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Article information
2021 , Volume 26, ¹ 3, p.86-106
Younsi-Abbaci L., Moulai M.
Stochastic optimization over the Pareto front by the augmented weighted Tchebychev program
In this paper, we propose a novel algorithm to deal with multi-objective stochastic integer linear programming problems (MOSILP). Given a stochastic linear function φ, we will optimize it over the full set of efficient solutions of a MOSILP. We convert the latter into an equivalent deterministic problem using uncertain aspirations which are inputs specified by the decision maker. For this purpose, we adopt a 2-stage recourse approach where an augmented weighted Tchebychev program is progressively optimized to generate an efficient solution, the value of the utility function φ is improved to enumerate all efficient solutions. The approach proposed here defines and solves a sequence of progressively more constrained integer linear programs, so that a new efficient solution is generated at each step of the algorithm. A numerical example is presented for illustration.
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Keywords: multiple objective, integer programming, stochastic linear programming, Tchebychev norm
doi: 10.25743/ICT.2021.26.3.006
Author(s):
Younsi-Abbaci Leila
Office: LaMOS Research Unit of the University of Bejaia
Address: 06000, Algiers, Algiers, Bejaia
Phone Office: (213) 657056798
E-mail: abbaci.leila@yahoo.fr
Moulai Mustapha
Office: University of Sciences and Technology Houari Boumediene
Address: 16111, Algiers, Algiers, Bab Ezzouar
E-mail: mmoulai@usthb.dz
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Bibliography link:
Younsi-Abbaci L., Moulai M. Stochastic optimization over the Pareto front by the augmented weighted Tchebychev program // Computational technologies. 2021. V. 26. ¹ 3. P. 86-106
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