A pheromone-rate-based analysis on the convergence time of ACO algorithm.

Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Based on the absorbing Markov chain model, we analyze the ACO convergence time in this paper. First, we present a general result for the estimation of convergence time to reveal the relationship between convergence time and pheromone rate. This general result is then extended to a two-step analysis of the convergence time, which includes the following: 1) the iteration time that the pheromone rate spends on reaching the objective value and 2) the convergence time that is calculated with the objective pheromone rate in expectation. Furthermore, four brief ACO algorithms are investigated by using the proposed theoretical results as case studies. Finally, the conclusions of the case studies that the pheromone rate and its deviation determine the expected convergence time are numerically verified with the experiment results of four one-ant ACO algorithms and four ten-ant ACO algorithms.

An improved biclustering algorithm and its application to gene expression spectrum analysis.

Cheng and Church algorithm is an important approach in biclustering algorithms. In this paper, the process of the extended space in the second stage of Cheng and Church algorithm is improved and the selections of two important parameters are discussed. The results of the improved algorithm used in the gene expression spectrum analysis show that, compared with Cheng and Church algorithm, the quality of clustering results is enhanced obviously, the mining expression models are better, and the data possess a strong consistency with fluctuation on the condition while the computational time does not increase significantly.