Energy Landscape Paving Method Research Articles

A new energy landscape paving heuristic for satellite module layouts

This article describes a study of the satellite module layout problem (SMLP), which is a three-dimensional (3D) layout optimization problem with performance constraints that has proved to be non-deterministic polynomial-time hard (NP-hard). To deal with this problem, we convert it into an unconstrained optimization problem using a quasi-physical strategy and the penalty function method. The energy landscape paving (ELP) method is a class of Monte-Carlo-based global optimization algorithm that has been successfully applied to solve many optimization problems. ELP can search for low-energy layouts via a random walk in complex energy landscapes. However, when ELP falls into the narrow and deep valleys of an energy landscape, it is difficult to escape. By putting forward a new update mechanism of the histogram function in ELP, we obtain an improved ELP method which can overcome this drawback. By incorporating the gradient method with local search into the improved ELP method, a new global search optimization method, nELP, is proposed for SMLP. Two representative instances from the literature are tested. Computational results show that the proposed nELP algorithm is an effective method for solving SMLP with performance constraints.

Heuristic-based energy landscape paving for the circular packing problem with performance constraints of equilibrium

The optimal layout problem of circle group in a circular container with performance constraints of equilibrium belongs to a class of NP-hard problem. The key obstacle of solving this problem is the lack of an effective global optimization method. We convert the circular packing problem with performance constraints of equilibrium into the unconstrained optimization problem by using quasi-physical strategy and penalty function method. By putting forward a new updating mechanism of the histogram function in energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method. Subsequently, by combining the IELP method and the local search (LS) procedure, we put forward a hybrid algorithm, denoted by IELP-LS, for the circular packing problem with performance constraints of equilibrium. We test three sets of benchmarks consisting of 21 representative instances from the current literature. The proposed algorithm breaks the records of all 10 instances in the first set, and achieves the same or even better results than other methods in literature for 10 out of 11 instances in the second and third sets. The computational results show that the proposed algorithm is an effective method for solving the circular packing problem with performance constraints of equilibrium.

Energy landscape paving with local search for global optimization of the BLN off-lattice model

The optimization problem for finding the global minimum energy structure is one of the main problems of protein structure prediction and is known to be an NP-hard problem in computational molecular biology. The low-energy conformational search problem in the hydrophobic-hydrophilic-neutral (BLN) off-lattice model is studied. We convert the problem into an unconstrained optimization problem by introducing the penalty function. By putting forward a new updating mechanism of the histogram function in the energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method. Subsequently, by combining the IELP method with the local search (LS) based on the gradient descent method, we propose a hybrid algorithm, denoted by IELP-LS, for the conformational search of the off-lattice BLN model. Simulation results indicate that IELP-LS can find lower-energy states than other methods in the literature, showing that the proposed method is an effective tool for global optimization in the BLN off-lattice protein model.

Heuristic energy landscape paving for protein folding problem in the three-dimensional HP lattice model

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology and biochemistry. However, the extremely difficult optimization problem arising from energy function is a key challenge in protein folding simulation. The energy landscape paving (ELP) method has already been applied very successfully to off-lattice protein models and other optimization problems with complex energy landscape in continuous space. By improving the ELP method, and subsequently incorporating the neighborhood strategy with the pull-move set into the improved ELP method, a heuristic ELP algorithm is proposed to find low-energy conformations of 3D HP lattice model proteins in the discrete space. The algorithm is tested on three sets of 3D HP benchmark instances consisting 31 sequences. For eleven sequences with 27 monomers, the proposed method explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases. For ten 48-monomer sequences, we find the lowest energies so far. With the achieved results, the algorithm converges rapidly and efficiently. For all ten 64-monomer sequences, the algorithm finds lower energies within comparable computation times than previous methods. Numeric results show that the heuristic ELP method is a competitive tool for protein folding simulation in 3D lattice model. To the best of our knowledge, this is the first application of ELP to the 3D discrete space.

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

The energy landscape paving (ELP) method is a class of heuristic global optimization algorithms based on Monte Carlo sampling. By incorporating the generation of an initial conformation based on a greedy strategy, the conformation update mechanism based on pull moves, and some heuristic off-trap strategies into an improved ELP method, we propose an alternative version of the ELP method, called the ELP-pull move method. We test the ELP-pull move method on both two-dimensional (2D) and 3D hydrophobic-hydrophilic protein-folding models. For ten 2D benchmark sequences of length ranging from 20 to 100, the proposed algorithm finds the lowest energies so far. Within the achieved results, the algorithm converges more rapidly and efficiently than previous methods. For all ten 3D sequences with a length of 64, the ELP-pull move method finds lower energies within comparable computational times. The numerical results demonstrate that our algorithm is a powerful method to study the lattice protein-folding model.

Monte Carlo Energy Landscape Paving and Basin Paving simulation of RNA T-loop hairpin

Conformational landscape of RNA T-loop hairpin has been investigated by Energy Landscape Paving (ELP) and Basin Paving (BP) Monte Carlo simulations. Both ELP and BP simulations use memory of the simulation to increase the probability of the states less visited. The unfolded structures of the RNA were obtained from the folded one by ELP method. Structures were folded from extended structures by BP method. Choice of different parameters, including the use of the end-to-end distance of RNA as a memory term, in the simulations to accelerate sampling is discussed. It has been found that both ELP and BP are highly efficient techniques for unfolding and folding RNA T-loop hairpin.

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

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.

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

The problem of packing circles into a larger containing circle is a kind of NP-hard problem. It is of high theoretical and practical value. Lacking powerful optimization method is the key obstacle to solving this problem. The energy landscape paving (ELP) method is a class of heuristic global optimization algorithm and a generation of Monte Carlo method. By incorporating new configuration update mechanism into ELP method, an improved energy landscape paving (ELP+) algorithm is put forward. The computational results, on two sets of instances taken from the literature, show the effectiveness of the proposed algorithm.