The normalized normal constraint method for generating the Pareto frontier

By Achille Messac, A. Ismail-Yahaya, Christopher A. Mattson. 2003

834 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d489a214696db69333b4d740ed5009e4d4c0e80a

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Citations in the corpus

On Ensuring that Intelligent Machines Are Well-Behaved (2017, background): “However, while algorithms exist to compute the Pareto frontier for a wide variety of multiobjective machine learning problems [Messac et al., 2003; Smits and Kotanchek, 2005; Pirotta et al., 2014], knowing the Pareto frontier does not provide a complete solution.”
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition (2007, methodology): “Several recent MOP decomposition methods such as Normal-Boundary Intersection Method [9] and Normalized Normal Constraint Method [10] can be classified as the BI approaches.”
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).”
Preventing undesirable behavior of intelligent machines (2019, background): “While algorithms exist to compute the Pareto frontier for a wide variety of multiobjective machine learning problems [66, 67, 68], knowing the Pareto frontier does not provide a complete solution.”
Sustainable supply chain network design: An optimization-oriented review☆ (2015, methodology): “[2011] use the normalized normal constraint method [Messac et al., 2013] and the subproblems are solved with IBM Ilog Cplex 9.”
Robust multi-objective optimal control of uncertain (bio)chemical processes (2011, methodology): “Þ single-objective optimization problems have to be solved when using equally spaced, convex weights (i.e., wiZ0 and Pm i wi ¼ 1) for WS, NBI, and (E)NNC with n the number of points between two individual minima and m the number of objectives considered by these methods.”
A multi-objective optimization for green supply chain network design (2011, methodology): “[22] to solve the multi-objective model.”
A new perspective on multiobjective optimization by enhanced normalized normal constraint method (2008, methodology): “To generate a set of Pareto solutions over the complete Pareto front, the approach presented in Messac and Mattson (2004) could be applied.”
The weighted sum method for multi-objective optimization: new insights (2010, methodology): “These two deficiencies are often answered with alternative methods for representing a Pareto optimal set (Das and Dennis 1998; Tappeta et al. 2000; Messac and Mattson 2002; Messac et al. 2003; Huang et al. 2007; Zhang et al. 2008).”
Robust multi-objective optimal switching control arising in 1,3-propanediol microbial fed-batch process (2017, background): “Moreover, a Pareto filter is designed to remove all non-global Pareto points whose definitions are given in [45].”
Smart Pareto filter: obtaining a minimal representation of multiobjective design space (2004, methodology): “[10] develop a Pareto filter to overcome deficiencies in Pareto set generation methods.”
MOEA/D with Adaptive Weight Adjustment (2014, background): “Many approaches have been developed to decompose a MOP into a set of scalar optimization problems (Das and Dennis, 1998; Miettinen, 1999; Messac et al., 2003; Zhang and Li, 2007; Zhang, Li, et al., 2010).”