Efficient algorithms for optimal designs - a unifying approach

In many research areas in both academia and industry, experimentation is performed as a means to establish new scientific results. For example, clinical trials are conducted to assess the efficacy of new treatments, or prototypes of new engines are tested to assess their fuel efficiency. It is well established that designing such experiments in a statistically optimal/efficient way will result in accurate conclusions from the data while at the same time saving resources since fewer runs of the experiment are needed. This not only saves the experimenters' costs, but also time, and may result in new treatments/technology reaching the market faster.

For many years, the field of optimal design of experiments was mostly concerned with theoretical advances, which characterised optimal designs, and in some special cases allowed finding optimal designs analytically. Usually these results were obtained on a case-by-case basis, for each model and optimality criterion separately. More recently, some unifying approaches were developed, which led to significant theoretical advances in the field.

However, in practice, most optimal design problems are too complicated to be solved analytically, and efficient algorithms for numerical design search are required. In particular, while the benefits of optimal designs have been well established in various application areas, practitioners cannot use optimal designs unless they are readily available to them. Therefore, it is essential to develop efficient algorithms and to incorporate them into an easy-to-use software package, which can find optimal designs quickly and to a good accuracy.

The current literature on algorithms for optimal designs resembles the theoretical design literature from decades ago in the sense that algorithms are usually found for specific problems on a case-by-case basis, and it is not clear which type of algorithm/construction method for algorithms will work best in which situation.

It seems that areas such as operational research and computer science have already developed many of the necessary tools for optimisation problems in a general context, which now need to be tailored towards design optimisation. It is time to bridge the gap between the statistical optimal design community and researchers working in the field of optimisation.

The ultimate goal is to develop new algorithms/tailor existing algorithms towards design search, within a large collaborative project between researchers in optimal design and in optimisation and users of optimal designs. We plan to assess these algorithms, and to implement the best ones in a software package available to users.

The proposed research will be a first step towards this goal. The PI will visit leading experts from all areas to start the dialogue. During the project, the PI will develop international collaborations, learn new techniques, meet potential further collaborators and users of the research, and co-ordinate the whole team of collaborators to find the best way forward. She will then take the lead on writing a large scale grant proposal involving all international collaborators to be visited and future users of the research outputs.

Deliverables of the proposed research will be the submission of a large scale collaborative grant proposal, and a shortlist of methods, which appear to be most promising for design search. This shortlist will in itself be useful to researchers in optimal design, since it gives some guidance on which algorithms to use. This may lead to finding optimal/efficient designs faster or with greater accuracy, which in turn benefits scientists in academia and industry who can conduct better experiments. Researchers in optimisation will benefit from a new application area for their research outputs.

When using optimal/efficient designs, the sample size in experiments/clinical trials can be reduced without compromising on the quality of the conclusions drawn from the data. It is therefore essential that optimal/efficient designs are readily available to the user community. The shortlist of promising algorithms, together with some guidance as to which algorithm will work well in which situation, will be available to researchers in design of experiments. Thus our research may result in the following benefits:

(1) Scientific experimentation at Universities: Researchers in design of experiments can use the shortlist to find optimal designs more quickly, which in turn benefits scientists in many areas such as engineering, (experimental) physics, chemistry, biology and medicine, for whose experiments/trials the optimal designs will be available earlier, and possibly to a better precision. This may lead to gaining important scientific understanding earlier. Where the use of an optimal design saves cost of experimentation, this may free up resources for further research.

(2) Scientific experimentation in Industry: Researchers in design of experiments can use the shortlist to find optimal designs more quickly, which in turn benefits scientists in many areas in industry, for whose experiments/trials the optimal designs will be available earlier, and possibly to a better precision. This may lead to new technology/treatments reaching the market faster, increasing competitiveness. Where the use of an optimal design saves cost of experimentation, this may be passed on to consumers.


[In stage 2 of our planned research, for which funding will be requested at a later time, we will provide an easy-to-use software package for finding optimal designs, which can be directly used by practitioners, possibly with some help from applied statisticians. We expect that this will lead to more widespread use of optimal designs in scientific experimentation in both academia and industry. So stage 2 will generate more impact. However, in order to progress to stage 2, the preliminary work of stage 1 is essential.]