Comment on: “Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential”

It is shown that the bound l-state solutions of the Klein-Gordon equation for the general scalar and vector Hulthén potentials obtained by Qiang et al. are valid only for q?1 and . We clarify the problem and give the correct solutions when 0<q<1 or q<0. In each case, we derive a transcendental quantization condition for the s-state energy levels.     

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.