A rank-based ant system algorithm for solving 0/1 knapsack problem

The 0/1 Knapsack Problem (KP), which is a classical NP-complete problem, has been widely applied to solving many real world problems. Ant system (AS), as one of the earliest ant colony optimization (ACO) algorithms, provides approximate solutions to 0/1 KPs. However, there are some shortcomings such as low efficiency and premature convergence in most AS algorithms. In order to overcome the shortcomings of AS, this paper proposes a rank-based AS algorithm, denoted as RAS to solve 0/1 KP. Taking advantages of the ranked ants with a higher profit, the pheromone of items will be updated with better solutions in RAS. Experimental results in different datasets show that this new kind of AS algorithm can obtain a higher efficiency and robustness when solving 0/1 KP.

A new physarum-based hybrid optimization algorithm for solving 0/1 knapsack problem

As a typical NP-complete problem, 0/1 Knapsack Problem (KP), has been widely applied in many domains for solving practical problems. Although ant colony optimization (ACO) algorithms can obtain approximate solutions to 0/1 KP, there exist some shortcomings such as the low convergence rate, premature convergence and weak robustness. In order to get rid of the above-mentioned shortcomings, this paper proposes a new kind of Physarum-based hybrid optimization algorithm, denoted as PM-ACO, based on the critical paths reserved by Physarum-inspired mathematical (PM) model. By releasing additional pheromone to items that are on the important pipelines of PM model, PM-ACO algorithms can enhance item pheromone matrix and realize a positive feedback process of updating item pheromone. The experimental results in two different datasets show that PM-ACO algorithms have a stronger robustness and a higher convergence rate compared with traditional ACO algorithms.

Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers

To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.

Molecular mechanism of the synergistic effects of vitrification solutions on the stability of phospholipid bilayers

The vitrification solutions used in the cryopreservation of biological samples aim to minimize the deleterious formation of ice by dehydrating cells and promoting the formation of the glassy state of water. They contain a mixture of different cryoprotective agents (CPAs) in water, typically polyhydroxylated alcohols and/or dimethyl sulfoxide (DMSO), which can damage cell membranes. Molecular dynamics simulations have been used to investigate the behavior of pure DPPC, pure DOPC, and mixed DOPC-β-sitosterol bilayers solvated in a vitrification solution containing glycerol, ethylene glycol, and DMSO at concentrations that approximate the widely used plant vitrification solution 2. As in the case of solutions containing a single CPA, the vitrification solution causes the bilayer to thin and become disordered, and pores form in the case of some bilayers. Importantly, the degree of thinning is, however, substantially reduced compared to solutions of DMSO containing the same total CPA concentration. The reduction in the damage done to the bilayers is a result of the ability of the polyhydroxylated species (especially glycerol) to form hydrogen bonds to the lipid and sterol molecules of the bilayer. A decrease in the amount of DMSO in the vitrification solution with a corresponding increase in the amount of glycerol or ethylene glycol diminishes further its damaging effect due to increased hydrogen bonding of the polyol species to the bilayer headgroups. These findings rationalize, to our knowledge for the first time, the synergistic effects of combining different CPAs, and form the basis for the optimization of vitrification solutions. © 2014 Biophysical Society.

Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations

A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equations within a thin rotating spherical shell were found as invariant and approximately invariant solutions. The model is used to describe a simple zonally averaged atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows. The model is superimposed by a stationary latitude dependent flow. Under the assumption of no friction, the perturbed model describes zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. In terms of nonlinear modeling for the NS equations, two small parameters are chosen for the viscosity and the rate of the earth’s rotation and exact solutions in terms of elementary functions are found using approximate symmetry analysis. It is shown that approximately invariant solutions are also valid in the absence of the flow perturbation to a zonally averaged mean flow.