## OSY

Osyczka and Kundu used the following six-variable
test problem: 

**Definition**

\begin{equation}
\newcommand{\boldx}{\mathbf{x}}
\begin{array}
\mbox{Minimize} & f_1(\boldx) = -\left[25(x_1-2)^2+(x_2-2)^2 + (x_3-1)^2+(x_4-4)^2  + (x_5-1)^2\right], \\
\mbox{Minimize} & f_2(\boldx) = x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 + x_6^2, 
\end{array}
\end{equation}

\begin{equation}
\begin{array}
\mbox{\text{subject to}} & C_1(\boldx) \equiv x_1 + x_2 - 2 \geq 0, \\
& C_2(\boldx) \equiv 6 - x_1 - x_2 \geq 0, \\
& C_3(\boldx) \equiv 2 - x_2 + x_1 \geq 0, \\
& C_4(\boldx) \equiv 2 - x_1 + 3x_2 \geq 0, \\
& C_5(\boldx) \equiv 4 - (x_3-3)^2 - x_4 \geq 0, \\
& C_6(\boldx) \equiv (x_5-3)^2 + x_6 - 4 \geq 0, \\[2mm]
& 0 \leq x_1,x_2,x_6 \leq 10,\quad 1 \leq x_3,x_5 \leq 5,\quad 0\leq x_4 \leq 6.
\end{array}
\end{equation}

**Optimum**

The Pareto-optimal region is a concatenation of
five regions. Every region lies on some of the constraints. However, for the
entire Pareto-optimal region, $x_4^{\ast} = x_6^{\ast} = 0$. 
In table below shows the other variable values in each of the five
regions and the constraints that are active in each region.



<div style="display: block;margin-left: auto;margin-right: auto;width: 40%;">

</div>

**Plot**


```python
from pymoo.factory import get_problem
from pymoo.util.plotting import plot

problem = get_problem("osy")
plot(problem.pareto_front(), no_fill=True)
```

ac29f0268b41f047ef1f47877e7948ea18628fcc
ipynb
Jupyter Notebook
source/problems/multi/osy.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-11T06:43:49.000Z
2021-11-10T13:36:09.000Z
source/problems/multi/osy.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-21T14:04:47.000Z
2022-03-07T13:46:09.000Z
source/problems/multi/osy.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-10-09T02:47:26.000Z
2022-02-10T07:02:37.000Z
Qwen/Qwen-72B
1. YES
2. YES