## 6 Case Analysis
### Establishment of Objective Function  
In the past, most evaluation methods of innovation performance focused on the measurement of three aspects of innovation output, innovation input, and innovation efficiency. The measurement is mainly carried out by DEA model or fuzzy comprehensive evaluation and the multi-objective optimization configuration is rarely used for research. By reading the measurement indicators of innovation performance and referring to the mature indicators through scholars' practice, this paper adopts the thinking indicators of innovation output, innovation input, and innovation industry agglomeration to measure the innovation performance of the innovation ecosystem for science and technology in defense in Shaanxi Province. The index system is established as follows. Relevant Shaanxi Province statistics from 2010 to 2020 were collected through the \"China Statistical Yearbook\", \"Shaanxi Provincial Statistical Yearbook\", the official website of Shaanxi Provincial Office of Science, Technology and Industry for National Defense, \"China National Defense White Paper\", etc. Using the entropy weighting method, the corresponding weights of each indicator were calculated. As shown in Table 6.  
Based on this, the objective function of innovation performance of the defense science and technology innovation ecosystem is established: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Primary Indicator** & **Secondary Indicator** & **Weight** & **Unit** \\ \hline \multirow{4}{*}{Innovation resource input C1} & Experimental development expenditure of R\&D funds for industrial enterprises above the scale C11 & 0.2074 & million \\ \cline{2-4}  & Internal expenditure of R\&D funds for defense science and technology industry C12 & 0.1646 & thousand \\ \cline{2-4}  & Internal expenditure on R\&D funding for research and development institutions C13 & 0.1956 & million \\ \cline{2-4}  & Internal expenditure on R\&D funds of higher education institutions C14 & 0.4324 & million \\ \hline \multirow{4}{*}{Innovation performance output C2} & Amount of valid invention patents for organizations of research and development C21 & 0.2509 & Pieces \\ \cline{2-4}  & Amount of valid invention patents at colleges and universities C22 & 0.2297 & Pieces \\ \cline{2-4}  & Above the scale, the number of legitimate innovation patents held by industrial businesses C23 & 0.3232 & Pieces \\ \cline{2-4}  & Number of defense invention patents granted C24 & 0.1961 & Pieces \\ \hline \multirow{4}{*}{Industrial agglomeration degree C3} & Proportion of the technology output of military-civilian integration innovation demonstration zones in the national output C31 & 0.1158 & \% \\ \cline{2-4}  & Construction degree of national defense science and technology innovation platform C32 & 0.1193 & \% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Innovation Performance Evaluation Indexes and Weights of Defense Science and Technology Innovation Ecosystem. Investment in innovation resources  
In an ecological system, it is one of the purposes of the ecosystem to obtain greater innovation performance and output with lower input of innovation resources, so the input of innovation resources should be minimized. \(x_{1i}\) represents the \(i\)th second-level index under the first first first-level index. The decision variable \(R\&D\exp^{indus}\) is the experimental development expenditure of R&D funds of industrial enterprises above the scale, \(R\&D\exp^{def}\) is internal expenditure of R&D funds for defense science and technology industry, \(R\&D\exp^{Cites}\) is internal expenditure on R&D funding for research and development institutions, \(R\&D\exp^{Hedu}\) is internal expenditure on R&D funds of higher education institutions.