Learning Outcomes
The implementation of numerical optimization in mechanical, manufacturing and process systems. Major emphasis is given in the optimization problem formulation using a single or multiple criteria using gradient based methods and non-gradient probabilistic methods.
General Competences
Apply knowledge in practice
Retrieve, analyse and synthesise data and information, with the use of necessary technologies
Adapt to new situations
Make decisions
Work autonomously
Work in teams
Work in an interdisciplinary team
Generate new research ideas
Appreciate diversity and multiculturality
Demonstrate social, professional and ethical commitment and sensitivity to gender issues
Be critical and self-critical
Advance free, creative and causative thinking
Course Content (Syllabus)
Optimization problem formulation
Decision hierarchy, selection of criteria, decision variables (continuous, discrete), mathematical model formulation, constraints, parameters
Applications (1st Assignment):
Manufacturing: Mechanical system model development
Energy: Thermal process model development.
Industrial management: Supply chain modellig.
Numerical Optimization (gradient-based)
Unconstrained and Constrained problems
Linear and non-linear programming
Linear and non-linear integer programming
Solution of optimality conditions, Optimal solution sensitivity
Applications (2nd Assignment) – Continuous decision variables (3rd Assignment) – Continuous and discrete decision variables
Manufacturing: Mechanical system optimization.
Energy: Heat exchanger network optimization.
Industrial management: Supply chain optimization.
Optimization using probabilistic methods (non-gradient methods)
Simulated annealing, genetic algorithms.
Applications (4th Assignment) – Implementation of probabilistic optimization methods
Manufacturing: Mechanical system optimization.
Energy: Heat exchanger network optimization.
Industrial management: Supply chain optimization.
Multi-objective optimization
Pareto front. Numerical optimization of multi-objective optimization problems.
Applications (5th Assignment) – Implementation of multi-objective optimization methods
Manufacturing: Mechanical system optimization.
Energy: Heat exchanger network optimization.
Industrial management: Supply chain optimization.
Optimization under uncertainty
Uncertainty characterization – Problem formulation and solution
Applications (6th Assignment) – Implementation of optimization methods under uncertainty.
Manufacturing: Mechanical system optimization.
Energy: Heat exchanger network optimization.
Industrial management: Supply chain optimization.
Optimization of dynamic problems
Time discretization. Decision vector parameterization. Numerical solution (direct methods, sequential method, multiple shooting)
Applications (4th Assignment) – Implementation of dynamic optimization methods.
Manufacturing: Mechanical system optimization.
Energy: Heat exchanger network optimization.
Industrial management: Supply chain optimization.
