The normalized normal constraint method for generating the Pareto frontier

• Published in: Structural and multidisciplinary optimization 2003-07, Vol.25 (2), p.86-98
• Main Authors: MESSAC, A, ISMAIL-YAHAYA, A, MATTSON, C. A
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Mapping; Mathematical programming; Mechanical engineering. Machine design; Multiple objective analysis; Numerical methods; Operational research and scientific management; Operational research. Management science; Pareto optimization; Pareto optimum
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-002-0276-1

The authors recently proposed the normal constraint (NC) method for generating a set of evenly spaced solutions on a Pareto frontier – for multiobjective optimization problems. Since few methods offer this desirable characteristic, the new method can be of significant practical use in the choice of an optimal solution in a multiobjective setting. This paper’s specific contribution is two-fold. First, it presents a new formulation of the NC method that incorporates a critical linear mapping of the design objectives. This mapping has the desirable property that the resulting performance of the method is entirely independent of the design objectives scales. We address here the fact that scaling issues can pose formidable difficulties. Secondly, the notion of a Pareto filter is presented and an algorithm thereof is developed. As its name suggests, a Pareto filter is an algorithm that retains only the global Pareto points, given a set of points in objective space. As is explained in the paper, the Pareto filter is useful in the application of the NC and other methods. Numerical examples are provided.