Help with % aritmetic operator [MIP problem]

[GJoe2]

I have this code:

# Crear el DataFrame con φ como cadenas de texto
varillas = pd.DataFrame({'φ(pulg)': ['3/8', '1/2', '3/4', '1']})

# Crear una nueva columna con los valores flotantes de φ
varillas['φ_float'] = varillas['φ(pulg)'].apply(lambda x: eval(x))

# Definir las conversiones
pulgadas_a_cm = 2.54  # 1 pulgada = 2.54 cm

# Calcular las áreas en cm² y los diámetros en cm
varillas['Area (cm²)'] = (varillas['φ_float'] ** 2) * np.pi * (pulgadas_a_cm / 2) ** 2
varillas['Diametro (cm)'] = varillas['φ_float'] * pulgadas_a_cm

# Redondear las áreas y diámetros a 2 decimales
varillas['Area (cm²)'] = varillas['Area (cm²)'].round(2)
varillas['Diametro (cm)'] = varillas['Diametro (cm)'].round(2)

from pulp import LpProblem, LpVariable, lpSum, LpMinimize
# Área total a cubrir
area_total_objetivo = 5.71

# Definir el problema de optimización
problema = LpProblem("Optimización_de_Varillas", LpMinimize)

# Crear las variables de decisión
variables_decision = LpVariable.dicts("Cantidad", varillas.index, lowBound=0, cat='Integer')

# Definir la función objetivo
problema += lpSum(variables_decision[i] * varillas.loc[i, 'Area (cm²)'] for i in varillas.index)

# Definir la restricción de área total
problema += lpSum(variables_decision[i] * varillas.loc[i, 'Area (cm²)'] for i in varillas.index) >= area_total_objetivo

# Resolver el problema de optimización
problema.solve()
print(problema)
# Imprimir la solución
print("Solución 1:")
for i, row in varillas.iterrows():
    cantidad = variables_decision[i].varValue
    if cantidad > 0:
        print(f"{int(cantidad)} varillas de φ {row['φ(pulg)']}")

print(f"Área total: {sum(variables_decision[i].varValue * row['Area (cm²)'] for i, row in varillas.iterrows())} cm²")

I want to add a condition where at least one value in "variables_decision" must be even (not counting values where solution is 0)
I tried % shenanigans:
[variables_decision[i] % 2
But pulp complain with:
TypeError: unsupported operand type(s) for %: 'LpVariable' and 'int'

Any advice is welcome, thanks in advance

[guifcoelho]

I think you need some integer variables:

Let var_multiples be some integer variables to cover the number of multiples of 2 (even numbers) for variables_decision

Then:

2 * var_multiples[i] <= variables_decision[i]
sum(var_multiples) >= 1

To get at least one even value, you need one variable to be greater or equal to 1.

I hope that helps. At least it is way to start.