These results are compared with the results of solving the instance 20×9-c by the improved NSGA-II, as shown in Tables8 Tables8
Similarly to Kao et al. [ 28], we show that solutions for instances of the form (X ∖ { x}, Y ∖ { y}, w) correspond to certain shortest paths in the residual flow network obtained when solving the instance (X, Y, w).
Table1 shows the results obtained by the model including the number of instances solved to optimality by the model in each problem size and the average computational time required to solve the instances.
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.
We solve the instances by using the CPLEX solver within the AIMMS development environment.
In addition, we report on the running time in seconds (t [ s]), the model CUT F needs to solve the instances of the mp/q group to optimality.
The obtained slow down factors indicate that the MTZ model is the most affected by increasing the costs of the core network: MTZ needs about 7 times more time to solve the instances to optimality, if the costs of the core network are multiplied by factor M=10.
A generalization of this game, called quasi-group completion [39], has already provided a means to studying heuristics that exploit structural properties, and may help to serve the same purpose in psychology.Theoretically, it can be computationally harder to detect structures than to solve the instance itself [40], [41].
In contrast, the Flow-RM was unable to solve the instance p5, regardless of the value of k considered.
RISOTTO [ 11] is the fastest algorithm in the family of suffix tree algorithms for PMS problem and can solve the instance (15, 5) in 100 minutes.
