Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier

By Achille Messac, Christopher A. Mattson. 2004

312 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f145edf2a7b91db4a085e105428f0fd6870bd3e2

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation (2006, methodology): “They also developed the normal constraint method (Messac and Mattson 2004), which generates uniformly distributed solutions along the Pareto front without missing any Pareto front regions.”
A new perspective on multiobjective optimization by enhanced normalized normal constraint method (2008, methodology): “When μ j is defined as in (7), also known as the pseudo nadir point (Messac and Mattson (2004)) in contrast with de true nadir point where μi N is defined as μi N = max x μi(x) subject to constraints (2).”
Adaptive weighted-sum method for bi-objective optimization: Pareto front generation (2005, background): “Messac and Mattson (2002, 2004) also developed the normal constraint method, which generates evenly distributed Pareto solutions along the entire Pareto front for n-dimensional problems.”
Efficient deterministic multiple objective optimal control of (bio)chemical processes (2009, methodology): “This class includes the classic convex Weighted Sum (WS) of the different objectives, but also encompasses novel methods as Normal Boundary Intersection (NBI) (Das and Dennis, 1998), or Normalised Normal Constraint (NNC) (Messac and Mattson, 2004).”
Performance indicators in multiobjective optimization (2018, background): “Evenness (ξ) [32] Given a point F (s), s ∈ S, in the Pareto front approximation, and considering the closest neighbor at a distance ds and the largest sphere of diameter ds such that F (s) and another point lie on the surface, we consider the set D = {ds , ds : s ∈ S}.”