"""
Weapons Assignment (WEAPONS)
This model determines an assignment of weapons to targets in order
to inflict maximum damage at minimal cost. This is a classic
NLP test problem.
Bracken, J, and McCormick, G P, Chapter 2. In Selected Applications of
Nonlinear Programming. John Wiley and Sons, New York, 1968, pp. 22-27.
Keywords: nonlinear programming, assignment problem, military application,
nlp test problem
"""
from __future__ import annotations
import os
import pandas as pd
from gamspy import Card
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Parameter
from gamspy import Problem
from gamspy import Product
from gamspy import Sense
from gamspy import Set
from gamspy import Sum
from gamspy import Variable
def main():
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
)
td_data = pd.DataFrame([
["icbm", "2", 0.05],
["icbm", "6", 0.15],
["icbm", "7", 0.10],
["icbm", "8", 0.15],
["icbm", "9", 0.20],
["icbm", "18", 0.05],
["mrbm-1", "1", 0.16],
["mrbm-1", "2", 0.17],
["mrbm-1", "3", 0.15],
["mrbm-1", "4", 0.16],
["mrbm-1", "5", 0.15],
["mrbm-1", "6", 0.19],
["mrbm-1", "7", 0.19],
["mrbm-1", "8", 0.18],
["mrbm-1", "9", 0.20],
["mrbm-1", "10", 0.14],
["mrbm-1", "12", 0.02],
["mrbm-1", "14", 0.12],
["mrbm-1", "15", 0.13],
["mrbm-1", "16", 0.12],
["mrbm-1", "17", 0.15],
["mrbm-1", "18", 0.16],
["mrbm-1", "19", 0.15],
["mrbm-1", "20", 0.15],
["lr-bomber", "1", 0.04],
["lr-bomber", "2", 0.05],
["lr-bomber", "3", 0.04],
["lr-bomber", "4", 0.04],
["lr-bomber", "5", 0.04],
["lr-bomber", "6", 0.10],
["lr-bomber", "7", 0.08],
["lr-bomber", "8", 0.09],
["lr-bomber", "9", 0.08],
["lr-bomber", "10", 0.05],
["lr-bomber", "11", 0.01],
["lr-bomber", "12", 0.02],
["lr-bomber", "13", 0.01],
["lr-bomber", "14", 0.02],
["lr-bomber", "15", 0.03],
["lr-bomber", "16", 0.02],
["lr-bomber", "17", 0.05],
["lr-bomber", "18", 0.08],
["lr-bomber", "19", 0.07],
["lr-bomber", "20", 0.08],
["f-bomber", "10", 0.04],
["f-bomber", "11", 0.09],
["f-bomber", "12", 0.08],
["f-bomber", "13", 0.09],
["f-bomber", "14", 0.08],
["f-bomber", "15", 0.02],
["f-bomber", "16", 0.07],
["mrbm-2", "1", 0.08],
["mrbm-2", "2", 0.06],
["mrbm-2", "3", 0.08],
["mrbm-2", "4", 0.05],
["mrbm-2", "5", 0.05],
["mrbm-2", "6", 0.02],
["mrbm-2", "7", 0.02],
["mrbm-2", "10", 0.10],
["mrbm-2", "11", 0.05],
["mrbm-2", "12", 0.04],
["mrbm-2", "13", 0.09],
["mrbm-2", "14", 0.02],
["mrbm-2", "15", 0.01],
["mrbm-2", "16", 0.01],
])
wa_data = pd.DataFrame([
["icbm", 200],
["mrbm-1", 100],
["lr-bomber", 300],
["f-bomber", 150],
["mrbm-2", 250],
])
tm_data = pd.DataFrame([
["1", 30],
["6", 100],
["10", 40],
["14", 50],
["15", 70],
["16", 35],
["20", 10],
])
mv_data = pd.DataFrame([
["1", 60],
["2", 50],
["3", 50],
["4", 75],
["5", 40],
["6", 60],
["7", 35],
["8", 30],
["9", 25],
["10", 150],
["11", 30],
["12", 45],
["13", 125],
["14", 200],
["15", 200],
["16", 130],
["17", 100],
["18", 100],
["19", 100],
["20", 150],
])
# Sets
w = Set(
m,
name="w",
records=["icbm", "mrbm-1", "lr-bomber", "f-bomber", "mrbm-2"],
description="weapons",
)
t = Set(
m,
name="t",
records=[str(i) for i in range(1, 21)],
description="targets",
)
# Parameters
td = Parameter(
m, name="td", domain=[w, t], records=td_data, description="target data"
)
wa = Parameter(
m,
name="wa",
domain=w,
records=wa_data,
description="weapons availability",
)
tm = Parameter(
m,
name="tm",
domain=t,
records=tm_data,
description="minimum number of weapons per target",
)
mv = Parameter(
m,
name="mv",
domain=t,
records=mv_data,
description="military value of target",
)
# Variables
x = Variable(
m,
name="x",
domain=[w, t],
type="Positive",
description="weapons assignment",
)
prob = Variable(
m, name="prob", domain=t, description="probability for each target"
)
tetd = Variable(m, name="tetd", description="total expected damage")
# Equations
maxw = Equation(m, name="maxw", domain=w, description="weapons balance")
minw = Equation(
m,
name="minw",
domain=t,
description="minimum number of weapons required per target",
)
probe = Equation(
m, name="probe", domain=t, description="probability definition"
)
etdp = Equation(
m,
name="etdp",
description="total expected damage alternate formulation",
)
etd = Equation(m, name="etd", description="total expected damage")
maxw[w] = Sum(t.where[td[w, t]], x[w, t]) <= wa[w]
minw[t].where[tm[t]] = Sum(w.where[td[w, t]], x[w, t]) >= tm[t]
probe[t] = prob[t] == 1 - Product(
w.where[td[w, t]], (1 - td[w, t]) ** x[w, t]
)
etdp[...] = tetd == Sum(t, mv[t] * prob[t])
etd[...] = tetd == Sum(
t, mv[t] * (1 - Product(w.where[td[w, t]], (1 - td[w, t]) ** x[w, t]))
)
war = Model(
m,
name="war",
equations=[maxw, minw, etd],
problem=Problem.NLP,
sense=Sense.MAX,
objective=tetd,
)
x.l[w, t].where[td[w, t]] = wa[w] / Card(t)
war.solve()
import math
assert math.isclose(war.objective_value, 1735.5696, rel_tol=0.001)
print(war.objective_value)
if __name__ == "__main__":
main()
