A Deep Insight into Advanced Optimization

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RUN Beyond the Metaphor:

An Efficient Optimization Algorithm Based on Runge Kutta Method

This algorithm attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics. The RUN utilizes the logic of slope variations computed by the RK method as a promising and logical searching mechanism for global optimization. This search mechanism benefits from two active exploration and exploitation phases for exploring the promising regions in the feature space and constructive movement toward the global best solution. Furthermore, an enhanced solution quality (ESQ) mechanism is employed to avoid the local optimal solutions and increase convergence speed.

Benefits of Runge Kutta Optimization (RUN)  

The optimization field suffers from the metaphor-based "pseudo-novel" or "fancy" optimization algorithms. Most of these cliche methods mimic animals' searching trends and possess a small contribution to the optimization process itself. Most of these cliche methods suffer from the locally efficient performance, biased verification methods on easy problems, and high similarity between their components' interactions. This study attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics.

Metaphor-free Language

RUN optimizer is a novel metaphor-free population-based optimization that employs a search mechanism based on the Runge Kutta (RK) method widely well-known in mathematics to boost both exploration and exploitation abilities.

Enhanced Solution Quality (ESQ)

The enhanced solution quality (ESQ) in the RUN algorithm utilizes the thus-far best solution to promote the quality of solutions and improve the convergence speed. The search mechanism and ESQ use two randomized variables to emphasize the importance of the best solution and move toward the global best solution, which can effectively balance the exploration and exploitation steps.

Unique Performance

The RUN provided very promising and competitive results, showing superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance

Runge Kutta Optimization (RUN) is a novel metaphor-free math-based Algorithm

Expert Systems with Applications 2021, 115079,
Developed for a better future by:
Iman Ahmadianfar, Ali Asghar Heidari, Huiling Chen, Amir H Gandomi, Xuefeng Chu

No Metaphor

Strong basis in math

Simple and reliable

Unlimited Post Publication Supports

Analysis and Basics of the Original RUN Optimization

The optimization field suffers from the metaphor-based "pseudo-novel" or "fancy" optimizers. Most of these cliché methods mimic animals' searching trends and possess a small contribution to the optimization process itself. Most of these cliché methods suffer from the locally efficient performance, biased verification methods on easy problems, and high similarity between their components' interactions. This study attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics. The proposed RUNge Kutta optimizer (RUN) was developed to deal with various types of optimization problems in the future. The RUN utilizes the logic of slope variations computed by the RK method as a promising and logical searching mechanism for global optimization. This search mechanism benefits from two active exploration and exploitation phases for exploring the promising regions in the feature space and constructive movement toward the global best solution. Furthermore, an enhanced solution quality (ESQ) mechanism is employed to avoid the local optimal solutions and increase convergence speed. The RUN algorithm's efficiency was evaluated by comparing with other metaheuristic algorithms in 50 mathematical test functions and four real-world engineering problems. The RUN provided very promising and competitive results, showing superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance. In optimizing the constrained engineering problems, the metaphor-free RUN demonstrated its suitable performance as well. The authors invite the community for extensive evaluations of this deep-rooted optimizer as a promising tool for real-world optimization. The source codes, supplementary materials, and guidance for the developed method will be publicly available.

This study was intended to develop a new optimizer (i.e., RUN) to be implemented and formulated with specific exploration and exploitation strategies. Despite the promising findings, it is recommended for future studies to use other well-known operators, such as the crossover operator, mutation operator, opposite-based learning method, and levy walks (LWs). A chaotic map (CMs) should also be considered when the EQS is used in each iteration. In addition, further improvement can be made by developing the multiobjective and binary versions of RUN for solving multiobjective and discrete optimization problems. Finally, other RK methods, such as the fourth-order RK contraharmonic mean method, can be considered in the RUN algorithm to enhance its efficiency.

RUN is an easy and simple free optimizer with secure basis and no metaphor that can be used for any class of problems. You just drop the codes to your software, add your objective function, and RUN it!

Download and RUN Matlab codes of Runge Kutta Optimization (RUN)
- Download and RUN Java codes of Runge Kutta Optimization (RUN)
- Download and RUN python codes of Runge Kutta Optimization (RUN) 
- Download brief RUN section and word file of Runge Kutta Optimization (RUN)
- Download Visio source files of Runge Kutta Optimization (RUN)
- Runge Kutta Optimization (RUN) is now available in github
- Runge Kutta Optimization (RUN) is now available in mathworks

RUN Beyond the Metaphor: An Efficient Optimization Algorithm Based on Runge Kutta Method
Expert Systems with Applications, 2021, 115079, https://doi.org/10.1016/j.eswa.2021.115079




We invite the community for extensive evaluations of this deep-rooted optimizer as a promising tool for real-world optimization.

The site was made by Ali Asghar Heidari