Sentence examples for instances can be solved from inspiring English sources
Nevertheless, for such cases often specific instances can be solved.
Difficult instances with up to 50 potential plants and 100 customers, and largest easy instances, can be solved in one CPU hour.
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.
This is possible because the Maximum Density Still Life Problem is in fact well behaved mathematically for sufficiently large n (around n>200) and if such very large instances can be solved, then there exist ways to construct provably optimal solutions for all n from a finite set of base solutions.
This problem is NP-hard, although in practice fairly large instances can be solved to optimality within reasonable running time.
Still, all instances can be solved in less than one second by the three algorithms mentioned above, which exploit low values of k.
This instance can be solved by any MILP solver (see, e.g., [17]) and we call this approach global MILP control.
Results for the instance with 10 items are not available anymore, but this instance can be solved by enumeration in a few seconds (there are 2=1024 possible solutions).
Moreover, from Table 3, notice that the algorithms in [19, 21] cannot solve the instances within two hours when (ngeq150) and (p=4), but all instances selected can be solved by the proposed algorithm within no more than two hours.
The size of the resulting optimization problems is far beyond the scale of problem instances that can be solved today even with the most powerful standard optimization solvers.
