An Enhanced Multioperator Runge–Kutta Algorithm for Optimizing Complex Water Engineering Problems

Abstract

Water engineering problems are typically nonlinear, multivariable, and multimodal optimization problems. Accurate water engineering problem optimization helps predict these systems’ performance. This paper proposes a novel optimization algorithm named enhanced multioperator Runge–Kutta optimization (EMRUN) to accurately solve different types of water engineering problems. The EMRUN’s novelty is focused mainly on enhancing the exploration stage, utilizing the Runge–Kutta search mechanism (RK-SM), the covariance matrix adaptation evolution strategy (CMA-ES) techniques, and improving the exploitation stage by using the enhanced solution quality (IESQ) and sequential quadratic programming (SQP) methods. In addition to that, adaptive parameters were included to improve the stability of these two stages. The superior performance of EMRUN is initially tested against a set of CEC-17 benchmark functions. Afterward, the proposed algorithm extracts parameters from an eight-parameter Muskingum model. Finally, the EMRUM is applied to a practical hydropower multireservoir system. The experimental findings show that EMRUN performs much better than advanced optimization approaches. Furthermore, the EMRUN has demonstrated the ability to converge up to 99.99% of the global solution. According to the findings, the suggested method is a competitive algorithm that should be considered in optimizing water engineering problems.

A Chaotic Multi‐Objective Runge–Kutta Optimization Algorithm for Optimized Circuit Design

“…The RUN is a fairly new optimizer designed in 2021. This algorithm has demonstrated superior performance to traditional metaphor-based algorithms, and thus, several researchers have proposed ways to improve its performance even more [7]. The RUN is a stochastic population-based algorithm [5].…”

“…(2) Development of a Searching Mechanism Using the Runge-Kutta Method. The RUN algorithm's searching mechanism is centered on the RK method and uses random solutions to perform searches in the search space, both globally and locally [3,5,7]. Like every other optimizer, this is the core of the program.…”

Dendritic Growth Optimization: A Novel Nature-Inspired Algorithm for Real-World Optimization Problems

“…Whether fine-tuning the hyperparameters of a deep neural network, optimizing supply chain logistics, or finding the most efficient route for delivery services, the need for efficient optimization techniques is abundant. To meet this demand, researchers and practitioners have turned to nature-inspired optimization methods, a class of algorithms that draw inspiration from natural processes to tackle complex optimization problems [ 1 , 2 , 3 , 4 , 5 ]. The diversity and complexity of optimization problems in scientific research and practical applications necessitate innovative solutions.…”

An Effective Runge-Kutta Optimizer Based on Adaptive Population Size and Search Step Size

“…This search approach makes use of two effective exploitation and exploration stages to find attractive areas in the search space and progress to the optimal global solution [13]. Despite RUN being a recent algorithm, it has demonstrated excellent performance in solving complex real-world problems such as parameters estimation of photovoltaic models [15,16], power systems [17,18], lithium-ion batteries management [19], identification of the optimal operating parameters for the carbon dioxide capture process in industrial settings [20], water reservoir optimization problems [21], resource allocation in cloud computing [22], and machine learning models parameters tuning [23] to name a few. However, it was noticed that the original RUN consumes more time in solving optimization problems without finding the optimal solution, and in high-dimensional problems, the search capabilities and convergence speed of the original RUN deteriorate.…”