Time-Constrained Travelling Tournament Problem Sample Clauses

Time-Constrained Travelling Tournament Problem. ‌ ≥ The first variant can actually be seen as a special case or specialisation of the K-RTTP. A concept B can be seen as a specialisation of a concept A if and only if: every instance of concept B is also an instance of concept A and instances of concept A which are not instances of concept B exist6. Since the time- constrained travelling tournament problem (TTP) covers the instances of the RTTP where K = 0 and solutions for the TTP are feasible for the K-RTTP for all K 0, the TTP can clearly be seen as a special case of the RTTP. These time-constrained problems are defined by the fact that each team plays exactly one game in each round. A competition of n teams, n is even, consists out of ∗ − 2 (n 1) rounds and in each round n/2 games are played. All other constraints, as well as the objective function, remain unchanged. The only difference is that some statements from the previous section become unnecessary since TTP is a time-constrained problem and byes do not occur, if n is even. Previous literature on the TTP shows that this problem is strongly NP-hard (Xxxxxxx & Xxxxxxxx, 2011). Since the TTP is a specialisation of the K-RTTP it is logical to assume that the K-RTTP will at least match the level of complexity of the TTP, i.e. the K-RTTP is also strongly NP-hard. NP-hard problems are at least as hard to solve as the hardest NP-problems, i.e. problems that can currently not be solved in polynomial time (Xxxxx & Xxxxxxx, 1979). Since complexity theory does not belong to the scope of this dissertation, it is sufficient to say that NP-hard problems require evaluation of an immense number of possibilities to determine the exact solution. Here, heuristics can effectively reduce the number of evaluations needed and play an invaluable role in obtaining solutions within a reasonable time frame (Pearl, 1984).
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