N-to-2-space mapping for visualization of search algorithm performance

Visualization of a search process can be an effective way to verify the performance of a search algorithm, especially in terms of its coverage of the search space and behavior near local optima. Planar and 3D surface graphs provide the best intuition, e.g., for highlighting "nearest neighbor" solutions. However, they cannot be directly applied to most search and optimization problems because of the high dimensionality of the search space. Building on insights from space-filling curves and their application for combinatorial optimization problems, This work presents a technique for mapping the solution space of hundred-variable combinatorial optimization problems into two-dimensions. Experimental results for electronics assembly optimization are presented as an example of this technique. Mathematical properties of the proposed N-to-2-space transformation are discussed, and several sample visualizations are presented.