A Scoping Review of Recent Fractional Programming Approaches and Ideas for Future Research

This paper aims to present a review of recent scientific ideas and developments in the field of fractional programming. The survey is designed to be prospective, to enable retrieving conclusions regarding current trends in fractional programming, and covers both theoretical results, and practical applications reported in the literature. We organize the solution approaches in certain categories with respect to their characteristics, emphasizing both similarities and differences among them. We also identify some challenges and research gaps that require further investigation. The main objective of the study is to provide an easy to follow survey of the field to researchers interested in advancing the applicability of fractional programming in various adjacent fields, thus, widening interdisciplinarity. The introspection in the recent literature, and suggestions for further research directions are mainly related to optimization in a fuzzy environment, data envelopment analysis, and multiple objective optimization with fractional objective functions.