  In the context of optimization, visualization techniques can be useful for
understanding the behaviour of optimization algorithms and can even provide a
means to facilitate human interaction with an optimizer. Towards this goal, an
image-based visualization framework, without dimension reduction, that
visualizes the solutions to large-scale global optimization problems as images
is proposed. In the proposed framework, the pixels visualize decision variables
while the entire image represents the overall solution quality. This framework
affords a number of benefits over existing visualization techniques including
enhanced scalability (in terms of the number of decision variables),
facilitation of standard image processing techniques, providing nearly infinite
benchmark cases, and explicit alignment with human perception. Furthermore,
image-based visualization can be used to visualize the optimization process in
real-time, thereby allowing the user to ascertain characteristics of the search
process as it is progressing. To the best of the authors' knowledge, this is
the first realization of a dimension-preserving, scalable visualization
framework that embeds the inherent relationship between decision space and
objective space. The proposed framework is utilized with 10 different mapping
schemes on an image-reconstruction problem that encompass continuous, discrete,
binary, combinatorial, constrained, dynamic, and multi-objective optimization.
The proposed framework is then demonstrated on arbitrary benchmark problems
with known optima. Experimental results elucidate the flexibility and
demonstrate how valuable information about the search process can be gathered
via the proposed visualization framework.
