Local-search based heuristics for advertisement scheduling

• Published in: R.A.I.R.O. Recherche opérationnelle Vol. 58; no. 4; pp. 3203 - 3231
• Main Authors: Costa da Silva, Mauro Roberto, Schouery, Rafael Crivellari Saliba
• Format: Journal Article
• Language: English
• Published: 08.08.2024
• ISSN: 0399-0559; 2804-7303
• DOI: 10.1051/ro/2024114

In the MAXSPACE problem, given a set of ads A , one wants to place a subset A ′ ⊆ A into K slots B 1 , …, B K of size L . Each ad A i ∈ A has size s i and 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 ∈ A ′ appears in exactly w i 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 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 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 , 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, and Tabu Search for MAXSPACE and MAXSPACE-RDWV. We compare our proposed algorithms with Hybrid-GA proposed by Kumar et al . [ Eur. J. Oper. Res . 173 (2006) 1067–1089]. We also created a version of Hybrid-GA for MAXSPACE-RDWV and compared it with our meta-heuristics. Some meta-heuristics like 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 our algorithms to run more iterations.