Simulation Optimization Through Regression or Kriging Metamodels

Abstract

This chapter surveys two methods for the optimization of real-world systems that are modelled through simulation. These methods use either linear regression metamodels, or Kriging (Gaussian processes). The metamodel type guides the design of the experiment; this design …xes the input combinations of the simulation model. These regression models uses a sequence of local …rst-order and second-order polynomials-known as response surface methodology (RSM). Kriging models are global, but are re-estimated through sequential designs. "Robust" optimization may use RSM or Kriging, and accounts for uncertainty in simulation inputs.

A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

“…Creating three optimization objectives. The prediction parameterf ,ĝ i and RMSE related to the objective and constraints can be calculated by the kriging model (see Equations (8) and (9)). The three optimization objectives in Equation (16) will be formed by the prediction parameters.…”

“…Based on single objective optimization, the EGO [7] algorithm can use the prediction objectiveŷ and standard deviationŝ of the kriging model to construct the infill sampling criterion EI shown in Equation (8).…”

“…The kriging-based EGO (efficient global optimization) method [7] and its extensions [8][9][10][11][12][13] have solved some optimization problems of expensive black-box objectives or constraints. Most of them are single-objective optimization approaches, which can only get one sampling point in per infill search loop.…”

Analysis of statistical model-based optimization enhancements in Generalized Self-Adapting Particle Swarm Optimization framework

“…In general, surrogate models of the original function are constructed to estimate its value at some point which is cheaper than making an evaluation of the true objective function. Kriging (Gaussian process) metamodel can be utilized as a standalone optimization technique [12]. The principle of its utilization is sequential approximation of the optimized function and designating the next sampling point.…”