2 Chapter 3Table 3.1. Table constructed to solve the problemTable 3.2. List of n objectsTable 3.3. Results of the recursive formulaTable 3.4. Demand and purchase pricesTable 3.5. Solution of the stock problem

3 Chapter 4Table 4.1. Characteristics of the random variables for the concrete beamTable 4.2. Results obtained with the FORM method for the concrete beam

4 Chapter 6Table 6.1. Material properties

5 Chapter 7Table 7.1. Results calculated with MatlabTable 7.2. Solution calculated with Matlab

6 Appendix 3Table A3.1. Optimization problems supported by the optimization toolbox

List of Illustrations

1 Chapter 1Figure 1.1. Bounded polyhedron (left) and unbounded polyhedron (right). For a co...Figure 1.2. Graphical solution. For a color version of this figure, see www.iste...Figure 1.3. Graphical solution with isoprofit lines. For a color version of this...

2 Chapter 2Figure 2.1. Branch-and-bound method Figure 2.2. Branch-and-cut methodFigure 2.3. Matrix A

3 Chapter 3Figure 3.1. Different cities. For a color version of this figure, see www.iste.c...Figure 3.2. DAG representing the dependencies between the different subproblems ...Figure 3.3. Level-dependent multilevel DAG for the shortest path problem. For a ...Figure 3.4. Level-independent multilevel DAG for the shortest path problem. For ...Figure 3.5. Graph corresponding to this problemFigure 3.6. Graph constructed from this problemFigure 3.7. Decision-chance tree for the insurance contract problem. For a color...Figure 3.8. Binary search tree for set A. For a color version of this figure, se...Figure 3.9. Five possible binary trees for list S. For a color version of this f...

4 Chapter 4Figure 4.1. Constructing a scenario tree. For a color version of this figure, se...Figure 4.2. Example of a tree structure. For a color version of this figure, see...Figure 4.3. Geometric representation of β_HL for a problem with two random variab...Figure 4.4. Most probable failure point. For a color version of this figure, see...Figure 4.5. Illustration of FORM. For a color version of this figure, see www.is...Figure 4.6. Diagram of the beam on simple supports of reinforced concrete

5 Chapter 5Figure 5.1. Different possible trips. For a color version of this figure, see ww...Figure 5.2. Problem with 85,900 towns. For a color version of this figure, see w...Figure 5.3. Various solving methodsFigure 5.4. Traveling salesman’s route through n townsFigure 5.5. VRPFigure 5.6. Final tour of the traveling salesman. For a color version of this fi...

6 Chapter 6Figure 6.1. Graphical solution. For a color version of this figure, see www.iste...Figure 6.2. Identification processFigure 6.3. Force/elongation for different optimization steps and plastic deform...

7 Chapter 7Figure 7.1. Methodology for optimizing structures modeled by finite elementsFigure 7.2. PlateFigure 7.3. Shape of the plate. For a color version of this figure, see www.iste...Figure 7.4. Optimized plate. For a color version of this figure, see www.iste.co...Figure 7.5. Triangular plateFigure 7.6. Initial and optimal shape. For a color version of this figure, see w...Figure 7.7. Position of the local optimum. For a color version of this figure, s...Figure 7.8. Graphs of the functions f and g. For a color version of this figure,...Figure 7.9. Contours of the functions f and g. For a color version of this figur...

8 Appendix 3Figure A3.1. Window that opens when calling optimtool. For a color version of th...Figure A3.2. Applications in the Optimization Toolbox