Piecewise Quadratic Approximation of the Non-Dominated Set for Bi-Criteria Programs.

Wiecek, Margaret M.; Wei Chen; Jinhuan Zhang

A procedure to approximate the non-dominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non-dominated point of interest and based on primal dual relationships associated with the weighted Tchebychefi scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed-form description of the non-dominated set. A numerical example is included.

CRITERION (Theory of knowledge); DECISION making; JUDGMENT (Psychology); MATHEMATICAL programming; MATHEMATICAL models

Journal of Multi-Criteria Decision Analysis, 2001, Vol 10, Issue 1, p35

1057-9214

Academic Journal

10.1002/mcda.287