💻 computer science

A high-efficiency adaptive Genghis Khan shark optimizer using novel strategies for static and dynamic complex engineering optimization

This paper proposes IGKSO, an enhanced Genghis Khan shark optimizer incorporating novel survival bonds, a light-dark interactive strategy, an adaptive parameter, and fish aggregation devices to effectively solve complex static and dynamic engineering optimization problems with improved accuracy and global search capabilities.

Original authors: Yuxuan Guo, Gang Hu, Mahmoud Abdel-salam

Published 2026-08-10

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CC BY 4.0

Original authors: Yuxuan Guo, Gang Hu, Mahmoud Abdel-salam

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to find the absolute best spot to set up a lemonade stand in a giant, chaotic city. The city is full of hidden alleys, dead ends, and sudden changes in the weather. If you just wander around randomly, you might get stuck in a small, quiet street with no customers (a "local trap"). If you try to calculate the perfect route using a rigid map, you might get confused because the city changes too fast. This is the daily struggle of optimization: finding the single best solution in a messy, complex world. Scientists use special computer programs called Meta-heuristic Algorithms to solve this. Think of these programs as teams of digital explorers. Instead of using a rigid map, they mimic nature—like how birds flock, ants find food, or sharks hunt—to explore the city, share information, and eventually zero in on the perfect spot. The goal is always the same: find the "global optimum," the one true best answer, without getting lost in the noise.

Now, meet the Genghis Khan Shark Optimizer (GKSO). In the world of these digital explorers, this algorithm is inspired by a specific type of shark that hunts in groups. The original shark algorithm was pretty good at navigating the city, but the researchers behind this new study, Yuxuan Guo, Gang Hu, and Mahmoud Abdel-salam, noticed it had some flaws. Sometimes the sharks got too comfortable and stopped looking for better spots; other times, they didn't adapt well when the "city" changed. They decided to upgrade the shark team into something they call IGKSO (Improved Genghis Khan Shark Optimizer).

Here is how they supercharged the sharks. First, they gave the sharks a new set of survival rules based on danger levels. Imagine the sharks have a built-in radar that measures how "dangerous" the current area is. If the danger is low, they keep hunting normally. But if the danger gets high (meaning they might be stuck in a bad spot), they trigger a self-protection mechanism. This is like a shark suddenly changing its color to blend in and escape a predator, allowing the algorithm to break free from a bad solution and start fresh.

To make this even smarter, the team added a "Light-Dark Interactive Strategy." Picture the sharks' skin changing color based on the sun. In the "light" mode, they explore widely, looking for new territories. In the "dark" mode, they focus intensely on refining their current spot. By switching between these two modes based on how much "light" (information) they have, the sharks balance between wandering around and digging deep, ensuring they don't miss the best spot.

They also introduced a Fish Aggregation Device (FAD) strategy. In the real ocean, fishermen use floating structures to attract fish. In this digital ocean, the algorithm uses these "devices" to gather the sharks together in high-quality groups. This helps the whole team organize better and find even better solutions faster. Finally, they made the sharks' speed and movement adaptive. Instead of running at a fixed speed, the sharks adjust their pace based on how the hunt is going, ensuring they don't run too fast and miss a turn, or move too slow and get left behind.

The researchers tested this new "super shark" against eleven other popular algorithms using a massive set of 29 complex math puzzles (known as the CEC2017 benchmark). The results were impressive: the IGKSO won or tied for the best performance on 41.38% of these puzzles, ranking first overall. It didn't just stop at math puzzles, though. The team also put the sharks to work on real-world engineering problems, like designing a transformer, optimizing a wind farm layout, and planning the path of a robot arm. In almost every case, the IGKSO found the cheapest, most efficient, or most accurate solution, often beating the other algorithms by a significant margin.

The paper suggests that by giving these digital sharks better survival instincts, a way to switch between exploring and focusing, and the ability to adapt their speed, we can solve some of the trickiest engineering problems we face today. While the results are based on computer simulations and mathematical models rather than physical experiments, the consistency of the results across different types of problems suggests this new method is a powerful tool for tackling complex challenges where finding the "perfect" answer is difficult. The authors are confident that this approach could be the key to unlocking better designs for everything from power grids to robotic systems in the future.

Technical Summary: A High-Efficiency Adaptive Genghis Khan Shark Optimizer Using Novel Strategies for Static and Dynamic Complex Engineering Optimization

Problem Statement
Optimization problems in engineering practice often involve nonlinearity, high dimensionality, real-time dynamics, and multi-modal characteristics. Traditional gradient-based methods frequently struggle with these complexities, particularly when objective functions are discontinuous, non-convex, or "black box," leading to convergence instability and entrapment in local optima. While Meta-heuristic Algorithms (MAs) offer a derivative-free alternative, they face challenges in dynamically balancing exploration (global search) and exploitation (local refinement). Specifically, the original Genghis Khan Shark Optimizer (GKSO), while effective, exhibits limitations: its self-protection mechanism is rigidly paired with a specific phase rather than being adaptable to dynamic threats; its scaling parameter $m$ is fixed, lacking universality across different problem landscapes; and it lacks mechanisms to dynamically alter population behavior to escape stagnation.

Methodology: The Improved Genghis Khan Shark Optimizer (IGKSO)
This study proposes IGKSO, an enhanced variant of GKSO designed to address static engineering optimization problems (SEOPs) and dynamic engineering optimization problems (DEOPs). The methodology introduces four novel strategies to refine the shark's survival and hunting behaviors:

Two Interdependent Survival Bonds: The authors restructure the optimization process into a new four-stage framework. Instead of a fixed sequence, the algorithm employs a "Global Danger Coefficient" and "Multiple Local Vigilance Factors" to determine the shark's behavior at any given moment. If the local vigilance factor exceeds the global danger coefficient, the shark performs standard hunting updates. Conversely, if the danger is high, the self-protection mechanism is triggered immediately, regardless of the stage. This dynamic integration allows the algorithm to escape local optima more effectively by simulating the shark's ability to flee predators at any time.
Light-Dark Interactive Strategy: Introduced in the new fourth stage, this strategy simulates the GKS's ability to change skin color based on light intensity to deter predators. Mathematically, this involves "brightening" and "darkening" updates (Eqs. 4.1 and 4.2) that adjust the shark's position based on normalized RGB color values and random interactions with other individuals. This mechanism is combined with the self-protection logic to further balance exploration and exploitation.
Adaptive Parameter $M$ : To overcome the rigidity of the fixed scaling parameter $m$ in the original GKSO, an adaptive parameter $M$ is designed. $M$ is dynamically calculated based on the intersection of the Global Danger Coefficient and the Local Vigilance Factor curves. This allows the olfactory intensity (OI) and convergence direction to adapt to the specific optimization environment, enhancing the search capability of individuals moving toward the best position.
Fish Aggregation Devices (FADs) Strategy: To prevent population stagnation and improve group organization, the FADs strategy is applied after the four main stages. It acts as an independent update mechanism that generates new candidate solutions by simulating fish gathering behavior. This introduces diversity into the population and guides individuals toward higher-quality solution regions.

Key Contributions

Algorithmic Enhancement: The proposal of IGKSO, which integrates the self-protection mechanism into a dynamic, four-stage survival model governed by danger coefficients rather than fixed phases.
Strategic Innovation: The introduction of the Light-Dark interactive strategy and the adaptive parameter $M$ , which collectively improve the algorithm's ability to balance exploration and exploitation in complex landscapes.
Comprehensive Validation: The study validates IGKSO against 11 other MAs (including recent variants like MSA, SBOA, and MTDE) across three distinct testing environments:
- Benchmark Functions: 29 functions from the CEC2017 suite (50 dimensions).
- Static Engineering Problems (SEOPs): Nine problems including frequency-modulated sound wave estimation, process flow sheeting, flywheel design, transformer design, two-reactor optimization, piston rod design, gas transmission compressor design, wind farm layout, and wing flipping design.
- Dynamic Engineering Problems (DEOPs): Two problems involving forced vibration of a beam and error minimization of a two-degree-of-freedom manipulator.

Experimental Results

CEC2017 Benchmarks: IGKSO achieved the best results on 41.38% of the 29 test functions (12 functions), ranking first overall with a mean rank of 2.414. It demonstrated superior convergence rates and stability compared to the original GKSO and other state-of-the-art algorithms.
Static Engineering Problems: IGKSO obtained optimal cost and statistical results (Best, Mean, Std) on all nine SEOPs. In several cases (e.g., Piston Rod Design and Wing Flipping Design), it achieved the lowest standard deviation among top-performing algorithms, indicating high robustness.
Dynamic Engineering Problems: For the beam vibration and manipulator error minimization problems, IGKSO achieved the minimum cost functions and demonstrated the smallest standard deviations, confirming its effectiveness in handling time-varying constraints and dynamic system states.

Significance and Claims
The paper claims that IGKSO is a "well-established and efficient method" for solving engineering optimization problems with complicated constraints. The authors assert that the proposed strategies successfully address the limitations of the original GKSO, particularly regarding the dynamic coordination of exploration and exploitation. By modeling the shark's survival rules more realistically through interdependent danger factors and adaptive parameters, the algorithm demonstrates a superior capacity to cast off local optima and navigate complex search spaces. The study concludes that IGKSO offers a significant advancement in meta-heuristic optimization, providing a robust tool for both static and dynamic engineering applications. Future work is suggested to extend IGKSO to feature selection, path planning, and curve shape optimization.

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