# Open Competency Optimization: A Human-Inspired Optimizer for the Dynamic Vehicle-Routing Problem
## 4 Experimental Studies
### Comparison with Other Metaheuristics
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline
**Technique Used** & **Eros** & **T1** & **T2** & **T3** & **T4** & **T5** & **T6** & **T7** \\ \hline \hline SGA & Avg best & \(2.1\times 10^{-5}\) & \(3.14\times 10^{-5}\) & \(58.0\times 10^{-5}\) & \(9.88\times 10^{-5}\) & \(0.91\times 10^{-5}\) & \(6.5\times 10^{-5}\) & \(0.94\times 10^{-5}\) \\  & Avg worst & 98.65 & 458.12 & 489.45 & 123.15 & 398.54 & 123.15 & 178.54 \\  & Avg mean & 34.17 & 83.91 & 185.22 & 32.54 & 94.28 & 123.15 & 78.54 \\  & STD & 10.48 & 13.02 & 15.12 & 11.02 & 12.46 & 21.78 & 44.38 \\ \hline HMGA & Avg best & \(2.04\times 10^{-7}\) & \(7.02\times 10^{-4}\) & \(4.65\times 10^{-7}\) & \(1.21\times 10^{-7}\) & \(3.57\times 10^{-7}\) & \(1.21\times 10^{-7}\) & \(10.57\times 10^{-6}\) \\  & Avg worst & 7.43 & 11.05 & 21.72 & 7.86 & 9.29 & 8.29 & 33.52 \\  & Avg mean & 6.76 & 10.31 & 19.62 & 8.27 & 12.26 & 17.29 & 25.83 \\  & STD & 3.16 & 8.09 & 11.25 & 2.63 & 8.61 & 7.37 & 12.83 \\ \hline RIGA & Avg best & \(1.68\times 10^{-7}\) & \(6.07\times 10^{-6}\) & \(4.96\times 10^{-7}\) & \(2.31\times 10^{-7}\) & \(4.67\times 10^{-7}\) & \(2.11\times 10^{-7}\) & \(11.97\times 10^{-6}\) \\  & Avg worst & 6.13 & 9.15 & 18.37 & 6.81 & 17.27 & 9.13 & 20.43 \\  & Avg mean & 4.36 & 11.31 & 18.92 & 8.37 & 10.21 & 15.08 & 11.13 \\  & STD & 2.62 & 7.07 & 10.35 & 2.23 & 6.51 & 6.45 & 10.53 \\ \hline \end{tabular}
\end{table} 
Table 4: Error values achieved for problem F2. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline
**Technique Used** & **Peaks (m)** & **Eros** & \multicolumn{6}{c}{**Times**} \\ \cline{3-8}  & & **T1** & **T2** & **T3** & **T4** & **T5** & **T6** & **T7** \\ \hline DASA & 10 & Avg best & \(4.17\times 10^{-3}\) & \(3.80\times 10^{-3}\) & \(3.80\times 10^{-5}\) & \(6.57\times 10^{-10}\) & \(5.56\times 10^{-10}\) & \(7.90\times 10^{-3}\) & \(3.55\times 10^{-14}\) \\  & Avg worst & \(5.51\) & \(3.85\times 10^{-10}\) & \(3.87\times 10^{-10}\) & \(9.17\times 10^{-1}\) & \(2.09\times 10^{-1}\) & \(4.71\times 10^{-1}\) & \(2.91\times 10^{-1}\) \\  & Avg mean & \(1.80\  
the sum of the best solutions found by the OCO algorithm after detecting dynamic changes following each iteration. \[P_{\text{off}}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{1}{R}\sum_{j=1}^{R}P_{ij}\right) \tag{26}\]  
Another factor added to this experimental study was the diversity factor defined by Equation (27), as follows:  
\[F_{\text{DIV}}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{1}{R}\sum_{j=1}^{R}\text{ DIV}_{ij}\right) \tag{27}\]  
\(DIV_{ij}\) is defined by Equation (27), as follows:  
\[\text{DIV}_{ij}=\frac{1}{N(N-1)}\sum_{p=1}^{N}\left(\frac{1}{R}\sum_{q\
eq p}^ {N}\left(1-\left(\frac{N-C_{pq}}{n+\text{avg}(NV_{p};NV_{q})}\right)\right)\right) \tag{28}\]  
\(N_{ep}\) and \(N_{eq}\) represent the numbers of vehicles for cities \(p\) and \(q\), respectively; \(N\) is the problem size, and \(N_{cpq}\) represents the number of common routes between cities \(p\) and \(q\). The test was performed on a real-life problem proposed by [PERSON], which is known as the benchmark in dataset F [45]. The OCO algorithm was tested on instances of dynamic vehicle routing from F-N45-k4, F-N72-k4, and F-N135-K7 [45]. These three bodies represent deliveries of groceries, tires, and accessories for service stations. The optimal values of these three instances were 724, 237, and 1162, respectively [46]. For each test mentioned above, N represents the number of customers (including the depot), while k is the number of vehicles. In this study, the solution was represented as a sequence of N customers to be served, which determined the relative allocation of K vehicles. We checked the capacity constraint of each vehicle starting from the first element of the vector that represented the solution; if it did not violate the constraint, we moved to the next element. If it violated the constraint in a vector element of the solution, we considered using another vehicle starting from that element and repeated the process until all customers were served.