Counterfactuals have become a popular technique nowadays for interacting with black-box machine learning models and understanding how to change a particular instance to obtain a desired outcome from the model. However, most existing approaches assume instant materialization of these changes, ignoring that they may require effort and a specific order of application. Recently, methods have been proposed that also consider the order in which actions are applied, leading to the so-called sequential counterfactual generation problem. In this work, we propose a model-agnostic method for sequential counterfactual generation. We formulate the task as a multi-objective optimization problem and present a genetic algorithm approach to find optimal sequences of actions leading to the counterfactuals. Our cost model considers not only the direct effect of an action, but also its consequences. Experimental results show that compared to state-of-the-art, our approach generates less costly solutions, is more efficient and provides the user with a diverse set of solutions to choose from.