As a preparation of a design standard regarding road facilities in terms of reliability based optimum design examples, such as cantilever columns for traffic lights, optimum design in deterministic and probabilistic ways for the foundation of traffic lights poles are proposed. Most of the previous study have focused on the foundation surrounded by cohesionless soil. However, the design would be governed by risky condition. Therefore the resistance by clay-soil is investigated compared with other design specifications. In deterministic optimization, GRG method is applied. It is found that both geometries of deep and shallow foundation provides optimum values. The resistance of cohesive soil is selected to represent the ultimate limit states, in terms of sliding, overturning and bearing pressures from super structures to the foundation under external loads. Example foundations with varying height of columns for traffic lights are optimized about 30% decreased embedded depth of foundation. The optimum coefficients of resistant and load factors may need to be developed with design load combinations in order to prepare design specifications as the next step.