On the normal boundary intersection method for generation of efficient front

Abstract

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points in multi-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. First, it presents alternate formulation of this algorithms, such that (weak) Pareto-optimality of solutions is guaranteed. This improvement makes these algorithm theoretically equivalent to other classical algorithms (like weighted-sum or ε-constraint methods), without losing its ability to generate a set of evenly spaced Efficient solutions. Second, an algorithm is presented so as to know beforehand about certain sub-problems whose solutions are not Pareto-optimal and thus not wasting computational effort to solve them. The relationship of the new algorithm with weighted-sum and goal programming method is also presented. © Springer-Verlag Berlin Heidelberg 2007.