## 5 Boom Configuration Optimization
### Optimization Approaches
#### 5.2.1 Heuristic Optimization Approach  
We here describe the developed heuristic optimization procedure for achieving a (near) optimal boom configuration. This is pursued in a three-step manner, as illustrated in Figure 5.  
In Step 1, only stress and fatigue are considered, buckling is considered separately in Step 2. This separation is possible since stress and fatigue only rely on the metal thicknesses, but not the stiffeners. For buckling, both thicknesses and stiffeners have to be taken into account. The first two steps operate solely on the segments: In these steps, the segments are considered to be completely independent of each other. In the case of a violation in the structural utility constraints, this independence assumption enables the enumeration of all of the more stable (i.e., thicker and/or more stiffeners) bottom/side/top segment configurations separately and to order them by segment costs to select for each bottom, side, and top the next cheapest segment configuration to update the boom configuration. Only in the third step the costs are optimized also including the welding costs of the boom (i.e., only here the complete objective function of Equation (4) is used). We next describe of each of the three steps. Note that the constraints in Equations (8) to (10) as well as in Equations (12) and (13), defining the admissible values of the plate thicknesses and the number of stiffeners, are fulfilled at any time, since the values are chosen in accordance with these sets. (1). Fulfilling utility of stress and fatigue (constraints in Equations (5) and (6))  
The optimization starts with an initial boom configuration, typically the cheapest possible one, i.e., no stiffeners and minimum plate thicknesses for each segment. The configuration is evaluated using the structural analysis tool. If the utilization of stress or fatigue is greater than one on the bottom, side or top of any segment, the respective segment configuration (and with it the boom configuration) is adapted by increasing the corresponding thickness to the next higher value. Whenever the number of stiffeners is larger than zero, it is set back to zero. The resulting boom configuration is then tested with the structural analysis tool. This process is repeated until no violations in the constraints of stress and fatigue are found, such that the procedure can continue with Step 2. In this step, no explicit cost evaluation is needed, since the thicknesses are only changed to the next higher value, which naturally is the next cheapest option. Note, however, that it might be possible that not all violated constraints of stress and fatigue would be necessary to be adapted simultaneously. It could be possible that it had been enough, e.g., to increase the value of one segment and reach no violation also for the consecutive segment, or to increase only certain values on the bottom and top and reach no violation on the sides. This, however, would yield an explosion of possibilities and thus of run time. Thus, in the heuristic, these values are increased simultaneously for all bottom, side, and top segments, where a violation occurred. This comes at a cost: the global optimum might be missed. (2). Fulfilling utility of buckling (constraint in Equation (7))  
The second step is divided into two sub-steps. (a). Taking constraints of Equations (11) and (14) into account  
Figure 5: Three-step heuristic optimization approach. Considering the boom configuration output of Step 1, if there are any violations in the utilization of buckling, or non-increasing plate thicknesses or the number of stiffeners, the boom configuration is updated as follows. For each segment \(i+1\) (i.e., starting from the segment closest to the head end), it is verified whether the thickness and/or the number of stiffeners of bottom, side or top is higher than the previous segment \(i\). If so, the respective thickness and/or the number of stiffeners of segment \(i+1\) is set to that value of segment \(i\).