Parametric approach for approximate efficiency of robust multiobjective fractional programming problems

• Published in: Mathematical methods in the applied sciences 2021-09, Vol.44 (14), p.11211-11230
• Main Author: Antczak, Tadeusz
• Format: Article
• Language: English
• Subjects: approximate efficiency; Dinkelbach approach; Efficiency; Mathematical programming; Optimization; Parametric statistics; robust methodology; Robustness (mathematics); scalarization; uncertain multiobjective fractional programming
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.7482

In this paper, a methodology is developed to solve an uncertain multiobjective fractional programming problem in the face of data uncertainty in the objective and constraint functions. We use the robust optimization approach (worst‐case approach) for finding ɛ‐efficient solutions of the associated robust multiobjective fractional programming problem defined as a robust (worst‐case) counterpart. For the robust multiobjective fractional programming problem constructed in the robust approach, In fact, in the parametric Dinkelbach approach. We define for the given multiobjective fractional programming problem its corresponding parametric robust vector optimization problem. Then, we establish both necessary and sufficient optimality conditions for a feasible solution to be an ɛ¯‐efficient solution (an approximate efficient solution) of the parametric robust vector optimization problem. Also we prove the relationship between ɛ‐efficiency of the robust multiobjective fractional programming problem (and thus ɛ‐efficiency of the considered uncertain multiobjective fractional programming problem) and ɛ¯‐efficiency of its corresponding parametric robust vector optimization problem constructed in the Dinkelbach approach. In order to prove this result, we also use a scalarization method. Thus, the equivalence between an approximate efficient solution of the parametric robust vector optimization problem and an approximate minimizer of its associated scalar optimization problem constructed in the used scalarization method is also established.