## 6 Conclusions  
The objective of this study was to compare the performance of four multi-objective optimization algorithms (AMOSA, MOABC, MSPSO, NSGA-II respectively) for a given spatial problem, namely evacuation planning. In our study, the evacuation problem was aiming to minimize the accumulated distance from high-risk zones to shelters and to minimize the total capacity overload cost of shelters. The higher the minimum fitness values of both capacity and distance are, the better are the obtained alternatives for assigning people to appropriate shelters.  
In terms of algorithm performance, all algorithms generated the optimization in a consistent way, and no results were obtained that could suggest that some of them were trapped in a local minimum. By evaluating the convergence speed of the fitness variation of the four algorithms (see Figure 8), we found that AMOSA and NSGA-II followed by MOABC converge faster and smoother towards the final optimal solutions. This justifies not only the competence of NSGA-II, which has been used in the literature to a larger extent than the other algorithms [60]. However, the competence of AMOSA and MOABC shows the capacity of solving multi-objective optimization problems including evacuation problems.  
Figure 9: Allocation maps of the shelters to building blocks from the case study area, when both capacity and distance objective functions are equally prioritized. (**1**) population allocation of AMOSA, (**2**) population allocation of MOABC, (**3**) population allocation of MSPSO, and (**4**) population allocation of NSGA-II.  
The presented metaheuristic methods and others of its type are not meant to find a'single perfect solution' but a set of 'good enough' solutions in an efficient way, and therefore, it is possible that a more optimal solution can be achieved by using alternative methods. Decision-makers must be aware of this aspect, in order to properly assess the benefits and limitations of these techniques.  
A suggestion for future work, as an alternative approach dealing with this type of spatial multi-objective optimization problems, is to modify the classical algorithms to better fit the problem in hand. For example, based on the results obtained by MOABC and the comparison made to other algorithms, MOABC could be an interesting algorithm to modify in order to solve complex problems such as evacuation planning. It is also important to consider the use of other methods, such as recoverable robustness, to solve evacuation planning. [PERSON] and [PERSON] [61] proposed a recoverable robust optimization approach for the weekly berth and quay crane planning problem. The results proved the strength of the proposed model for solving a spatial problem.  
O.N. was responsible for methodology, implementation, testing and analysis, and writing; [PERSON] contributed in formal analysis and editing; [PERSON] contributed in implementation, analysis, and editing; [PERSON] was responsible for supervision and conceptualization; [PERSON] was responsible for idea development and conceptualization, coordination, supervision, reconstruction, and editing the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Swedish International Development Agency (SIDA) through the University of Rwanda-Sweden Program, GIS Sub-Program. Grant Agreement between Sweden, the Government of Rwanda and the University of Rwanda (UR) regarding the \"University of Rwanda and Sweden Research Partnership 2019-2024\" Sida Contribution No 11277.  
The authors would like to express their thanks to the University of Rwanda, Lund University, and SIDA Partnership Program for their financial support of this research.  
The authors declare no conflicts of interest.