## 6 Conclusions  
Bi-criteria optimization plays an important role when the specifics of the solved problem do not allow using a simple model minimizing only one objective function. A common example can be found in emergency medical service design, which was the core application domain of our research.  
Specifically, the emergency medical service system design faces two contradictory quality criteria. First, the system objective follows the idea of minimizing the response time of the system to an average user and comes from the statistical fact that minimization of the average response time saves the largest number of lives in total. Nevertheless, this criterion does not take into account worse-located and less populated dwelling places, for which the response time may considerably exceed an acceptable value. That is why the fairness criterion has been simultaneously applied to minimize disutility perceived by the worst-situated minorities.  
This paper was focused on providing the responsible authorities with a finite collection of non-dominated system designs from which the final solution can be chosen.  
Since searching for the optimal Pareto front proved to be very demanding, the attention of operations researchers has been focused on the development of heuristic methods, which could approximate the original Pareto front in a much shorter time. In addition to the theoretical explanation, we provided the readers with the results of numerical experiments in order to evaluate the quality of the proposed algorithms. Based on the reported results, a conclusion can be made that the suggested algorithm significantly extends the state-of-the-art solving tools for specific location problems in which two contradictory objectives need to be optimized.  
Future studies in this area of science may focus on building new algorithms that would produce a close approximation of the Pareto front of non-dominated system designs or on modifying certain existing techniques to obtain findings that are more accurate. The promising research direction can be seen in the application of self-learning methods for heuristic parameter adjustment.  
M.K.: data analysis, mathematical modeling, numerical experiments, implementation, and revising the article. J.J.: conceptualization, design of the study, methodology, data analysis, and drafting of the article. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Slovak Research and Development Agency, grant number APVV-19-0441, and by the Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the Slovak Academy of Sciences, grant numbers VEGA 1/0216/21, \"Designing of emergency systems with conflicting criteria using tools of artificial intelligence\"; VEGA 1/0077/22, \"Innovative prediction methods for optimization of public service systems\"; and VEGA 1/0654/22, \"Cost-effective design of combined charging infrastructure and efficient operation of electric vehicles in public transport in sustainable cities and regions\".  
The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Ethics Committee of the University of Zilina (protocol code 2/3/2023) on 2 March 2023.  
Presented results do not contain studies with human or animal subjects. Informed Consent Statements are not relevant for this study.  
The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.  
Both authors of the manuscript declare that they have no conflict to report. In addition, we declare that the presented results do not contain studies with human or animal subjects.