An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle

Protein-folding simulations of the hydrophobic-hydrophilic model by combining pull moves with energy landscape paving

“…This is achieved by performing low-temperature MC simulations, but with a modified energy expression designed to steer the search away from regions that have already been explored. This means that if a conformation c is hit, the energy E(c) is increased by a "penalty", and replaced by energy )) , ELP has been applied successfully to rough energy landscapes for finding low-energy conformations in the off-lattice protein folding problems [23][24][25] and the circular packing problems [26,27]. In ELP minimization, the sampling weight of a local minimum conformation decreases with the time that system stays in that minimum, and consequently the probability to escape the minimum increases.…”

“…The accumulated histogram function H(E, t) from all previously visited energy at the MC sweeps helps the simulation escape local entrapments and surpass high-energy barrier easier. However, in ELP, there exists a technical flaw [26,27].…”

“…To overcome this shortcoming, Refs. [26] and [27] give an improvement on ELP. In the improved ELP, the acceptability of the new conformation …”

“…ELP is an improved Monte Carlo global optimization method, and has been successfully applied to solving off-lattice protein models [23][24][25] and circular packing problems [26,27]. By incorporating generation of initial conformation based on greedy strategy, conformation update mechanism based on pull moves and some heuristic off-trap strategies into the improved ELP method, a new version of ELP, called ELP-pull moves, is put forward to solve the protein folding problem in HP lattice model.…”

Orthogonal packing of identical rectangles within isotropic convex regions

“…In [25,26], Packmol was introduced as successful tool for building initial configurations for molecular dynamics simulations, based on the packing of spheres by nonlinear optimization. Hybrid methods that combine nonlinear models with heuristics have also been considered in [21,22,24,28,31,32], among others, for packing identical or different circular pieces within several types of objects. In [36], mixed integer linear and nonlinear formulations for staged cutting problems and 2-stage two-dimensional guillotine cutting patterns are reviewed.…”