A collection of bivariate nonlinear optimisation test problems with graphical representations. (1st September 2020)

• Record Type: Journal Article
• Authors: Simionescu, Petru A.
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 10:Number 4(2019)
• Page Start: 365
• Page End: 398
• Publication Date: 2020-09-01
• Subjects: nonlinear optimisation -- inequality constrains -- objective functions -- all optima -- visualisation; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

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.