Estimation of distribution algorithms (EDAs) constitute a new branch of evolutionary optimization algorithms that were developed as a natural alternative to genetic algorithms (GAs). Several studies have demonstrated that the heuristic scheme of EDAs is effective and efficient for many optimization problems. Recently, it has been reported that the incorporation of mutation into EDAs increases the diversity of genetic information in the population, thereby avoiding premature convergence into a suboptimal solution. In this study, we propose a new mutation operator, a transpose mutation, designed for Bayesian structure learning. It enhances the diversity of the offspring and it increases the possibility of inferring the correct arc direction by considering the arc directions in candidate solutions as bi-directional, using the matrix transpose operator. As compared to the conventional EDAs, the transpose mutation-adopted EDAs are superior and effective algorithms for learning Bayesian networks.

There are many methods for separating and purifying proteins from dilute solutions, such as salting out/precipitation, adsorption/chromatography, foam fractionation, and droplet fractionation. In order to determine the optimal condition for a selected separation and purification process, an objective function is developed. The objective function consists of three parameters, which are the protein mass recovery, the separation ratio, and the enzymatic activity ratio. In this paper the objective function is determined as a function of the pH of the bulk solution for egg albumin, cellulase, and sporamin (for foam fractionation) and invertase ( for droplet fractionation). It is found that the optimal pH for all the systems except for cellulase is near their isoelectric point.