# smoof-package: smoof: Single and Multi-Objective Optimization test... In smoof: Single and Multi-Objective Optimization Test Functions

 smoof-package R Documentation

## smoof: Single and Multi-Objective Optimization test functions.

### Description

The smoof R package provides generators for huge set of single- and multi-objective test functions, which are frequently used in the literature to benchmark optimization algorithms. Moreover the package provides methods to create arbitrary objective functions in an object-orientated manner, extract their parameters sets and visualize them graphically.

### Some more details

Given a set of criteria \mathcal{F} = \{f_1, \ldots, f_m\} with each f_i : S \subseteq \mathbf{R}^d \to \mathbf{R} , i = 1, \ldots, m being an objective-function, the goal in Global Optimization (GO) is to find the best solution \mathbf{x}^* \in S. The set S is termed the set of feasible soluations. In the case of only a single objective function f, - which we want to restrict ourself in this brief description - the goal is to minimize the objective, i. e.,

\min_{\mathbf{x}} f(\mathbf{x}).

Sometimes we may be interested in maximizing the objective function value, but since min(f(\mathbf{x})) = -\min(-f(\mathbf{x})), we do not have to tackle this separately. To compare the robustness of optimization algorithms and to investigate their behaviour in different contexts, a common approach in the literature is to use artificial benchmarking functions, which are mostly deterministic, easy to evaluate and given by a closed mathematical formula. A recent survey by Jamil and Yang lists 175 single-objective benchmarking functions in total for global optimization [1]. The smoof package offers implementations of a subset of these functions beside some other functions as well as generators for large benchmarking sets like the noiseless BBOB2009 function set [2] or functions based on the multiple peaks model 2 [3].

### References

[1] Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation, Vol. 4, No. 2, pp. 150-194 (2013). [2] Hansen, N., Finck, S., Ros, R. and Auger, A. Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions. Technical report RR-6829. INRIA, 2009. [3] Simon Wessing, The Multiple Peaks Model 2, Algorithm Engineering Report TR15-2-001, TU Dortmund University, 2015.

smoof documentation built on March 31, 2023, 11:48 p.m.