We were inspired to furnish information concerning the promising applicability of a hybrid approach involving artificial neural networks (ANNs), with manifold network functions, and a meta-heuristic optimization algorithm for prediction of soil compaction indices. The employed network functions were the prevailed feed-forward network and the novel cascade-forward network algorithms to accommodate multivariate inputs of wheel load, tire inflation pressure, number of passage, slippage, and velocity each at three different levels for estimating the study objectives of soil compaction (i.e. penetration resistance and soil sinkage). The experimentations were carried out in a soil bin facility utilizing a single wheel-tester. Each ANN trials was developed merely and then by merging with the recently introduced evolutionary optimization technique of imperialist competitive algorithm (ICA). The results were compared on the basis of a modified performance function (MSEREG) and coefficient of determination (R2). Our results elucidated that hybrid ICA–ANN further succeeded to denote lower modeling error amongst which, cascade-forward network optimized by ICA managed to yield the highest quality solutions.