# Decision-Maker's Preference-Driven Dynamic Multi-Objective Optimization
## 3 Experimental Setup
### Algorithm Setup
#### 3.1.1 Decision-Maker's Preference Incorporation  
The different procedures and how they are used with a DMOA for the preference-driven search process are presented in Figure 1. Before the normal run of the DMOA starts, the a priori preference incorporation procedure is used to define the DM's preference. During the run of the DMOA, any of the constraint managing approaches can be used. If a small environment change occurs, the DMOA's change response approach is executed during the normal DMOA run. However, if the change is large, requiring a change in the boundary box placement, the interactive preference incorporation procedure is first completed before the DMOA's change response approach is executed during the normal DMOA run. A Priori Preference Incorporation: A single run of the algorithm is executed. A series of POFs is presented to the DM. The DM selects one of these POFs, and then selects one of the points on the POF, which will become his \(\mathbf{x}_{p}\) and \(\mathbf{p}\), i.e., the preferred decision/solution vector and the preferred outcome, respectively. This preference, together with the radius of the bounding box specified by the DM during the bootstrap procedure (refer to Algorithm 3), is used to drive the DMOA's search to optimize the DMOA's under the constraints of the DM's preferences. The time complexity of the bootstrap procedure is similar to the time complexity of the DMOA that is used to produce the POSs. ```
1:procedureBootStrap(freq, severity, iteration, F)
2: Call DMOA(freq, severity, iteration, F)
3:\(\triangleright\) DMOA returns \(\{\text{POS}_{t}^{k}\}\), \(\forall k=1,\ldots,n\)
4:\(\triangleright\) where \(k\) is the \(k\)th environment change
5:\(i\leftarrow\text{DMChooseIn}(1,\ldots,n)\)\(\triangleright\) DM indicates their preferred POS
6:\(\mathbf{x}_{p}\leftarrow\text{DMChooseIn}(POS_{t}^{k})\)\(\triangleright\) DM indicates their preferred solution
7:\(\triangleright\)\(\text{P}\leftarrow\text{F}(\mathbf{x}_{p},t)\)\(\triangleright\) DM's preference is formulated
8: DM Choose box radius, \(\mathbf{r}\leftarrow\text{random}()\)\(\triangleright\) DM indicates their preferred boundary box size
9: return (\(\mathbf{x}_{p}:\mathbf{p}:\mathbf{r}\))
```  
**Algorithm 3** Bootstrap Procedure  
Interactive Preference Incorporation: A significant change in the environment may occur where the resulting POF may shift in such a way that the DM preference, \(\mathbf{p}\), is no longer part of the new POF. In this scenario, the DM interactively redefines the position of the bounding box ensuring that its preference lies on the new POF. A few scenarios  
Figure 1: Preference-driven search process of a DMOA. may emerge when this shift of the POF occurs. The initial preferred outcome, \(p\), may no longer lie on the new POF, but the functional value of the corresponding decision variable, \(x_{p}\), may still lie on the new POF. The second possibility is that both \(p\) and the functional value of \(x_{p}\) do not lie on the new POF. In both cases, a new bounding box position needs to be defined. The interactive redefinition of the bounding box position is presented in Algorithm 4. The time complexity of the interactive preference incorporation procedure is a constant value, i.e., low time complexity.