Multiple Penalties and Multiple Local Surrogates for Expensive Constrained Optimization

This article proposes an evolutionary algorithm using multiple penalties and multiple local surrogates (MPMLS) for expensive constrained optimization. In each generation, MPMLS defines and optimizes a number of subproblems. Each subproblem penalizes the constraints in the original problem using a different penalty coefficient and has its own search subregion. A local surrogate is built for optimizing each subproblem. Two major advantages of MPMLS are: 1) it can maintain good population diversity so that the search can approach the optimal solution of the original problem from different directions and 2) it only needs to build local surrogates so that the computational overhead of the model building can be reduced. Numerical experiments demonstrate that our proposed algorithm performs much better than some other state-of-the-art evolutionary algorithms.