TITLE:
A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone
AUTHORS:
El-Desouky Rahmo, Marcin Studniarski
KEYWORDS:
Multiobjective Optimization, Scalarization Function, Generalized Jacobian, Vector Critical Point
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.2,
February
24,
2017
ABSTRACT: 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.