Let G = (V0; V1 ; V2; E) be a 3-layer graph. The 3-layer drawings of G in which V0 , V1 , and V2 are placed on 3 parallel lines and each edge in E is drawn using one straight line segment, are studied. A generalization of the linear arrangement problem which we call the 3-layer pseudo linear arrangement problem is introduced, and it is shown to be closely related to the 3-layer crossing number....

This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining t...

this paper presents a strategy for using harmony search algorithm in facility layout optimization problems. in this paper an adapted harmony search algorithm is developed for solving facility layout optimization problems. this method finds an optimal facility arrangement in an existing layout. two real-world case studies are employed to demonstrate the efficiency of this model. a comparison is ...