Multiobjective nonlinear optimization method ``vector simplex'' (Q2722335)

The paper generalizes a method for unconstrained nonlinear optimization problems, which is based on sequential modifications of simplices formed by candidate solutions as suggested by \textit{W. Spendley, G. R. Hext} and \textit{F. R. Himsworth} [Technometrics 4, 441-461 (1962; Zbl 0121.35603)] and \textit{J. A. Nelder} and \textit{R. Mead} [Computer J. 7, 308-313 (1965; Zbl 0229.65053)], to multi-objective unconstrained nonlinear optimization problems. In analogy to the single-objective case a set \(U\) is sequentially modified in order to obtain an approximation of the complete set of Pareto optimal solutions. A bi-objective example problem illustrates the procedure and indicates the need for further improvements of the resulting approximation. This is realized by the incorporation of a neighborhood search improving upon the originally obtained solution set.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00047].