Combinatorial optimization for user interface design

Combinatorial optimization offers a rigorous but powerful approach to user interface design problems, defining problems mathematically such that they can be algorithmically solved. Design is defined as algorithmic combination of design decisions to obtain an optimal solution defined by an objective function. There are strong rationale for this method. First, core concepts such as 'design task', 'design objective', and 'optimal design' become explicit and actionable. Second, solutions work well in practice, even for some problems traditionally out of reach of manual solutions. The method can assist in the generation, refinement, and adaptation of design. However, mathematical expression of HCI problems has been challenging and curbed applications. This chapter introduces combinatorial optimisation from user interface design point of view, and addresses two core challenges: 1) mathematical definition of design problems and 2) expression of evaluative knowledge such as design heuristics and predictive models of interaction.