Most chemical processes are operated under continuously changing conditions and thus the optimal operating conditions change with time. On-line optimization techniques of various types which are used to track these kinds of moving optimum, have sparked significant interest in recent years. However, most of these strategies deal only with static optimum or optimum that move so slowly that they can be considered static.The model-based optimization algorithms, such as SQP, use first-principle models to optimize the process in a sequential steady-state mode, and hence rely on accurate process models. But for many circumstances, a process model is either too complex or expensive to obtain or changes quickly with time. This can limit the model-based approach and points to the 'direct search' optimization methods, since for these methods no explicit model is required. Moreover, direct search methods need very few new measurements to calculate a new movement toward the optimum. However, little work has been done on optimizing dynamic systems with moving optima using direct search methods. In this work, the traditional Nelder-Mead simplex method is modified and extended to allow tracking of moving optima, which results in a so-called dynamic simplex algorithm. Various simulation examples demonstrate the capability and flexibility of this new direct search algorithm in tracking moving optima in multiple dimensions. (C) 2003 Elsevier Ltd. All rights reserved.