General 0-1 fractional programming with conditional fractional terms for design of food frequency questionnaires

Optimising an important methodological tool in nutritional epidemiology gives rise to a general 0–1 fractional programming problem with more than 200 fractional terms. All fractional terms are conditional, i.e. in every feasible solution only a subset of the fractional terms is actually defined. Existing literature does not provide a solution method. We extend known reformulation approaches to reformulate the general 0–1 fractional programming problem such that it can be solved by standard MILP software. Practical instances were solved fast.