8007
2021
eng
521
554
93
article
Mathematical Methods of Operations Research
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The Maximum Diversity Assortment Selection Problem
In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP is to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2D-KP literature.
Mathematical Methods of Operations Research
https://doi.org/10.1007/s00186-021-00740-2
yes
urn:nbn:de:0297-zib-81039
2021-04-16
Felix Prause
Felix Prause
Kai Hoppmann-Baum
Boris Defourny
Thorsten Koch
Hoppmann, Kai
Koch, Thorsten
MODAL-GasLab
MODAL-Gesamt
Prause, Felix
Applied Algorithmic Intelligence Methods
MODAL-EnergyLab
MODAL-MobilityLab