Algorithm 1: Complete Optimization Algorithm Pseudocode

$$\begin{array}{cc}\hfill & 1\mathrm{Input}:\text{Budget}∕\text{Cost function};\text{Constraint Bounds and Data Types}\mathbf{l},\mathbf{u},\mathbf{c};\text{Number of sampling points per}\hfill \\ \hfill & \text{iteration}{n}_j;\text{Number of iterations}M,\text{exploration coefficient}{e}_j;\text{Maximum cost and regularization}\hfill \\ \hfill & \text{parameters}c,\lambda ;\text{Mesh},\text{gradient descent},\text{and acquisition function parameters}(\text{see Table 1})\hfill \\ \hfill & 2\text{Initialize empty data matrix},\mathrm{X},\text{surrogate loss and cost function}\widehat{L},\widehat{C}\hfill \\ \hfill & 3\text{Sample initial latin hypercube design of size}{n}_0\text{while maintaining cost constraints},\text{add to data matrix X}\hfill \\ \hfill & 4\text{In parallel},\text{simulate points in data matrix X according to the underlying biological problem and generate}\hfill \\ \hfill & \text{scoress}\hfill \\ \hfill & 5\text{Train Gaussian process model for loss function (and},\text{if necessary},\text{the cost function) using X}\hfill \\ \hfill & 6\text{Sort X by score}\hfill \\ \hfill & 7\mathbf{while}M>0\mathbf{do}\hfill \\ \hfill & \begin{array}{c}8\hfill \\ 9\hfill \\ \hfill \\ 10\hfill \\ \hfill \\ 11\hfill \\ 12\hfill \\ 13\hfill \\ 14\hfill \\ 15\hfill \\ 16\hfill \\ 17\hfill \end{array}\mid \begin{array}{c}\text{Sample latin hypercube of large size}(\text{e.g.}100\ast n_j)\hfill \\ \text{Get LCB acquisition function values for this sample and pick}{n}_j\ast e_j\text{new search points based on minimal}\hfill \\ \text{values and cost constraints}\hfill \\ \text{Generate remaining}{n}_j-n_j\ast e_j\text{points via mesh search and gradient descent steps using surrogate and}\hfill \\ \text{current data matrix along with a priori parameter values}\hfill \\ \text{Add new points to X}\hfill \\ \text{In parallel},\text{simulate new points in X according to biological knowledge and generate scores}\hfill \\ \text{Update mesh size and gradient descent parameters}\hfill \\ \text{Sort data matrix X by score}\hfill \\ \text{Update surrogate Gaussian process models using new data point scores}\hfill \\ M=M-1\hfill \\ \text{Check stopping criterion and}\mathbf{break}\text{if criterion is met}\hfill \end{array}\phantom{\mid }\hfill \\ \hfill & 18\mathbf{end}\hfill \\ \hfill & 19\mathrm{Output}:\text{Ranked matrix of study designs},\text{Surrogate model}\hfill \end{array}$$