## 1 Introduction  
Optimization problems of all sorts arise in quantitative disciplines, ranging from computer science and engineering to operations research and economics. Thus, the development of solution methods has been of interest in mathematics for many centuries. The goal of optimization methods is to find an optimal (globally optimal) or near-optimal solution with low computational effort. We can distinguish between two different types of optimization methods: deterministic or exact methods that can guarantee finding the global optimal solution and heuristic methods where there is no such guarantee and a local optimal is usually obtained instead. The deterministic approach has a solid mathematical formulation, provides exact solutions, and can be used to solve optimization problems where the computational effort grows polynomially with respect to the problem size. The situation is different if the problem is NP-hard as the required computational effort grows exponentially. In this case, the optimization problems can become intractable or impractical to solve using deterministic methods. Heuristic optimization methods, on the other hand, can overcome such problems as they have shown good performance for many NP-complete problems and complex optimization tasks of practical relevance. The terms heuristic or metaheuristic are commonly associated with random search algorithms. Random search algorithms refer to a set of optimization methods that implement some kind of randomness or probability (typically in the form of a pseudo-random number) in the definition of the iterative search strategy. This family of methods includes genetic algorithms (GA) [1; 2; 3], particle swarm optimization (PSO) [4; 5; 6], differential evolution (DE) [7; 8; 9; 10], ant colony optimization (ACO) [4; 11], harmony search (HS) [12; 13], simulated annealing [14], tabu search [15], and many others. The introduced randomness in random search algorithms possesses several advantages that add robustness to the solution strategy. It can significantly increase the solution's convergence speed and make the method less sensitive to modeling errors. Furthermore, it may enable the method to escape a local optimum and push the search towards the global solution. Therefore, random search algorithms are very useful for ill-structured global optimization problems where the objective function may be nonconvex, nondifferentiable, and possibly, discontinuous over a continuous, discrete, or mixed continuous-discrete domain. Nevertheless, they offer no guarantee that a global optimal solution will be obtained. Although numerous heuristic optimization methods have been proposed thus far in the literature, surprisingly, new methods are still being proposed almost every day. These new methods may differ from existing ones, but the major question is whether they make a real difference or a significant improvement. Often, a newly proposed optimization algorithm is simply a replica of an existing method with a few extra parameters or rules that are supposed to improve or \"optimize\" its performance. However, adding more complexity is not always a good idea as the fine-tuning of the newly introduced parameters ends up being another optimization problem by itself. In the present paper, we introduce a new optimization method: pure random orthogonal search (PROS), which is simple, elegant, fast, easy to understand and implement, and truly parameterless. The performance of the new proposed strategy is investigated in comparison to pure random search (PRS) as well as three other established and well-known optimization methods, namely genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE). Due to the simplicity and the lack of parameters of PROS, this method can set a benchmark for other optimization algorithms that have a higher degree of complexity and require the definition of one or more parameters. The remainder of the paper is organized as follows.