Ravigneaux planetary gear [17]: 1 small sun gear; 2- 3 broad planet gear; 4 large sun gear; 5 narrow planet gear; 6 ring gear. 

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... imposed integer values (as it is the case with gear- teeth numbers), they may be considered from the beginning integers [35], or a continuous-variable nonlinear programming problem can be solved first and then a supplementary search for integer optimum values performed in the vicinity of the continuous optimum found [32]. In the present paper the former approach will be adopted, and the problem of synthesizing a 3+1 speed planetary transmission of the Ravigneaux type solved with the aid of an Estimation of Distribution Algorithm. Fig. 1 shows a planetary transmission of the Ravigneaux type with 3 forward gears and 1 reverse used in automobiles. A kinematic diagram of the transmission is also available in Fig. 2, where the broad planet gear is shown as two distinct gears 2 and 3. Based on the clutch/brake activation required in each gear (Table 1), it becomes evident that for the first and reverse gears the planet carrier is immobile and the equivalent transmission is a fixed-axle one with the following gear rations: i 1 = N 6 N 4 (1) and i R = − ( N 2 N 6 ) ( N 1 N 4 ) . (2) In the third gear, the planet carrier, sun gears and ring gear rotate together as a whole: i 3 = 1 (3) i.e. a direct drive, which ensures a maximum mechanical efficiency of the transmission. The second gear configuration is the only case when the transmission works as a planetary gear set; considering the planet carrier c immobile, three basic gear ratios can be defined as ...