Engineering Optimization

21Multiple OF and Constraint Applications

21.1 Introduction

Often there are multiple and diverse objectives in an optimization. You might want to balance several competing objectives by combining them into one OF, and the question is “How to combine diverse and opposing objectives?” Here are some examples:

Find the best route for an automobile road trip: This seems like a simple statement, but how does one interpret best? There are diverse measures of desirability (goodness) and they have disparate units:

• Minimize cost (fuel, meals, nights, tolls)—$
• Minimize travel time—hours
• Maximize scenery and tranquility—what units?
• Maximize safety (slower, back roads, no traffic, proximity to assistance, not isolated, probability of an accident)—what units?

The turnpike might be the answer to minimizing travel time, but tolls and gas consumption and impact of an accident may prompt you to prefer another road.

Find the best design for a manufacturing plant: Again, this simple concept could have many meanings:

• Maximize profitability (DCFROI, NPV, LTROA).
• Minimize capital cost.
• Minimize risk.
• Minimize resource utilization and waste generation.
• Maximize security.
• Maximize flexibility.
• Maximize operability.

Minimizing capital might conflict with risk, waste, flexibility, and operability objectives.

Find the best automobile design: Again, there are many meanings:

• Maximize gas mileage.
• Maximize carrying capacity.
• Maximize useful life.
• Minimize purchase cost.
• Maximize safety.

And again, the objectives ...