选择

形式

$$y=OneOf((x_1,c_1),(x_2,c_2),..,(x_i,c_i))=\{\begin{array}{ll}{x}_1,& c_1\\ \\ x_2,& c_2\\ \\ ⋮\\ \\ x_i,& c_i\end{array}$$

其中，$c_i$ 应当有且仅有一个成立。

导出符号

$$y=\sum _{i}masking(x_i,c_i)$$

$masking(x_i,c_i)$ 可参考 掩码函数。

数学模型

$$s.t.\sum _i{c}_i=1$$

样例

选择

kotlin

import kotlinx.coroutines.*
import fuookami.ospf.kotlin.utils.math.*
import fuookami.ospf.kotlin.core.frontend.variable.*
import fuookami.ospf.kotlin.core.frontend.expression.polynomial.*
import fuookami.ospf.kotlin.core.frontend.expression.symbol.linear_function.*
import fuookami.ospf.kotlin.core.frontend.inequality.*
import fuookami.ospf.kotlin.core.frontend.model.mechanism.*
import fuookami.ospf.kotlin.core.backend.plugins.scip.*

val x = URealVar("x")
x.range.geq(Flt64.two)
x.range.leq(Flt64.five)
val condition1 = IfFunction(x geq Flt64.three, name = "c1")
val condition2 = IfFunction(x leq Flt64.one, name = "c2")
val oneOf = OneOfFunction(
    listOf(
        AbstractOneOfFunction.Branch(
            condition1,
            LinearPolynomial(Flt64.zero),
            "ifc1"
        ),
        AbstractOneOfFunction.Branch(
            condition2,
            LinearPolynomial(Flt64.one),
            "ifc2"
        )
    ),
    name = "one_of"
)
val solver = ScipLinearSolver()

val model1 = LinearMetaModel()
model1.add(x)
model1.add(condition1)
model1.add(condition2)
model1.add(oneOf)
model1.minimize(x)
val result1 = runBlocking { solver(model1) }
assert(result1.value!!.obj eq Flt64.three)

val model2 = LinearMetaModel()
model2.add(x)
model2.add(condition1)
model2.add(condition2)
model2.add(oneOf)
model2.maximize(oneOf)
val result2 = runBlocking { solver(model2) }
assert(result2.value!!.obj eq Flt64.zero)

二择

kotlin

import kotlinx.coroutines.*
import fuookami.ospf.kotlin.utils.math.*
import fuookami.ospf.kotlin.core.frontend.variable.*
import fuookami.ospf.kotlin.core.frontend.expression.polynomial.*
import fuookami.ospf.kotlin.core.frontend.expression.symbol.linear_function.*
import fuookami.ospf.kotlin.core.frontend.inequality.*
import fuookami.ospf.kotlin.core.frontend.model.mechanism.*
import fuookami.ospf.kotlin.core.backend.plugins.scip.*

val x = URealVar("x")
x.range.geq(Flt64.two)
x.range.leq(Flt64.five)
val condition = IfFunction(x geq Flt64.three, name = "c")
val ifElse = IfElseFunction(
    IfElseFunction.Branch(
        polynomial = x,
        name = "if"
    ),
    IfElseFunction.Branch(
        polynomial = LinearPolynomial(Flt64.zero),
        name = "else"
    ),
    condition,
    name = "if_else"
)
val solver = ScipLinearSolver()

val model1 = LinearMetaModel()
model1.add(x)
model1.add(condition)
model1.add(ifElse)
model1.addConstraint(x geq Flt64.three)
model1.maximize(ifElse)
val result1 = runBlocking { solver(model1) }
assert(result1.value!!.obj eq Flt64.five)

val model2 = LinearMetaModel()
model2.add(x)
model2.add(condition)
model2.add(ifElse)
model2.minimize(ifElse)
val result2 = runBlocking { solver(model2) }
assert(result2.value!!.obj eq Flt64.zero)
assert(result2.value!!.solution[0] ls Flt64.three)

val model3 = LinearMetaModel()
model3.add(x)
model3.add(condition)
model3.add(ifElse)
model3.addConstraint(x eq Flt64.two)
model3.maximize(ifElse)
val result3 = runBlocking { solver(model3) }
assert(result3.value!!.obj eq Flt64.zero)

完整实现请参考：

• Kotlin

完整样例请参考：

• Kotlin