Local-Search Based Heuristics for Advertisement Scheduling
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In the MAXSPACE problem, given a set of ads A, one wants to place a subset A' of A into K slots B_1, ..., B_K of size L. Each ad A_i in A has a size s_i and a frequency w_i. A schedule is feasible if the total size of ads in any slot is at most L, and each ad A_i in A' appears in exactly w_i slots. The goal is to find a feasible schedule that maximizes the sum of the space occupied by all slots. We introduce MAXSPACE-RDWV, which is a MAXSPACE generalization that has release dates, deadlines, variable frequency, and generalized profit. In MAXSPACE-RDWV each ad A_i has a release date r_i >= 1, a deadline d_i >= r_i, a profit v_i that may not be related with s_i*w_i and lower and upper bounds w^min_i and w^max_i for frequency. In this problem, an ad may only appear in a slot B_j with r_i <= j <= d_i. In this paper, we present some algorithms based on meta-heuristics Greedy Randomized Adaptive Search Procedure (GRASP), Variable Neighborhood Search (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 for this problem. Some meta-heuristics, like GRASP, have had better results than Hybrid-GA for both problems.
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