## 2 Problem Formulation
### Multi-User Evaluation  
The fitness function stated in Equation (5) has two clearly different parts: a quantitative evaluation of solutions given by material handling costs and geometrical feasibility, and a qualitative evaluation assigned by the DM. Therefore, it would be necessary that the DM would evaluate each one of the candidate solutions in the whole reef and water but, since the number of individuals to be evaluated can be high, human intervention is critically limited due to the necessary time to perform it and by the fatigue caused to the DM. Hence, it is necessary to implement a strategy to free the DM from such a tiresome task. In this way, a clustering method has been implemented in order to show to the DM only a small group formed by nine solutions, distributing the valuation to the rest of the individuals  
Figure 2: Facility layout codification example. proportionally to their similarity to the main nine that have been actually assessed by the DM. The clustering algorithm used is Fuzzy c-Means [53] and it is explained in detail in [PERSON] et al. [54]. This work has used the implementation of c-Means developed in the library Peach. The strategy followed to organize the human intervention during the algorithm execution is as follows: during the first generations, the intervention of the DMs is required in every one of them until one solution that satisfies completely the DM's requirements appears. Once this occurs, the algorithm runs by itself, without the intervention of the DMs, for a prefixed number of iterations (this number can be set for each problem and can be changed during the execution time) in which human evaluations are automatically assigned according to the previously assigned ones. Therefore, the DM's fatigue is limited as much as possible without losing his/her contribution to guide the process. Furthermore, the intervention of several DMs who have their own preferences regarding the characteristics of the problem is allowed. Thus, every time that the intervention of the DM is required during the algorithm process, it is possible to choose a different one. In this way, it is possible to organize the intervention of 1 to \(m\) human evaluators sequentially one by one, changing the DM each time that the algorithm requires the human intervention, or to allow a particular DM to guide the evolution of the algorithm during several generations in a row, or even to allow the intervention of the \(m\) human evaluators in a random way (see flow diagram in Figure 3). According to the flow diagram of Figure 3, the algorithm begins with a random generation of individuals representing the whole population. Afterwards, the individuals of the population are grouped into nine clusters according to [PERSON] et al. [54] and the human intervention can be required or not. The human intervention is required for every generation in which no individuals have appeared satisfying the DMs' requirements, and every certain number of prefixed generations if any individual satisfying the DMs' requirements has already appeared during the previous generations. Furthermore, every time that the human intervention is required, the algorithm asks whether the same DM will be maintained or a change will take place and the DM who will perform the evaluation is indicated if there is a change. Continuing with the development of the algorithm, the quantitative values of every one of the individuals in the population are calculated and incorporated into the general evaluation function. Finally, the reproduction and selection processes are performed, and the algorithm finishes, or the depredation is carried out and a new generation starts. The way in which the scores assigned by each one of the DMs are distributed among the corals is as follows: in the case where there is a single evaluator, only the nine individuals representative of the clusters (centers) are actually evaluated, and the scores are distributed to the rest of the population proportionally to their similitude with respect to the nine centers, as mentioned before.