MultiObjectiveLineSearches.jl

MultiObjectiveLineSearches.jl provides line searches for multiobjective optimization. Given a point, a search direction and the objective values at the point, a line search looks for a step size along the direction that satisfies an acceptance condition on all objectives. The available method, BackTracking, uses an Armijo-type sufficient decrease condition. The package has no runtime dependencies and requires Julia 1.11 or later.

Installation

The package is not registered. Add it from its GitHub repository:

import Pkg
Pkg.add(url = "https://github.com/VectorOptimizationGroup/MultiObjectiveLineSearches.jl")

See the installation guide for project environments and local checkouts.

Quick Example

using MultiObjectiveLineSearches

function objectives!(values, x)
    values[1] = (x[1] - 1)^2
    values[2] = (x[1] - 1)^2 + 1
    return nothing
end

x = [0.0]; d = [3.0]; Fx = [1.0, 2.0]; slopes = [-6.0, -6.0]

search = configure_linesearch(BackTracking(), Float64)
x_trial = similar(x); F_trial = similar(Fx)

result = perform_linesearch!(search, objectives!, x, d, Fx, slopes,
                             x_trial, F_trial; factor = maximum(slopes))
result.success  # true; x_trial and F_trial hold the accepted point and values

Documentation

The MultiObjectiveLineSearches.jl documentation contains the quick start, the usage guide, the mathematical formulation of each line search with its literature sources, the API reference, and the bibliography. Instructions for building it locally are in docs/README.md.

Run the tests from the package directory:

julia --project -e 'using Pkg; Pkg.test()'

Highlights

• Backtracking for an Armijo-type sufficient decrease condition in every objective, with safeguarded quadratic interpolation.
• Typed, reusable configurations and in-place searches with caller-owned buffers.
• Structured diagnostics: step, termination reason, evaluation and reduction counts.
• Formulations related to the multiobjective literature, with executable examples.

Citation

If you use MultiObjectiveLineSearches.jl in research, please cite the software using the metadata in CITATION.cff.

License

MultiObjectiveLineSearches.jl is distributed under the MIT License.