Research Proposal: Meta-heuristics in Robust Optimisation

我的研究是基于开发在不确定情况下执行优化的方法。我的工作是解决一般问题。给定用于支持明智决策的某种形式的模型(例如，某个问题的后勤解决方案的模型，或铁路时刻表问题的模型，...)优化用于确定模型中将产生最佳结果的值，即最佳后勤解决方案或最佳时间表。然而，我们假设问题中存在一些不确定性，所以如果我们可以非常准确地定义解决方案，但又非常敏感，那么我们希望避免得到一个很好的结果-因此，如果我们更改解决方案的一小部分，结果会恶化很多。我们对不确定性所做的假设将我们的工作归入了“稳健优化”的范畴。因为我们不对我们的方法可以应用到的模型的性质做出任何假设，所以我们致力于“元启发式”(通用的基于规则的方法)领域。这与Marc的工作不同，例如，Marc的工作主要是数学编程--对你想要应用优化的模型做出了一些特定的假设，这是一个限制，但这意味着你可能比我更一般类型的方法更能找到最优解决方案。

My research is based on developing approaches for performing optimisation under uncertainty. I work on general problems. Given some form of model that is being used to support informed decision making (e.g. a model of a logistical solution to some problem, or a model of a railway timetabling problem, ....) optimisation is used to identify the values in the model that will produce the best results i.e. the best logistical solution or best timetable. However we assume that there is some uncertainty in the problem so we want to avoid getting a result that is good if we can define the solution very accurately, but is highly sensitive - so that if we change a small part of the solution the result deteriorates a lot. The assumptions we make about the uncertainty puts our work under a category of 'robust optimisation'. Because we don't make any assumptions about the nature of the models our approaches can be applied to, we are working in the area of 'metaheuristics' (general rule-based approaches). This is as opposed to, for example, Marc's work which is primarily in 'mathematical programming' - there some specific assumptions are made about the models you want to apply optimisation to, which is a limitation, but means that you may be better able to find an optimal solution than you can for my more general types of approach.