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.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.