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In the real-time decision-making and local planning process of autonomous vehicles in dynamic environments, the autonomous driving system may fail to find a reasonable policy or even gets trapped in some situation due to the complexity of…
Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral…
\textit{Weighted shortest processing time first} (WSPT) is one of the best known algorithms for total weighted completion time scheduling problems. For each job $J_j$, it first combines the two independent job parameters weight $w_j$ and…
Fine-tuning a pre-trained model (such as BERT, ALBERT, RoBERTa, T5, GPT, etc.) has proven to be one of the most promising paradigms in recent NLP research. However, numerous recent works indicate that fine-tuning suffers from the…
In recent years, combining neural networks with local search heuristics has become popular in the field of combinatorial optimization. Despite its considerable computational demands, this approach has exhibited promising outcomes with…
Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem,…
In traditional assembly lines, it is reasonable to assume that task execution times are the same for each worker. However, in sheltered work centres for disabled this assumption is not valid: some workers may execute some tasks considerably…
Frontier AI models have achieved remarkable progress, yet recent studies suggest they struggle with compositional reasoning, often performing at or below random chance on established benchmarks. We revisit this problem and show that widely…
We investigate deterministic non-preemptive online scheduling with delayed commitment for total completion time minimization on parallel identical machines. In this problem, jobs arrive one-by-one and their processing times are revealed…
The capacitated Vehicle Routing Problem with structured Time Windows (cVRPsTW) is concerned with finding optimal tours for vehicles with given capacity constraints to deliver goods to customers within assigned time windows. In our problem…
This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…
Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…
Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and…
The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…
In this paper we combine the k-means and/or k-means type algorithms with a hill climbing algorithm in stages to solve the joint stratification and sample allocation problem. This is a combinatorial optimisation problem in which we search…
In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with…
We present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem…
This paper investigates the optimization of the Vehicle Routing Problem for Security Dispatch (VRPSD). VRPSD focuses on security and patrolling applications which involve challenging constraints including precise timing and strict time…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…