Pareto optimal front determination

ParetoOptimalFront.py

"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_ParetoOptimalFront.html
## LICENSETYPE: Demo
## MODELTYPE: NLP


Pareto optimal front determination

For more details please refer to Chapter 2 (Gcode2.16), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: NLP
--------------------------------------------------------------------------------
Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
"""

from __future__ import annotations

import os

from gamspy import (
    Card,
    Container,
    Equation,
    Model,
    Number,
    Parameter,
    Set,
    Variable,
)
from gamspy.math import sqr


def main():
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
    )

    # VARIABLES #
    of1 = Variable(m, name="of1", type="free")
    of2 = Variable(m, name="of2", type="free")
    x1 = Variable(m, name="x1", type="free")
    x2 = Variable(m, name="x2", type="free")

    # EQUATIONS #
    eq1 = Equation(m, name="eq1", type="regular")
    eq2 = Equation(m, name="eq2", type="regular")
    eq3 = Equation(m, name="eq3", type="regular")
    eq4 = Equation(m, name="eq4", type="regular")

    eq1[...] = 4 * x1 - 0.5 * sqr(x2) == of1
    eq2[...] = Number(-1) * sqr(x1) + 5 * x2 == of2
    eq3[...] = 2 * x1 + 3 * x2 <= 10
    eq4[...] = 2 * x1 - x2 >= 0

    x1.lo[...] = 1
    x1.up[...] = 2
    x2.lo[...] = 1
    x2.up[...] = 3

    pareto1 = Model(
        m,
        name="pareto1",
        equations=m.getEquations(),
        problem="nlp",
        sense="max",
        objective=of1,
    )
    pareto2 = Model(
        m,
        name="pareto2",
        equations=m.getEquations(),
        problem="nlp",
        sense="max",
        objective=of2,
    )

    # COUNTER SET #
    counter = Set(m, name="counter", records=[f"c{c}" for c in range(1, 22)])

    # REPORTING PARAMETERS #
    E = Parameter(m, name="E")
    report = Parameter(m, name="report", domain=[counter, "*"])
    ranges = Parameter(m, name="ranges", domain="*")

    pareto1.solve()
    ranges["OF1max"] = of1.l
    ranges["OF2min"] = of2.l

    pareto2.solve()
    ranges["OF2max"] = of2.l
    ranges["OF1min"] = of1.l

    for idx, c in enumerate(counter.toList()):
        E[...] = (ranges["OF2max"] - ranges["OF2min"]) * (idx) / (
            Card(counter) - 1
        ) + ranges["OF2min"]
        of2.lo[...] = E
        pareto1.solve()
        report[c, "OF1"] = of1.l
        report[c, "OF2"] = of2.l
        report[c, "E"] = E

    print("Report:  \n", report.pivot().round(4), "\n")
    print("Ranges:  \n", ranges.toDict(), "\n")


if __name__ == "__main__":
    main()