Main Concepts RTTSA Sample Clauses

Main Concepts RTTSA. ‌ Time-Relaxed Travelling Tournament Simulated Annealing (RTTSA) uses the same concepts and is structured in a similar way as its time-constrained counterpart (TTSA). This section will briefly cover these concepts to provide clarity on where the proposed adaptations will fit in. RTTSA aims to perform a search in the neighbourhood of a given schedule in order to obtain a schedule with a better objective function value. The neighbourhood of a schedule S can be defined as the set of all possible schedules S′ that can be obtained by performing one of the nine defined move operators (Section 3.4). The concepts of the first five move operators (SwapHomes, SwapRounds, SwapTeams, PartialSwapRounds, PartialSwapTeams) are already implemented in the TTSA algorithm for the time-constrained TTP, but required some adaptations in order to cope with byes (Section 3.4.1). Two other move operators (GroupingAwayUsingByes, SwapByes) are obtained from previous work on the RTTP (Xxxxx-Xxxxxxx & Xxxx, 2015). Finally, building on top of the existing move operators, two new operators are proposed (ExtendAwayTrip, FlipSchedule). In order to perform the neighbourhood search of a solution, a simulated annealing metaheuristic is used (Xxxxxxxxxxx et al., 1983). Pseudocode for the RTTSA algorithm is shown in Algorithm 1. Line 7 to line 43 make clear that the main structure of the proposed RTTSA algorithm is in line with a standard simulated annealing meta-heuristic. For a given temperature T , the algorithm selects one of the moves and generates the schedule S′. If S′ has at least one violation and at most the number of allowed violations (in this case, S′ is called semi-feasible) the repairSchedule method (Section 4.1.5.3) is applied in order to try restore the feasibility of schedule S′. Next, the algorithm determines if the objective function value (cost) of the, potentially repaired, schedule S′ is lower than the cost of schedule S or is lower than the cost of the best feasible or infeasible schedule encountered at that point in the algorithm. If this is the case, TTSA applies the move, if not, the move still has a certain probability of being accepted. Note that strictly infeasible schedules (nbv > nbvAllowed) also can be accepted. This is done to ensure that infeasible regions are also covered during the search. However, when schedule S′ is entirely equal to schedule S in terms of both distance and scheduled matches, the move will always be rejected (see Section 4.1.5.3 for more ...
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