## 1 Introduction  
Optimization refers to the process of systematically examining or solving a problem by selecting real or integer values within a defined range and placing them into the function in order to minimize or maximize a real function. Thus, it is the process of modifying the inputs or characteristics of a device to determine the minimum or maximum output or result of the experiment [1, 2]. The process is called a cost function, objective function or fitness function; the input consists of variables and the output is the cost or fitness function [3]. The combinatorial explosion that characterizes optimization issues sometimes renders them intractable as their size increases, compelling researchers to employ heuristic or approximation techniques to generate near-optimal solutions in a reasonable amount of time [4]. There are many different optimization algorithms for solving the problem. The Traveling Salesman Problem (TSP) is the one of test for discrete optimization problems [5]. Although the TSP is a canonical benchmark for evaluating the performance of metaheuristics in permutation-based discrete optimization, it does not universally represent all problem classes [6]. In discrete domains, problems such as multidimensional knapsack [7], job-shop scheduling [8], and cutting stock tasks [9] serve as established benchmarks, each targeting distinct algorithmic features such as constraint handling, resource allocation, or combinatorial explosion. Therefore, while the TSP provides a meaningful framework for testing exploration-exploitation balance in discrete settings, it can not be generalized to all metaheuristic benchmarking scenarios. Likewise, in continuous optimization, standardized test suites such as Levy [10], HyperSphere [11], Rastrigin [12], Rosenbrock, Griewank, and Ackley [13] functions are extensively used due to their complex landscapes, including multimodality, separability, and non-convexity. The TSP involves finding the shortest possible route that visits a set of cities and returns to the origin [14]. It is only one prominent example, though; there are numerous other well-known applications, such as the Vehicle Routing Problem (VRP) for fleet management [15], the Quadratic Assignment Problem (QAP) [16] for facility location, and other intricate scheduling tasks [17]. With test functions, we can comprehend how well an optimization technique performs in continuous optimization situations. Test functions are helpful for assessing the precision, robustness, convergence rate, and overall performance of optimization methods [18]. Test functions such as Levy and HyperSphere (Sphere) are functions that are often used to evaluate the performance of continuous optimization problems [19]. There are a number of different methods as metaheuristics for the solution of an optimization problem. Some are inspired by natural processes. As noted in [20], traditional exact algorithms can solve smaller instances optimally, but because of the exponential expansion in the solution space, they frequently struggle to handle large-scale variants. For large-scale and extremely complicated discrete optimization tasks, metaheuristics--whether or not they are inspired by nature--have therefore proven invaluable [21]. Over the past three decades, nature-inspired algorithms have become increasingly popular as reliable solutions to combinatorial problems in a variety of fields [22]. In this work, we introduced a new optimization technique inspired by nature. Using the TSP, we evaluated the performance of our optimization technique on discrete optimization problems. We showed how it performs on continuous optimization problems with using Levy and Hypersphere test functions. Metaheuristic techniques for TSP-based scheduling optimization problems were thoroughly reviewed by [PERSON] and [PERSON] [23]. They presented the top 15 metaheuristics that have the most impact on TSP solution. Their review indicated that the Genetic Algorithm (GA) has the most impact on the TSP. Additionally, GA outperformed the second algorithm by 38%.