Local-Search Based Heuristics for Advertisement Scheduling
Abstract
In the MAXSPACE problem, given a set of ads A, one wants to place a subset A' of A into K slots B1, ..., BK of size L. Each ad Ai in A has size si and frequency wi. A schedule is feasible if the total size of ads in any slot is at most L, and each ad Ai in A' appears in exactly wi slots. The goal is to find a feasible schedule that maximizes the space occupied in all slots. We introduce MAXSPACE-RDWV, a MAXSPACE generalization with release dates, deadlines, variable frequency, and generalized profit. In MAXSPACE-RDWV each ad Ai has a release date ri >= 1, a deadline di >= ri, a profit vi that may not be related with si and lower and upper bounds wmini and wmaxi for frequency. In this problem, an ad may only appear in a slot Bj with ri <= j <= di, and the goal is to find a feasible schedule that maximizes the sum of values of scheduled ads. This paper presents some algorithms based on meta-heuristics GRASP, VNS, Local Search, and Tabu Search for MAXSPACE and MAXSPACE-RDWV. We compare our proposed algorithms with Hybrid-GA proposed by Kumar et al. (2006). We also create a version of Hybrid-GA for MAXSPACE-RDWV and compare it with our meta-heuristics. Some meta-heuristics, such as VNS and GRASP+VNS, have better results than Hybrid-GA for both problems. In our heuristics, we apply a technique that alternates between maximizing and minimizing the fullness of slots to obtain better solutions. We also applied a data structure called BIT to the neighborhood computation in MAXSPACE-RDWV and showed that this enabled ours algorithms to run more iterations.