[PhD proposal 2021] Meta-modelling for multi-scale global optimization for process synthesis problems


Team OPTIMIST, Loria
Supervisor : Bernardetta ADDIS (HDR)


Global optimization, mathematical programming, black-box optimization


Many optimization problems arising from real applications ask for optimizing the design (and the management) of physical systems to attain a given objective in terms of quality of the product or overall gain/costs. An emblematic example is the optimization problems arising from process synthesis.

“Process synthesis is the assembly and interconnection of units into a process network – involving different physical and chemical phenomena to transform raw material and energy inputs into desired outputs – with the goal of optimizing economic, environmental, and/or social objectives” (from [1])

The challenge in applying optimization to process synthesis is two-fold:

  • determine/derive correct models representing the overall system
  • develop efficient optimization methods to optimize the proposed models.

These two steps are strictly interlaced. Indeed, the chosen model will highly influence the efficiency of the optimization method and which kind of methods can be used to solve the problem.
If the model is a “classical” mathematical programming one, then state-of-the-art solvers, or math-heuristics based on them, can be used. On the contrary, if the model is a black-box one (in the case of data coming from a simulator or experiments), derivative-free methods can be more suitable.

The major difficulty in solving process synthesis problems is related to two different aspects. First, process synthesis represents a large family of problems, that are very different from each other. Secondly, even considering a specific case, the complexity of the overall system is quite impressive.

These features prevent having a unified strategy to solve these problems. Furthermore, even if models for specific cases exist, they are often not enough detailed to be of practical use.

In the current state of the art, different decomposition strategies are present. These approaches are of two types:
the ones based on different scales of the system [1,2], from a high level/simplified representation to reach rigorous models,
the ones considering the process as composed of interconnected functional units [3,4].

The main idea of the thesis is to combine these two decomposition strategies to take advantage of the already existing knowledge on solving some specific process synthesis problems and, at the same time, to keep the size and complexity of the sub-problems reasonable for the current state-of-the-art solvers, without losing the necessary level of detail.

The work of the thesis will focus from some specific case studies to develop a meta-modeling framework to consider both decomposition strategies. The interconnection will be possible between sub-blocks of possibly different scales (grid connectivity). This meta-model will be the base to build upon a global optimization strategy.

The global optimization strategy will “autonomously” decide which parts of the meta-model optimize and which scale use for each of them. Using machine learning techniques to guide the search process are a promising perspective, as already shown by some recent research both in global optimization [5] and in discrete optimization [6].


Excellent programming skills
Good mathematical programming and optimization knowledge

non-linear optimization

Desired (but not compulsory):
global optimization
knowledge of the pyomo library

The candidate must be fluent in English (thesis in collaboration with Italy).


[1] Qi Chen and I.E. Grossmann. Recent developments and challenges in optimization-
based process synthesis. Annual Review of Chemical and Biomolecular Engineering,
8(1):249–283, 2017. PMID: 28375774.

[2] Lorenz T. Biegler, Yi dong Lang, and Weijie Lin. Multi-scale optimization for
process systems engineering. Computers & Chemical Engineering, 60:17 – 30, 2014.

[3] Ligang Wang, Philip Voll, Matthias Lampe, Yongping Yang, and André Bardow.
Superstructure-free synthesis and optimization of thermal power plants. Energy,
91:700 – 711, 2015.

[4] Thibaut Neveux. Ab-initio process synthesis using evolutionary programming.
Chemical Engineering Science, 185:209 – 221, 2018.

[5] A. Cassioli, D. Di Lorenzo, M. Locatelli, F. Schoen, and M. Sciandrone. Ma-
chine learning for global optimization. Computational Optimization and Applications,
51(1):279–303, Jan 2012.

[6] Andrea Lodi and Giulia Zarpellon. On learning and branching: a survey. TOP,
25(2):207–236, Jul 2017.

How to apply

Deadline: May 25, 2021 (midnight Paris time)

Applications must be sent as soon as possible.
Send a file with the following documents:

  • Your CV;
  • A cover letter/motivation letter describing your interest in this topic;
  • A brief description (one-page maximum) of your Master’s thesis (or equivalent) or work in progress if not yet completed;
  • Your diplomas and transcripts for the Bachelor’s and Master’s degrees (or the last 5 years);

In addition, a letter of recommendation from the person who supervised or has supervised your Master’s thesis (or research project or internship) is welcome.

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