# MOA-HiGHS Unsupported Objective Function

**URL:** <https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [July 5, 2024, 4:57pm UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672 "2024-07-05T16:57:47Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![jhannyj](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@jhannyj](https://discourse.julialang.org/u/jhannyj)\
**Post date:** [July 5, 2024, 4:57pm UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672/1 "2024-07-05T16:57:47Z")

</div>

Hi all. I’m pretty new to Julia optimization. I have this problem:

```julia
model = Model(HiGHS.Optimizer)
@variable(model, x[1:n] >= 0)
@constraint(model, A' * x .>= f)
@objective(model, Min, b' * x)

```

which works perfectly when using the HiGHS optimizer alone, but I want to find multiple solutions, so I’ve been trying to use MOA as follows

```julia
model = Model()
@variable(model, x[1:n] >= 0)
@constraint(model, A' * x .>= f)
@objective(model, Min, b' * x)

set_optimizer(model, () -> MOA.Optimizer(HiGHS.Optimizer))
set_attribute(model, MOA.Algorithm(), MOA.Dichotomy())
set_attribute(model, MOA.SolutionLimit(), 2)

```

but when I call optimize, I get the following error

```julia
ERROR: MathOptInterface.UnsupportedAttribute{MathOptInterface.ObjectiveFunction{MathOptInterface.ScalarAffineFunction{Float64}}}: Attribute MathOptInterface.ObjectiveFunction{MathOptInterface.ScalarAffineFunction{Float64}}() is not supported by the model.
Stacktrace:
  [1] bridge_type(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, F::Type{…})
    @ MathOptInterface.Bridges C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Bridges\lazy_bridge_optimizer.jl:520
  [2] concrete_bridge_type(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, F::Type{…})
    @ MathOptInterface.Bridges.Objective C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Bridges\Objective\bridge.jl:68
  [3] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, attr::MathOptInterface.ObjectiveFunction{…}, func::MathOptInterface.ScalarAffineFunction{…})
    @ MathOptInterface.Bridges C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Bridges\bridge_optimizer.jl:1187
  [4] _pass_attribute(dest::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, src::MathOptInterface.Utilities.UniversalFallback{…}, index_map::MathOptInterface.Utilities.IndexMap, attr::MathOptInterface.ObjectiveFunction{…})
    @ MathOptInterface.Utilities C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Utilities\copy.jl:51
  [5] pass_attributes(dest::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, src::MathOptInterface.Utilities.UniversalFallback{…}, index_map::MathOptInterface.Utilities.IndexMap)
    @ MathOptInterface.Utilities C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Utilities\copy.jl:38
  [6] default_copy_to(dest::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, src::MathOptInterface.Utilities.UniversalFallback{…})
    @ MathOptInterface.Utilities C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Utilities\copy.jl:503
  [7] copy_to
    @ C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Bridges\bridge_optimizer.jl:455 [inlined]
  [8] optimize!
    @ C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\MathOptInterface.jl:84 [inlined]
  [9] optimize!(m::MathOptInterface.Utilities.CachingOptimizer{…})
    @ MathOptInterface.Utilities C:\Users\JHANNY\.julia\packages\MathOptInterface\2CULs\src\Utilities\cachingoptimizer.jl:316
 [10] optimize!(model::Model; ignore_optimize_hook::Bool, _differentiation_backend::MathOptInterface.Nonlinear.SparseReverseMode, kwargs::@Kwargs{})
    @ JuMP C:\Users\JHANNY\.julia\packages\JuMP\Gwn88\src\optimizer_interface.jl:457
 [11] optimize!
    @ C:\Users\JHANNY\.julia\packages\JuMP\Gwn88\src\optimizer_interface.jl:409 [inlined]

```

which I think doesn’t really make sense since HiGHS does support ScalarAffineFunction{Float64}, and the problem can be solved perfectly fine without using MOA.

Thanks for the help!

---

<div class="post-metadata">

**Author:** ![slwu89](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/slwu89/32/217323_2.png) [@slwu89](https://discourse.julialang.org/u/slwu89)\
**Post date:** [July 5, 2024, 5:49pm UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672/2 "2024-07-05T17:49:21Z")

</div>

The `MultiObjectiveAlgorithms.jl` package (`MOA`) is for problems with more than one objective but your optimization problem only has a single objective. In the examples using MOA, the 3rd argument to `@objective` is a vector of objectives: [Simple multi-objective examples · JuMP](https://jump.dev/JuMP.jl/stable/tutorials/linear/multi_objective_examples/#Bi-objective-linear-problem)

---

<div class="post-metadata">

**Author:** ![jhannyj](https://avatars.discourse-cdn.com/v4/letter/j/e8c25b/32.png) [@jhannyj](https://discourse.julialang.org/u/jhannyj)\
**Post date:** [July 5, 2024, 5:55pm UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672/3 "2024-07-05T17:55:31Z")

</div>

Ah I see. Is there some way that I can find multiple solutions from a single objective if the optimal solution is non-unique?

---

<div class="post-metadata">

**Author:** ![slwu89](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/slwu89/32/217323_2.png) [@slwu89](https://discourse.julialang.org/u/slwu89)\
**Post date:** [July 5, 2024, 8:17pm UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672/4 "2024-07-05T20:17:21Z")

</div>

Hmm, if you have access to Gurobi or CPLEX it seems like those solvers support a solution pool: [Finding multiple feasible solutions | JuMP](https://jump.dev/tutorials/2021/11/02/tutorial-multi-jdf/)

I’m not sure if any of the common open source solvers support such a feature.

---

<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:** [July 13, 2024, 12:46am UTC](https://discourse.julialang.org/t/moa-highs-unsupported-objective-function/116672/5 "2024-07-13T00:46:39Z")

</div>

Hi @jhannyj, welcome to the forum 😄

MOA is for solving multi-objective (vector-valued) optimization problems, not for finding multiple solutions to a scalar-valued optimization problem.

HiGHS does not support finding multiple solutions.

You could do something like this, where you solve once, add a constraint on optimal objective value, and then try to find a diversity of solutions:

```Julia
using JuMP, HiGHS
import MultiObjectiveAlgorithms as MOA
model = Model(HiGHS.Optimizer)
@variable(model, x[1:n] >= 0)
@constraint(model, A' * x .>= f)
@objective(model, Min, b' * x)
optimize!(model)
@constraint(model, b' * x == objective_value(model))
@objective(model, Min, x) # objective is now a vector
set_optimizer(model, () -> MOA.Optimizer(HiGHS.Optimizer))
optimize!(model)
[value(x; result = i) for i in 1:result_count(model)]

```