A novel desirability function for multi-response optimization and its application in chemical engineering

In many aspects of modern engineering (processes, products, and systems)InIn many aspects of modern engineering (processes, products, and systems) there is a need to optimize multiple responses simultaneously, rather than optimizing one response at a time. The optimization of each individual response may generate as many different results as the responses, which is considered in the study. Then, it may be impossible to decide whether one solution is better than the other. On the other hand, some improvement in one response can significantly degrade at least one or more responses. There are a number of multi-response optimization techniques available. Among these multi-response optimization techniques, the desirability-based approaches take a prominent place because they are less sophisticated, easy to understand and implement, and more flexible with respect to other existing approaches, due to which they are very popular among researchers and practitioners. There are many different formulations of the desirability function. Unfortunately, most desirability functions known in the literature are piecewise, non-differentiable functions. In this paper, a novel desirability function is proposed, which is continuous and differentiable in its domain. This function is more suitable for applying some of the efficient gradient-based optimization methods. The efficiency and accuracy of the proposed method were analyzed on two chemical processes that were studied extensively in the literature.