internship

Heuristics for Mixed-Integer Nonlinear Programming

Heuristics and algorithms for Mixed-Integer nonlinear programs.

why join artelys?

Artelys implements quantitative decision support solutions, using mathematical decision support models and algorithms: statistics, data analysis, artificial intelligence, numerical optimization and operations research. Our activities applied to the key sectors of Energy, Transport, Mobility, Health and more generally to the public sector place Artelys as a key player in the ecological transition through the support and advice it provides to private companies and public institutions.

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.

Description

This internship focuses on solving mixed-integer nonlinear problems (MINLP). A major challenge when solving such problems is the ability to quickly compute good solutions. A key to getting such solutions and improve the resolution time is heuristics executed during the branch-and-bound search. Knitro already includes a large number of heuristics (feasibility pump, complementarity constraints, rounding, diving, etc.)

The internship will focus on one of the following subjects:

Study the state of the art and design, implement and benchmark new heuristics for MINLP.

Investigate algorithms and heuristic techniques for globalization in order to find a global optimum (or a better local optimum) on non-convex models.

The developed algorithms will be tested on various Mixed-Integer nonlinear programming applications from the literature in particular in the energy field with hydro energy system scheduling, gas transmission and compression, power system or water network optimization.

what we are looking for

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.

Required skills:

Knowledge of discrete optimization techniques, heuristics and meta-heuristics

Programming in C and C++

Fluent in English

Additional relevant skills:

Knowledge of convex optimization and nonlinear programming

Knowledge of linear and mixed-Integer linear programming

Combinatorial optimization, graph theory, computational complexity

Skills in algorithms design and implementation

Programming in Python, R, Java

Fluent in French

Benefits

The intership will take place in our Paris office and may lead to a long-term job offer.

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