Rounding Function (Round to Nearest)

Function Form

$$y=\text{Round}(x,d)=\lceil \frac{x}{d}\rfloor$$

Additional Variables

$q\in \mathbb{Z}$: Integer part of $\frac{x}{d}$.

$r\in [-\frac{|d|}{2},\frac{|d|}{2})$: Remainder part of $\frac{x}{d}$.

Derived Symbol

$$y=q$$

Mathematical Model

$$\begin{array}{rl}\text{s.t.}& x=d\cdot q+r\end{array}$$

Code Example

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 = RealVar("x")
x.range.leq(Flt64.five)
x.range.geq(Flt64.two)
val rounding = RoundingFunction(x, Flt64(0.7), "rounding")
val solver = ScipLinearSolver()

val model1 = LinearMetaModel()
model1.add(x)
model1.add(rounding)
model1.minimize(rounding)
val result1 = runBlocking { solver(model1) }
assert(result1.value!!.obj eq Flt64.three)
assert(result1.value!!.solution[0].roundTo(5) leq Flt64(2.45))

val model2 = LinearMetaModel()
model2.add(x)
model2.add(rounding)
model2.maximize(rounding)
val result2 = runBlocking { solver(model2) }
assert(result2.value!!.obj eq Flt64(7.0))
assert(result2.value!!.solution[0].roundTo(5) geq Flt64(4.55))

Complete Implementation Reference:

• Kotlin

Complete Example Reference:

• Kotlin