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Performance

In most Nosy studies, computation time is dominated by optimisation in the solver, not by Nosy's model generation. If model generation itself becomes noticeable, the usual Julia advice applies: keep code type-stable, avoid unnecessary allocations, and work with functions. See Julia's Performance Tips for the general toolbox.

In problems with a very large number of variables, the creation of variable names may take a non-negligible time. If you do not need the variable names, you can use the function set_string_names_on_creation from the package JuMP.

JuMP.set_string_names_on_creation(model(sim(snapshot)), false)

The levers below mostly target solver time by reducing model size, dropping irrelevant tiny coefficients, or improving numerical conditioning. Nosy's defaults preserve the mathematical model exactly.

Objective Cleanup

optimize! can filter small objective coefficients before sending the objective to JuMP. The threshold is read from the simulation option objthreshold. Its default is 0, which preserves every coefficient without rounding. Set a positive threshold to opt in to filtering and rounding:

using Nosy
using HiGHS

s = Sim(HiGHS.Optimizer; objthreshold=1e-8)

The threshold is relative to the largest absolute objective coefficient. Terms below the threshold are removed, and Nosy emits a warning if any terms are dropped. This is useful when tiny numerical terms accumulate in a large objective and add noise without changing the economics of the problem.

Use this carefully: if a coefficient is small because the unit scale is small but the term is still meaningful, increasing objthreshold may change the model.

Constraint Cleanup And Scaling

By default, Sim wraps optimiser constructors in Nosy's constraint scaling bridge:

s = Sim(HiGHS.Optimizer; constraint_scaling=true)

The bridge rewrites scalar affine constraints before they reach the solver. For each constraint row, it:

  • scales the row so that the geometric mean of the smallest and largest finite nonzero absolute values is equal to scalingtarget.

This row scaling is enabled by default and is mathematically lossless. Setting expthreshold to a positive value additionally removes coefficients, left-hand-side constants, and right-hand-side bounds below expthreshold * maxabs, where maxabs is the largest finite coefficient in that row.

The defaults are:

s = Sim(
    HiGHS.Optimizer;
    constraint_scaling=true,
    expthreshold=0.0,
    scalingtarget=1.0,
)

This is an MOI bridge, so it changes the representation of scalar affine constraints passed to the optimiser. It does not rewrite variable bounds, integrality constraints, vector constraints, quadratic constraints, or nonlinear constraints.

To disable this bridge:

s = Sim(HiGHS.Optimizer; constraint_scaling=false)

Small Bound Cleanup

Nosy can also fix nonnegative variables to zero when their upper bound is at most boundthreshold. The default is 0, which disables this cleanup. Set a positive threshold to opt in:

s = Sim(HiGHS.Optimizer; boundthreshold=1e-4)

This can reduce model size when preprocessing has created tiny-capacity variables. As with objective cleanup, the threshold should be consistent with the units of the model.

Unit Commitment Masks

UnitCommitment can create many variables and constraints, especially on long meshes. Setting integer=true does not by itself create more constraints, but it turns the commitment decisions into integer variables and can make the optimisation problem much harder for the solver. When starts or shutdowns only need to be considered at selected timesteps, use startupmask and shutdownmask to avoid creating unnecessary event variables.

# Only allow starts every four hours.
startupmask = falses(8760)
startupmask[1:4:end] .= true

# Only allow shutdowns every four hours for the single downtime type.
shutdownmask = [copy(startupmask)]

uc = UnitCommitment(
    "output",
    0.4;
    startup=2,
    shutdown=1,
    uptime=6,
    downtime=4,
    integer=true,
    startupmask=startupmask,
    shutdownmask=shutdownmask,
)

The masks should have one Boolean value per timestep in the simulation mesh. startupmask=false disallows startups at that timestep. Each vector in shutdownmask applies to one shutdown type; its length must match the number of downtime alternatives.

Model archetype simplifications

Some models offer a simplified version of the equations, which can help reduce the computational burden of the optimization. In particular, the BasicStorage and LazyStorage constructors have the simplified keyword argument, which slightly changes the expression of the level as a function of the flows by using the simpler "energy" formalism instead of the "power" formalism.

Please validate before using the simplified=true argument in production.

Time mesh

The number of optimization variables is generally linear with the number of timesteps. Depending on the model's goal, there can be two types of time-related simplifications:

  • reducing the duration of the TimeMesh: you can define a smaller temporal horizon, e.g. sub-annual duration.
  • using a coarser TimeMesh, with all or some of the night steps lasting more than one hour.

The Time section of the documentation provides more detail on how to use a custom TimeMesh.