Modeling with Optimization and Simulation

Abstract

Earlier chapters have already developed several examples demonstrating how an optimal property can characterize a computational study. For instance, optimization was used in the method of least squares in Sects. 3.1 and 3.2, the development of principal component analysis in Sect. 3.4, the examples and techniques in Chap. 4, and the design of radiotherapy treatments in Sect. 8.2. This chapter introduces two models associated with optimization and simulation, the latter of which is regularly employed within a search for optimality, see Sects. 4.3.1 (simulated annealing) and 4.3.2 (genetic algorithms) as examples. The first model of this chapter optimizes the selection of stocks for a portfolio, where stock prices are stochastic and simulated. The second model uses simulation to predict abrupt changes in a material property. We specifically study the Ising model to computationally illustrate magnetic phase transitions. Both models are famous and have had profound impacts.