# Developments, Trends, and Challenges in Optimization of Ship Energy Systems
## 4 Historical Development of Optimization of Ship Energy Systems
### Objective Functions  
Both single- and multiobjective optimization appears in the articles of Table 1. In order to have a concise picture, the objective functions grouped by type are written in Table 4, together with the articles that apply each objective function.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Objective Function** & **Articles** \\ \hline \multicolumn{2}{c}{**Thermodynamic objectives–single objective optimization**} \\ \hline Total irreversibility (min) & 3 \\ \hline Energy efficiency (max) & 4, 12, 21, 23 \\ \hline Exergetic efficiency (max) & 13 \\ \hline Exergy destruction (min) & 56 \\ \hline Power output (max) & 26 \\ \hline Net power output (max) & 5, 9, 18, 20 \\ \hline Equivalent power output (max) & 45 \\ \hline Fuel consumption (min) & 6, 11, 14, 34, 38, 39 \\ \hline Work required for a process (min) & 25 \\ \hline Maximum temperature of the system (min) & 33 \\ \hline \(\dot{W}_{att}/\Delta\Sigma\)x (max) & 42 \\ \hline \multicolumn{2}{c}{**Environmental objectives–single objective optimization**} \\ \hline EEOI (min) & 32 \\ \hline \multicolumn{2}{c}{**Economic objectives–single objective optimization**} \\ \hline Net present value (max) & 1, 7, 17, 43, 44, 46 \\ \hline Total cost of the system (min) & 2, 22, 35, 41, 54 \\ \hline Total cost of electric energy (min) & 28, 29 \\ \hline Investment cost + operation cost + NOx tax (min) & 10 \\ \hline Capital + fuel + maintenance + emissions cost & 36 \\ \hline Cost of fuel + cost of battery (min) & 15 \\ \hline Levelized energy cost (min) & 16 \\ \hline Present worth cost (min) & 27, 46, 48 \\ \hline \multicolumn{2}{c}{**Multiobjective optimization**} \\ \hline \multicolumn{2}{c}{(i) Total cost (min), (ii) CO2 emissions (min)} & 8 \\ \hline \multicolumn{2}{c}{(i) Exergetic efficiency (max), (ii) total unit product cost (min)} & 19 \\ \hline \multicolumn{2}{c}{(i) Fuel consumption (min), (ii) emissions (min), (iii) difference between initial and final} & 24 \\ \multicolumn{2}{c}{state of charge of the batteries (min)} & \multicolumn{1}{c}{} \\ \hline Life cycle quantities: (i) cost (min), (ii) CO2 emissions (min), (iii) SOx emissions (min), (iv) & 30 \\ \multicolumn{2}{c}{NOx emissions (min)} & \multicolumn{1}{c}{} \\ \hline \multicolumn{2}{c}{(i) Fuel consumption (min), (ii) CO2 emissions (min), (iii) power safety margin (max)} & 31 \\ \hline \multicolumn{2}{c}{(i) Fuel consumption (min), (ii) CHG emissions (min)} & 40 \\ \hline Life cycle quantities: (i) cost (min), (ii) CO2 emissions (min) & 47, 50 \\ \hline \multicolumn{2}{c}{(i) Total annual cost (min), (ii) Size of system (min)} & 49 \\ \hline Weighted summation of (i) battery degradation, (ii) voltage fluctuation, (iii) energy losses & 51 \\ \multicolumn{2}{c}{(iv) device cost} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Objective functions and articles. (The numbers are those written in the first column of Table 1. Explanations of symbols and abbreviations are written after Section 7 Closure.).  
As seen in Table 4, several objective functions have been used, while multiobjective optimization starts gaining ground with a variety of objective functions and their combinations.