Partial Swap Rounds Sample Clauses

Partial Swap Rounds. ‌ The last move operator proposed by Xxxxxxxxxxxxxxx et al. (2006) is called PartialSwapRounds and is determined by one team ti and two rounds, rx and ry. The move will swap the opponents of team ti in rounds rx and ry. This swap will create a schedule that falls outside the search space, which calls for an ejection chain to restore the violations on C1 and C2 (Section 2.1). It is sufficient to find the connected component which contains the games of ti, in rx and ry. A connected component is a graph where the nodes represent the teams and where an edge connects two teams that play against each other in rx or ry (see e.g. Figure 2). All teams in this connected component must have their games swapped (Anagnostopoulos et al., 2006). The opponents on the other hand might have to change their location to meet the requirements for the new match-up. This will create a new schedule that falls within the search space. The matches of only two rounds will be altered for this move operator. − − − − − − The example in Table 10 again requires some additional clarification. Swapping the games of t1 in r6 and r10 will lead to a schedule that does not meet the requirements of a double round-xxxxx tournament. The connected component that contains the games of t1 in r6 and r10 (t1 t4,t1 t2) also includes the arcs t4 t6,t5 t6,t5 t3,t3 t2 (Figure 2). Since it is necessary to swap the games in r6 and r10 of all other nodes in the connected component, the matches of the other teams involved: t2, t3, t4, t5 and t6 in r6 and r10 should be swapped. The resulting schedule is part of both the search and solution space. However, the latter is not guaranteed by this operator. T/R 1 2 3 4 5 6 7 8 9 10 2 -5 6 1 3 -4 -3 4 5 -6 -1 4 -3 -5 -6 1 2 -1 -2 3 5 6 5 2 4 -3 -6 -1 6 1 -2 -4 3 6 -1 -2 4 5 -3 -5 3 1 2 -4 T/R 1 2 3 4 5 6 7 8 9 10 2 -5 6 1 3 -4 -1 4 5 -6 -3 4 -3 -5 -6 1 2 6 -2 3 5 -1 6 -1 -2 4 5 -3 -4 3 1 2 -5 Table 10: Example PartialSwapRounds(S, t1, r6, r10) t1 − t2 t2 t1 t1 − t4 t4 t3 − t2 t3 t4 − t6 t6 t5 − t3 t5 t5 − t6 Figure 2: Connected Component PartialSwapRounds(S, t1, r6, r10)