## 5 Simulation Results
### Comparisons  
To reveal the efficiency and quality of the EHOO approach, three optimization methods, particle swarm optimization (PSO), genetic algorithm (GA) and evolutionary strategies (ES), were utilized to resolve the large problem. In the employed PSO [31], the maximum allowable velocity was 0.5; the inertia factor was 1; both cognitive factor and social factor were 2.05; and the population size was 100. In the applied GA [32], a real-value coding was adopted to represent an integer-valued solution. A roulette wheel selection, a single point crossover with probability 0.8, and a mutation with probability 0.03 were adopted. The population size was 100. In the employed ES [33], the population size was 100, the offspring size was 200, and the mutated time constant was \(1/\sqrt{15}\). The rate of self-adaptation in ES depends on the choice of the mutated time constant. Empirical as well as theoretical investigations suggest to choose it as \(1/\sqrt{K}\), where \(K\) is the dimension of a solution vector. The accurate evaluation was utilized to evaluate the objective value of a solution vector for three optimization methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**N** & \(\mathbf{x}^{\star}\) & **Cost** & \(g_{0}(\mathbf{x})\) & **CPU Times (sec.)** \\ \hline
40 & [22,22,22,22,  
We simulated 30 individual runs for the large problem. Because three competing methods should execute a very long period of time to obtain the optimum, the search processes were stopped after they spent 100 min of consumed CPU time. Figure 6 displays the computing efficiencies and solution qualities using four approaches over 30 individual runs. The \"*\" point with coordinates (1.93, 538.6) shown in Figure 6 represents the pair of consumed CPU time and average obtained objective value obtained using the EHOO for the case \(N=40\). The progressions of the average best-so-far objective value of (28) and the corresponding consumed CPU times at the end of every iteration of three heuristic methods are also shown in Figure 6. The progressions of these values associated with PSO, GA and ES are plotted as solid line with triangles \"----\", solid line with circles \"----\", and solid line with crosses \"----\", respectively. Table 5 reveals that the average best-so-far objective values computed  
diversification and intensification. The RMTS metamodel evaluated a solution vector in a short computing time. The EHOO method utilized the IEHO for diversification with the AOCBA for intensification. The EHOO method was applied to minimize the staffing cost in a one-period multi-skill call center, which was formulated as a SICOP. The EHOO method was compared to three optimization methods--PSO, GA and ES--with accurate evaluation. The superb solution that was resulted by the EHOO method had a high quality with favorable computing efficiency. Experimental results demonstrate that most of the objective values obtained by the EHOO method are close to the optimum in 30 individual runs. The EHOO method usually obtains a near optimum even though it does not provide a globally optimal solution. Future research will continue to focus on the improvement of OO method to resolve more complex stochastic optimization problems, such as portfolio optimization with stochastic dominance constraints and optimal reinsurance-investment problems.  
[PERSON]-[PERSON] conceived and designed the experiments; [PERSON]-[PERSON] performed the experiments; [PERSON]-[PERSON] analyzed the data; [PERSON]-[PERSON] contributed reagents/materials/analysis tools; [PERSON]-[PERSON] wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This research work is supported in part by the Ministry of Science and Technology in Taiwan, R.O.C., under Grant MOST108-2221-E-324-018.  
The authors declare no conflicts of interest.