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In this paper, a new stochastic optimization algorithm is introduced, called Driving Training-Based Optimization (DTBO), which mimics the human activity of driving training. The fundamental inspiration behind the DTBO design is the learning process to drive in the driving school and the training of the driving instructor. DTBO is mathematically modeled in three phases: (1) training by the driving instructor, (2) patterning of students from instructor skills, and (3) practice. The performance of DTBO in optimization is evaluated on a set of 53 standard objective functions of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and IEEE CEC2017 test functions types. The optimization results show that DTBO has been able to provide appropriate solutions to optimization problems by maintaining a proper balance between exploration and exploitation. The performance quality of DTBO is compared with the results of 11 well-known algorithms. The simulation results show that DTBO performs better compared to 11 competitor algorithms and is more efficient in optimization applications.

In this paper, a new bio-inspired metaheuristic algorithm called Zebra Optimization Algorithm (ZOA) is developed; its fundamental inspiration is the behavior of zebras in nature. ZOA simulates the foraging behavior of zebras and their defense strategy against predators' attacks. The ZOA steps are described and then mathematically modeled. ZOA performance in optimization is evaluated on sixty-eight benchmark functions, including unimodal, high-dimensional multimodal, fixed-dimensional multimodal, CEC2015, and CEC2017. The results obtained from ZOA are compared with the performance of nine well-known algorithms. The simulation results show that ZOA can solve optimization problems by creating a suitable balance between exploration and exploitation and has a superior performance compared to nine competitor algorithms. ZOA's ability to solve real-world problems has been tested on four engineering design problems, namely, tension/compression spring, welded beam, speed reducer, and pressure vessel. The optimization results show that ZOA is an effective optimizer in determining the values of the design variables of these problems compared to the nine competitor algorithms.

Metaheuristic algorithms have a wide range of applications in handling optimization problems. In this study, a new metaheuristic algorithm, called the chef-based optimization algorithm (CBOA), is developed. The fundamental inspiration employed in CBOA design is the process of learning cooking skills in training courses. The stages of the cooking training process in various phases are mathematically modeled with the aim of increasing the ability of global search in exploration and the ability of local search in exploitation. A collection of 52 standard objective functions is utilized to assess the CBOA’s performance in addressing optimization issues. The optimization results show that the CBOA is capable of providing acceptable solutions by creating a balance between exploration and exploitation and is highly efficient in the treatment of optimization problems. In addition, the CBOA’s effectiveness in dealing with real-world applications is tested on four engineering problems. Twelve well-known metaheuristic algorithms have been selected for comparison with the CBOA. The simulation results show that CBOA performs much better than competing algorithms and is more effective in solving optimization problems.

This paper proposes a new nature-inspired metaheuristic algorithm called Clouded Leopard Optimization (CLO), which mimics the natural behavior of clouded leopards in the wild. The fundamental inspiration of CLO is derived from two ways of natural behaviors of the clouded leopard, including hunting strategy and daily resting on trees. CLO is mathematically modeled in two phases of exploration and exploitation, based on the simulation of these two natural behaviors. CLO performance is evaluated in solving sixty-eight benchmark functions, including unimodal, multimodal, CEC 2015, and CEC 2017 types. The performance of CLO in solving optimization problems is compared with the performance of ten famous metaheuristic algorithms. The simulation results show that the proposed CLO approach with high ability in exploration, exploitation, and balancing between them has a high capability in optimization applications. Simulation results show that CLO performs better in most test functions than competitor algorithms. In addition, the implementation of CLO on four engineering design issues demonstrates the capability of the proposed approach in real-world applications.

This paper proposes a new nature-based metaheuristic algorithm called Fennec Fox Optimization (FFA), mimicking two natural behaviors of the animal Fennec Fox in nature. Concretely, Fennec's digging ability and escape strategy from wild predators were the fundamental inspiration for the proposed FFA. The mathematical model of FFA is presented in two phases based on imitating these two behaviors. First, the efficiency of FFA was evaluated in the optimization of sixty-eight standard benchmark functions and four engineering design problems. Second, FFA performance is challenged against eight wellknown optimization algorithms. The optimization results show that FFA perfectly balances exploration and exploitation in searching for the global optimum. Hence, FFA can provide suitable solutions to optimization problems. The comparison of results indicates the superiority of FFA in most objective functions over competitor algorithms in providing the optimal solution.

This paper introduces a new human-based metaheuristic algorithm called Sewing Training-Based Optimization (STBO), which has applications in handling optimization tasks. The fundamental inspiration of STBO is teaching the process of sewing to beginner tailors. The theory of the proposed STBO approach is described and then mathematically modeled in three phases: (i) training, (ii) imitation of the instructor’s skills, and (iii) practice. STBO performance is evaluated on fifty-two benchmark functions consisting of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and the CEC 2017 test suite. The optimization results show that STBO, with its high power of exploration and exploitation, has provided suitable solutions for benchmark functions. The performance of STBO is compared with eleven well-known metaheuristic algorithms. The simulation results show that STBO, with its high ability to balance exploration and exploitation, has provided far more competitive performance in solving benchmark functions than competitor algorithms. Finally, the implementation of STBO in solving four engineering design problems demonstrates the capability of the proposed STBO in dealing with real-world applications.

Let ( F n ) n ≥ 0 be the sequence of the Fibonacci numbers. The order (or rank) of appearance z ( n ) of a positive integer n is defined as the smallest positive integer m such that n divides F m . In 1975, Sallé proved that z ( n ) ≤ 2 n , for all positive integers n. In this paper, we shall solve the Diophantine equation z ( n ) = ( 2 − 1 / k ) n for positive integers n and k.