Numerical Optimization Solver development

Focus on Mixed Integer Second Order Cone Programs (MISOCP) and Mixed Integer convex nonlinear programs (convex MINLP)

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Artelys is an international company based in France (HQ), with offices in Brussels (Belgium), Chicago (US) and Montréal (Canada).  Artelys is specialized in optimization, decision-making and modeling. Relying on their high level of expertise in quantitative methods, Artelys’ consultants deliver efficient solutions to complex business problems. They provide services to numerous industries: Energy & Environment, Logistics & Transportation, Telecommunications, Finance, Defense, etc.

Artelys offers a wide variety of services, including software solutions (optimization solvers, business specific solutions & specific software developments), consulting, project management assistance, training, etc. For instance, Artelys develops Knitro, a state-of-the-art nonlinear optimization solver, and also the Artelys Crystal software suite which addresses specific business problems (especially in the energy sector and planning) including optimization and visualization tools.

The company was founded with an ambition to provide sound quantitative analysis for daily business decisions and its reputation and growth rely on a number of key values such as competence and experience, commitment to deliver and client satisfaction.


Artelys Knitro is a state-of-the-art nonlinear optimization solver. It addresses all classes of optimization problems with very high performances and versatility. The solver is in permanent development and more features as well as problem specializations are regularly added to the solver, improving its performances steadily over the years.

Artelys has a major part of its activities in Power Systems modelling and optimization. The problem arising in Power Systems network, namely Optimal Power Flow (OPF) problems, are a very challenging class of nonlinear optimization programs for existing optimization solvers. Being able to efficiently solve OPF is critically important for the safe and efficient operation of electric power systems. This problem is becoming even more crucial (and complex) with the increasing integration of renewable energy sources and distributed storage. The nonlinear optimization solver Artelys Knitro is highly efficient at tackling such nonlinear problems. Other industrially relevant problems appear in the optimal management and design of water, oil and gas networks.

Recently, promising approaches have been proposed for solving the Alternating Current OPF problems in transmission networks by means of Sum-Of-Squares (SOS) relaxations, SOS techniques provide a global optimum of the network optimization problem along with a global optimality certificate, which is more valuable from the perspective of a Transmission System Operator. Other methods based on conic optimization have been explored by academic researchers in the case of transmission and distribution networks.

Yet, these problems are still difficult to solve to (global) optimality when integrating all of the desired parameters. For instance, the AC optimal transmission-switching problem involves mixed-integer constraints and can be turned into a mixed-integer SOCP. Network design and transmission expansion planning problems typically involve binary variables. This class of problems is handled by means of Branch-and-Bound algorithms, in which convex or linear relaxations are solved for every node.

In the case of optimal power flow problems, it has been observed that piecewise linear relaxations may fail at providing good performance. Therefore, the use of polynomial relaxations for deriving strong lower bounds is a promising research direction.

The purpose of the engineer will be to develop novel practical algorithms for solving mixed-integer nonlinear programs arising in power systems optimization with a particular focus on MISOCP and problems arising from polynomial relaxations.

As part of a young and dynamic high-level R&D IT team, your mission will be to:

  • Design and develop various decision support functions and optimization models
  • For a given problem, study the state of the art and enumerate, prototype and compare various resolution methods (exact or approximate, relaxations, branch-and-bound, branch-and-cut, mixed integer variables, complementarities, constraint programming, etc.)
  • Design and implement the chosen solutions, with a strong requirement for reliability and numerical efficiency
  • Integrate and test these features into the nonlinear optimization solver Artelys Knitro

The candidate will also integrate the POEMA network and have the opportunity to participate in the network activities.


The candidate must have a master’s degree in computer science and/or applied mathematics. You should have a solid background in Operations Research. You are curious and enthusiast to exploit your computer development skills and your knowledge of optimization research.

Operational on various contexts and real issues. Rigorous and passionate, you show initiative and imagination and already have an ease in programming in programming and scientific languages (C/C++, Python, R, Julia).

The candidate should be fluent in English. Knowledge of French is an asset.


The position is funded under the H2020-MSCA-ITN-2018 call and is part of the Marie Sklodowska-Curie Actions — Innovative Training Networks (ITN) funding scheme. Specific degree and mobility conditions apply in relation to this grant:

  • Have — at the date of recruitment — a Master’s degree in Computer Science, Mathematics or Engineering (or any equivalent diploma).
  • Should have — at the date of recruitment — less than 4 years of a research career, and not have a doctoral degree. The 4 years are measured from the date when they obtained the degree which would formally entitle them to embark on a PhD.
  • Trans-national mobility: The applicant — at the date of recruitment — should not have resided in France for more than 12 months in the 3 years immediately prior to recruitment, and not have carried out their main activity (work, studies, etc.) in that country.

The duration of the job is until 31/12/2022 in our Paris office.


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