A nonlinear multidimensional knapsack problem in the optimal design of mixture experiments

D-Optimal Design for a Causal Structure for Completely Randomized and Random Blocked Experiments

“…In this paper, we assume that there are no constraints on the treatments or on the exogenous variables. However, if there are constraints on the treatments, such as if one of the treatments is limited, then the optimality criteria can be adjusted as is done in the univariate case, which is known as the optimal design of mixture experiments problem [13,[34][35][36][37].…”

Bayesian I-optimal designs for choice experiments with mixtures

“…This means that, even if a Bayesian optimal design is desired, the moments matrix needs to be computed only once in the design creation process, reducing the computational burden. The elements of the moments matrix W u can be obtained using the following formula given in Goos et al [32], Goos et al [33], and DeGroot [34]:…”

Optimal design of mixture experiments for general blending models

“…Duarte et al [59] formulated optimal exact design for Dand A-optimality criteria as a Mixed Integer Nonlinear Programming (MINLP) problem and solved it employing global and local MINLP solvers. Goos et al [60] compared a variable neighborhood search (VNS) algorithm and a MINLP approach to tackle the problem of identifying D-and I-optimal designs for mixture experiments.…”

“…Coetzer and Haines [67] proposed an approach that involves transforming the search for design points over a polytope to a search over a regular simplex with dimension equal to the number of vertices of the polytope. Syafitri et al [68] proposed a VNS algorithm which Goos et al [60] compare to a MINLP based formulations. The approach in this study is grounded on mathematical programming.…”