Complements of Operational Research

Academic year
Subject Area
Advanced Computational Methods
Language of Instruction
Other Languages of Instruction
Mode of Delivery
ECTS Credits
2nd Cycle Studies - Mestrado

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.

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 of combinatorial nature

Work Placement(s)



1. Integer programming (I). 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. Multiobjective programming with integer variables.

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

Mini Tests: 20.0%
Exam: 80.0%


- Hillier, F.S., G.J. Lieberman. "Introduction to Operations Research", McGraw-Hill, 2010.


- Bronson, R., G. Naadimuthu. "Investigação Operacional", Colecção Schaum, McGraw-Hill Portugal, 2001.


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


- Michalewicz, Z., D.B. Fogel. "How to Solve It: Modern Heuristics", Springer, 2002.


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


- Chang, Y.L. "WinQSB, Decision Support Software for M/OM (v. 2.0)", Wiley, 2003.


- Oliveira, R., J. S. Ferreira (Coord.), “Investigação operacional em ação: casos de aplicação”, Imprensa da Universidade de Coimbra, 2014.


- Antunes, C.H., M.J. Alves, J. Clímaco. “Multiobjective Linear and Integer Programming”, EURO Advanced Tutorials on