Iterative search methods, such as the Box complex method, can be used for inverse shape design problems. In the present article, an improved version of the Box complex method is proposed specifically for computational fluid dynamics-based optimization of fluid flow ducting elements. The original Box complex method is improved by (1) assigning non-uniform weights for the estimation of the centroid, (2) using a reduced reflection factor for accelerated convergence, and (3) introducing measures to prevent premature breakdown of the iterative process. The success of the improved Box complex method over the original Box complex method is demonstrated on two benchmark functions and by applying it to two fluid flow problems of engineering. The improved method is shown to substantially accelerate the convergence with approximately 50% reduction in computational effort for the T-junction and manifold problems. © 2016 Informa UK Limited, trading as Taylor & Francis Group.