Analysis of Constrained Optimization Problems by the SCE-UA with an Adaptive Penalty Function

Abstract

Evolutionary algorithms are used to solve optimization problems in a wide range of fields and are considered to be global optimization algorithms. However, evolutionary algorithms are limited in that they cannot be used to solve optimization problems with constraints. Additional methods to implement constraints must be used with these algorithms when solving constrained optimization problems. The purpose of the study is to improve the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm to include constraints. An adaptive penalty function that is easy to implement, free of parameter tuning, and guaranteed to find a solution for every problem at every run was used to impose constraints on the SCE-UA. The modified SCE-UA was validated by application to two constrained optimization problems. The algorithm was also applied to an automatic calibration of the storm water management model (SWMM), which is a hydrological model. An automatic calibration by unconstrained optimization (the original SCE-UA) was not able to properly simulate the observed data. On the other hand, the modified SCE-UA with the adaptive penalty function produced results superior to those obtained using unconstrained optimization. That is the reason why the calibration was advanced to improve the limitation of the unconstrained optimization by imposing constraints. The constrained optimization module modified by embedding the adaptive penalty function could help in solving various constrained optimization problems in the water resources engineering field.