Chris Child

Syed Mahbubul Huq, Daniel Brito, Daniel Sikar et al.

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.

Chris Child, Lam Ngo

The DeeP-Mod framework builds an environment model using features from a Deep Dynamic Programming Network (DDPN), trained via a Deep Q-Network (DQN). While Deep Q-Learning is effective in decision-making, state information is lost in deeper DQN layers due to mixed state-action representations. We address this by using Dynamic Programming (DP) to train a DDPN, where Value Iteration ensures the output represents state values, not state-action pairs. Extracting features from the DDPN preserves state information, enabling task and action set independence. We show that a reduced DDPN can be trained using features extracted from the original DDPN trained on an identical problem. This reduced DDPN achieves faster convergence under noise and outperforms the original DDPN. Finally, we introduce the DeeP-Mod framework, which creates an environment model using the evolution of features extracted from a DDPN in response to actions. A second DDPN, which learns directly from this feature model rather than raw states, can learn an effective feature-value representation and thus optimal policy. A key advantage of DeeP-Mod is that an externally defined environment model is not needed at any stage, making DDPN applicable to a wide range of environments.