# Multi-Objective Combinatorial Optimization

**URL:** https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604
**Category:** Optimization (Mathematical)
**Tags:** question
**Created:** [May 8, 2017, 8:57pm UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604 "2017-05-08T20:57:56Z")
**Posts on this page:** 5
**Page:** 1

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### Author: ![KrishnaKanhaiya](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/krishnakanhaiya/32/443_2.png) [@KrishnaKanhaiya](https://discourse.julialang.org/u/KrishnaKanhaiya)
#### Post date: [May 8, 2017, 8:57pm UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604/1 "2017-05-08T20:57:56Z")

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I have a problem statement where I have to maximize multiple (2 or more than 2) objective functions simultaneously and the some of the variables involved are discrete whereas the remaining are continuous. Is there any julia pacage that can fulfill my needs?

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### Author: ![jkbest2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jkbest2/32/7350_2.png) [@jkbest2](https://discourse.julialang.org/u/jkbest2)
#### Post date: [May 9, 2017, 6:09am UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604/2 "2017-05-09T06:09:28Z")

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The [JuliaOpt](http://www.juliaopt.org/) organization is a good place to start for anything optimization-related in Julia. They provide interfaces to a number of standard solvers for linear, mixed and higher-order programs. I’ve never used it, but [MultiJuMP.jl](https://github.com/anriseth/MultiJuMP.jl) looks like something you might be interested in. It doesn’t appear to be part of JuliaOpt, but builds on their interface and model-building interface.

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### Author: ![adowling2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/adowling2/32/539_2.png) [@adowling2](https://discourse.julialang.org/u/adowling2)
#### Post date: [May 10, 2017, 4:18pm UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604/3 "2017-05-10T16:18:02Z")

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I have solved some mixed integer (combinatorial) multi-objective optimization problems in the past using Julia and JuMP.

Paper:  
[http://www.sciencedirect.com/science/article/pii/S0098135416300965](http://www.sciencedirect.com/science/article/pii/S0098135416300965)

Julia code for all of the examples in the paper:

> <https://github.com/zavalab/JuliaBox/tree/master/MultiStakeholder>
>
> //github.com/zavalab/JuliaBox/tree/master/MultiStakeholder

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### Author: ![miles.lubin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/miles.lubin/32/279_2.png) [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)
#### Post date: [May 10, 2017, 9:11pm UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604/4 "2017-05-10T21:11:55Z")

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> [@adowling2](#):
>
> I have solved some mixed integer (combinatorial) multi-objective optimization problems in the past using Julia and JuMP.
> 
> Paper:  
> [http://www.sciencedirect.com/science/article/pii/S0098135416300965](http://www.sciencedirect.com/science/article/pii/S0098135416300965)

Where’s the citation to JuMP? 🙂

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### Author: ![adowling2](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/adowling2/32/539_2.png) [@adowling2](https://discourse.julialang.org/u/adowling2)
#### Post date: [May 10, 2017, 9:24pm UTC](https://discourse.julialang.org/t/multi-objective-combinatorial-optimization/3604/5 "2017-05-10T21:24:43Z")

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Oops. We included the JuMP citation is our subsequent papers.
