Abstract
The distributive power of the arithmetic operators: multiplication, division, addition, and subtraction, gives the arithmetic optimization algorithm (AOA) its unique ability to find the global optimum for optimization problems used to test its performance. Several other mathematical operators exist with the same or better distributive properties, which can be exploited to enhance the performance of the newly proposed AOA. In this paper, we propose an improved version of the AOA called nAOA algorithm, which uses the high-density values that the natural logarithm and exponential operators can generate, to enhance the exploratory ability of the AOA. The addition and subtraction operators carry out the exploitation. The candidate solutions are initialized using the beta distribution, and the random variables and adaptations used in the algorithm have beta distribution. We test the performance of the proposed nAOA with 30 benchmark functions (20 classical and 10 composite test functions) and three engineering design benchmarks. The performance of nAOA is compared with the original AOA and nine other state-of-the-art algorithms. The nAOA shows efficient performance for the benchmark functions and was second only to GWO for the welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD).
Highlights
Optimization techniques are popular for solving real-world problems
Several other mathematical operators exist, which have the same or better distributive properties, which could be exploited to enhance the performance of arithmetic optimization algorithm (AOA). This motivated us to use the high-density values that the natural logarithm and exponential operators can generate to enhance the exploratory ability of AOA
The benchmark functions can be divided into unimodal, multimodal, fixed-dimension multimodal, and composite functions
Summary
Optimization techniques are popular for solving real-world problems. Finding solution to these complex, nonlinear, and multimodal real-world problems usually requires reliable optimization techniques, such as metaheuristic algorithms, which have proved to be a reliable optimization technique for such problems. Nature has inspired many metaheuristic algorithms; they solve optimization problems by mimicking natural phenomena These phenomena cover a range of natural processes from such areas as biology, physics, chemistry and swarms (population-based) [1,2]. The randomly generated search agents are evolved by combining the best individuals after every iteration during the search process Examples of these bio-inspired metaheuristic algorithms include genetic algorithms (GA) [3], the artificial algae algorithm (AAA) [4], and the evolution strategy (ES) [5]. The distributive power of the arithmetic operators gives the AOA its unique ability to find the global optima for optimization problems used to test its performance.
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