh, M. A new method for optimizing a linear function over the efficient set of a multiobjective integer program. European Journal Of Operational Research. 260, 904-919 (2017)
- Bongo, M. & Sy, C. A Bi-Objective Integer Linear Optimization Model for Post- Departure Aircraft Rerouting Problem. Intelligent And Transformative Production In Pandemic Times: Proceedings Of The 26th International Conference On Production Research. pp. 453-462 (2023)
- Caballero, R., Cerdá, E., Munoz, M., Rey, L. & Stancu-Minasian, I. Efficient solution concepts and their relations in stochastic multiobjective programming. Journal Of Optimization Theory And Applications. 110 pp. 53-74 (2001)
- Caballero, R., Cerdá, E., Mar Munoz, M. & Rey, L. Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems. European Journal Of Operational Research. 158, 633-648 (2004)
- Chaabane, D. & Mebrek, F. Optimization of a linear function over the set of stochastic efficient solutions. Computational Management Science. 11, 157-178 (2014)
- Dos Santos, F. & Oliveira, F. An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming. European Journal Of Operational Research. 275, 677-693 (2019)
- Ecker, J. & Kouada, I. Finding all efficient extreme points for multiple objective linear programs. Mathematical Programming. 14, 249-261 (1978)
- Ecker, J. & Song, J. Optimizing a linear function over an efficient set. Journal Of Optimization Theory And Applications. 83, 541-563 (1994)
- Jorge, J. An algorithm for optimizing a linear function over an integer efficient set. European Journal Of Operational Research. 195, 98-103 (2009)
- Kall, P., Wallace, S. & Kall, P. Stochastic programming. (Springer,1994)
- Moayedi, M. & Sadeghian, R. A multi-objective stochastic programming approach with untrusted suppliers for green supply chain design by uncertain demand, shortage, and transportation costs. Journal Of Cleaner Production. 408 pp. 137007 (2023)
- Motati, L. Multi-Objective Optimization Frameworks for Healthcare Resource Allocation Using Bayesian Decision Models Multi-Objective Optimization Frameworks for Healthcare Resource Allocation Using Bayesian Decision Models. Journal Of Artificial Intelligence Research And Applications. 6, 1-34 (2026)
- Liu, X., Feng, Y., Ding, N., Li, R. & Chen, X. Multi-criteria Scheduling in Parallel Environment with Learning Effect. Foundations Of Computing And Decision Sciences. 49, 3-20 (2024)
- Li, C. & Grossmann, I. An improved L-shaped method for two-stage convex 0–1 mixed integer nonlinear stochastic programs. Computers & Chemical Engineering. 112 pp. 165-179 (2018)
- Lokman, B. Optimizing a linear function over the nondominated set of multiobjective integer programs. International Transactions In Operational Research. 28, 2248-2267 (2021)
- Ouaïl, F., Chergui, M. & Moulaıï, M. An Exact Method for Optimizing a Linear Function over an Integer efficient Set. International Journal Of Mathematical And Computational Methods. 2 (2017)
- Philip, J. Algorithms for the vector maximization problem. Mathematical Programming. 2, 207-229 (1972)
- Pirouz, B. & Guerriero, F. Multi-objective Stochastic Optimization with AI Predictions on Management of Battery Energy. Learning And Intelligent Optimization: 18th International Conference, LION 18, Ischia Island, Italy, June 9–13, 2024, Revised Selected Papers. 14990 pp. 475 (2025)
- Rasmi, S. & Türkay, M. GoNDEF: an exact method to generate all nondominated points of multi-objective mixed-integer linear programs. Optimization And Engineering. 20 pp. 89-117 (2019)
- Sierra-Altamiranda, A., Charkhgard, H., Eaton, M., Martin, J., Yurek, S. & Udell, B. Spatial conservation planning under uncertainty using modern portfolio theory and Nash bargaining solution. Ecological Modelling. 423 pp. 109016 (2020)
- Steuer, R. Multiple Criteria Optimization: Theory, Computation, and Application. (John Wiley & Sons,1986)
- Syah, R., Elveny, M., Soerjati, E., Guerrero, J., Jowad, R., Suksatan, W., Aravindhan, S., Voronkova, O. & Mavaluru, D. Optimizing the multi-level locationassignment problem in queue networks using a multi-objective optimization approach. Foundations Of Computing And Decision Sciences. 47, 177-192 (2022)
- Sylva, J. & Crema, A. A method for finding the set of non-dominated vectors for multiple objective integer linear programs. European Journal Of Operational Research. 158, 46-55 (2004)
- Tamby, S. & Vanderpooten, D. Enumeration of the nondominated set of multiobjective discrete optimization problems. INFORMS Journal On Computing. 33, 72-85 (2021)
- Teghem, J. Multiobjective and stochastic linear programming. Foundations Of Control Engineering. 8, 225-232 (1983)
- Teghem, J. “Strange”: An Interactive Method for Multiobjective Stochastic Linear Programming, and “Strange-Momix” Its Extension to Integer Variables. Stochastic Versus Fuzzy Approaches To Multiobjective Mathematical Programming Under Uncertainty. pp. 103-115 (1990)
- Tırınk, S. Multi-Objective Optimization in Sustainable Energy. Optimization In Sustainable Energy: Methods And Applications. pp. 267-289 (2026)
- Van Slyke, R. & Wets, R. L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal On Applied Mathematics. 17, 638-663 (1969)
- Vafadarnikjoo, A., Moktadir, M., Paul, S. & Ali, S. A novel grey multi-objective binary linear programming model for risk assessment in supply chain management. Supply Chain Analytics. 2 pp. 100012 (2023)
DOI: https://doi.org/10.2478/fcds-2026-0012 | Journal eISSN: 2300-3405 (formerly 0867-6356) | Journal ISSN: 0867-6356
Language: English
Page range: 377 - 403
Submitted on: Feb 13, 2026
Accepted on: Aug 21, 2026
Published online: Oct 11, 2026
Published in print: Sep 1, 2026
Published by: Poznan University of Technology
In partnership with: Paradigm Publishing Services
Keywords:
Related subjects:
© 2026 Ilias Badaoui, Mustapha Moulaï, published by Poznan University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.