Many innovative ameliorating techniques including chemical stabilization have been in practice for enhancing the behavior of expansive clays. However, cement and lime are quite effective and successful chemical additives. Based on an experimental investigation, this paper discusses the influence of cement and lime on significant index and swelling properties of expansive clays. Cement and lime were mixed in various quantities (depending on chemicals) with highly swelling montmorillonitic expansive clays for investigating the variation of liquid limit (LL), plasticity index (PI), free swell index (FSI), rate of heave, swell potential (S%), and compression index (Cc). In geotechnical designs, the compression index is one of the major parameters to determine settlements in soils. This paper employed the heuristic models for the prediction of Cc of blended expansive clays. Particle swarm optimization (PSO) is an efficient and inspired computational search for various engineering disciplines. Hence, the PSO technique is used to estimate the compression index value from available data using a linear model. With availability of limited test data, close estimation is possible with PSO for the prediction of Cc. In the linear model Cc equation, the effect of additional coefficients chosen in the PSO prediction model is the key factor presented in this paper.