Optimization Tools for Systems Development

This set of vocabulary flashcards covers concepts from Lecture 6A on optimization tools, including problem components, categorization, solution techniques, and software used in Civil Engineering systems design.

Objective function

The goal in optimization problems to maximize utility or minimize disutility.

Constraints

The limitations within which decisions are made, including financial (budgets), physical (right-of-way), institutional, and political considerations.

Decision variables

The factors adjusted by engineers to maximize utility or minimize disutility; also known as design, input, or control variables.

Optimization under certainty

A level of certainty where the system outcome in response to a certain stimulus is known.

Optimization with risk

A type of optimization under uncertainty where the probability ($p$) of each possible outcome is known.

Optimization with true uncertainty

A type of optimization under uncertainty where the probability ($p$) of each possible outcome is not known.

Single-criterion optimization

An optimization problem categorized by having only one criterion being considered.

Multi-criteria optimization

An optimization problem categorized by having more than one criterion being considered.

Discrete-variable optimization

Optimization where decision variables are count variables (e.g., number of production units) or binary variables (e.g., whether to select a resource).

Continuous-variable optimization

Optimization where the decision variables can take on any value within a range rather than discrete increments.

Network-level optimization

Optimization categorized by the level of management involving an entire system network.

Project-level optimization

Optimization categorized by the level of management involving a specific individual project.

Feasible Region

The unshaded region on a graph where all points satisfy all the constraining functions of a linear programming problem.

Critical Boundary

The line representing the equation of an inequality constraint used to define the edge of a feasible region.

Vertices

The corner points of a feasible region where intersecting lines yield potential problem solutions.

Optimal solution

The set of decision variable values that yields the maximum or minimum value of the objective function.

Vertex Technique

A manual or graphical solution method where vertices are identified and substituted into the objective function to find the optimum.

Simultaneous Equations Method

A solution method using substitution or elimination to find the vertices of the feasible region by solving constraints simultaneously.

Simplex method

A technique employed within linear algebra and matrix methods to help in the rapid solution of optimization problems.

GAMS

A software program where the user specifies objective functions and constraints in an input file to find optimal values and model statistics.

MS Solver

An optimization tool that uses a constraints matrix and initial seed values for control variables to determine the optimum value of $Z$.

CPLEX

A powerful optimization program used mainly for linear programming that requires constraints to be rewritten in forms such as $ax + by + c = 0$.

Redundant constraint

A constraint that, if dropped, does not change the feasible region because it does not form a unique boundary of the feasible solution space.

Binding constraint

A constraint that forms the optimal corner point of the feasible solution space.

Non-linear Programming

Optimization where the constraints are non-linear; the optimal solution is not necessarily a vertex of the feasible region.