## 5 Illustrative Example
### Identification of GIVs  
For each performance indicator, the set of GIVs must be determined. The conflict associated with each performance indicator is determined in the first step. Thus, the following results are obtained:  
* Reconfiguration time (#1): adaptation speed versus automation level (GEP #9 versus GEP #38 in TRIZ language (see TRIZ-MC, p. 280, [32]));
* Module availability (#2): the time required for reconfiguration versus the waste of modules (GEP #9 versus GEP #23 in TRIZ language (see TRIZ-MC, p. 280, [32]));
* Number of interfaces/module (#3): convenience in use versus complexity of solution (GEP #33 versus GEP #36 in TRIZ language (see TRIZ-MC, p. 280, [32]));
* Number configurations (#4): adaptability versus waste of functional units (GEP #35 versus GEP #23 in TRIZ language (see TRIZ-MC, p. 280, [32]));
* Granularity (#5): adaptability versus complexity of control and precision (GEP #35 versus GEP #37 in TRIZ language (see TRIZ-MC, p. 280, [32])). For the contradictions above, the GIVs revealed by TRIZ-MC [32] are put into evidence in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance** & **GIV Position in** & **GIV Description (See TRIZ Table of 40 GIVs, p. 284, [32])** \\ \hline \hline \#1 & \#10 & Perform in advance arrangements of components \\  & \#18 & Use the “resonance frequency” \\ \hline \multirow{4}{*}{\#2} & \#10 & Perform in advance arrangements of components \\  & \#13 & Inversion (e.g., from mobile into immobile or vice \\  & \#28 & Replace the rigid system with a flexible one \\  & \#38 & Strong interactions (e.g., enrich the system with \\  & & elements) \\ \hline \multirow{4}{*}{\#3} & \#12 & Ensure equipotentiality \\  & \#17 & Multilayer assembly and multidimensional motions \\  & \#26 & Use simple copies instead of a compact, complex \\  & \#32 & Use some additive elements \\ \hline \multirow{4}{*}{\#4} & \#2 & Extract the disturbing part from the system \\  & \#10 & Perform in advance arrangements of components \\  & \#13 & Inversion (e.g., from mobile into immobile or vice \\  & \#15 & Create interchangeable modules with automatic \\  & & adjustment \\ \hline \#5 & \#1 & Increase the level of segmentation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GIVs for the case study under consideration. GIV #10 occurs three times in Table 1. Considering the value weights of the associated performance indicators, \(\beta_{1}=0.11\), \(\beta_{2}=0.25\) and \(\beta_{4}=0.24\), the rank of GIV #10 is \(b(\#10)=0.60\). Similarly, with the logic above, the ranks of the other GIVs from Table 1 are determined. They are \(b(\#18)=0.11\), \(b(\#13)=0.49\), \(b(\#28)=0.25\), \(b(\#38)=0.25\), \(b(\#12)=0.26\), \(b(\#17)=0.26\), \(b(\#26)=0.26\), \(b(\#32)=0.26\), \(b(\#2)=0.24\), \(b(\#15)=0.24\), \(b(\#1)=0.14\). Thus, GIVs in the subset belonging to each performance indicator can be ordered, starting with the highest rank. In cases where the ranks of two GIVs in the subset are of the same value, the position of GIVs in the subset is given randomly. For example, all GIVs belonging to performance indicator #3 in Table 1 have the same rank. Thus their order in the subset may be [#26, #32, #12, #17]. Based on the calculated ranks, the result of ordering GIVs is illustrated in Table 2. Symbols associated with GIVs in Table 2 are taken from Figure 11.  
Addition \(\oplus\) and subtraction- in Equations (8) and (9) using the symbols from Table 2 are further exemplified. In this respect, it is assumed for example, that particle #1 in the swarm at iteration \(t\) is defined by the following GIVs of the performance indicators: performance indicator #1 by GIV #10, performance indicator #2 by GIV #28, performance indicator #3 by GIV #17, performance indicator #4 by GIV #2, performance indicator #5 by GIV #1.