1. An optical network design apparatus for designing path routing across an optical network including an asymmetric optical hub which has a plurality of ports and of which a number of connections between the ports is limited, the apparatus comprising: a memory configured to store a connection limit corresponding to the number of connections between the ports; and a processor configured to provisionally design a traffic path across the optical network independently of a connection limit to which the number of connections of the asymmetric optical hub is limited, to calculate a penalty allowance with respect to a penalty limit of the provisionally designed traffic path, the penalty limit being a hub facility hop count or transmission delay allowed for the traffic path and the penalty allowance being a value of the allowance, relative to the penalty limit, of a penalty of the traffic path, to calculate, with respect to the asymmetric optical hub, an additional penalty caused on a detour path which is derived by replacing a port with a replacement port in the asymmetric optical hub, to generate, if an asymmetric optical hub is included in the detour path, asymmetric optical hub information about the asymmetric optical hub included in the detour path, the asymmetric optical hub information being connection information about the connection of the asymmetric optical path included in the detour path, to generate, based on the connection limit, the calculated penalty allowance, the calculated additional penalty, and the generated asymmetric optical hub information, a constraint condition for adopting the traffic path satisfying the connection limit and the penalty limit, and to calculate the traffic path by mathematical programming under the generated constraint condition.