Multiobjective Optimization in Fractional Calculus: Theoretical and Computational Advances

Abstract

Multiobjective optimization in fractional calculus has made important developments, mainly due to the addition of fractional operators to complex optimization methods. Some recent research has applied fractional differential-difference operators to generalize traditional optimization ideas, forming new groups of functions known as local fractional Univex functions. As a result, people can build strong, weak, and converse duality theorems for multiobjective fractional problems, which provide advancement in solving mathematically complex non-convex and non-smooth optimization problems. Robust optimization methods have been applied to multiobjective fractional programming to consider uncertain data and to introduce conditions called ε-optimality and robust ε-saddle points for weakly efficient solutions. With regard to computation, using Branch-and-Cut methods has made it possible to speed up optimization on linear fractional functions by removing inadequate solutions from efficient sets of integer quadratic problems. Such numerical methods have made it easier to solve fractional derivatives with great precision and now support applications in wave propagation, models of viscoelastic materials, and machine learning. New optimization techniques make it easier to solve multiple challenges by lowering computational effort without sacrificing the accuracy of results. All these changes together join theory and practice, giving new tools to areas where mismatched objectives and fractional mathematics are important