A new optimization algorithm for non-convex problems

Optimization is an important technique in many fields of research. In most cases, researchers study processes and analyze them in order to determine the parameters that will optimize a system. In fact, some systems are harder to analyze and optimize than others. Continuous non-convex system problem is considered one of the most difficult problems that can be solved using the conventional analytical methods; particularly, when it is difficult to calculate derivatives directly. For this reason, many meta-heuristic optimization methods have been devised and modified to solve these problems. In this paper, we propose an approach that can be used alternatively for solving continuous non-convex optimization problems. The method introduced in this paper is named as Average Uniform Algorithm (AUA). The idea behind the algorithm is based on a mathematical approach unlike other meta-heuristic algorithms that are inspired by nature such as Genetic Algorithm (GA), Simulated Annealing (SA), and Ant Colony (ACO). The algorithm is principally constructed using the uniform distribution to generate random solutions, and then averaging the best solutions to develop one good solution that will give the optimal value for the non-convex function. Throughout the paper, the algorithm will be delineated with examples. In the final phase of the research, the results of AUA will be discussed and compared with the results of other optimization methods.