## 5 Conclusions  
The proposed PROS algorithm is a new, fast, simple and parameterless stochastic optimization strategy that has shown surprisingly positive results despite its simplicity. A total of 12 multi-dimensional mathematical test functions with various levels of complexity have been used to thoroughly test the algorithm. The results indicate that the PROS algorithm achieves significantly good performance and a relatively fast convergence speed when compared with other well-established and more complex optimization methods, such as GA, PSO and DE. In general, it appears that the PROS strategy exhibits good exploration capabilities but shows some difficulties on the exploitation phase. However, the main advantages of PROS are the following: (i) lack of user-defined parameters; (ii) good computational efficiency; and (iii) its exceptional easiness of implementation. The right usage and correct implementation of optimization algorithms often requires a high level of expertise that can take a long time to be obtained. In contrast, the PROS algorithm requires a minimum level of mathematical knowledge and programming skills while still providing a clear, reliable, elegant and powerful search strategy. Therefore, it can be easily implemented and used even by non-experts in optimization problems, in various applied sciences fields. Additionally, the method can serve as a benchmarking tool for evaluating the performance of other optimization methods. We can claim that if an optimization algorithm \"OA\" is more complex than PROS but it exhibits poorer performance in the same problem or in a series of selected problems, then according to Occam's razor it can be concluded that OA is not a good alternative since it adds unnecessary complexity without significantly improving performance. Of course, complexity cannot be measured directly or precisely, and it is not easy to be quantified in general. Yet, it still makes sense to claim that in optimization algorithms complexity has to do with (a) the number of parameters that need to be adjusted for the algorithm to work properly in a set of problems; and (b) the difficulty of implementation of the algorithm on a computer code. Given these criteria, PROS is certainly simpler and less complex than most well-known state-of-the-art optimization methods, yet still effective. Future DirectionsThe PROS algorithm was presented in this paper in its simplest form. Based on our research, we believe that there are various ways to further improve the algorithm's performance by searching in a smarter way while keeping the basic search idea. Nevertheless, by doing so, perhaps some extra parameters will need to be added. One idea is to include more search directions when updating the candidate solution. Presently, the search is only in orthogonal principal directions, i.e., the new position of the candidate solution differs only in one of the design variables. Instead of that, the search could follow another, possibly random direction in the design space in each iteration. Another idea is to use a different method when sampling a new position. Based on the experience obtained during the search, we can use another distribution that describes the problem more accurately compared to the uniform distribution used in this work. Alternatively, one could employ a population of agents instead of a single solution in each iteration, rendering the method a population-based method, based on specific rules on how the population is updated in each iteration. Conceptualization, N.P.B. and V.P. ; methodology, V.P. ; software, V.P. and G.S., validation, V.P. and N.P.B. ; formal analysis, V.P. and N.P.B. ; investigation, V.P., N.P.B. and G.S. ; resources, V.P., N.P.B. and G.S. ; data curation, V.P., N.P.B. and G.S. ; writing--original draft preparation, V.P., N.P.B. and G.S. ; writing--review and editing, V.P. ; visualization, V.P. and G.S. ; supervision, V.P. ; project administration, V.P. ; funding acquisition, V.P. and G.S. All authors have read and agreed to the published version of the manuscript.