A computationally efficient metamodeling approach for expensive multiobjective optimization

Abstract

This paper explores a new metamodeling framework that may collapse the computational explosion that characterizes the modeling of complex systems under a multiobjective and/or multidisciplinary setting. Under the new framework, a pseudo response surface is constructed for each design objective for each discipline. This pseudo response surface has the unique property of being highly accurate in Pareto optimal regions, while it is intentionally allowed to be inaccurate in other regions. In short, the response surface for each design objective is accurate only where it matters. Because the pseudo response surface is allowed to be inaccurate in other regions of the design space, the computational cost of constructing it is dramatically reduced. An important distinguishing feature of the new framework is that the response surfaces for all the design objectives are constructed simultaneously in a mutually dependent fashion, in a way that identifies Pareto regions for the multiobjective problem. The new framework supports the puzzling notion that it is possible to obtain more accuracy and radically more design space exploration capability, while actually reducing the computation effort. This counterintuitive metamodeling paradigm shift holds the potential for identifying highly competitive products and systems that are well beyond today's state of the art.

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

“…As can be seen, most of the problems considered are limited to two or three objective functions except [52] with five objective functions. As mentioned earlier, since the method in [16] hybridizes both the sequential and the adaptive frameworks, we discuss it in Section 7. Step 1: Input: Initial sample points…”

“…, k, is defined as z i e = f (x i e ) (see Figure 1). A hyperplane passing through all extreme solutions is called a utopia hyperplane [16].…”

Surrogate Modeling for Uncertainty Assessment with Application to Aviation Environmental System Models

“…However, as discussed in [17], neural networks are computationally expensive to create and are best suited for deterministic problems. More recent advances in surrogate modeling methods, such as the pseudo response surface methodology [18], address some of the computational challenges associated with high-dimensional input spaces by requiring the surrogate to be accurate only in some regions of the design space (e.g., near the Pareto front). However, even with these advances, surrogate modeling for systems with thousands or millions of inputs remains out of reach.…”

“…Though Eq. (18) states that the convergence to a normal distribution occurs as N ! 1, it is common in statistical practice to assume Y may be appropriately modeled with a normal distribution when N 30 [20].…”

SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems

“…Similarly, Akhtar and Shoemaker (2016) Datta and Regis (2016) introduced SMES-RBF, which is a surrogate-assisted evolutionary strategy for constrained multiobjective optimization problems with black-box objective and constraint functions. Messac and Mullur (2008) introduced a computationally efficient algorithm that uses surrogate models and that is not based on evolutionary algorithms. However, the authors have not published implementations of these algorithms.…”