# HiGHS solver \>100x slower than Gurobi with bilinear big-m relaxation

**URL:** <https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, gurobi\
**Created:** [May 29, 2024, 8:00am UTC](https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905 "2024-05-29T08:00:07Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![this\_josh](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/this_josh/32/42679_2.png) [@this\_josh](https://discourse.julialang.org/u/this_josh)\
**Post date:** [May 29, 2024, 8:00am UTC](https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905/1 "2024-05-29T08:00:07Z")

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I’m not sure where to put this as it’s not specifically an issue, and I’m not sure who would improve it.  
For my research I need to solve a bilinear model and I’d like to use an open-source solver ideally.

> **Rough example of my constraints**
>
> My constraint is like xy==0. I relax this using big\_M to roughly
> 
> ```julila
> @variable(model, 0 <= x[1:n])
> @variable(model, y[1:n] <= 0)
> @variable(model, 0 <= u[1:n] <= 1, binary=true)
> @constraint(model, big_m_x, x .≤ 10 .* (1 .- u))
> @constraint(model, big_m_y, -10 .* u .≤ y)
> 
> ```

I’ve formulated a MWE example (see below), in this scenario Gurobi solves the problem in 0.4s while HiGHS takes 40-60 seconds which is \>100 times slower. As my actual problem is much bigger than the example below HiGHs become prohibitively slow.

I appreciate Gurobi is often quicker than HiGHS, but not usually by this much, it seems like my HiGHs implementation is missing a trick?

> **MWE**
>
> Note I haven’t gone through this MWE thoroughly, it just serves to demonstrate the timing scenario and is roughly similar to my actual problem
> 
> ```julia
> using JuMP, HiGHS, Gurobi
> 
> function create_model(n, nl, solver)
> if solver==:H
> model = Model(HiGHS.Optimizer)
> elseif solver==:G
> model = Model(Gurobi.Optimizer)
> end
> if nl
> @variable(model, 0 <= x[1:n] <= 10)
> @variable(model, -10 <= y[1:n] <= 0)
> @constraint(model, [i=1:n], x[i]*y[i] ==0)
> 
> else
> @variable(model, 0 <= x[1:n])
> @variable(model, y[1:n] <= 0)
> @variable(model, 0 <= u[1:n] <= 1, binary=true)
> @constraint(model, big_m_x, x .≤ 10 .* (1 .- u))
> @constraint(model, big_m_y, -10 .* u .≤ y)
> 
> end
> 
> @objective(model, Min, sum(x[i] + -2*y[i] for i in 1:n))
> @constraint(model, [i=1:n], x[i] - y[i] >= 1)
> @constraint(model, [i=1:n], x[i] - y[i] <= 15)
> 
> return model
> end
> 
> n = 100_000
> model = create_model(n,false,:G)
> 
> optimize!(model)
> 
> # Gurobi = 0.4
> # HiGHS = 58.6
> solve_time(model)
> objective_value(model)
> sum(value.(model[:x]))
> sum(value.(model[:y]))
> 
> ```
> 
> with
> 
> ```julia
> (jl_MPgoHK) pkg> st
> Status `/private/var/folders/63/lgx7112n3b58qj9r923y2v680000gp/T/jl_MPgoHK/Project.toml`
> [2e9cd046] Gurobi v1.2.3
> [87dc4568] HiGHS v1.9.0
> [4076af6c] JuMP v1.22.1
> 
> ```

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**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:** [May 29, 2024, 9:43am UTC](https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905/2 "2024-05-29T09:43:14Z")

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This is probably expected behavior.

You should expect that HiGHS is 10-100× slower than Gurobi.

It will be missing a trick, but because Gurobi is closed source, we don’t know which one(s).

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**Author:** ![this\_josh](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/this_josh/32/42679_2.png) [@this\_josh](https://discourse.julialang.org/u/this_josh)\
**Post date:** [May 29, 2024, 10:14am UTC](https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905/3 "2024-05-29T10:14:41Z")

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I see, usually I’ve found it to be more like 10x, so found this up to 150x difference noteworthy. But as you say, we cannot find what is causing this disparity.

Unfortunately, I do not have a good enough understanding of HiGHS to try investigating beyond changing parameters, which has made little difference.

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**Author:** ![ohmsweetohm1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ohmsweetohm1/32/49126_2.png) [@ohmsweetohm1](https://discourse.julialang.org/u/ohmsweetohm1)\
**Post date:** [October 22, 2025, 6:24pm UTC](https://discourse.julialang.org/t/highs-solver-100x-slower-than-gurobi-with-bilinear-big-m-relaxation/114905/4 "2025-10-22T18:24:08Z")

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Since this is basically a set of `n` optimization problems, `HiGHS` seems to be bad at detecting this and making use of it.