Characterising constrained continuous optimisation problems

Real-world optimisation problems are usually constrained in some way. These constraints essentially modify the search space and can have a significant impact on the success of algorithms during optimisation. This paper proposes the notion of a violation landscape as a concept for analysing the nature of constrained continuous search spaces. A number of numerical measures are proposed for characterising constrained problems and these are tested on the CEC 2010 benchmark suite of constrained real-parameter optimisation problems. It is shown that for many constrained problems and algorithms, the features of the violation landscape are more relevant in terms of understanding algorithm performance than the features of the fitness landscape.