Complements of Operational Research

Recommended Prerequisites

Linear Algebra, Calculus, Fundamentals of Operational Research.

Teaching Methods

Theoretical and methodological concepts are presented in tutorial lectures, being motivated by real-world problems and illustrated with application examples.
Software (commercial and public domain) packages are used to obtain solutions to the mathematical models, thus freeing the students for the more creative tasks of problem formulation, model building and critical analysis of results.
Assignments will be offered, involving the development of mathematical models for a real-world problem and the generation of the optimal solutions or the characterization of the nondominated frontier.

Learning Outcomes

Providing the students with methodological and application competences in the context of optimization in engineering problems, enlarging the range of problems addressed in Fundamentals of Operational Research, in particular by considering integer variables and multiple objective functions in optimization problems. In addition, meta-heuristic approaches are introduced to deal with complex optimization problems, in particular of combinatorial and/or nonlinear nature.

Work Placement(s)

No

Syllabus

1.Integer programming (IP). Applications of IP. IP models. Use of binary variables in mathematical programming models. Methods to solve IP problems. The "branch-and-bound" algorithm. IP with binary variables. The Balas’ algorithm. The 0-1 knapsack problem. Problem reformulation. Stability of the optimal solution in IP models.
2. Multi-objective linear programming. Revisiting the goal programming model. Concepts of non-dominated solutions. Scalarization processes. Interactive methods. The STEM method. The Interval Criterion Weights method. Multiobjective programming with integer variables. Supported and unsupported nondominated solutions.
3. Meta-heuristics in optimization problems. Tabu search. Simulated annealing. Genetic algorithms. Main steps of a genetic algorithm. Genetic operators. Particle swarm optimization. Differential evolution.

Head Lecturer(s)

Rita Cristina Girão Coelho da Silva

Assessment Methods

Assessment
Mini Tests: 20.0%
Exam: 80.0%

Bibliography

-Hillier, F. S., G. J. Lieberman. Introduction to Operations Research, McGraw-Hill, (11^th ed.), 2021.

- Henggeler Antunes, C., M. J. Alves, J. Clímaco. Multiobjective Linear and Integer Programming, EURO Advanced Tutorials on Operational Research, Springer, 2016.

- Clímaco, J., C. H. Antunes, M. J. Alves. Programação Linear Multiobjectivo, Imprensa da U. de Coimbra, 2003.

- Michalewicz, Z., D. B. Fogel. How to Solve It: Modern Heuristics, Springer (2^nd ed.), 2004.

- Gaspar-Cunha, A., R. Takahashi, C. H. Antunes (Coord.). Manual de Computação Evolutiva e Meta-heurística“, Imprensa da U. de Coimbra, 2012.

-Hillier, F., M. Hillier. Introduction to Management Science and Business Analytics: A Modeling and Case Studies Approach with Spreadsheets (7th ed.), McGraw-Hill, 2023.

-H. A. Taha, Operations Research: An Introduction (11th edition), Pearson, 2023.

-R. C. Oliveira, J. S. Ferreira. Investigação operacional em ação: casos de aplicação. Imprensa da U. de Coimbra, 2014.