Heuristics for Combinatorial Optimisation

这个研究项目将基于组合优化领域，特别关注算法图论和启发式。众所周知，这个领域中的问题在运输、物流、时间表和制造等领域有许多实际应用。这些问题中的许多也被认为是np困难的，因此需要使用启发式和近似方法。该博士项目将专注于设计、实现和测试该问题领域的一系列算法，重点关注将在学生早期阶段决定的具体问题。在此过程中，我们将寻求加深我们对问题领域的理解，并在适当的情况下将其与其他图理论问题和结果联系起来。在博士期间，学生将研究几种解决组合优化问题的方法，包括整数规划、启发式和元启发式。这样的技术将被用于解决这个问题。也将有机会学习如何查询在线地图和绘图api来收集和利用现实世界的数据。在这些项目中会有一个重要的编码元素（很可能是c++和Python），学生将在运行大规模实验和统计分析结果方面变得有经验。更广泛地说，学生将在批判性思维、解决复杂问题和正确决策方面变得经验丰富。他们将培养深入挖掘文献所需的研究技能，以找到可信和相关的信息。所有这些技能在学术界内外都是高度可转移的，尤其是在分析和数据科学领域。拟议的奖学金包括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全面回顾而得出。重要的成果将通过以第一作者命名的学生出版记录，帮助他们发展研究组合。完成后，期望的目标是学生在论文之外至少发表了一篇期刊论文。还将提供辅导课教学的机会。该项目的必修教学内容也将由NATCOR提供，这是一系列在英国不同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，在那里他们将向同龄人展示他们的作品。学生也将被鼓励在他们的博士学位期间寻求出版物。这将有助于提高他们的写作技巧，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本质，以及我们对它们的理解和学习的渴望，使这成为一个非常重要的研究领域。我们希望这个学生至少有一篇论文发表在四星级期刊上，并在会议论文集中有额外的产出。随着研究的进展，学生也将在研讨会和会议上发表演讲

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