Basin filling algorithm for the circular packing problem with equilibrium behavioral constraints

Abstract

With the background of the satellite module layout design, the circular packing problem with equilibrium behavioral constraints is a layout optimization problem and NP-hard problem in math. For lack of a powerful optimization method, this problem is hard to solve. The energy landscape paving (ELP) method is a class of stochastic global optimization algorithms based on the Monte Carlo sampling. Based on the quasiphysical strategy and the penalty function method, the problem is converted into an unconstrained optimization problem. Here by combining the improved ELP method, the gradient method based on local search and the heuristic configuration update mechanism, a new global search algorithm, basin filling algorithm, is put forward. The numerical results show that the proposed algorithm is effective to solving the circular packing problem with equilibrium behavioral constraints, and is easy to be popularized to other layout optimization problems. CitationLiu J F, Li G. Basin filling algorithm for the circular packing problem with equilibrium behavioral constraints.

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.…”

Iterated tabu search for the circular open dimension problem

“…Cutting and packing (C&P) problems are widely encountered in practical applications, such as paper industry (Fraser and George, 1994), wireless communication (Adickes et al, 2002), marine transport (Birgin et al, 2005), aircraft designing (Liu and Li, 2010), material cutting (He et al, 2012), etc. They generally consist of cutting (or packing) a set of small items from (or into) a large object so as to minimize the wasted portion.…”