Shape optimization of airfoils involves highly expensive, nonlinear objective(s) and constraint functions often with functional and slope discontinuity that limits the efficient use of gradient-based methods for its solution. Gradient-based methods are not capable of generating a set of pareto solutions as required in multiobjective problems as they work with a single solution and improve it through successive iterations. Population-based, zero-order, stochastic optimization methods are therefore an attractive choice for shape optimization problems as they are easy to implement and effective for highly nonlinear problems. We present a swarm algorithm that is applicable for optimization problems in general, but is here explored for airfoil design optimization studies. The algorithm is based on a sociobehavioral model, and it offers the designer the desired flexibility to solve various unconstrained/constrained, single-/multiobjective forms of the airfoil shape optimization problem. The algorithm handles objectives and constraints separately via pareto ranking and is thus immune to problems of scaling and aggregation that commonly affect penalty-function-based constraint handling schemes. Three different airfoil design optimization problems have been solved to illustrate the algorithm's flexibility and its computational efficiency, which compare favorably with existing stochastic search methods.