Towards an abstract parallel branch and bound machine

Many (parallel) branch and bound algorithms look very different from each other at first glance. They exploit, however, the same underlying computational model. This phenomenon can be used to define branch and bound algorithms in terms of a set of basic rules that are applied in a specific (predefined) order. In the sequential case, the specification of Mitten's rules turns out to be sufficient for the development of branch and bound algorithms. In the parallel case, the situation is a bit more complicated. We have to consider extra parameters such as work distribution and knowledge sharing. Here, the implementation of parallel branch and bound algorithms can be seen as a tuning of the parameters combined with the specification of Mitten's rules. These observations lead to generic systems, where the user provides the specifications of the problem to be solved, and the system generates a branch and bound algorithm running on a specific architecture. We will discuss some proposals that appeared in the literature. Next, we raise the question whether the proposed models are flexible enough. We analyze the design decisions to be taken when implementing a parallel branch and bound algorithm. It results in a classification model, which is validated by checking whether it captures existing branch and bound implementations. Finally, we return to the issue of flexibility of existing systems, and propose to add an abstract machine model to the generic framework. The model defines a virtual parallel branch and bound machine, within which the design decisions can be expressed in terms of the abstract machine. We will outline some ideas on which the machine may be based, and present directions of future work.