Typical Constrained Optimization Formulation in Evolutionary Computation Not Suitable for Expensive Optimization

The typical formulation of a constrained optimization problem (COP), which has the constraint form of (mathbf {g}(mathbf {x})le mathbf {0}), has widely used in evolutionary computation field. However, it is not suitable for Gaussian processes (GPs) based expensive optimization. In this paper, a more general and suitable formulation of the COP, which has the constraint form of (mathbf {l_{g}} le mathbf {g}(mathbf {x})le mathbf {u_{g}}), is recommended for the expensive optimization. Modeling a real world COP as a typical formulation will probably introduce additional constraints and dependencies among the objective and constraints while that as a suitable one introduces none additional. In the case of typical formulation, the additional constraints and dependencies have to be handled and the handling would cost additional computational resource, especially, the additional dependencies would lead to degenerating the performance of expensive optimization technologies since most of the technologies are based on the assumption of mutual independency among the objective and constraints. Experiments show that the performance of the expensive optimization technologies in the aspect of precision on solving the problems with suitable formulation is better than that with typical one. However, we could not verify the expense of additional computational resource since there are few expensive optimization technologies dealing with dependent objective and constraints.