Partial Swap Teams Sample Clauses

Partial Swap Teams. ‌ The move operator PartialSwapTeams of Anagnostopoulos et al. (2006) involves one round, rx, and two teams, ti and tj. A precondition for this move is that ti and tj do not play each other in round rx but have 2 different opponents, e.g. ta and tbn respectively. It does not matter if they play at home or away. The move will start by swapping both matches, ti − ta and tj − tb to ti − tb and tj − ta. After the swap, a schedule will appear that violates some hard constraints (C1 and C2 (Section 2.1)) of a double round-xxxxx tournament. To restore those violations, an ejection chain is called upon. This chain starts by searching the round ra where the original match ti tb was planned. In ra, the matchups of ti and tj are swapped again. Matches tc ti and td tj will now become td ti and tc tj. After this swap, the ejection chain searches again for the round where the match td ti was originally planned and swaps the matchups for both ti and tj. This procedure is repeated until the circle is complete, i.e. we arrive again in round rx. After the ejection chain is applied, a schedule will be produced that is part of the search space (but not necessarily of the solution space). The maximum number of rounds where matches can be swapped is equal to R 2, because the rounds where ti and tj have a match-up will never change. For every involved round, two matches will be altered. The example of this move operator in Table 9 requires some additional clarification. After matches t4 t2 and t3 t6 are changed to t6 t2 and t3 t4 in r5 a schedule appears that is not a part of the search space. An ejection chain is invoked to make sure that the new schedule is again part of the search space. First, the round of the initial match t3 t4 is determined, here r1. In r1, the original matches t3 t4 and t1 t6 are replaced by t3 t6 and t1 t4. Next, the round of initial match t1 t4 is determined, here r6. Also for this round the original matches t1 t4 and t5 t6 are replaced by t1 t6 and t5 t4. This procedure repeats itself for r2, r7, r8, r4 and r9, in that particular order. The matches in r9 were originally t4 t5 and t6 t2 and are replaced by t6 t5 and t4 t2. The match t4 t2 was originally planned to be played in r5, the initial round. After this last swap, the circle is complete and the schedule is again part of the search space. However, the resulting schedule is not part of the solution space because the atmost constraint is violated by team 4 in round 10. A fourth consecutive home gam...