A graph H is an isometric subgraph of G if dH(u, v) = dG(u, v), for every pair u, v ∈ V (H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i ≥ 1. We give an equivalent condition to sequentially dist...

This paper considers the job scheduling problem in virtual manufacturing cells (VMCs) with the goal of minimizing two objectives namely, makespan and total travelling distance. To solve this problem two algorithms are proposed: traditional non-dominated sorting genetic algorithm (NSGA-II) and knowledge-based non-dominated sorting genetic algorithm (KBNSGA-II). The difference between these algor...

green space, as a social development indicator has environmental, social, cultural, economical, and skeletal aspects and to be able to play its role effectively, the first and most important step is to select an appropriate site for it. site selection necessitates stability analysis of urban green space. the main three steps are identifying stability factors, ahp-based weighting factors and lay...