Author(s)

El-Desouky Rahmo^1,2*, Marcin Studniarski³

¹Department of Mathematics, Faculty of Science, Taif University, Khurma, Kingdom of Saudi Arabia.
²Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.
³Faculty of Mathematics and Computer Science, University of Lódé, Lódé, Poland.

We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

Multiobjective Optimization, Scalarization Function, Generalized Jacobian, Vector Critical Point

Rahmo, E. and Studniarski, M. (2017) A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone. Applied Mathematics, 8, 154-163. doi: 10.4236/am.2017.82013.