The main reason for the efficiency decrease at part load conditions for four-stroke spark-ignition (SI) engines is the flow restriction at the cross-sectional area of the intake system. Traditionally, valve-timing has been designed to optimize operation at high engine-speed and wide open throttle conditions. Several investigations have demonstrated that improvements at part load conditions in engine performance can be accomplished if the valve-timing is variable. Controlling valve-timing can be used to improve the torque and power curve as well as to reduce fuel consumption and emissions. In this paper, a group method of data handling (GMDH) type neural network and evolutionary algorithms (EAs) are firstly used for modelling the effects of intake valve-timing (V-1) and engine speed (N) of a spark-ignition engine on both developed engine torque (T) and fuel consumption (Fc) using some experimentally obtained training and test data. Using such obtained polynomial neural network models, a multi-objective EA (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity preserving mechanism are secondly used for Pareto based optimization of the variable valve-timing engine considering two conflicting objectives such as torque (T) and fuel consumption (Fc). The comparison results demonstrate the superiority of the GMDH type models over feedforward neural network models in terms of the statistical measures in the training data, testing data and the number of hidden neurons. Further, it is shown that some interesting and important relationships, as useful optimal design principles, involved in the performance of the variable valve-timing four-stroke spark-ignition engine can be discovered by the Pareto based multi-objective optimization of the polynomial models. Such important optimal principles would not have been obtained without the use of both the GMDH type neural network modelling and the multi-objective Pareto optimization approach. (c) 2006 Elsevier Ltd. All rights reserved.