# MathOptInterface and MultiObjectiveAlgorithms functionality to implement a multiobjective algorithm (AUGMECON)

**URL:** <https://discourse.julialang.org/t/mathoptinterface-and-multiobjectivealgorithms-functionality-to-implement-a-multiobjective-algorithm-augmecon/136243>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [March 17, 2026, 8:12pm UTC](https://discourse.julialang.org/t/mathoptinterface-and-multiobjectivealgorithms-functionality-to-implement-a-multiobjective-algorithm-augmecon/136243 "2026-03-17T20:12:02Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Josa9321](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/josa9321/32/12170_2.png) [@Josa9321](https://discourse.julialang.org/u/Josa9321)\
**Post date:** [March 17, 2026, 8:12pm UTC](https://discourse.julialang.org/t/mathoptinterface-and-multiobjectivealgorithms-functionality-to-implement-a-multiobjective-algorithm-augmecon/136243/1 "2026-03-17T20:12:02Z")

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Hi.

I’m currently working on adapting an AUGMECON implementation in JuMP to use the MultiObjectiveAlgorithms module as its base. As part of this process, I’m adjusting AUGMECON to follow the MOA structure and implementing the tests from the MOA package (only the basic tests, not those from vOptLib). However, I’m encountering a couple of errors trying to do so.

The first issue appears in `test_vectornonlinearfunction` (MOA). The AUGMECON method requires adding the sum of the surplus variables (s\_i) to the main objective:

\max f\_1 + \epsilon \sum\_{i=2}^p \frac{s\_i}{r\_i}

The problem is that I’m trying to add a ScalarAffineFunction (the surplus sum) to a ScalarNonlinearFunction (f\_1) as following:

```julia
    objective_term = -algorithm.penalty * sum(surplus_variables[o-1] / (ranges_set[o][1] - ranges_set[o][end]) for o in 2:m)

    MOI.set(inner, MOI.ObjectiveFunction{typeof(objs_set[1])}(), objs_set[1] + objective_term)

```

Which produces the error when I run the `test_vectornonlinearfunction` test from MOA:

```julia
MethodError: no method matching +(::MathOptInterface.ScalarNonlinearFunction, ::MathOptInterface.ScalarAffineFunction{Float64})

```

I looked at other algorithms implemented in MOA, but I still couldn’t find a clear way to construct a valid expression that combines f\_1 with the sum of the surplus variables.

Also, for S-AUGMECON, I have \max f\_1 + \epsilon \sum\_{i=2}^p \frac{f\_i}{r\_i}. If the objective functions have different types, I anticipate that the same bug will appear. Would be the same solution than for AUGMECON?

The second issue is related to the time limit. Even when I set a time limit, the solver still runs until the problem is fully solved, apparently ignoring the limit:

`MOI.set(model, MOI.TimeLimitSec(), 0.0)`.

I checked other algorithms in MOA and didn’t notice anything specific related to setting or enforcing time limits, so I assumed that this was something handled automatically rather than within the algorithm implementation. However, in my case it doesn’t seem to be working.

Could someone help me understand what might be missing in these two cases?

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 17, 2026, 8:39pm UTC](https://discourse.julialang.org/t/mathoptinterface-and-multiobjectivealgorithms-functionality-to-implement-a-multiobjective-algorithm-augmecon/136243/2 "2026-03-17T20:39:48Z")

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Hi @Josa9321, please open an issue (or better yet, a pull request, don’t worry if it is only half-finished and not working) in MultiObjectiveAlgorithms.jl. It’ll be easier to discuss there.

> objective\_term = -algorithm.penalty \* sum(surplus\_variables[o-1] / (ranges\_set[o][1] - ranges\_set[o][end]) for o in 2:m)

The main issue is that you can’t use Julia’s operator overloading to construct expressions like this.

You need to do something like:

```Julia
sum_terms = map(2:m) do o
    return MOI.ScalarAffineTerm{Float64}(
        -algorithm.penalty / (ranges_set[o][1] - ranges_set[o][end]),
        surplus_variables[o-1],
    )
end
objective_term = MOI.ScalarAffineFunction(sum_terms, 0.0)
new_obj = MOI.Utilities.operate(+, Float64, objs_set[1], objective_term)
MOI.set(inner, MOI.ObjectiveFunction{typeof(new_obj)}(), new_obj)

```

> The second issue is related to the time limit. Even when I set a time limit, the solver still runs until the problem is fully solved, apparently ignoring the limit:

Are you calling `_check_premature_termination(model)`?