Direct search methods: then and now

Simulation-Based Sailboat Trajectory Optimization Using on-Board Heterogeneous Computers

“…All of these, together with non-linear programming (NLP), have become the bases for many effective trajectory optimization methods that are commonly classified as either direct or indirect (see, for instance, [4,19,33,37]). The indirect methods, based on the calculus of variations, aim for solutions that satisfy the necessary conditions of optimality.…”

From landscapes to waterscapes: A PSE for landuse change analysis

“…There are direct search [44] and simplicial pattern search [49] algorithms that only require candidate points to be ranked; these methods coupled with statistical response surface methodology [31] can be very effective for the type of problems with sparse and noisy data encountered in landuse models. There is certainly research work to be done on improved optimization techniques, but standard tools could be integrated with existing models quite quickly.…”

S⁴W: globally optimized design of wireless communication systems

“…Jones et al [9] named the algorithm after one of its key steps-dividing rectangles. DIRECT is a pattern search method that is categorized as a direct search technique by Lewis et al [10]. Generally speaking, "pattern search methods are characterized by a series of exploratory moves that consider the behavior of the objective function at a pattern of points" [10], which are chosen as the centers of rectangles in the DIRECT algorithm.…”

“…DIRECT is a pattern search method that is categorized as a direct search technique by Lewis et al [10]. Generally speaking, "pattern search methods are characterized by a series of exploratory moves that consider the behavior of the objective function at a pattern of points" [10], which are chosen as the centers of rectangles in the DIRECT algorithm. This center-sampling strategy reduces the computational complexity, especially for higher dimensional problems.…”