Learning-Driven Combinatorial Optimization for Efficient Resource Allocation

This dissertation investigates the integration of learning mechanisms within combinatorial optimization to design efficient, adaptive, and human-centric decision-support systems. Motivated by real-world resource allocation scenarios and aligned with the national vision for data-driven governance, the research develops the methodological foundations of the Learning-Driven Combinatorial Optimization (LDCO) paradigm, which views optimization as an iterative, knowledge-enhancing process. Within this framework, the thesis introduces new models, metaheuristics, software tools, and interactive AI-based optimization methodologies. The first contribution concerns the introduction and study of the Soft Capacity Bin Packing Problem (SCBPP), a new combinatorial optimization problem that inherits structural similarities from both classical Bin Packing and Number Partitioning Problems. Unlike traditional formulations, the SCBPP models resource allocation through flexible capacity constraints, allowing both under-utilization and controlled over-utilization of heterogeneous bins, with deviations penalized directly in the objective function. Several heuristic and metaheuristic strategies are developed, including a fast constructive approach and two variants based on the Carousel Greedy (CG) framework. Extensive experiments confirm that these methods achieve high-quality solutions in milliseconds and outperform exact solvers on medium and large instances, with successful applications to real digital preservation workflows. Building on this foundation, the thesis presents a multi-language open-source implementation of the CG algorithm (Python, R, MATLAB, Julia), designed to ensure reproducibility and facilitate its adoption in diverse optimization settings. The methodological trajectory then advances with the proposal of the Data-Dependent Carousel Greedy (DDCG), a novel metaheuristic that explicitly extends the classical CG by incorporating data-profiling metrics to guide the search adaptively. DDCG has been benchmarked against state-of-the-art algorithms for the Minimum Label Spanning Tree (MLST) problem, achieving superior results and demonstrating the benefits of integrating learning mechanisms within a light-weight greedy architecture. The final contribution explores the integration of Large Language Models (LLMs) within optimization workflows. A human-centered methodology is developed in which LLMs act as cognitive interfaces, enabling decision-makers to express requirements, constraints, and preferences in natural language while interacting with optimization models. After validating this approach in a real industrial case study, the methodology is applied once again to the SCBPP, thereby closing the experimental loop of the thesis. This final investigation demonstrates how LLM-driven reasoning can support and reinterpret heuristic optimization processes, reinforcing the coherence and generality of the LDCO paradigm.