## 4 Case Studies  
In order to test the optimization effect of the MSO for the OED of combined heat and power-thermal-wind-photovoltaic systems, this paper introduces nine commonly used heuristic algorithms which are highly independent from a specific mathematical model, including biogeography-based optimization (BBO) [27], cultural algorithms (CA) [28], firefly algorithms (FA) [29], genetic algorithms (GA) [11], the grey wolf optimizer (GWO) [14], moth-flame optimization (MFO) [30], particle swarm optimization (PSO) [12], simulated annealing (SA) [31] and a teach-learn based optimization algorithm (TLBO) [32].  
Figure 5: Execution procedure of the multi-searcher optimization (MSO) for optimal energy dispatch (OED).  
Through trial-and-error, the main parameters of different algorithms are given in Table 1. All the simulations were undertaken in MATLAB R2016b on a personal computer with an Intel(R) Core TM i7 CPU at 3.4 GHz with 16 GB of RAM.  
In order to assure a fair comparison, all the parameters of each algorithm have been carefully set based on two rules, as follows:  
(1) Common parameters: The maximum iteration number and the population size are the common parameters of all of the algorithms, which should be set to the same values for each algorithm. Generally speaking, both a larger maximum iteration number and a larger population size can effectively obtain a higher quality optimum, however, this consumes more computation time. Hence, these two parameters were set to achieve a proper balance between the optimum quality and the computation time. Through trial-and-error, they were set to be 300 and 150 for all the algorithms, respectively.  
(2) Independent parameters: Each algorithm has its own parameters, e.g., the crossover probability of GA and the maximum velocity of PSO. These parameters can be determined according to the optimum quality with the given maximum iteration number and population size. Through trial-and-error, the optimal parameters are given in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{BBO} & Number of habitats & 150 \\  & Keep rate & 0.2 \\  & Mutation & 0.1 \\ \hline \multirow{3}{*}{CA} & Population size & 150 \\  & Acceptance ratio & 0.35 \\ \hline \multirow{3}{*}{FA} & Number of fireflies & 150 \\  & Light absorption coefficient & 1 \\  & Attraction coefficient base value & 2 \\  & Mutation coefficient & 0.2 \\  & Mutation coefficient damping ratio & 0.98 \\ \hline \multirow{3}{*}{GA} & Population size & 150 \\  & Mutation probability & 0.1 \\  & Crossover probability & 0.75 \\  & Generation gap & 0.8 \\ \hline GWO & Population size & 150 \\ \hline MFO & Total number of moths & 150 \\ \hline \multirow{3}{*}{PSO} & Inertia weight & 1 \\  & Inertia weight damping ratio & 0.99 \\  & Personal learning coefficient & 1.5 \\  & Global learning coefficient & 2.0 \\ \hline \multirow{3}{*}{SA} & Maximum number of sub-iterations & 20 \\  & Initial temp. & 0.1 \\ \cline{1-1}  & Temp. reduction rate & 0.99 \\ \cline{1-1}  & Number of neighbors per individual & 5 \\ \cline{1-1}  & Mutation rate & 0.5 \\ \hline TLBO & Population size & 150 \\ \hline \multirow{3}{*}{MSO} & Number of global searchers & 150 \\ \cline{1-1}  & Number of local searchers & 30 \\ \cline{1-1}  & Maximum search radius & 1.414 \\ \cline{1-1}  & Minimum search radius & 1e-4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the most important parameters used for different algorithms.