GDPopt LOA appears to mishandle maximization objective sense

[bernalde]

Summary

gdpopt.loa appears to mishandle objective sense in the discrete OA master for a maximization GDP. In a GDPlib methanol benchmark, the algebraically equivalent formulations minimize(-profit) and maximize(profit) produce different GDPopt LOA solutions. The maximization form terminates after one iteration at a negative-profit local solution, while the minimization-of-negative-profit form finds the expected positive-profit solution from the Turkay/Grossmann LOA paper.

This was discovered while working on GDPlib:

• GDPlib upstream tracker: Track GDPopt LOA objective-sense discrepancy SECQUOIA/gdplib#114
• GDPlib PR preserving the workaround and adding sign-convention documentation: Fix methanol GDPopt solve options SECQUOIA/gdplib#113
• Original paper reference used by the benchmark: Turkay and Grossmann, "Logic-based MINLP algorithms for the optimal synthesis of process networks", Computers & Chemical Engineering, 1996, DOI 10.1016/0098-1354(95)00219-7

Environment

• Pyomo version: 6.10.0
• Python: 3.12 in the GDPlib Pixi environment
• GDPopt call:

pyo.SolverFactory("gdpopt").solve(
    m,
    algorithm="LOA",
    mip_solver="gams",
    nlp_solver="gams",
    tee=False,
)

GAMS was locally available for both MIP and NLP roles.

Reproducer

This uses GDPlib PR #113 because it exposes m.profit separately from the solver objective.

import pyomo.environ as pyo
import pyomo.gdp as gdp
from gdplib.methanol.methanol import build_model


def solve_case(label, maximize_profit):
    m = build_model()
    if maximize_profit:
        m.objective.deactivate()
        m.max_profit_objective = pyo.Objective(expr=m.profit, sense=pyo.maximize)
    res = pyo.SolverFactory("gdpopt").solve(
        m,
        algorithm="LOA",
        mip_solver="gams",
        nlp_solver="gams",
        tee=False,
    )
    active = [
        d.name
        for d in m.component_data_objects(
            gdp.Disjunct, active=True, sort=True, descend_into=True
        )
        if pyo.value(d.indicator_var)
    ]
    print(f"CASE: {label}")
    print(f"termination: {res.solver.termination_condition}")
    print(
        "objective:",
        pyo.value(m.objective)
        if m.objective.active
        else pyo.value(m.max_profit_objective),
    )
    print(f"profit: {pyo.value(m.profit)}")
    print(f"iterations: {getattr(res.solver, 'iterations', None)}")
    print(f"active: {active}")
    print(f"feed1: {pyo.value(m.flows[1])}")
    print(f"feed2: {pyo.value(m.flows[2])}")
    print(f"product_flow: {pyo.value(m.flows[23])}")
    print(f"purity: {pyo.value(m.component_flows[23, 'CH3OH'] / m.flows[23])}")
    print("---")


solve_case("minimize_negative_profit", maximize_profit=False)
solve_case("maximize_profit", maximize_profit=True)

Observed output:

CASE: minimize_negative_profit
termination: optimal
objective: -1793.4292381783353
profit: 1793.4292381783353
iterations: 15
active: ['cheap_reactor', 'expensive_feed_disjunct', 'single_stage_recycle_compressor_disjunct', 'two_stage_feed_compressor_disjunct']
feed1: 0
feed2: 3.408977431099573
product_flow: 1.0
purity: 0.9
---
CASE: maximize_profit
termination: optimal
objective: -242.05445652916296
profit: -242.05445652916296
iterations: 1
active: ['cheap_feed_disjunct', 'cheap_reactor', 'two_stage_feed_compressor_disjunct', 'two_stage_recycle_compressor_disjunct']
feed1: 4.820913073983858
feed2: 0
product_flow: 1.0
purity: 0.9
---

Expected behavior

minimize(-profit) and maximize(profit) should produce equivalent GDPopt behavior, modulo normal local NLP solver tolerances and nonconvex local-solution limitations. They should not cause the LOA master to pursue the opposite economic direction or terminate after one iteration at a dominated negative-profit solution.

The minimize(-profit) result matches the expected scale from Turkay/Grossmann Example 3, which reports an optimal profit around $1.794M/yr.

Suspected source location

In Pyomo 6.10.0, pyomo.contrib.gdpopt.loa.GDP_LOA_Solver._setup_augmented_penalty_objective() appears to create the discrete OA objective with minimization sense unconditionally:

discrete_problem_util_block.oa_obj = Objective(sense=minimize)

Then _update_augmented_penalty_objective() updates only the expression:

discrete_problem_util_block.oa_obj.expr = (
    discrete_objective.expr + OA_penalty_expr
)

The slack penalty sign is adjusted for maximize/minimize, and bound bookkeeping elsewhere appears objective-sense-aware, but the active OA master objective sense itself may remain minimization even when the original objective is maximization.

Suggested next step

This GDPlib model is larger than ideal for a Pyomo regression test. The next useful step is to reduce this to a small standalone GDP where minimize(-f) and maximize(f) diverge under gdpopt.loa, then test whether setting the OA objective sense to the original objective sense fixes the issue.