This paper presents a new method with an evolutionary approach to some parts of integrated-circuit (IC) design. This study, however, is focused on application-specific integrated circuits (ASICs), which need an even more sophisticated design (in terms of size, speed and low-power) because of their specific uses. Optimally scheduled operations are not necessarily optimally allocated to units. To enable optimal allocation we need to consider some allocation criteria while the scheduling is being done. Therefore, algorithms with concurrent scheduling and allocation produce the best results. It is obvious that we have to deal with a trade-off between the quality of the solution and its design time. The main part of the paper is a presentation of an improved method of the evolutionary search for the optimal design of ICs. The evolutionary approach considers scheduling and allocation constraints and ensures a globally optimal solution in a reasonable time. The evaluation of our method shows that the evolutionary method is able to find a solution that is more appropriate in terms of all the considered and important objectives than is the case when working with classical deterministic methods.