# An Innovative Hybrid Approach Producing Trial Solutions for Global Optimization
###### Abstract  
Global optimization is critical in engineering, computer science, and various industrial applications as it aims to find optimal solutions for complex problems. The development of efficient algorithms has emerged from the need for optimization, with each algorithm offering specific advantages and disadvantages. An effective approach to solving complex problems is the hybrid method, which combines established global optimization algorithms. This paper presents a hybrid global optimization method, which produces trial solutions for an objective problem utilizing a genetic algorithm's genetic operators and solutions obtained through a linear search process. Then, the generated solutions are used to form new test solutions, by applying differential evolution techniques. These operations are based on samples derived either from internal line searches or genetically modified samples in specific subsets of Euclidean space. Additionally, other relevant approaches are explored to enhance the method's efficiency. The new method was applied on a wide series of benchmark problems from recent studies and comparison was made against other established methods of global optimization. optimization; differential evolution; genetic algorithm; line search; evolutionary techniques; stochastic methods; hybrid methods +
Footnote †: journal: applied sciences  
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agriculture, in sugarcane production applications [6]; and in economics, for comprehensive techno-economic analyses [7]. Optimization methods can be categorized into deterministic [8] and stochastic [9] methods based on how they approach solving the problem. The techniques belonging to the category of deterministic methods are mainly the so-called interval methods [10]. Stochastic methods utilize randomness to explore the solution space, while in interval methods, the set \(S\) is divided into smaller regions that may contain the global minimum based on certain criteria. Recently, a comparison between deterministic and stochastic methods was proposed by [PERSON] et al. [11]. There are a series of stochastic optimization methods called evolutionary methods, which attempt to mimic a series of natural processes. Such methods include the genetic algorithms [12]; the differential evolution method [13]; the Particle Swarm Optimization (PSO) method used, for example, in solving feature selection problems [14]; the Ant Colony Optimization method used, for example, in the traveling salesman problem [15]; the Fish Swarm Algorithm, which is inspired by the ecological behaviors of fish breeding in the wild, i.e., their prey, swarming, and monitoring behaviors [16]; the Dolphin Swarm Algorithm, based on the natural behavior of sparrows and dolphins [17]; the Whale Optimization Algorithm (WOA) algorithm [18], etc. Also, due to the wide spread of parallel computing units [19], a variety of research papers related to evolutionary techniques have appeared that use such processing units [20]. Genetic algorithms were formulated by [PERSON] [21] and his team, and they create random candidate solutions for the optimization problem. These solutions are modified through a series of operators that mimic natural processes, such as mutation, selection and crossover. Genetic algorithms have been widely used in areas such as networking, for indoor 5G network design using a machine learning model for path loss estimation [22]; robotics, for digital twin robots [23]; the energy conservation issues of the speed of a high SI motor fueled with butanol-gasoline blends [24], etc. They can be combined with machine learning to solve complex problems, such as training a feed-forward artificial neural network [25]. Furthermore, differential evolution (DE) is used in symmetric optimization problems [26] and in problems that are discontinuous and noisy and change over time.