Engineering Optimization

24Stochastic Objective Functions

24.1 Introduction

A deterministic function returns the exact same value each time it is given the same inputs. What is the value of 3 times 4 (in base 10 arithmetic)? Whether last year or next year, whether in Barbados or on the Moon, whether by human or by computer, the answer is 12. By contrast a stochastic function does not return the same value when given supposedly identical conditions. If I roll this cubical die, what value will appear? Even if I do it, in one setting in the same location, trying my best to be repeatable, the answer is a 1 or a 2 or a … or a 6. This stochastic function returns one of 6 values with an equal probability. It does not consistently return the same value.

How does this relate to optimization? Following are several example situations:

Example 1

Consider that a fast‐food business wants to determine the optimum amount of salt on fried potato strings. This is a single DV application, and the OF will be customer rating. Each batch of fries is hand‐salted by counting the shakes of the salt canister. Since each batch of fries does not have exactly the same number or orientation of fries and each shake of salt does not deliver exactly the same amount of salt, there is batch‐to‐batch variation in salt per fry. There is even greater variation within each sample of fries from the batch given to any customer. The data will be obtained experimentally by asking customers to rate the fries—too salty, just right, and not ...