Title: A collection of bivariate nonlinear optimisation test problems with graphical representations

Authors: Petru A. Simionescu

Addresses: College of Science and Engineering, Texas A&M University Corpus Christi, 6300 Ocean Dr., Corpus Christi, Texas, 78412, USA

Abstract: Plotting objective functions, whenever possible, allows constraint activity, modality and convexity, as well as landscape features like basins, plateaus, valleys and saddle points, to be intuitively identified. Knowledge of these properties allow researchers to best select a set of functions for rating existing optimisation algorithms, when developing new search algorithms or for their control parameter tune-up. This paper offers a selection of 30 bivariate constrained objective functions accompanied by graphical representations. It is the first time a significant number of constrained-functions with their plots are gathered in one place. Also provided are the minima, maxima (global and local) and saddle point information of these functions, very useful in 'all optima' studies.

Keywords: nonlinear optimisation; inequality constrains; objective functions; all optima; visualisation.

DOI: 10.1504/IJMMNO.2020.110704

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.4, pp.365 - 398

Received: 30 May 2019
Accepted: 08 Mar 2020

Published online: 28 Oct 2020 *

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