Optimization Methods and Artificial Intelligence

1. Introduction 1.1. Formulation of the optimization problem. Linear-, quadratic- and non-linear programming. 1.2 Constraints in equality and inequality form.
2. Linear planning 2.1. Solution of linear plenning problem. The simplex method. 2.2. Dual problem, optimality conditions. 2.3. Transportation problem. 2.4. Integer programming. Methods of cutting planes.
3. Gradient methods. 3.1.Steepest descent method. 3.2. Newton method 3.3 Quasi Newton and Gauss-Newton methods. 3.4. The Kuhn-Tucker condtions 3.5. The Langrange multipliers method
4. Utilizing artificial intelligence in optimization
5. Global optimization techniques. Population methods. 5.1. Genetic algorithm. 5.2. Particle swarm optimization. 5.3. Ant colony optimization. 5.4. Local search 5.4.1. Hill Climbing 5.4.2. Simulated annealing 5.4.3 Tabu search
6. Hybrid algorithms 6.1. GA+Gradient 6.2. GA+local search
7. Function approximation, responce surface. 7.1. Artificial neural networks 7.2. Least square method
8. Multicriteria optimization 8.1. Pareto concept 8.2.Combining optimality criteria
9. Sensitivity analysis.

NB! This course will take place in autumn semester 2024/2025 which starts on 2nd of September and ends 26th of January (you can find that information under Start date section). The real course start and end dates will be announced at the beginning of September at the latest.

After completing this course, the student:

• applies traditional optimization methods in engineering;
• adjusts and applies global optimization methods and integer programming tools;
• adjusts and applies hybrid and local search algorithms in engineering;
• applies multicriteria optimization methods;
• adjusts and applies artificial intelligence algorithms in optimization;
• applies optimization software tools;
• applies sensitivity analysis for solving engineering problems.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

Optimization course covers different topics/areas like: AI, Stat. Mechanical engineering, Risk Analysis.

• 1. Singiresu S Rao, Engineering Optimization Theory and Practice, Fifth Edition
• 2020 John Wiley & Sons, Inc, DOI:10.1002/9781119454816
• 2. Joaquim R. R. A. Martins Andrew Ning,Engineering Design Optimization, 2022
• 3. Amir H. Gandomi and Laith Abualigah , Eds., Evolutionary Process for Engineering Optimization,
• 2022, 286p, https://doi.org/10.3390/books978-3-0365-4772-5

lectures, practices