Making decisions despite uncertainty thanks to stochastic optimization
Stochastic? Borrowed from ancient Greek, this word comes from the Greek stokhastikos, which means “conjectural.” In mathematics, it refers to anything based on chance or probability.
Everyone makes decisions under uncertainty. Should we take an umbrella, invest our savings, or plan a long trip? These choices are made without knowing for sure what the future holds. In industry, and particularly in the energy sector, these uncertainties are multiplied. Fluctuating demand, volatile prices, irregular production linked to renewable energies…
Operators must constantly adapt. This is where stochastic optimization comes in, a mathematical discipline that models complex problems in which some data is not known in advance but is described by probability laws.
In other words, no one tries to predict exactly what will happen: the aim is to make the best decision on average, or to control risks to an acceptable level, given what could happen.
Planning the electricity system
Every day, energy operators have to decide how much electricity to produce tomorrow, next week or in six months’ time. These decisions involve committing resources (thermal power plants, dams, renewable energies, etc.) but also anticipating random events: a heatwave, soaring gas prices, a wind turbine spinning slower than expected, etc.
For example:
- A hydroelectric power plant that releases water today affects the potential output of downstream power plants tomorrow (this is known as temporal and spatial coupling).
- The growing share of renewable energies, which are more difficult to predict, reinforces the importance of dynamic and flexible production management.
- Demand varies according to the season, the day of the week, social behavior, and other factors.
In this context, stochastic optimization makes it possible to create mathematical models that take all these factors into account and to derive robust strategies, i.e., strategies that will work well even if future conditions prove unfavorable.
The Center for Applied Mathematics, bridging theory and practice
The Center for Applied Mathematics (CMA) at Mines Paris – PSL is a recognized player in the field of optimization. Welington de Oliveira develops approaches ranging from the most fundamental mathematical optimization theory to cutting-edge algorithms. He also contributes to the scientific community by serving on the editorial boards of prestigious journals in the field of mathematical optimization.
Working with industrial players in the energy sector, he leads CIFRE (Conventions Industrielles de Formation par la Recherche) thesis projects in which doctoral students work at the interface between science and industry. Collaboration between academia and industry makes it possible to answer complex and concrete questions, such as:
- How can the expansion of a gas or electricity network be planned in an uncertain context?
- How can investments in energy infrastructure be made while controlling financial risks?
- How can a system as vast as an oil supply chain or a natural gas distribution network be modeled?
Proof of this fruitful collaboration can be found in the publication of Methods of Nonsmooth Optimization in Stochastic Programming, a scientific work co-authored with Wim van Ackooij, a researcher at EDF. This book perfectly illustrates the dual focus of this research, which is both academic and industrial.
Algorithms for solving large-scale problems
While stochastic optimization equations can be elegantly formulated, solving them is another matter entirely. The problems are often:
- Very large: with thousands or even millions of variables to take into account.
- Non-convex: they can have several “valleys” and “peaks,” making it difficult to find an overall optimum.
To meet these challenges, Welington de Oliveira and his colleagues are designing specialized algorithms capable of guaranteeing reliable results within reasonable time frames. These methods are known as “convergence-guaranteed”: they ensure that, even in a complex environment, the best possible solution will eventually be found.
Mathematics for research with a double impact: science and industry
The value of this work goes beyond the performance of the algorithms. It lies above all in the concrete impact on the energy strategy of a player such as EDF. Thanks to these tools, it becomes possible to:
- Better anticipate peaks in consumption or production.
- Optimize investments in new infrastructure.
- Reduce costs related to uncertainty.
- Strengthen the robustness of decisions in the face of climate or geopolitical change.
The project led by Welington de Oliveira perfectly illustrates the approach of Mines Paris – PSL at Mines Paris Research Day: promoting research that combines academic excellence and industrial application.
By combining the most advanced mathematical knowledge with the real needs of industry, this collaboration with EDF demonstrates the potential of dual-impact research.
Stochastic optimization is not an abstract discipline reserved for mathematicians alone. It is an essential lever for building the energy systems of tomorrow, capable of responding to ever more numerous and uncertain challenges.
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