A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 867-886.

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

DOI : 10.1051/ro/2017058
Classification : 90C29, 90C70, 49M15
Mots-clés : Fuzzy multiobjective problem, Newton method, Pareto optimal solution, Generalized Hukuhara differentiability, Critical point
Ghaznavi, Mehrdad 1 ; Hoseinpoor, Narges 1 ; Soleimani, Fatemeh 1

1 
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     author = {Ghaznavi, Mehrdad and Hoseinpoor, Narges and Soleimani, Fatemeh},
     title = {A {Newton} method for capturing {Pareto} optimal solutions of fuzzy multiobjective optimization problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {867--886},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {3},
     year = {2019},
     doi = {10.1051/ro/2017058},
     zbl = {1423.90241},
     mrnumber = {3975703},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2017058/}
}
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Ghaznavi, Mehrdad; Hoseinpoor, Narges; Soleimani, Fatemeh. A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 867-886. doi : 10.1051/ro/2017058. http://www.numdam.org/articles/10.1051/ro/2017058/

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