OptimizationProblem

Optimization problem

Description

An OptimizationProblem object describes an optimization problem, including variables for the optimization, constraints, the objective function, and whether the objective is to be maximized or minimized. Solve a complete problem using solve.

Tip

For the full workflow, see Problem-Based Optimization Workflow.

Creation

Create an OptimizationProblem object by using optimproblem.

Warning

The problem-based approach does not support complex values in the following: an objective function, nonlinear equalities, and nonlinear inequalities. If a function calculation has a complex value, even as an intermediate value, the final result might be incorrect.

Properties

Description — Problem label

'' (default) | string | character vector

Problem label, specified as a string or character vector. The software does not use Description. It is an arbitrary label that you can use for any reason. For example, you can share, archive, or present a model or problem, and store descriptive information about the model or problem in the Description property.

Example: "Describes a traveling salesman problem"

Data Types: char | string

ObjectiveSense — Indication to minimize or maximize

'minimize' (default) | 'min' | 'maximize' | 'max'

Indication to minimize or maximize, specified as 'minimize' or 'maximize'. This property affects how solve works.

You can use the short name 'min' for 'minimize' or 'max' for 'maximize'.

Example: 'maximize'

Data Types: char | string

Variables — Optimization variables in object

structure of OptimizationVariable objects

This property is read-only.

Optimization variables in the object, specified as a structure of OptimizationVariable objects.

Data Types: struct

Objective — Objective function

scalar OptimizationExpression | structure containing scalar OptimizationExpression

Objective function, specified as a scalar OptimizationExpression or as a structure containing a scalar OptimizationExpression. Incorporate an objective function into the problem when you create the problem, or later by using dot notation.

prob = optimproblem('Objective',5*brownies + 2*cookies)
% or
prob = optimproblem;
prob.Objective = 5*brownies + 2*cookies

Constraints — Optimization constraints

OptimizationConstraint object | OptimizationEquality object | OptimizationInequality object | structure containing OptimizationConstraint, OptimizationEquality, or OptimizationInequality objects

Optimization constraints, specified as an OptimizationConstraint object, an OptimizationEquality object, an OptimizationInequality object, or as a structure containing one of these objects. Incorporate constraints into the problem when you create the problem, or later by using dot notation:

constrs = struct('TrayArea',10*brownies + 20*cookies <= traysize,...
    'TrayWeight',12*brownies + 18*cookies <= maxweight);
prob = optimproblem('Constraints',constrs)
% or
prob.Constraints.TrayArea = 10*brownies + 20*cookies <= traysize
prob.Constraints.TrayWeight = 12*brownies + 18*cookies <= maxweight

Remove a constraint by setting it to [].

prob.Constraints.TrayArea = [];

Object Functions

evaluate	Evaluate optimization expression or objectives and constraints in problem
issatisfied	Constraint satisfaction of an optimization problem at a set of points
optimoptions	Create optimization options
prob2struct	Convert optimization problem or equation problem to solver form
show	Display information about optimization object
solve	Solve optimization problem or equation problem
solvers	Determine default and valid solvers for optimization problem or equation problem
varindex	Map problem variables to solver-based variable index
write	Save optimization object description

Examples

Create and Solve Maximization Problem

Create a linear programming problem for maximization. The problem has two positive variables and three linear inequality constraints.

prob = optimproblem('ObjectiveSense','max');

Create positive variables. Include an objective function in the problem.

x = optimvar('x',2,1,'LowerBound',0);
prob.Objective = x(1) + 2*x(2);

Create linear inequality constraints in the problem.

cons1 = x(1) + 5*x(2) <= 100;
cons2 = x(1) + x(2) <= 40;
cons3 = 2*x(1) + x(2)/2 <= 60;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;

Review the problem.

show(prob)

  OptimizationProblem : 

	Solve for:
       x

	maximize :
       x(1) + 2*x(2)


	subject to cons1:
       x(1) + 5*x(2) <= 100

	subject to cons2:
       x(1) + x(2) <= 40

	subject to cons3:
       2*x(1) + 0.5*x(2) <= 60

	variable bounds:
       0 <= x(1)
       0 <= x(2)

Solve the problem.

sol = solve(prob);

Solving problem using linprog.

Optimal solution found.

sol.x

ans = 2×1

    25
    15

Version History

Introduced in R2017b

R2024a: OptimizationProblem supports evaluate and issatisfied

You can now evaluate optimization expressions and constraints using evaluate and issatisfied for OptimizationProblem objects. Evaluate at a set of points in an OptimizationValues object, or at a single point in a structure.

The value of a constraint depends on the constraint type. An equation is equivalent to an == constraint. For expressions L and R:

Constraint Type	Value
L <= R	L – R
L >= R	R – L
L == R	abs(L – R)

For details, see the evaluate and issatisfied reference pages.