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The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…
Heuristics have achieved great success in solving combinatorial optimization problems~(COPs). However, heuristics designed by humans require too much domain knowledge and testing time. Since Large Language Models~(LLMs) possess strong…
We present Model Predictive Trees (MPT), a receding horizon tree search algorithm that improves its performance by reusing information efficiently. Whereas existing solvers reuse only the highest-quality trajectory from the previous…
The container relocation problem is a challenging combinatorial optimisation problem tasked with finding a sequence of container relocations required to retrieve all containers by a given order. Due to the complexity of this problem,…
We formulate the Resource-Constrained Project Scheduling Problem (RCPSP) as optimal search over the reachability graph of a Timed Transition Petri Net with Resources, using relative-delay tokens so that scheduling decisions correspond to…
Learning a well-informed heuristic function for hard task planning domains is an elusive problem. Although there are known neural network architectures to represent such heuristic knowledge, it is not obvious what concrete information is…
The Job Shop Scheduling Problem (JSSP) is a well-known optimization problem in manufacturing, where the goal is to determine the optimal sequence of jobs across different machines to minimize a given objective. In this work, we focus on…
The Capacitated Vehicle Routing Problem (CVRP), a fundamental combinatorial optimization challenge, focuses on optimizing fleet operations under vehicle capacity constraints. While extensively studied in operational research, the NP-hard…
Recent advancements have significantly enhanced the performance of large language models (LLMs) in tackling complex reasoning tasks, achieving notable success in domains like mathematical and logical reasoning. However, these methods…
Tree search methods have demonstrated impressive performance in code generation. Previous methods combine tree search with reflection that summarizes past mistakes to achieve iterative improvement. However, these methods face significant…
Monte Carlo tree search (MCTS) is one of the most capable online search algorithms for sequential planning tasks, with significant applications in areas such as resource allocation and transit planning. Despite its strong performance in…
Complete tree search is a highly effective method for tackling MIP problems, and over the years, a plethora of branching heuristics have been introduced to further refine the technique for varying problems. Recently, portfolio algorithms…
Recent studies explored integrating state-space search algorithms with Language Models (LM) to perform look-ahead on the token generation process, the ''Tree-of-Thoughts'' (ToT), generated by LMs, thereby improving performance on…
Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a…
The integration of Large Language Models (LLMs) into evolutionary frameworks has established a new paradigm for automated heuristic discovery. Despite their promise, these methods typically search in the discrete space of program syntax,…
Metaheuristic search methods have proven to be essential tools for tackling complex optimization challenges, but their full potential is often constrained by conventional algorithmic frameworks. In this paper, we introduce a novel approach…
Cutting and Packing problems are occurring in different industries with a direct impact on the revenue of businesses. Generally, the goal in Cutting and Packing is to assign a set of smaller objects to a set of larger objects. To solve…
Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…
Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities, yet their standard generation process -- auto-regressive token prediction -- is inherently myopic and prone to cascading errors. To address this, the…
This paper is concerned with the container pre-marshalling problem, which involves relocating containers in the storage area so that they can be efficiently loaded onto ships without reshuffles. In reality, however, ship arrival times are…