Edinburgh Napier University

  The ability to generate example instances from a domain is important in order to benchmark algorithms and to generate data that covers an instance-space in order to train machine-learning models for algorithm selection. Quality-Diversity (QD) algorithms have recently been shown to be effective in generating diverse and discriminatory instances with respect to a portfolio of solvers in various combinatorial optimisation domains. However these methods all rely on defining a descriptor which defines the space in which the algorithm searches for diversity: this is usually done manually defining a vector of features relevant to the domain. As this is a limiting factor in the use of QD methods, we propose a meta-QD algorithm which uses an evolutionary algorithm to search for a nonlinear 2D projection of an original feature-space such that applying novelty-search method in this space to generate instances improves the coverage of the instance-space. We demonstrate the effectiveness of the approach by generating instances from the Knapsack domain, showing the meta-QD approach both generates instances in regions of an instance-space not covered by other methods, and also produces significantly more instances.