8.7 Binary and Integer Design Variables

Core idea¶

Binary and Integer Design Variables must be treated as a system-level decision rather than an isolated technique. For sensor and actuator selection for a flexible structure, suspension alternatives, and hybrid-powertrain topology, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are $a\in\{0,1\}^m$, continuous $p$, and controller design $c$. The chapter-level formulation is

For this section, trace how the choice changes actuator set, the active constraints, and the implementable engineering design. A method is useful only when its assumptions are explicit and its result answers the same system question as the baseline.

Engineering interpretation¶

Ask three questions:

1. Which physical, informational, computational, or economic resource changed?

2. Which objective component or active constraint made the change valuable?

3. Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to enforce logic. Record units and assumptions before optimization, report component objectives and margins afterward, and verify the result using an independent calculation or higher-fidelity model.

Activity 8.7: quantify binary and integer design variables¶