Minimax reference point approach and its application for multiobjective optimisation

In multiobjective optimisation, one of the most common ways of describing the decision maker's preferences is to assign targeted values (goals) to conflicting objectives as well as relative weights and priority levels for attaining the goals. In linear and convex decision situations, traditional goal programming provides a pragmatic and flexible manner to cater for the above preferences. In certain real world decision situations, however, multiobjective optimisation problems are non-convex. In this paper, a minimax reference point approach is developed which is capable of handling the above preferences in non-convex cases. The approach is based on ∞-norm formulation and can accommodate both preemptive and non-preemptive goal programming. A strongly non-linear multiobjective ship design model is presented and fully examined using the new approach. This simulation study is aimed to illustrate the implementation procedures of the approach and to demonstrate its potential application to general multiobjective optimisation problems.