A parallel genetic algorithm is developed for the design of morphing aircraft structures using tendon actuated compliant truss. The wing structure in this concept is made of solid members and cables. The solid members are connected through compliant joints so that they can be deformed relatively easily without storing much strain energy in the structure. The structure is actuated using cables to deform into a required shape. Once the structure is deformed, the cables are locked and hence carry loads. Previously an octahedral unit cell made of cables and truss members was developed to achieve the required shape change of a morphing wing developed at NASA. It was observed that a continuously deformable truss structure with required morphing capability can be achieved by a cellular geometry tailored to local strain deformation. A wing structure made of these unit cells was sized for a representative aircraft and was found to be suitable. This paper describes the development of new unit cell designs that fit the morphing requirements using topology optimization. A ground structure approach is used to set up the problem. A predetermined set of points is selected and the members are connected in between the neighboring nodes. Each member in this ground structure has four possibilities, 1) a truss member, 2) a cable that morphs the structure into a required shape, 3) a cable that is antagonistic and brings it back to the original shape 4) a void, i.e., the member doesn't exist in the structure. This choice is represented with a discrete variable. A parallel genetic algorithm is used as an optimization approach to optimize the variables in the ground structure to get the best structural layout. The parallelization is done using a master slave process. A fitness function is used to calculate how well a structural layout fits the design requirements. In general, a unit cell that has lesser deflection under external loads and higher deflection under actuation has a higher fitness value. Other requirements such as having fewer cables and achieving a required morphing shape are also included in the fitness function. The finite element calculations in the fitness function can be done using either linear or nonlinear analysis. The paper discusses the different ways of formulating the fitness function and the results thereof.