Table 5 A comparison of the optimal fleet size in different static and uncertain scenarios. The values for MC2-FSEA and MC12-FSEA are averaged fleet sizes ! standard deviations. UNCeRTaINTY IN TRaVel TIMe (MC1-FSea) UNCeRTaINTY IN PROCeSSING aND TRaVel TIMe (MC12-FSea) PORT NUMbeR OF CONTaINeRS STaTIC (FSea) UNCeRTaINTY IN PROCeSSING TIMe (MC2-FSea) lOW HIGH lOW HIGH A 100 10 10.53!0.49 10.20 12.90 10.46!0.49 12.86!0.53 200 14 15.10!0.53 14.30 18.77 15.00!0.67 18.61!0.58 B 300 16 16.30!0.64 16.20 20.05 16.20!0.47 20.10!0.59 100 15 15.83!0.45 15.07 20.22 15.59!0.60 20.87!0.75 200 17 17.13!0.42 17.27 23.57 17.27!0.65 23.46!0.64 300 17 17.70!0.52 17.24 24.84 17.88!0.55 24.44!0.47 As can be seen in Fig. 9, in most cases the robust fleet sizes found by MC12-FSEA are very close to the optimal robust fleet sizes found by the simulation. In 8/12 scenarios the robust solutions found by the two approaches are identical. In the other four scenarios (three from port A under high disruptions), EA underestimates the fleet size, but the differences are not significant: between one and four vehicles and the difference in discharging time is less than 20 minutes. The possible reason for the EA to underestimate in the scenarios of port A under high disruptions is that these are the most complex scenarios. There might be some other factors in these scenarios that the EA model has not considered. The results prove that MC12-FSEA is able to accurately estimate the optimal robust fleet size in the majority of cases. Discharging Time (min) Port A - Low Disruption Rate 230 210 190 170 150 130 110 90 70 50 30 10 300 Containers 200 Containers 100 Containers 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 Discharging Time (min) 270 Port B - Low Disruption Rate 240 Robust Fleet Size by Simulation Robust Fleet Size by MC12-FSEA 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Fleet Size 360 320 Port B - High Disruption Rate 280 210 240 180 200 150 160 120 120 90 60 80 30 40 0 In this research, we have developed an evolutionary algorithm able to identify the suitable number of vehicles in environments with shuttle transportation tasks (ESTTs), in both static and uncertain situations. We considered the travel time of vehicles and the processing time of machines to be the main sources of uncertainty. In the static case we compared the results of our algorithm, FSEA, Port A - High Disruption Rate 240 220 200 180 160 140 120 100 80 60 40 20 Fleet Size 300 IX. Conclusion 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 Fleet Size 0 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 Fleet Size FIGURe 9 Average discharging time of vessels in simulation for the instances in Table 5. The robust fleet sizes found by MC12-FSEA for each instance are shown as black circles and the optimal fleet sizes found by simulation are shown as red squares. 68 IEEE ComputatIonal IntEllIgEnCE magazInE | FEbruary 2016