Heuristics for Combinatorial Optimisation

该研究项目将基于组合优化领域，特别关注算法图论和算法学。已知该领域内的问题在诸如运输、物流、布线和制造等领域中具有许多实际应用。这些问题中的许多也被认为是NP难的，因此需要使用启发式和近似方法。这个博士项目将专注于设计，实施和测试在这个问题领域的一系列算法，专注于将在学生的早期阶段决定的具体问题。在此过程中，我们将寻求加深对问题领域的理解，并在适当的情况下，与其他图论问题和结果建立联系。 在这个博士学位期间，学生将研究解决组合优化问题的几种方法，包括整数规划，数学和元数学。然后将针对此问题实施此类技术。还将有机会学习如何询问在线地图和图形API，以收集和利用真实世界的数据。在这些项目中将有一个重要的编码元素（最有可能是C++和Python），学生将在运行大规模实验和统计分析结果方面获得经验。更一般地说，学生将成为经验丰富的批判性思维，解决复杂问题，并正确决策。他们将发展深入挖掘文献所需的研究技能，以找到可靠和相关的信息。所有这些技能在学术界内外都是高度可转移的，特别是在分析和数据科学领域。拟议的奖学金涉及理论和实验工作的结合。理论结果将通过对文献、数学思想和监督讨论的彻底审查得出。显著的结果将通过与命名为第一作者的学生出版物记录，帮助开发他们的研究组合。完成后，预期的目标是学生除了论文外还至少发表了一篇期刊。还将提供在辅导课上授课的机会。该计划的必修课也将由NATCOR提供，这是一系列在不同英国大学教授的为期一周的住宿课程。这些将用于向学生介绍重要的研究技能和方法，并将有助于推进和拓宽他们在该领域的知识。学生还将参加国际会议，在那里他们将展示他们的工作给他们的同龄人。还将鼓励学生在博士期间寻求出版物。这将有助于提高他们的写作技能，并使他们获得修改和辩护工作的经验。 从数学和数据科学的角度来看，图和网络在现代世界中无处不在的性质，以及我们对理解和学习它们的渴望，使其成为一个非常重要的研究领域。我们希望这个学生奖学金至少有一篇论文在4-星星杂志上发表，加上会议论文集的额外产出。随着研究的进展，学生还将参加研讨会和会议报告

This research project will be based in the area of combinatorial optimisation, with a particular focus on algorithmic graph theory and heuristics. Problems within this field are known to have many real-world applications in areas such as transportation, logistics, timetabling, and manufacturing. Many of these problems are also known to be NP-hard, and therefore require the use of heuristic and approximate methods. This PhD project will focus on designing, implementing, and testing a range of algorithms in this problem area, focusing on specific problems that will be decided upon in the early stages of the studentship. In doing this, we will seek to deepen our understanding of the problem area and, where appropriate, make connections to other graph-theoretical problems and results. During this PhD, the student will research several methods for tackling combinatorial optimisation problems, including integer programming, heuristics, and metaheuristics. Such techniques will then be implemented for this problem. There will also be opportunities to learn how to interrogate online mapping and graphing APIs to collect and exploit real-world data. There will be a significant element of coding in these projects (most likely C++ and Python) and the student will become experienced in running large scale experiments and statistically analysing results. More generally, the student will become experienced in critical thinking, complex problem solving, and correct decision-making. They will develop the research skills needed to dig deeply into the literature in order to find credible and relevant information. All of these skills are highly transferrable inside and outside of academia, particularly in areas of analytics and data science. The proposed studentship involves a combination of both theoretical and experimental work. Theoretical results will be derived via a thorough review of the literature, mathematical thought, and supervisory discussions. Significant results will be documented through publication with the student named as first author, helping to develop their research portfolio. Upon completion, the desired aim is for the student to have achieved at least one journal publication in addition to their thesis. Opportunities to teach in tutorial sessions will also be provided. A compulsory taught element of the programme will also be provided by NATCOR, a series of week-long residential courses taught at different UK universities. These will be used to introduce the student to important research skills and methods and will help to advance and broaden their knowledge in the field. The student will also attend international conferences, where they will present their work to their peers. The student will also be encouraged to seek publications during their PhD. This will aid the improvement of their writing skills and allow them to gain experience in revising and defending work. From a mathematical and data science perspective, the ubiquitous nature of graphs and networks in the modern world, together with our desire to understand and learn from them, makes this a very important area of study. We expect this studentship to result in at least one paper to be published in a 4-star journal, plus additional output in conference proceedings. Seminars and conference presentations will also be given by the student as the research progresses