## 5 Computational Experiments  
This section describes the experimental setup designed to evaluate the performance of our BR-GRASP and BR-ILS algorithms. To the best of our knowledge, this is the first work solving a rich and realistic version of the multi-period product display problem with dynamic attractiveness. Hence, we had to generate a complete set of benchmarks with different characteristics to comprehensively evaluate and test the proposed algorithms. These characteristics are: number of articles (\(|I|\)), number of display tables (\(|T|\)), number of collections (\(|C|\)), and number of items per display table (\(n\)). For small-sized instances (aimed at being solved using non-linear exact methods), we set \(|I|\in\{25,50,75,100\}\), \(|T|\in\{2,3,4\}\), \(|C|=5\), \(|H|\in\{2,3,4\}\), and \(n=6\). Each of these instances was named according to these specifications. Thus, for example, instance 75i-5c-4p-4t-6 it consists of 75 items, 5 collections, 4 periods, 4 tables per period, and 6 items per table. Similarly, for the large-sized instances we set \(|I|\in\{500,1000,1500,2000\}\), \(|T|\in\{5,10\}\), \(|C|=4\), \(|H|=12\), and \(n=10\). Each of these instances was named according to these specifications. Thus, for example, instance a500m5i1 consists of 500 products and 5 tables. The last index represents different instances using the same combination of items and tables. For the purpose of numerical experimentation, most of the specific inputs in these instances (e.g., initial attractiveness values, dependencies between pairs of products, item prices, and associated collection) have been randomly generated. In order to facilitate reproducibility of the experiments, all these instances and inputs are publicly available at [[https://www.researchgate.net/publication/330675091_instancesMPPDPDA](https://www.researchgate.net/publication/330675091_instancesMPPDPDA)]([https://www.researchgate.net/publication/330675091_instancesMPPDPDA](https://www.researchgate.net/publication/330675091_instancesMPPDPDA)). Although all input data is available in the previous link, an overview of these inputs is provided next for the case of the large-sized instances. The final selling price of each product is generated according to a uniform distribution in the range \([10,150]\) (monetary units). The profit-margin percentage for each product follows a uniform distribution in the range \([10\%,35\%]\). The price and profit margin are considered to generate the absolute profit, which is used to check whether the respective constraints are satisfied. The initial attractiveness value for each item and the between-items dependencies are generated according to a uniform distribution in the range \([10,100]\) and \([-35,35]\), respectively. Regarding the considered constraints, the subset of selected products at each table should cover at least 20% of each collection. Regarding prices, the items are categorized into two different categories: those with a cost inferior to 60 monetary units are considered as non-expensive items. The rest are considered expensive. In our experiments, we required that the selected subset at each table should include at least 50% of expensive products. Finally, for each table, the profit margin per table is set at 100 monetary units or more. To account for the 'novelty factor', when a product is displayed on a table during a given period, its attractiveness value is decreased by 10% for the next period (always considering that the minimum attractiveness value that a product can reach is bounded by the modeling parameter \(a\geq 0\)). Conversely, if a product is not displayed at a given period, its attractiveness value increases by 3% for the next period (up to a maximum value given by the modeling parameter \(b>a\)). After some initial tests, a geometric probability distribution with a parameter \(\beta\) randomly chosen in the interval \((0.80,0.99)\) was used for the biased-randomization process during the solution-construction stage.