Journal of Global Optimization https://doi.org/10.1007/s10898-019-00812-y Multidimensional frontier visualization based on optimization methods using parallel computations Alexander P. Afanasiev 1,2,3,4 · Vladimir E. Krivonozhko 2,3,5 · Andrey V. Lychev 2 · Oleg V. Sukhoroslov 1,4 Received: 1 March 2018 / Accepted: 19 July 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In data envelopment analysis, methods for constructing sections of the frontier have been recently proposed to visualize the production possibility set. The aim of this paper is to develop, prove and test the methods for the visualization of production possibility sets using parallel computations. In this paper, a general scheme of the algorithms for constructing sec- tions (visualization) of production possibility set is proposed. In fact, the algorithm breaks the original large-scale problems into parallel threads, working independently, then the piece- wise solution is combined into a global solution. An algorithm for constructing a generalized production function is described in detail. Keywords Data envelopment analysis (DEA) · Parallel algorithms · Efficient frontier · Frontier visualization Mathematics Subject Classification 90C08 · 90B30 · 68W10 · 91B74 · 90C29 1 Introduction Despite the rapid development of information technologies in the last decade, relatively simple methods (based on ratio analysis) are used for performance evaluation of large complex systems (regions, financial organizations, municipalities, universities, etc.). In this approach, B Vladimir E. Krivonozhko KrivonozhkoVE@mail.ru 1 Centre for Distributed Computing, Institute for Information Transmission Problems, Russian Academy of Sciences, Nakhimovsky Prospekt 36-1, Moscow, Russia 117218 2 National University of Science and Technology MISiS, Leninskiy Prospekt 4, Moscow, Russia 119049 3 Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, Russia 119991 4 National Research University Higher School of Economics, Myasnitskaya str., 20, Moscow, Russia 101000 5 Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov st. 44-2, Moscow, Russia 119333 123