Multi-objective optimization for power markets

Why join Artelys?

Artelys is a company specialized in mathematical optimisation, quantitative decision-making, and scientific modeling. Relying on its high-level expertise in quantitative methods, Artelys delivers efficient solutions to complex business problems and provides services to numerous industries: energy, transportation, telecommunications, manufacturing, etc. Artelys is an international company with offices in France, Canada, Belgium, Spain and the USA.

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 Artelys Knitro, a state-of-the-art solver for nonlinear and mixed-integer nonlinear optimization. Artelys is one of the major partners of FICO who develops FICO® Xpress Optimization which includes the world’s foremost mathematical modeling / programming language and a full range of powerful optimization engines.

internship description

The TERRE project (Trans-European Replacement Reserves Exchange) aims at developing an IT platform for the market clearing of services exchanged between the European producers and transmission systems operators. Artelys is responsible for providing the platform’s market clearing engine. The algorithm goes through the resolution of complex and large mathematical optimization problems, which take into account the offers of the various suppliers, balancing requests and fairness goals between the actors. Receiving and matching bids and demands every hour of the day, the robustness and performance of the optimization engine are very strongly constrained: results are to be provided within 3 minutes for a problem containing up to 500,000 offers – including complex offers.

The problem is formulated as several mixed integer linear program and mixed integer quadratic programs. The main objectives of these problems include a set of market rules that are implemented as soft constraints with different priorities, such as the maximization of the economic surplus, the cross-border flow minimization or the maximization of the traded volume.  These market rules are defined in the objective function in order to maximize their satisfaction with an associated penalty in case of constraint violation. In other words, the problem solved is a multi-objective optimization problem with lexicographic ordering between the objectives.

Current approach requires to sequentially solve several very similar optimization problems. We would like to explore other options. Especially, using properties of the simplex algorithm, “efficient pivots” could be used to embed these objectives into a single problem and solve it efficiently. FICO® Xpress Optimization has recently released a feature supporting such pivoting when using its multi-objective optimization API. The goal of the internship is to modify the market clearing algorithm in order to exploit this new feature and benchmark it with respect to performance, solutions quality and robustness.


The candidate must be in his/her last year of master’s degree in computer science and/or applied mathematics with a solid background in Operations Research. An interest in power systems and energy markets will be strongly appreciated.

Required skills: 

  • Knowledge of linear and mixed-integer linear programming
  • Knowledge of mixed-integer programming solvers
  • Knowledge of Java or Python
  • Appreciated competence:

  • Interest in programming
  • Interest in energy markets and general energy field
  • Knowledge of mathematical modelling and optimization languages
  • Fluent in French

    The duration of the internship is 6 months. The internship will take place in our Paris or Lyon offices. The internship may lead to a long-term job offer.


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