In the design and operation of chemical processes, multiple objectives are frequently encountered, i.e., profit vs. environmental impacts, safety vs. flexibility. Under these circumstances, the design task can be formulated as a multi-objective optimization (MOO) problem. Moreover, when facing the challenge of uncertainties, how to identify the optimal solution will be even more challenging.

In decision-making under uncertainty, many stochastic programming (SP) based methods have been developed. Most approaches assume that some key parameters (e.g., mean and variance) and/or probability distributions (e.g., normal distribution) or the prior distribution (Bayesian statistics) can be identified and used to describe variation and probability.

Under severe uncertainty, the available information about the target parameters/variables might be incomplete or very vague. Instead of having accurate historian data for these variables, a probability distribution in which the characteristic parameters like mean, standard deviation and variance might be given by a range rather than a fixed value. However, so far there is no algorithm available for conducting multi-objective multi-criterion decision-analysis/decision-making when severe uncertainty is expressed in such a way.

In this work, the authors developed a novel algorithm POSU for calculating the Pareto optimal solution under severe uncertainty. An appropriate selection criterion is developed to select the most appropriate set of solution. Case studies were conducted to demonstrate the efficacy of the algorithm.