mip

package
v1.4.0 Latest Latest
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 Go to latest Published: Mar 6, 2024 License: Apache-2.0 Imports: 8 Imported by: 0

Documentation

Overview

Package mip provides a general interface for solving mixed integer linear optimization problems using a variety of back-end solvers. The base interface is the Model which is a collection of variables, constraints and an objective. The interface Solver is constructed by mip.NewSolver. The solver can be invoked using Solver.Solve and returns a Solution.

A new Model is created: 

d := mip.NewModel()

Var instances are created and added to the model: 

x := d.NewFloat(0.0, 100.0)
y := d.NewInt(0, 100)

Constraint instances are created and added to the model: 

c1 := d.NewConstraint(mip.GreaterThanOrEqual, 1.0)
c1.NewTerm(-2.0, x)
c1.NewTerm(2.0, y)

c2 := d.NewConstraint(mip.LessThanOrEqual, 13.0)
c2.NewTerm(-8.0, x)
c2.NewTerm(10.0, y)

The Objective is specified: 

d.Objective().SetMaximize()
d.Objective().NewTerm(1.0, x)
d.Objective().NewTerm(1.0, y)

A Solver is created and invoked to produce a Solution: 

solver, _ := mip.NewSolver("backend_solver_identifier", mipModel)
solution, _ := solver.Solve(mip.DefaultSolverOptions())

Index

Examples

Constants

This section is empty.

Variables

This section is empty.

Functions

func Format added in v0.26.0 

func Format(
	options any,
	solution any,
	solverSolution Solution,
) schema.Output

Format the MIP solution into the output format that the runner expects. The solution represents the decisions that were made by the solver, translated into the domain of the problem.

Types

type Bool added in v0.20.0 

type Bool interface {
	Int
	// contains filtered or unexported methods
}

Bool a Var which can take two values, zero or one. A bool variable is also an int variable which can have two values zero and one.

type Constraint 

type Constraint interface {
	// Name returns assigned name. If no name has been set it will return
	// a unique auto-generated name.
	Name() string
	// NewTerm adds a term to the invoking constraint, invoking this API
	// multiple times for the same variable will take the sum of coefficients
	// of earlier added terms for that variable
	//
	// 		m := mip.NewModel()
	//
	// 		x := m.NewFloat(10.0, 100.0)
	//
	// 		c := m.NewConstraint(mip.LessThanOrEqual, 123.4)
	// 		c.NewTerm(1.0, x)  	 // results in 1.0 * x <= 123.4 in solver
	// 		c.NewTerm(2.0, x)    // results in 3.0 * x <= 123.4 in solver
	NewTerm(coefficient float64, variable Var) Term
	// RightHandSide returns the right-hand side of the invoking constraint.
	RightHandSide() float64
	// Sense returns the sense of the invoking constraint.
	Sense() Sense
	// SetName assigns name to invoking constraint
	SetName(name string)
	// Term returns a term for variable with the sum of all coefficients of
	// defined terms for variable. The second return argument defines how many
	// terms have been defined on the objective for variable.
	Term(variable Var) (Term, int)
	// Terms returns a copy slice of terms of the invoking constraint,
	// each variable is reported once. If the same variable has been
	// added multiple times the sum of coefficients is reported for that
	// variable.
	Terms() Terms
}

Constraint specifies a relation between variables a solution has to comply with. A constraint consists out of terms, a sense and a right hand side.

For example: 

2.5 * x + 3.5 * y <= 10.0

The less than operator is the sense The value 10.0 is the right hand side 

2.5 * x and 3.5 * y are 2 terms in this example
Example (Equal) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	c := model.NewConstraint(mip.Equal, 1.0)

	fmt.Println(c.Sense())
	fmt.Println(c.RightHandSide())
	fmt.Println(c)
}

Output:
1
1
= 1
Example (GreaterThanEqual) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	c := model.NewConstraint(mip.GreaterThanOrEqual, 1.0)

	fmt.Println(c.Sense())
	fmt.Println(c.RightHandSide())
	fmt.Println(c)
}

Output:
2
1
>= 1
Example (LessThanOrEqual) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	c := model.NewConstraint(mip.LessThanOrEqual, 1.0)
	c.SetName("constraint")
	fmt.Println(c.Sense())
	fmt.Println(c.RightHandSide())
	fmt.Println(c)
	fmt.Println(c.Name())
}

Output:
0
1
<= 1
constraint
Example (Terms) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v := model.NewBool()
	c := model.NewConstraint(mip.Equal, 1.0)

	t1 := c.NewTerm(1.0, v)
	t2 := c.NewTerm(2.0, v)

	fmt.Println(t1.Var().Index())
	fmt.Println(t1.Coefficient())
	fmt.Println(t2.Coefficient())
	fmt.Println(len(c.Terms()))
	fmt.Println(c.Terms()[0].Coefficient())
	fmt.Println(c)
	fmt.Println(c.Term(v))
}

Output:
0
1
2
1
3
3 B0 = 1
3 B0 2

type Constraints 

type Constraints []Constraint

Constraints slice of Constraint instances.

type ControlOptions added in v0.30.0 

type ControlOptions struct {
	Bool   string `` /* 175-byte string literal not displayed */
	Float  string `` /* 178-byte string literal not displayed */
	Int    string `` /* 172-byte string literal not displayed */
	String string `` /* 181-byte string literal not displayed */
}

ControlOptions allow the user to define solver-specific parameters. The parameters' names and types must be known beforehand so that the correct type is used.

func (ControlOptions) MarshalJSON added in v0.30.0 

func (controlOptions ControlOptions) MarshalJSON() ([]byte, error)

MarshalJSON implements the json.Marshaler interface.

func (ControlOptions) ToTyped added in v0.30.0 

func (controlOptions ControlOptions) ToTyped() (*TypedControlOptions, error)

ToTyped converts the string-based control options into fully typed options.

type CustomResultStatistics added in v0.26.0 

type CustomResultStatistics struct {
	// Constraints in the matrix, i.e. the number of constraints.
	Constraints int `json:"constraints,omitempty"`
	// Provider of the solution.
	Provider SolverProvider `json:"provider,omitempty"`
	// Status of the solution.
	Status string `json:"status,omitempty"`
	// Variables in the matrix, i.e. the number of variables.
	Variables int `json:"variables,omitempty"`
}

CustomResultStatistics is an example of custom statistics that can be added to the output and used in experiments.

func DefaultCustomResultStatistics added in v0.26.0 

func DefaultCustomResultStatistics(model Model, solution Solution) CustomResultStatistics

DefaultCustomResultStatistics creates default custom statistics for a given solution.

type Float added in v0.20.0 

type Float interface {
	Var
	// contains filtered or unexported methods
}

Float a Var which can take any value in an interval.

type GapOptions added in v0.30.0 

type GapOptions struct {
	// Absolute gap.
	Absolute float64 `` /* 228-byte string literal not displayed */
	// Relative gap.
	Relative float64 `` /* 235-byte string literal not displayed */
}

GapOptions specifies the gap stopping criteria.

type Int added in v0.20.0 

type Int interface {
	Var
	// contains filtered or unexported methods
}

Int a Var which can take any integer value in an interval.

type MIPOptions added in v0.30.0 

type MIPOptions struct {
	// Gap stopping criteria.
	Gap GapOptions `json:"gap" usage:"Gap stopping criteria."`
}

MIPOptions are options specific to MIP problems. LP problems do not use these options.

type Model 

type Model interface {
	// Constraints returns a copy slice of all constraints.
	Constraints() Constraints
	// Copy returns a copy of the model.
	Copy() Model
	// NewBool adds a bool variable to the invoking model,
	// returns the newly constructed variable.
	NewBool() Bool
	// NewFloat adds a float var with bounds [lowerBound,
	// upperBound] to the invoking model, returns the newly constructed
	// var.
	NewFloat(
		lowerBound float64,
		upperBound float64,
	) Float
	// NewInt adds an integer var with bounds [loweBound,
	// upperBound] to the invoking model, returns the newly constructed
	// var.
	NewInt(
		lowerBound int64,
		upperBound int64,
	) Int
	// NewConstraint adds a constraint with sense and right-hand-side value rhs
	// to the invoking model. All terms for existing and future variables
	// are initially zero. Returns the newly constructed constraint.
	// A constraint where all terms remain zero is ignored by the solver.
	NewConstraint(sense Sense, rhs float64) Constraint
	// Objective returns the objective of the model.
	Objective() Objective
	// Vars returns a copy slice of all vars.
	Vars() Vars
}

Model manages the variables, constraints and objective.

Example (Copy) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	model.Objective().SetMaximize()
	model.NewBool()
	model.NewFloat(1.0, 2.0)
	model.NewBool()
	model.NewConstraint(mip.Equal, 0.0)

	copyModel := model.Copy()

	fmt.Println(len(copyModel.Vars()))
	fmt.Println(len(copyModel.Constraints()))
	fmt.Println(copyModel)
}

Output:
3
1
maximize
      0: = 0
      0: B0 [0, 1]
      1: F1 [1, 2]
      2: B2 [0, 1]
Example (Empty) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	fmt.Println(len(model.Constraints()))
	fmt.Println(len(model.Vars()))
	fmt.Println(len(model.Objective().Terms()))
	fmt.Println(model.Objective().IsMaximize())
	fmt.Println(model)
}

Output:
0
0
0
false
minimize
Example (Queries) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	model.NewBool()
	model.NewFloat(1.0, 2.0)
	model.NewBool()
	model.NewConstraint(mip.Equal, 0.0)

	fmt.Println(len(model.Vars()))
	fmt.Println(len(model.Constraints()))
	fmt.Println(model)
}

Output:
3
1
minimize
      0: = 0
      0: B0 [0, 1]
      1: F1 [1, 2]
      2: B2 [0, 1]

func NewModel 

func NewModel() Model

NewModel creates an empty MIP model.

type Objective 

type Objective interface {
	// IsLinear returns true if the invoking objective is a linear function.
	IsLinear() bool
	// IsMaximize returns true if the invoking objective is a maximization
	// objective.
	IsMaximize() bool
	// IsQuadratic returns true if the invoking objective is a quadratic function.
	IsQuadratic() bool
	// NewTerm adds a term to the invoking objective, invoking this API
	// multiple times for the same variable will take the sum of coefficients
	// of earlier added terms for that variable.
	//
	// 		m := mip.NewModel()
	// 		x := m.NewFloat(10.0, 100.0)
	//
	// 		m.Objective().SetMaximize()			// results in: maximize -
	// 		m.Objective().NewTerm(1.0, x)		// results in: maximize 1.0 * x
	// 		m.Objective().NewTerm(2.0, x)		// results in: maximize 3.0 * x
	NewTerm(coefficient float64, variable Var) Term
	// NewQuadraticTerm adds a new quadratic term to the invoking objective,
	// invoking this API multiple times for the same variables will take the sum
	// of coefficients of earlier added terms for that variable.
	//
	//      m := mip.NewModel()
	//      x1 := m.NewFloat(10.0, 100.0)
	//      x2 := m.NewFloat(10.0, 100.0)
	//
	//      m.Objective().SetMaximize()
	//      // results in: maximize -
	//      m.Objective().NewQuadraticTerm(1.0, x1, x1)
	//      // results in: maximize 1.0 * x1^2
	//      m.Objective().NewQuadraticTerm(1.0, x1, x2)
	//      // results in: maximize 1.0 * x1^2 + x1x2
	//      m.Objective().NewQuadraticTerm(1.0, x2, x1)
	//      // results in: maximize 1.0 * x1^2 + 2.0 * x1x2
	NewQuadraticTerm(coefficient float64, variable1, variable2 Var) QuadraticTerm
	// SetMaximize sets the invoking objective to be a maximization objective.
	SetMaximize()
	// SetMinimize sets the invoking objective to be a minimization objective.
	SetMinimize()
	// Term returns a term for a given variable together with the sum of the
	// coefficients of all terms referencing that variable. The second return
	// argument defines how many terms have been defined on the objective for
	// the given variable.
	Term(variable Var) (Term, int)
	// Terms returns a copy slice of terms of the invoking objective,
	// each variable is reported once. If the same variable has been
	// added multiple times the sum of coefficients is reported for that
	// variable. The order of the terms is not specified and is not guaranteed
	// to be the same from one invocation to the next.
	Terms() Terms
	// QuadraticTerm returns a quadratic term for a given pair of variables
	// together with the sum of the coefficients of all quadratic terms
	// referencing that variable. The second return argument defines how many
	// quadratic terms have been defined on the objective the given pair of
	// variables.
	QuadraticTerm(variable1, variable2 Var) (QuadraticTerm, int)
	// QuadraticTerms returns a copy slice of quadratic terms of the invoking
	// objective, each variable pair is reported once. If the same pair has been
	// added multiple times the sum of coefficients is reported for that
	// variable. The order of the terms is not specified and is not guaranteed
	// to be the same from one invocation to the next.
	QuadraticTerms() QuadraticTerms
}

Objective specifies the objective of the model. An objective consists out of terms and a specification if it should be maximized or minimized.

For example: 

maximize 2.5 * x + 3.5 * y

2.5 * x and 3.5 * y are 2 terms in this example.

Example (Sense) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	model.Objective().SetMaximize()

	fmt.Println(model.Objective().IsMaximize())
	fmt.Println(model.Objective())

	model.Objective().SetMinimize()

	fmt.Println(model.Objective().IsMaximize())
	fmt.Println(model.Objective())
}

Output:
true
maximize
false
minimize
Example (Terms) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v1 := model.NewBool()
	v2 := model.NewBool()

	fmt.Println(len(model.Objective().Terms()))

	t1 := model.Objective().NewTerm(2.0, v1)
	fmt.Println(t1)
	t2 := model.Objective().NewTerm(1.0, v1)
	fmt.Println(t2)
	t3 := model.Objective().NewTerm(3.0, v2)
	fmt.Println(t3)

	fmt.Println(t1.Var().Index())
	fmt.Println(t1.Coefficient())

	fmt.Println(t2.Var().Index())
	fmt.Println(t2.Coefficient())

	fmt.Println(t3.Var().Index())
	fmt.Println(t3.Coefficient())

	terms := model.Objective().Terms()
	fmt.Println(len(terms))
	for _, term := range terms {
		fmt.Println(term.Var(), term.Coefficient())
	}
	fmt.Println("isMaximize: ", model.Objective().IsMaximize())
}

Output:
0
2 B0
1 B0
3 B1
0
2
0
1
1
3
2
B0 3
B1 3
isMaximize:  false
Example (TermsToString) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	m := mip.NewModel()
	x0 := m.NewBool()
	x1 := m.NewBool()
	x2 := m.NewBool()
	x3 := m.NewBool()
	z := m.Objective()
	z.NewTerm(3, x2)
	z.NewTerm(2, x1)
	z.NewTerm(1, x0)
	fmt.Println(z)
	fmt.Println(z.Term(x0))
	z.NewTerm(1, x0)
	fmt.Println(z.Term(x0))
	fmt.Println(z.Term(x3))
}

Output:
minimize   1 B0 + 2 B1 + 3 B2
1 B0 1
2 B0 2
0 B3 0

type QuadraticTerm added in v0.20.4 

type QuadraticTerm interface {
	// Coefficient returns the coefficient value of the invoking term.
	Coefficient() float64
	// Var1 returns the first variable.
	Var1() Var
	// Var2 returns the second variable.
	Var2() Var
}

QuadraticTerm consists of a coefficient and two vars. It should be interpreted as the product of a coefficient and the two vars.

type QuadraticTerms added in v0.20.4 

type QuadraticTerms []QuadraticTerm

QuadraticTerms is a slice of QuadraticTerm instances.

type Sense 

type Sense int64

Sense defines the constraint operator between the left-hand-side and the right-hand-side. 

const (
	// LessThanOrEqual is used to define a less than or equal constraint
	// 		c, _ := d.NewConstraint(mip.LessThanOrEqual, 123.4)
	//
	// 		c.NewTerm(1.0, x)  	 // results in 1.0 * x <= 123.4 in solver
	LessThanOrEqual Sense = iota
	// Equal is used to define an equality constraint
	// 		c, _ := d.NewConstraint(mip.Equal, 123.4)
	//
	// 		c.NewTerm(1.0, x)  	 // results in 1.0 * x = 123.4 in solver
	Equal
	// GreaterThanOrEqual is used to define a greater or equal constraint
	// 		c, _ := d.NewConstraint(mip.	GreaterThanOrEqual, 123.4)
	//
	// 		c.NewTerm(1.0, x)  	 // results in 1.0 * x >= 123.4 in solver
	GreaterThanOrEqual
)

Sense of a Constraint.

type Solution 

type Solution interface {
	// HasValues returns true if the solver was able to associate values with
	// variables.
	HasValues() bool
	// IsInfeasible returns true if the solver has proven that the model
	// defines an infeasible solution, otherwise returns false.
	IsInfeasible() bool
	// IsNumericalFailure returns true if the solver encountered a numerical
	// failure, otherwise returns false. Numerical failures can have different
	// causes and depend on the underlying solver provider.
	IsNumericalFailure() bool
	// IsOptimal returns true if the solver has proven that the solution
	// is one of the optimal solutions, otherwise returns false.
	IsOptimal() bool
	// IsSubOptimal returns true if the solver sub-optimal conform the
	// model of the underlying solver, otherwise false.
	IsSubOptimal() bool
	// IsTimeOut returns true if the solver returned due to a time limit
	// before reaching a conclusion, otherwise returns true.
	IsTimeOut() bool
	// IsUnbounded returns true if the solver proved the solution is
	// unbounded, otherwise returns false. An unbounded solution is
	// a solution that can be improved by changing a variable in a
	// direction it is not limited by bounds.
	IsUnbounded() bool
	// ObjectiveValue return the value of the objective, the value should only
	// be used if HasValues returns true. Returns 0.0 if HasValues is false.
	ObjectiveValue() float64
	// Provider of the solver that produced the invoking solution.
	Provider() SolverProvider
	// RunTime returns the duration it took for the Solver.Solve to return
	// this solution
	RunTime() time.Duration
	// Value returns the value the solver has associated with the variable
	// in the invoking solution. the value should only be used if HasValues
	// returns true. Returns math.MaxFloat64 if HasValues is false.
	Value(variable Var) float64
}

Solution contains the results of a Solver.Solve invocation.

type SolveOptions 

type SolveOptions struct {
	// Duration is the maximum duration of the solver. A duration limit of 0 is
	// treated as infinity.
	Duration time.Duration `json:"duration" usage:"Maximum duration of the solver." default:"30s"`
	// Verbosity of the solver in the console.
	Verbosity Verbosity `json:"verbosity" usage:"{off, low, medium, high} Verbosity of the solver in the console." default:"off"`
	// MIP-specific options.
	MIP MIPOptions `json:"mip" usage:"Options specific to MIP problems. Linear problems do not use these options."`
	// Control options for the specific solver.
	Control ControlOptions `json:"control" usage:"Options to control a specific solver, as defined by the provider."`
}

SolveOptions are options that can be cionfigured for any solver.

type Solver 

type Solver interface {
	// Solve is the entrypoint to solve the model associated with
	// the invoking solver. Returns a solution when the invoking solver
	// reaches a conclusion.
	Solve(options SolveOptions) (Solution, error)
}

Solver for a MIP problem.

func NewSolver 

func NewSolver(provider SolverProvider, model Model) (Solver, error)

NewSolver returns a new Solver implemented by the given provider.

type SolverProvider 

type SolverProvider string

SolverProvider identifier for a back-end solver. 

const (
	// Highs is the [HiGHS] open-source solver.
	//
	// [HiGHS]: https://highs.dev
	Highs SolverProvider = "highs"
	// Xpress is the [FICO Xpress] commercial solver.
	//
	// [FICO Xpress]: https://www.fico.com/en/products/fico-xpress-optimization
	Xpress SolverProvider = "xpress"
)

type Term 

type Term interface {
	// Coefficient returns the coefficient value of the invoking term.
	Coefficient() float64
	// Var returns the variable of the term.
	Var() Var
}

Term is the building block of a constraint and an objective. A term consist of a coefficient and a var and should be interpreted as the product of coefficient and the var in the context of the constraint or objective.

type Terms 

type Terms []Term

Terms is a slice of Term instances.

type TypedControlOption added in v0.30.0 

type TypedControlOption[T string | float64 | int | bool] struct {
	// Name of the option.
	Name string `json:"name"`
	// Value for the option. The value's type is defined by how the control
	// option is instantiated.
	Value T `json:"value"`
}

TypedControlOption defines a generic way to specify a control parameter for a solver.

type TypedControlOptions added in v0.30.0 

type TypedControlOptions struct {
	Bool   []TypedControlOption[bool]    `json:"bool"`
	Float  []TypedControlOption[float64] `json:"float"`
	Int    []TypedControlOption[int]     `json:"int"`
	String []TypedControlOption[string]  `json:"string"`
}

TypedControlOptions is the typed equivalent to ControlOptions for configuring a solver's parameters.

type Var 

type Var interface {
	// Index is a unique number assigned to the var. The index corresponds
	// to the location in the slice returned by Model.Variables().
	Index() int
	// IsBool returns true if the invoking variable is a bool variable,
	// otherwise it returns false.
	IsBool() bool
	// IsFloat returns true if the invoking variable is a float
	// variable otherwise false.
	IsFloat() bool
	// IsInt returns true if the invoking variable is an int variable
	// otherwise false.
	IsInt() bool
	// LowerBound returns the lowerBound of the invoking variable.
	//
	// Lower bounds of variables are limited by the lower bounds of the
	// underlying solver technology. The lower bound used will be the maximum
	// of the specification and the lower bound of the solver used.
	LowerBound() float64
	// Name returns assigned name. If no name has been set it will return
	// a unique auto-generated name.
	Name() string
	// SetName assigns name to invoking var
	SetName(name string)
	// UpperBound returns the upperBound of the invoking variable.
	//
	// Upper bounds of variables are limited by the upper bounds of the
	// underlying solver technology. The upper bound used will be the minimum
	// of the specification and the upper bound of the solver used.
	UpperBound() float64
}

Var represents the entities on which the solver has to make a decision without violating constraints and while optimizing the objective. Vars can be of a certain type, bool, float or int.

Float vars can take a value of a float quantity Int vars are vars that must take an integer value (0, 1, 2, ...) Bool vars can take two values, zero or one.

Example (Bool) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v := model.NewBool()

	fmt.Println(v.LowerBound())
	fmt.Println(v.UpperBound())
	fmt.Println(v.IsFloat())
	fmt.Println(v.IsInt())
	fmt.Println(v.IsBool())
	fmt.Println(v)
}

Output:
0
1
false
true
true
B0
Example (Float) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v := model.NewFloat(-1.0, 1.0)

	fmt.Println(v.LowerBound())
	fmt.Println(v.UpperBound())
	fmt.Println(v.IsFloat())
	fmt.Println(v.IsInt())
	fmt.Println(v.IsBool())
	fmt.Println(v)
}

Output:
-1
1
true
false
false
F0
Example (Int) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v := model.NewInt(-1, 1)

	fmt.Println(v.LowerBound())
	fmt.Println(v.UpperBound())
	fmt.Println(v.IsFloat())
	fmt.Println(v.IsInt())
	fmt.Println(v.IsBool())
	fmt.Println(v)
	v.SetName("v")
	fmt.Println(v)
}

Output:
-1
1
false
true
false
I0
v
Example (Vars) 
package main

import (
	"fmt"

	"github.com/nextmv-io/sdk/mip"
)

func main() {
	model := mip.NewModel()

	v0 := model.NewBool()
	v1 := model.NewInt(-1, 1)
	v2 := model.NewFloat(-1.0, 1.0)

	fmt.Println(v0.Index())
	fmt.Println(v1.Index())
	fmt.Println(v2.Index())
	fmt.Println(len(model.Vars()))
}

Output:
0
1
2
3

type Vars 

type Vars []Var

Vars is a slice of Var instances.

type Verbosity added in v0.20.0 

type Verbosity string

Verbosity specifies the level of verbosity of the back-end solver. 

const (
	// Off logs nothing.
	Off Verbosity = "off"
	// Low logs essentials, depends on the back-end solver.
	Low Verbosity = "low"
	// Medium logs essentials plus high level events,
	// depends on the back-end solver.
	Medium Verbosity = "medium"
	// High logs everything the underlying logs,
	// depends on the back-end solver.
	High Verbosity = "high"
)

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