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Could somebody help me on this issue with work. I tried different code many times in vain.

\documentclass[twocolumn]{svjour3}          % twocolumn
%
\smartqed  % flush right qed marks, e.g. at end of proof
%
\usepackage{graphicx}
%
% \usepackage{mathptmx}      % use Times fonts if available on your TeX system
%
% insert here the call for the packages your document requires
\usepackage{latexsym}
\usepackage{amssymb,mathtools}
%\usepackage{amstext}
\usepackage{stmaryrd}
% etc.
\begin{document}

\begin{equation*}
\begin{aligned}
 Minimize \quad& F=(f_1(x,y),f_2(x,y))\\
 With \quad& 0\leq x,y\leq1\\
 & f_1(x,y)=x\\
 & f_2(x,y)=(1+10y)\left(1-\left(\frac{x}{1+10y}\right)^2-\\
 &\frac{x}{1+10y}sin(2p\pi x)\right),
\end{aligned}
\end{equation*}

\end{document}
1

I do not see where the problem is.

Using:

\documentclass[twocolumn]{svjour3}
\usepackage{graphicx}
\usepackage{latexsym}
\usepackage{amssymb,mathtools,lipsum}
\usepackage{stmaryrd}
\begin{document}
\lipsum[1-2]
\begin{equation*}
\begin{aligned}
 \mathrm{Min}\  & F=(f_1(x,y),f_2(x,y))\\
 \mathrm{s.t.}\ & 0\leq x,y\leq1\\
                & f_1(x,y)=x\\
                & f_2(x,y)=(1+10y)(1-(\frac{x}{1+10y})^2- \\
                &\frac{x}{1+10y}\sin(2p\pi x)),
\end{aligned}
\end{equation*}
\lipsum[1-2]
\end{document}

I have no problem. Notice that I removed all \left and \right. If you want larger delimiters use \bigl and \bigr

You should post MWE instead of snippets. The W means working, which is not the case for your code.

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