The equation-oriented (EO) approach is widely used for process simulation and optimization. Nevertheless, large-scale EO models consist of a huge number of nonlinear equations and make the solution procedure a challenging and time-consuming task. For most gradient-based numerical algorithms, function evaluations are the dominant step during the solution procedure. Here, a parallel computation method is developed for function evaluations within EO optimization strategies. After dividing the equations into several groups, function evaluations are calculated by using multiple threads on a parallel hardware platform simultaneously. Theoretical analysis for the speedup ratio is conducted. The implementation of the proposed method on a multi-core processor platform as well as a graphics processing unit (GPU) platform is then presented with several case studies. Numerical results are compared and discussed to show that the multi-core processor implementation has good computational performance, whereas the GPU implementation only achieves computational acceleration under relatively specific conditions. (C) 2016 Elsevier Ltd. All rights reserved.