## 4 Heuristic Optimization Techniques Analysis  
The numerous demands make it difficult to include cogeneration units in the economic dispatch of the power system. The cogeneration units' mutual dependence on each other'sheat-power capacity makes it difficult to economically dispatch cogeneration units into the power grid due to the numerous demands (for both heat and electricity). Researchers have put forth a variety of heuristic methods for optimizing the CHPED problem. The many heuristic methods proposed for CHPED optimization are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ref. No.** & \begin{tabular}{c} **Optimization** \\ **Techniques** \\ \end{tabular} & **Constraints** & \
\begin{tabular}{c} **Taken Case Study for** \\ **Optimization** \\ \end{tabular} &
\begin{tabular}{c} **Advantages and** \\ **Disadvantages** \\ \end{tabular} \\ \hline
[1] 1994 & Quadratic programming & Generation limits & \
\begin{tabular}{c} 15 traditional power \\ units, 9 boilers, and \\ 15 co-generation units \\ \end{tabular} &
\begin{tabular}{c} Fast response and does not \\ depend on the size of the data \\ \end{tabular} \\ \hline
[2] 1996 & Lagrangian relaxation & \
\begin{tabular}{c} Power balance and \\ generation limits \\ \end{tabular} & 7-unit system &
\begin{tabular}{c} Best suitable for small \\ generating unit system \\ optimization \\ \end{tabular} \\ \hline
[3] 2013 & Benders decomposition & Inequality constraint & 4- and 5-unit systems &
\begin{tabular}{c} Performing well for a small \\ data set \\ \end{tabular} \\ \hline
[4] 2009 & SPSO & Equality and inequality & 4 units &
\begin{tabular}{c} Best performing for small \\ test data \\ \end{tabular} \\ \hline
[5] 2011 & Bee colony & Generation limits & 4 units & Fast and effective \\ \hline
[6] 2012 & Artificial immune system & Power balance and generation limits & 4 units &
\begin{tabular}{c} Gives an optimum solution \\ and takes less CPU time, but \\ does not test the big test \\ data set. \\ \end{tabular} \\ \hline
[7] 2013 & Firefly algorithm &
\begin{tabular}{c} Power balance and \\ generation limits \\ \end{tabular} & 4 units & Simple and effective \\ \hline
[8] 2011 & Mesh adaptive direct search & Power balance and generation limits & \
\begin{tabular}{c} Single- as well as \\ multi-heat area and \\ power area systems \\ \end{tabular} &
\begin{tabular}{c} Conceptually, it is very \\ straightforward, easily \\ implementable, and \\ computationally effective. \\ \end{tabular} \\ \hline
[9] 2015 & TVAC-PSO & \
\begin{tabular}{c} Valve point, generation \\ limit, power balance, \\ and heat balance \\ \end{tabular} & 4- and 84-unit system &
\begin{tabular}{c} Effective for CHPED issues \\ that are non-convex and \\ non-linear \\ \end{tabular} \\ \hline
[10] 2015 & Crisscross optimization &
\begin{tabular}{c} Valve point, \\ transmission losses, \\ and prohibited \\ operating zones \\ \end{tabular} & 4,7, 24, and 48 units & Effective for large test data also \\ \hline
[11] 2016 & Exchange market &
\begin{tabular}{c} Valve-point loss along \\ with power balance \\ and generation limits \\ \end{tabular} & 4,5, 7, 24, and 48 units & Powerful and robust algorithm \\ \hline
[12] 2017 & WOA & \
\begin{tabular}{c} Valve-point effect, \\ generation limits \\ \end{tabular} & 24, 84, and 96 units &
\begin{tabular}{c} Easily handles large test data \\ and gives a global solution \\ \end{tabular} \\ \hline
[13] 2019 & IGA-NCM & Power balance & 4-, 5-, 7-, 24- and 48-unit system &
\begin{tabular}{c} It can handle small and large \\ data and give optimal \\ solutions easily. \\ \end{tabular} \\ \hline
[14] 2019 & Advanced modified PSO & \
\begin{tabular}{c} Valve-point effect, \\ power balance, and \\ generation limits \\ \end{tabular} & 4- and 7-unit system &
\begin{tabular}{c} The suggested technique can \\ locate the ideal solution and \\ avoid local minima. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different optimization approaches used for the solution of the CHPED problem.