MAS report LP

mas_report_lp.py

#!/usr/bin/env python
# -*- coding: UTF-8 -*-

# PuLP is an LP modeler written in Python.
# PuLP can generate MPS or LP files and call GLPK, COIN CLP/CBC, CPLEX,
# and GUROBI to solve linear problems.

import pulp
from pulp import (
    LpMaximize,
    LpMinimize,
    LpProblem,
    LpVariable,
    LpStatus,
    value,
)


def main():
    # https://cw.felk.cvut.cz/wiki/_media/courses/ae4m36mas/report_fixed.pdf
    mas_report_agent()
    mas_report_bandita()


def mas_report_agent():
    print "mas_report_agent:"
    r = LpVariable("r", 0, 1)
    v_I20 = LpVariable("v_I20", 0, 100)
    v_I21 = LpVariable("v_I21", 0, 100)
    v_I21 = LpVariable("v_I21", 0, 100)
    r_UI11 = LpVariable("r_UI11", 0, 1)
    r_UI11_UI12 = LpVariable("r_UI11_UI12", 0, 1)
    r_UI11_UI12_RI13 = LpVariable("r_UI11_UI12_RI13", 0, 1)
    r_UI11_UI12_RI13_RI14 = LpVariable("r_UI11_UI12_RI13_RI14", 0, 1)
    r_UI11_UI12_RI15 = LpVariable("r_UI11_UI12_RI15", 0, 1)
    r_UI11_UI12_RI15_RI16 = LpVariable("r_UI11_UI12_RI15_RI16", 0, 1)
    r_RI11 = LpVariable("r_RI11", 0, 1)
    r_RI11_RI17 = LpVariable("r_RI11_RI17", 0, 1)
    r_RI11_RI17_UI18 = LpVariable("r_RI11_RI17_UI18", 0, 1)
    r_RI11_RI17_UI18_UI19 = LpVariable("r_RI11_RI17_UI18_UI19", 0, 1)
    r_RI11_RI17_UI10 = LpVariable("r_RI11_RI17_UI10", 0, 1)
    r_RI11_RI17_UI10_UI11 = LpVariable("r_RI11_RI17_UI10_UI11", 0, 1)
    prob = LpProblem("mas_report_agent", LpMaximize)
    prob += v_I20, "objective"
    prob += v_I20 <= v_I21, "-"
    prob += v_I21 <=    5 * r_UI11_UI12_RI13_RI14 \
                     + 11 * r_RI11_RI17_UI18_UI19, "E1"
    prob += v_I21 <=  5.5 * r_RI11_RI17_UI10_UI11 \
                     + 10 * r_UI11_UI12_RI15_RI16, "E2"
    prob += r == 1
    prob += r == r_UI11 + r_RI11
    prob += r_UI11 == r_UI11_UI12
    prob += r_UI11_UI12 == r_UI11_UI12_RI13
    prob += r_UI11_UI12_RI13 == r_UI11_UI12_RI13_RI14
    prob += r_UI11_UI12 == r_UI11_UI12_RI15
    prob += r_UI11_UI12_RI15 == r_UI11_UI12_RI15_RI16
    prob += r_RI11 == r_RI11_RI17
    prob += r_RI11_RI17 == r_RI11_RI17_UI18
    prob += r_RI11_RI17_UI18 == r_RI11_RI17_UI18_UI19
    prob += r_RI11_RI17 == r_RI11_RI17_UI10
    prob += r_RI11_RI17_UI10 == r_RI11_RI17_UI10_UI11
    status = prob.solve(pulp.GLPK(msg=0))
    assert LpStatus[status] == "Optimal"
    print "  game value:", value(v_I20)
    print "  r_UI11:", value(r_UI11)
    print "  r_RI11:", value(r_RI11)
    assert value(v_I20) == 7.85714


def mas_report_bandita():
    print "mas_report_bandita:"
    v_20 = LpVariable("v_20", -100, 100)
    v_11 = LpVariable("v_11", -100, 100)
    v_12 = LpVariable("v_12", -100, 100)
    v_13 = LpVariable("v_13", -100, 100)
    v_14 = LpVariable("v_14", -100, 100)
    v_15 = LpVariable("v_15", -100, 100)
    v_16 = LpVariable("v_16", -100, 100)
    v_17 = LpVariable("v_17", -100, 100)
    v_18 = LpVariable("v_18", -100, 100)
    v_19 = LpVariable("v_19", -100, 100)
    v_110 = LpVariable("v_110", -100, 100)
    v_111 = LpVariable("v_111", -100, 100)
    r = LpVariable("r", 0, 1)
    r_E1 = LpVariable("r_E1", 0, 1)
    r_E2 = LpVariable("r_E2", 0, 1)
    prob = LpProblem("mas_report_bandita", LpMaximize)
    prob += v_20, "objective"
    prob += v_20 <= v_11, "-"
    prob += v_11 <= v_12,             "U11"
    prob += v_12 <= 0 + v_13 + v_15,  "U11_U12"
    prob += v_13 <= v_14,             "U11_U12_R13"
    prob += v_14 <= -5 * r_E1,        "U11_U12_R13_R14"
    prob += v_15 <= v_16,             "U11_U12_R15"
    prob += v_16 <= -10 * r_E2,       "U11_U12_R15_R16"
    prob += v_11 <= v_17,             "R11"
    prob += v_17 <= 0 + v_18 + v_110, "R11_R17"
    prob += v_18 <= v_19,             "R11_R17_U18"
    prob += v_19 <= -11 * r_E1,       "R11_R17_U18_U19"
    prob += v_110 <= v_111,           "R11_R17_U110"
    prob += v_111 <= -5.5 * r_E2,     "R11_R17_U110_U111"
    prob += r == 1
    prob += r == r_E1 + r_E2
    status = prob.solve(pulp.GLPK(msg=0))
    assert LpStatus[status] == "Optimal"
    print "  game value:", value(v_20)
    print "  r_E1:", value(r_E1)
    print "  r_E2:", value(r_E2)
    assert value(v_20) == -7.85714


if __name__ == "__main__":
    main()

output.txt

mas_report_agent:
  game value: 7.85714
  r_UI11: 0.52381
  r_RI11: 0.47619
mas_report_bandita:
  game value: -7.85714
  r_E1: 0.428571
  r_E2: 0.571429