A Novel Enhanced Arithmetic Optimization Algorithm for Global Optimization

Abstract

The arithmetic optimization algorithm (AOA) is based on the distribution character of the dominant arithmetic operators and imitates addition ( $A$ ), subtraction ( $S$ ), multiplication ( $M$ ) and division ( $D$ ) to find the global optimal solution in the entire search space. However, the basic AOA has some drawbacks of premature convergence, easily falls into a local optimal value, slow convergence rate, and low calculation precision. To improve the overall optimization ability and overcome the drawbacks of the basic AOA, an enhanced AOA (EAOA) based on the Lévy variation and the differential sorting variation is proposed to solve the function optimization and the project optimization. The Lévy variation increases population diversity, broadens the optimization space, enhances the global search ability and improves the calculation precision. The differential sorting variation filters out the optimal search agent, avoids search stagnation, enhances the local search ability and accelerates the convergence rate. The EAOA realizes complementary advantages of the Lévy variation and the differential sorting variation to avoid falling into the local optimum and the premature convergence. The sixteen benchmark functions and five engineering design projects are applied to verify the effectiveness and feasibility of the EAOA. The EAOA is compared with other algorithms by minimizing the fitness value, such as artificial bee colony, ant line optimizer, cuckoo search, dragonfly algorithm, moth-flame optimization, sine cosine algorithm, water wave optimization and arithmetic optimization algorithm. The experimental results show that the overall optimization ability of the EAOA is superior to that of other algorithms, the EAOA can effectively balance the exploration and the exploitation to obtain the best solution. In addition, the EAOA has a faster convergence rate, higher calculation precision and stronger stability.

Keywords

• Arithmetic optimization algorithm
• Lévy variation
• differential sorting variation
• benchmark function
• engineering design