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https://github.com/lanl-ansi/alpine.jl
A Julia/JuMP-based Global Optimization Solver for Non-convex Programs
https://github.com/lanl-ansi/alpine.jl
global-optimization julia-language minlp minlp-solver mixed-integer-nonlinear-programming mixed-integer-programming non-convex-optimization nonlinear-optimization optimization optimization-algorithms
Last synced: about 1 month ago
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A Julia/JuMP-based Global Optimization Solver for Non-convex Programs
- Host: GitHub
- URL: https://github.com/lanl-ansi/alpine.jl
- Owner: lanl-ansi
- License: other
- Created: 2016-10-20T18:08:33.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2024-10-07T23:20:08.000Z (about 1 month ago)
- Last Synced: 2024-10-12T22:23:35.882Z (about 1 month ago)
- Topics: global-optimization, julia-language, minlp, minlp-solver, mixed-integer-nonlinear-programming, mixed-integer-programming, non-convex-optimization, nonlinear-optimization, optimization, optimization-algorithms
- Language: Julia
- Homepage: https://lanl-ansi.github.io/Alpine.jl/latest/
- Size: 5.15 MB
- Stars: 244
- Watchers: 22
- Forks: 39
- Open Issues: 10
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.md
- Citation: CITATION.bib
Awesome Lists containing this project
README
# Alpine, a global solver for non-convex MINLPs
[](https://github.com/lanl-ansi/Alpine.jl/actions/workflows/ci.yml)
[](https://codecov.io/gh/lanl-ansi/Alpine.jl)
[](https://lanl-ansi.github.io/Alpine.jl/latest/)
[](https://juliahub.com/ui/Packages/Alpine/TRSJF)
ALPINE (glob(AL) o(P)timization for mixed-(I)nteger programs with (N)onlinear (E)quations), is a novel global optimization solver that uses an adaptive, piecewise convexification scheme and constraint programming methods to solve non-convex Mixed-Integer Non-Linear Programs (MINLPs) efficiently. MINLPs are typically "hard" optimization problems which appear in numerous applications (see [MINLPLib.jl](https://github.com/lanl-ansi/MINLPLib.jl)).
Alpine is entirely built upon [JuMP](https://github.com/jump-dev/JuMP.jl) and [MathOptInterface](https://github.com/jump-dev/MathOptInterface.jl) in Julia, which provides incredible flexibility for usage and further development.
Alpine globally solves a given MINLP by:
* Analyzing the problem's expressions (objective & constraints) and applies appropriate convex relaxations and polyhedral outer-approximations
* Performing sequential optimization-based bound tightening (OBBT) and an iterative MIP-based adaptive partitioning scheme via piecewise polyhedral relaxations with a guarantee of global convergence
Upon Alpine's convergence, for a given relative gap tolerance `ε`, the user is guaranteed that the global optimal solution is in the `ε`-neighborhood of the solution found by the solver.
## Installation
Install Alpine using the Julia package manager:
```julia
import Pkg
Pkg.add("Alpine")
```
## Usage with JuMP
Use Alpine with [JuMP](https://github.com/jump-dev/JuMP.jl) as follows:
```julia
using JuMP, Alpine, Ipopt, HiGHS
ipopt = optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0)
highs = optimizer_with_attributes(HiGHS.Optimizer, "output_flag" => false)
model = Model(
optimizer_with_attributes(
Alpine.Optimizer,
"nlp_solver" => ipopt,
"mip_solver" => highs,
),
)
```
## Documentation
For more details, see the [online documentation](https://lanl-ansi.github.io/Alpine.jl/latest/).
## Support problem types
Alpine can currently handle MINLPs with polynomials in constraints and/or in the objective. Currently, there is no support for exponential cones and Positive Semi-Definite (PSD) cones in MINLPs. Alpine is also a good fit for subsets of the MINLP family, for example, Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs), Non-Linear Programs (NLPs), etc.
For more details, check out this [video](https://www.youtube.com/watch?v=mwkhiEIS5JA) on Alpine.jl at [JuMP-dev 2018](http://www.juliaopt.org/meetings/bordeaux2018/).
## Underlying solvers
Though an MIP-based bounding algorithm implemented in Alpine is quite involved, most of the computational bottleneck arises in the underlying MIP solvers. Since every iteration of Alpine solves an MIP sub-problem, which is typically a convex MILP/MIQCQP, Alpine's run time heavily depends on the run-time of these solvers. For the best performance of Alpine, we recommend using the commercial solver [Gurobi](https://www.gurobi.com), which is available [free](https://www.gurobi.com/academia/academic-program-and-licenses/) for academic purposes. However, due to the flexibility offered by [JuMP](https://github.com/jump-dev/JuMP.jl), the following MIP and NLP solvers are supported in Alpine:
| Solver | Julia Package |
|--------------------------------------------------------------------------------|--------------------------------------------------------------|
| [Gurobi](http://gurobi.com/) | [Gurobi.jl](https://github.com/jump-dev/Gurobi.jl) |
| [CPLEX](https://www.ibm.com/analytics/cplex-optimizer) | [CPLEX.jl](https://github.com/jump-dev/CPLEX.jl) |
| [HiGHS](https://highs.dev/) | [HiGHS.jl](https://github.com/jump-dev/HiGHS.jl)
| [Cbc](https://projects.coin-or.org/Cbc) | [Cbc.jl](https://github.com/jump-dev/Cbc.jl) |
| [Ipopt](https://projects.coin-or.org/Ipopt) | [Ipopt.jl](https://github.com/jump-dev/Ipopt.jl) |
| [Bonmin](https://projects.coin-or.org/Bonmin) | [Bonmin.jl](https://github.com/jump-dev/AmplNLWriter.jl) |
| [Artelys KNITRO](http://artelys.com/en/optimization-tools/knitro) | [KNITRO.jl](https://github.com/jump-dev/KNITRO.jl) |
| [Xpress](https://www.fico.com/en/products/fico-xpress-optimization) | [Xpress.jl](https://github.com/jump-dev/Xpress.jl)
## Bug reports and support
Please report any issues via the GitHub [issue tracker](https://github.com/lanl-ansi/Alpine.jl/issues).
All types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc.
## Challenging Problems
We are seeking out hard benchmark instances for MINLPs. Please get in touch either by opening an issue or [privately](https://harshangrjn.github.io/#contact) if you would like to share any hard instances.
## Citing Alpine
If you find Alpine useful in your work, we kindly request that you cite the following papers ([PDF](http://harshangrjn.github.io/pdf/JOGO_2018.pdf), [PDF](http://harshangrjn.github.io/pdf/CP_2016.pdf))
```bibtex
@article{alpine_JOGO2019,
title = {An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs},
author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell and Sundar, Kaarthik},
journal = {Journal of Global Optimization},
year = {2019},
issn = {1573-2916},
doi = {10.1007/s10898-018-00734-1},
}
@inproceedings{alpine_CP2016,
title = {Tightening {McCormick} relaxations for nonlinear programs via dynamic multivariate partitioning},
author = {Nagarajan, Harsha and Lu, Mowen and Yamangil, Emre and Bent, Russell},
booktitle = {International Conference on Principles and Practice of Constraint Programming},
pages = {369--387},
year = {2016},
organization = {Springer},
doi = {10.1007/978-3-319-44953-1_24},
}
```
If you find the underlying piecewise polyhedral formulations implemented in Alpine useful in your work, we kindly request that you cite the following papers ([link-1](https://doi.org/10.1016/j.orl.2020.12.002), [link-2](http://www.optimization-online.org/DB_HTML/2022/07/8974.html)):
```bibtex
@article{alpine_ORL2021,
title = {Piecewise polyhedral formulations for a multilinear term},
author = {Sundar, Kaarthik and Nagarajan, Harsha and Linderoth, Jeff and Wang, Site and Bent, Russell},
journal = {Operations Research Letters},
volume = {49},
number = {1},
pages = {144--149},
year = {2021},
publisher = {Elsevier}
}
@article{alpine_OptOnline2022,
title={Piecewise Polyhedral Relaxations of Multilinear Optimization},
author={Kim, Jongeun and Richard, Jean-Philippe P. and Tawarmalani, Mohit},
eprinttype={Optimization Online},
date={2022}
}
```