A geometric approach to anytime constraint solving for TCSPs

Temporal constraint satisfaction problems (TCSPs) are typically modelled as graphs or networks. Efficient algorithms are only available to find solutions for problems with limited topology. In this paper, we propose constraint geometry as an alternative approach to modeling TCSPs. Finding solutions to a TCSP is transformed into a search problem in the corresponding n-dimensional space. Violations of constriants can be measured in terms of spatial distances. As a result, approximate solutions can be identified when it is impossible or impractical to find exact solutions. A real-numbered evolutionary algorithm with special mutation operators has been designed to solve the general class of TCSPs. It can render approximate solutions at any time and improve the solution quality if given more time. Experiments on hundreds of randomly generated problems with representative parameters showed that the algorithm is more efficient and robust in comparison with the path-consistency algorithm.