The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such a combination should outperform the single heuristics. This article presents a GA-based method that produces general hyper-heuristics that solve two-dimensional regular (rectangular) and irregular (convex polygonal) bin-packing problems. A hyper-heuristic is used to define a highlevel heuristic that controls low-level heuristics. The hyper-heuristic should decide when and where to apply each single low-level heuristic, depending on the given problem state. In this investigation two kinds of heuristics were considered: for selecting the figures (pieces) and objects (bins), and for placing the figures into the objects. Some of the heuristics were taken from the literature, others were adapted, and some other variations developed by us. We chose the most representative heuristics of their type, considering their individual performance in various studies and also in an initial experimentation on a collection of benchmark problems. The GA included in the proposed model uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyperheuristics, when tested with a large set of benchmark problems, produce outstanding results for most of the cases. The testbed is composed of problems used in other similar studies in the literature. Some additional instances for the testbed were randomly generated.

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This paper proposes an adaptation, to the two-dimensional irregular bin packing problem of the Djang and Finch heuristic (DJD), originally designed for the one-dimensional bin packing problem. In the two-dimensional case, not only is it the case that the piece's size is important but its shape also has a significant influence. Therefore, DJD as a selection heuristic has to be paired with a placement heuristic to completely construct a solution to the underlying packing problem. A successful adaptation of the DJD requires a routine to reduce computational costs, which is also proposed and successfully tested in this paper. Results, on a wide variety of instance types with convex polygons, are found to be significantly better than those produced by more conventional selection heuristics.

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Gamification is usually understood as a pedagogical strategy that favors student engagement and motivation. Traditionally it is composed of dynamics, mechanics, and components. The purpose of this study was to compare Engineering and Economics and Social Sciences undergraduate students in their performance (grades), motivation, quality of assignments, participation, and emotion when their teachers used gamification as an innovative teaching method during the COVID-19 pandemic. Pearson correlations, Principal Component Analysis (PCA), and Mann–Whitney test were conducted. Additionally, four students were interviewed to describe the emotional downside of the lockdown. The main results indicate that there are higher positive relationships among variables in the Engineering undergraduate students rather than in Economics and Social Sciences and show that emotion poorly correlates with performance, especially for the Economics and Social Sciences students, as many have a negative attitude toward learning mathematics. Additionally, gender and scholarship status are not differential factors. Gamification proved to be a useful pedagogical strategy to promote participation and enhance motivation among undergraduate students, particularly in a context of academic confinement. This study gives teachers an idea of the benefits and extent to which gamification can be used in the classroom.