A sequential approach for unconstrained optimization via a partitioning technique

Abstract

In this paper, an alternative optimization strategy incorporating the ideas of lexicographic optimization and evolutionary algorithms is presented. The given optimization problem is approximated by others in which priorities are given. Under the sequential optimization method, they are optimized, not exhaustively, in order to produce an initial point for the given problem. An important role in the proposed approach plays the way of generating the involved problems and the given priorities on them. General principles to produce the objective functions of the involved problems are proposed. An algorithm named LexOpt Algorithm, which implements the suggested process, is given. Numerical results via LexOpt Algorithm, on a set of widely used test problems show noticeable promising convergence behaviour of the proposed strategy in comparison with the utilized optimization methods.

Keywords:

• optimization
• iterative methods
• partition
• lexicographic optimization
• splitting a function

2010 AMS Subject Classifications::

• 90C30
• 90C29
• 65K10