Many problems related to systems biology remain computationally hard (their difficulty increases exponentially with instance size), meaning that a brute force computational approach will only be tractable for small instance sizes.
Task size is the price interval that the small instance needs to finish the task.
In this instance, size does matter.
Next, select an instance size.
The results are presented based on the VMs sizes: Small instances (Fig. 36), Medium instances (Fig. 37), Large instances (Fig. 38), and Xlarge instances (Fig. 39).
In what follows, we refer to these instance sizes as "tiny", "small", "medium", and "large".
For example, Rackspace has the best performance for the small instances, but not the best for the other instances' sizes.
(5) We propose exact solution in GAMS for solving small-size instances and metaheuristic solution methods, non-dominated sorting genetic algorithm II (NSGA-II), based on the new formulation, providing the means to solve large-size instances, and to compute tight gaps for small instances.
Numerical experiments on randomly-generated data show that, first, only very small instances can be solved efficiently using the mathematical model and, second, our heuristic produces high-quality solutions and solves real-size instances in a reasonable computing time.
Although exact algorithms are appropriate for instances with small size, they are not often suitable for real instances owing to the computational time required to obtain an optimal solution.
