Problem decomposition
Block Coordinate Descent is the decomposition strategy at the foundation of Sim::OPT. Instead of treating all design variables as one indivisible optimization problem, variables are grouped into smaller search blocks. These blocks may overlap, so a variable may participate in more than one local exploration.
The purpose is not merely computational convenience. The decomposition can express a designer’s understanding of the problem: which variables should be explored together, which relationships should be revisited, and in what order information should propagate through the search.
Sequential and parallel progression
In a sequential block search, the preferred state obtained from one block can become the context for the next. This corresponds to an inexact Gauss-Seidel interpretation of block coordinate search.
Blocks can also be explored from a common state and their results subsequently combined, corresponding to an inexact Jacobi interpretation. Sim::OPT can therefore intermix sequential and parallel search structures in the same exploration.
Overlapping blocks
Overlap allows information to be transmitted through shared variables. A variable explored in one block can later be reconsidered in another context rather than being permanently fixed after a single local decision.
This is particularly useful in design problems whose variables belong simultaneously to several physical or functional relationships.
Reference
Gian Luca Brunetti (2016), “Cyclic overlapping block coordinate search for optimizing building design”, Automation in Construction, 71, 242–261. DOI: 10.1016/j.autcon.2016.08.014.