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optimizationbenchmarkproblems.jl's Introduction

Oabp - Optimization Algorithm Benchmark Problems (OABP)

Simple problems

Supported Dimensions: any.

name Definition Solution Optima
sphere $f(x) = \sum_{i=1}^n x_i^2$ $x_i = 0$ 0
sphere64 $f(x) = \sum_{i=1}^n (x_i - 64)^2$ $x_i = 64$ 0
rosenbrok $f(x) = \sum_{i=1}^{n-1} \left( 100(x_{i+1} - x_i^2)^2 + (x_i - 1)^2 \right)$ $x_i = 1$ 0
ackley $f(x) = -20 \exp \left( -0.2 \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2} \right) - \exp \left( \frac{1}{n} \sum_{i=1}^n \cos(2\pi x_i) \right) + 20 + e$ $x_i = 0$ 0
rastrigin $f(x) = 10n + \sum_{i=1}^n \left( x_i^2 - 10 \cos(2\pi x_i) \right)$ $x_i = 0$ 0
griewank $f(x) = \frac{1}{4000} \sum_{i=1}^n x_i^2 - \prod_{i=1}^n \cos \left( \frac{x_i}{\sqrt{i}} \right) + 1$ $x_i = 0$ 0
schwefel $f(x) = 418.9829n - \sum_{i=1}^n x_i \sin \left( \sqrt{\vert x_i \vert} \right)$ $x_i = 0$ 0
zakharov $f(x) = \sum_{i=1}^n x_i^2 + \left( \sum_{i=1}^n 0.5ix_i \right)^2 + \left( \sum_{i=1}^n 0.5ix_i \right)^4$ $x_i = 0$ 0
levy* $f(x) = \sin^2(\pi w_1) + \sum_{i=1}^{n-1} (w_i - 1)^2 \left( 1 + 10 \sin^2(\pi w_i + 1) \right) + (w_n - 1)^2 \left( 1 + \sin^2(2 \pi w_n) \right)$ $x_i = 1$ 0
stybtang** $f(x) = \sum_{i=1}^n \left( x_i^4 - 16x_i^2 + 5x_i \right)$ $x_i = 2.903534$ -39.16599n
trid*** $f(x) = \sum_{i=1}^{d} [ (x_i - 1)^2 - \sum_{j=1}^{i-1} x_j x_{j+1} ]$ $x_i = i(n+1-i)$ $-n(n+4)(n-1)/6$

* $w_i = 1 + \frac{x_i - 1}{4}$

**, *** optima modified to 0

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