region are concentrated in a much higher number of dwelling places such as city quarters, towns, villages, and hamlets. If a user's request for service is made, then a system dispatcher assigns the demand to the closest available center, and the associate response time is approximately proportional to the distance from the assigned service provider to the client's place. Average response time is one of the common criteria to minimize. Because the individual dwelling places significantly differ in the distance from the nearest service center, this inequality raises different goals, which the public representatives apply when designing the system. As already mentioned, a commonly used quality criterion is the minimal average response time to user requests. This so-called system criterion ensures maximal efficiency of the service system, but it may cause the following problem: even if the average response time is minimal, there may be some locations shared by such users who are very far from any located service center. Although all users of the system contribute to the building and operational costs, not all of them have equal access to the service. Users from less densely populated areas, in particular, find this approach unfair because, despite contributing the same amount to system costs as the others, they live considerably further away from the nearest center than the average. Several solidarity criteria have been developed in response to the users' need for equity in service accessibility [14; 15]. However, if we optimized only a fair criterion defined in any way, the previously mentioned system criterion may get worse. From this small example, it is obvious that it is not possible to satisfy all at once, especially if the requirements are in conflict. Simultaneous optimization of both criteria is hard, and it may bring serious difficulties to the associated solving process. Let us focus on the output of the EMS system design. If we wanted to consider two (or even more) conflicting criteria, it would not be possible to bring only one solution to the location problem as a result. Such a situation could cause unintentional contradictions and reluctance to come up with a consensus acceptable to all partners involved. From the viewpoint of final decision-making and the possibility of finding a suitable compromise, we needed to bring more system designs, not just one. The basic premise is that for any final judgment, a particular set of solutions known as the _Pareto front_ is presented. Such a collection of system designs is represented by the Pareto front of solutions, which cannot be improved in one of the criteria without at least one of the other criteria deteriorating [16; 17; 18; 19; 20; 21; 22]. In general, determining the exact Pareto set is very time-demanding [18; 19]. To reduce computation time and complexity, the approximate Pareto front should be used instead of the complete one. The construction of the exact Pareto front of non-dominated EMS system designs represents a severe computational difficulty. The scientific topic of this paper aims at possible ways to obtain a good approximation of the original Pareto front. In addition to the theoretical explanation, we provide the readers with the results of numerical experiments to evaluate the quality of the proposed algorithms. Contrary to [20], the keystones are obtained using solutions from the area of feasible solutions, and from this starting solution, by minimization, we have achieved members, which are near the Pareto front. Thus, we use a reverse approach. In the current form of the presented algorithm, we do not use any learning process as in [21], but it is a good direction for future development. The structure of this paper is organized as follows. In the following section, we discuss the conflicting objectives and the idea of non-dominated solutions to EMS design problems. The third section is devoted to the suggested swap algorithm and non-dominated solution set.