Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers

By Achille Messac, Glynn J. Sundararaj, R. Tappeta, John E. Renaud. 2000

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Simultaneous Optimization of Mean and Standard Deviation (2010, methodology): “As Messac et al. (2000) proved, using exponents for assigning priorities to responses is more effective than using a constant of proportionality like in the weighted square sum–based methods.”
Desirability function approach: A review and performance evaluation in adverse conditions (2011, background): “Moreover, the analyst must be aware that points in non-convex response surfaces cannot be captured by weighted sums like those of the objective functions tested here [45], even if the proposed measures are used.”
Studies on a biobjective robust design optimization problem (2009, background): “When an optimizing function is of a higher order than second, it is known that obtaining non-dominated solutions is usually unlikely (see, Tind and Wiecek (1999), Messac et al. (2000) and Mattson and Messac (2003)).”
A review of multi-objective optimization: Methods and its applications (2018, unknown): “In the weighted-sum method (Cohon, 1983; Das & Dennis, 1997; Kim & de Weck, 2005; Messac, Sukam, & Melachrinoudis, 2000a; Messac, Sundararaj, Tappeta, & Renaud, 2000b; Odu & Charles-Owaba, 2013; Triantaphyllou, Shu, Sanchez, & Ray, 1998), all problems are combined into one problem using a weighted…”