No abstract

In this paper, we present a multi-surrogates assisted memetic algorithm for solving optimization problems with computationally expensive fitness functions. The essential backbone of our framework is an evolutionary algorithm coupled with a local search solver that employs multi-surrogate in the spirit of Lamarckian learning. Inspired by the notion of 'blessing and curse of uncertainty' in approximation models, we combine regression and exact interpolating surrogate models in the evolutionary search. Empirical results are presented for a series of commonly used benchmark problems to demonstrate that the proposed framework converges to good solution quality more efficiently than the standard genetic algorithm, memetic algorithm and surrogate-assisted memetic algorithms.

This paper presents a study on Hierarchical Surrogate-Assisted Evolutionary Algorithm (HSAEA) using different global surrogate models for solving computationally expensive optimization problems. In particular, we consider the use of Gaussian Process (GP) and Polynomial Regression (PR) methods for approximating the global fitness landscape in the surrogateassisted evolutionary search. The global surrogate model serves to pre-screen the EA population for promising individuals. Subsequently, these potential individuals undergo a local search in the form of Lamarckian learning using online local surrogate models. Numerical results are presented on two multi-modal benchmark test functions. The results obtained show that both PR-HSAEA and GP-HSAEA converge to good designs on a limited computational budget. Further, our study also shows that the GP model is suitable for global surrogate modeling in HSAEA if the evaluation function is very expensive in computations. On moderately expensive problems, the PR method may serve to generate better efficiency than using GP.

Evolutionary frameworks that employ approximation models or surrogates for solving optimization problems with computationally expensive fitness functions may be referred as Surrogate-Assisted Evolutionary Algorithms (SAEA). In this paper, we present a study on the effects of uncertainty in the surrogate on SAEA. In particular, we focus on both the 'curse of uncertainty' and 'blessing of uncertainty' on evolutionary search, a notion borrowed from 'curse and blessing of dimensionality' in [1]. Here, the 'curse of uncertainty' refers to impairments due to the errors in the approximation. The 'blessing of uncertainty' is less explicitly discussed in the literature, but refers to the benefits of approximation errors on evolutionary search. Empirical studies suggest that approximation errors lead to convergence at false global optima, but prove to be beneficial in some cases.

This paper presents enhancements to a surrogateassisted evolutionary optimization framework proposed earlier in the literature for solving computationally expensive design problems on a limited computational budget [l]. The main idea of our former framework was to couple evolutionary algorithms with a feasible sequential quadratic programming solver in the spirit of Lamarckian learning, including a trustregion approach for interleaving the true fitness function with computationally cheap local surrogate models during gradientbased search. In this paper, we propose a hierarchical snrrogateassisted evolutionary optimization framework for accelerating the convergence rate of the original surrogate-assisted evolutionary optimization framework. Instead of using the exact high-fidelity fitness function during evolutionary search, a Kriging global surrogate model is used to screen the population for individuals that will undergo Lamarckian learning. Numerical results are presented for two multi-modal benchmark test functions to show that the proposed approach leads to a further acceleration of the evolutionary search process.