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In the bin-packing problem with minimum color fragmentation (BPPMCF), we are given a fixed number of bins and a collection of items, each associated with a size and a color, and the goal is to avoid color fragmentation by packing items with the same color within as few bins as possible. This problem emerges in areas as diverse as surgical scheduling and group event seating. We present several optimization models for the BPPMCF, including baseline integer programming formulations, alternative integer programming formulations based on two recursive decomposition strategies that utilize decision diagrams, and a branch-and-price algorithm. Using the results from an extensive computational evaluation on synthetic instances, we train a decision tree model that predicts which algorithm should be chosen to solve a given instance of the problem based on a collection of derived features. Our insights are validated through experiments on the aforementioned applications on real-world data. Summary of Contribution: In this paper, we investigate a colored variant of the bin-packing problem. We present and evaluate several exact mixed-integer programming formulations to solve the problem, including models that explore recursive decomposition strategies based on decision diagrams and a set partitioning model that we solve using branch and price. Our results show that the computational performance of the algorithms depends on features of the input data, such as the average number of items per bin. Our algorithms and featured applications suggest that the problem is of practical relevance and that instances of reasonable size can be solved efficiently. [ABSTRACT FROM AUTHOR]

Completion time requirements are often imposed on a classification task. In practice, the desired completion time for classifying a subject may depend on its label (target) value. For example, a timely diagnosis is important for an illness that requires immediate medical attention. It is common in medical diagnoses, therefore, to set completion times based on the severity level of the illness. In this study, we use “label-dependent" completion time requirements to formulate a new classification problem for cost-sensitive decision tree induction by adding “late constraints" to control the rate of tardy classifications for each label value. Adding the late constraints generalizes and enriches the decision tree induction problem, but also poses a challenge to developing an efficient solution algorithm because the conventional approach based on the “divide-and-conquer" strategy cannot be used. We develop a novel algorithm that relaxes the late constraints and iteratively solves a series of cost-sensitive decision tree problems under systematically-generated late penalties. The results of an extensive numerical experiment show that the proposed algorithm is effective in finding the optimal or a near-optimal solution. [ABSTRACT FROM AUTHOR]