Complete Search Method Sample Clauses

Complete Search Method. ‌ A first RTTP algorithm, the Complete Search Method, was created by Xxxxxxx and Xxxxxxx (2014). This technique can be seen as the first heuristic approach that can present solutions for an extensive amount of RTTP instances. Xxxxxxx and Xxxxxxx abandoned the brute force-method and came up with an algorithmic approach for the problem. Their method contains several tools: branch-and-bound, metaheuristics and dynamic programming. The branch and bound method is used to generate solutions round by round. Metaheuristics are added to the algorithm to improve the bounds of the solution. Dynamic programming on its turn is used to compute the independent lower bounds quickly and efficiently after each iteration. The operators used by the method are SwapHomesRTTP, SwapRoundsRTTP and SwapTeamsRTTP (Section 3.4.1). Generating schedules is done round by round, i.e. all games of round rx must be fixed before moving on to round rx+1. By doing this, restrictions can be detected much earlier and excess calculations are avoided. A branch will not be further investigated if the sum of the current cost and the independent lower bound of a candidate is higher than the upper bound. This independent lower bound of all teams is the sum of the optimal schedule for every team, ignoring any restrictions or validity constraints (Easton, Nemhauser, & Trick, 2002). In order to calculate this independent lower bound, a dynamic programming approach is used to determine the optimal distance for each team given their location and the amount of matches they have already played. Finally, hill-climbing metaheuristics are used to improve bounds. When a local minimum is reached, random perturbations are applied until a new minimum is reached or until a number of iterations is performed. Each iteration consists of applying one of the move operators to the schedule and checking if this generates a new better schedule. The three transformations (or operators) do not cover the complete search space and as a consequence lead to suboptimal solutions. In addition, some auxiliary data structures are stored to check several constraints in a fast way. These data structures consist of the current location, last opponent, number of byes used, number of consecutive home or away games and a matrix to check if a game has already been scheduled. Using the complete search method, competitive solutions are found for NL4, NL6 and NL8 with up to 3 byes. A noteworthy finding is the longer runtime of the RTTP in com...
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