A multi-objective adaptive surrogate modelling-based optimization algorithm for constrained hybrid problems

Many multi-objective optimization problems in integrated environmental modelling and management involve not only continuous decision variables but also variables like integers and/or discrete variables. Furthermore, the optimization problems are often subject to various constraints. Solving this kind of constrained hybrid problems usually requires a huge number of model evaluations that can be computationally expensive. This study presents an algorithm known as multi-objective adaptive surrogate modelling-based optimization for constrained hybrid problems (MO-ASMOCH). It incorporates several evolutionary operators to handle different types of decision variables and uses a classification surrogate model to deal with model constraints. MO-ASMOCH was evaluated against the widely used NSGA-II method on three engineering design problems and three water distribution system design problems with up to 30 dimensions. The results showed that MO-ASMOCH is able to obtain nondominated solutions of similar quality as that of NSGA-II using much fewer model evaluations.