Evaluating LLMs for Combinatorial Optimization: One-Phase and Two-Phase Heuristics for 2D Bin-Packing

This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs with evolutionary algorithms to generate and refine heuristic solutions iteratively. Through comprehensive experiments comparing LLM generated heuristics against traditional approaches (Finite First-Fit and Hybrid First-Fit), we demonstrate that LLMs can produce more efficient solutions while requiring fewer computational resources. Our evaluation reveals that GPT-4o achieves optimal solutions within two iterations, reducing average bin usage from 16 to 15 bins while improving space utilization from 0.76-0.78 to 0.83. This work contributes to understanding LLM evaluation in specialized domains and establishes benchmarks for assessing LLM performance in combinatorial optimization tasks.

The Misclassification Likelihood Matrix: Some Classes Are More Likely To Be Misclassified Than Others

This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering techniques to measure the distances between the predictions of a trained neural network and class centroids. By analyzing these distances, the MLM provides a comprehensive view of the model's misclassification tendencies, enabling decision-makers to identify the most common and critical sources of errors. The MLM allows for the prioritization of model improvements and the establishment of decision thresholds based on acceptable risk levels. The approach is evaluated on the MNIST dataset using a Convolutional Neural Network (CNN) and a perturbed version of the dataset to simulate distribution shifts. The results demonstrate the effectiveness of the MLM in assessing the reliability of predictions and highlight its potential in enhancing the interpretability and risk mitigation capabilities of neural networks. The implications of this work extend beyond image classification, with ongoing applications in autonomous systems, such as self-driving cars, to improve the safety and reliability of decision-making in complex, real-world environments.

When to Accept Automated Predictions and When to Defer to Human Judgment?

Ensuring the reliability and safety of automated decision-making is crucial. It is well-known that data distribution shifts in machine learning can produce unreliable outcomes. This paper proposes a new approach for measuring the reliability of predictions under distribution shifts. We analyze how the outputs of a trained neural network change using clustering to measure distances between outputs and class centroids. We propose this distance as a metric to evaluate the confidence of predictions under distribution shifts. We assign each prediction to a cluster with centroid representing the mean softmax output for all correct predictions of a given class. We then define a safety threshold for a class as the smallest distance from an incorrect prediction to the given class centroid. We evaluate the approach on the MNIST and CIFAR-10 datasets using a Convolutional Neural Network and a Vision Transformer, respectively. The results show that our approach is consistent across these data sets and network models, and indicate that the proposed metric can offer an efficient way of determining when automated predictions are acceptable and when they should be deferred to human operators given a distribution shift.

Evaluation of autonomous systems under data distribution shifts

We posit that data can only be safe to use up to a certain threshold of the data distribution shift, after which control must be relinquished by the autonomous system and operation halted or handed to a human operator. With the use of a computer vision toy example we demonstrate that network predictive accuracy is impacted by data distribution shifts and propose distance metrics between training and testing data to define safe operation limits within said shifts. We conclude that beyond an empirically obtained threshold of the data distribution shift, it is unreasonable to expect network predictive accuracy not to degrade