A solution to the Shell standard control problem is presented in this paper, based on genetic algorithms (GAs). The proposed scheme includes two discrete-time PID controllers with integral anti-windup and a multivariable Smith predictor to provide the required process output regulation, while the process input minimisation problem is analytically solved on-line, by estimating the unmeasured disturbances entering the process and solving the associated linear programming problem. This, as well as the presence of constraints in the process manipulated variables, results in a complex, non-linear closed-loop system and hence, the manual tuning of the PID controllers according to some given performance specifications becomes a difficult task. GAs are successfully applied to the automatic tuning of the PID controllers according to the given specifications, using a specially formulated objective function which quantifies the controller performance in terms of time-domain bounds on the closed-loop system responses. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.