Abstract
Abstract Arithmetic optimization algorithm (AOA) is one of the recently proposed population-based metaheuristic algorithms. The algorithmic design concept of the AOA is based on the distributive behavior of arithmetic operators, namely, multiplication (M), division (D), subtraction (S), and addition (A). Being a new metaheuristic algorithm, the need for a performance evaluation of AOA is significant to the global optimization research community and specifically to nature-inspired metaheuristic enthusiasts. This article aims to evaluate the influence of the algorithm control parameters, namely, population size and the number of iterations, on the performance of the newly proposed AOA. In addition, we also investigated and validated the influence of different initialization schemes available in the literature on the performance of the AOA. Experiments were conducted using different initialization scenarios and the first is where the population size is large and the number of iterations is low. The second scenario is when the number of iterations is high, and the population size is small. Finally, when the population size and the number of iterations are similar. The numerical results from the conducted experiments showed that AOA is sensitive to the population size and requires a large population size for optimal performance. Afterward, we initialized AOA with six initialization schemes, and their performances were tested on the classical functions and the functions defined in the CEC 2020 suite. The results were presented, and their implications were discussed. Our results showed that the performance of AOA could be influenced when the solution is initialized with schemes other than default random numbers. The Beta distribution outperformed the random number distribution in all cases for both the classical and CEC 2020 functions. The performance of uniform distribution, Rayleigh distribution, Latin hypercube sampling, and Sobol low discrepancy sequence are relatively competitive with the Random number. On the basis of our experiments’ results, we recommend that a solution size of 6,000, the number of iterations of 100, and initializing the solutions with Beta distribution will lead to AOA performing optimally for scenarios considered in our experiments.
Highlights
Optimization techniques have been applied successfully in many real-world problems
We evaluate the influence of different initialization schemes on the performance of the newly proposed
This article tested the influence of solution size, the number of iterations, and other initialization schemes on Arithmetic optimization algorithm (AOA)
Summary
Optimization techniques have been applied successfully in many real-world problems. These real-world problems are usually complex, with multiple nonlinear constraints and multimodal nature. Solving these complex, nonlinear, and multimodal problems usually requires reliable optimization techniques. The common taxonomy is bioinspired and physical based (based on physical phenomena such as physics and chemistry) [3]. Another taxonomy is inspired by swarm intelligence, evolution, physics-based, and human based [4]. Metaheuristic algorithms are modeled after natures’ best features, and many attributed their popularity to this fact and their ability to find nearoptimal solutions [5]
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