In this paper, we present AMS-DEMO, an asynchronous master-slave implementation of DEMO, an evolutionary algorithm for multi-objective optimization. AMS-DEMO was designed for solving time-intensive problems efficiently on both homogeneous and heterogeneous parallel computer architectures. The algorithm is used as a test case for the asynchronous master-slave parallelization of multi-objective optimization that has not yet been thoroughly investigated. Selection lag is identified as the key property of the parallelization method, which explains how its behavior depends on the type of computer architecture and the number of processors. It is arrived at analytically and from the empirical results. AMS-DEMO is tested on a benchmark problem and a time-intensive industrial optimization problem, on homogeneous and heterogeneous parallel setups, providing performance results for the algorithm and an insight into the parallelization method. A comparison is also performed between AMS-DEMO and generational master-slave DEMO to demonstrate how the asynchronous parallelization method enhances the algorithm and what benefits it brings compared to the synchronous method.