💻 computer science

Bombardier Beetle Optimizer: A Novel Bio-Inspired Algorithm for Global Optimization

This paper proposes the Bombardier Beetle Optimizer (BBO), a novel bio-inspired algorithm that mimics the beetle's chemical defense and escape mechanisms to achieve superior convergence rates and solution quality compared to existing metaheuristic algorithms on CEC 2017 benchmark tests.

Original authors: Hisham A. Shehadeh, Mohd Yamani Idna Idris, Iqbal H. Jebril

Published 2026-06-10

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CC BY 4.0

Original authors: Hisham A. Shehadeh, Mohd Yamani Idna Idris, Iqbal H. Jebril

Original paper licensed under CC BY 4.0 (http://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

The Big Picture: Finding the Best Spot in a Maze

Imagine you are trying to find the absolute lowest point in a massive, foggy, mountainous landscape. This is what computer scientists call an "optimization problem." You want to find the perfect solution (the bottom of the valley), but the terrain is tricky. There are many small dips (local minima) that look like the bottom but aren't, and the fog makes it hard to see the whole map.

For years, computers have used different "strategies" to navigate this maze. Some act like a flock of birds (PSO), others like a wolf pack (GWO), and some even mimic historical disasters like Chernobyl (CDO).

This paper introduces a new strategy called the Bombardier Beetle Optimizer (BBO). It's a new way for computers to search for answers, inspired by a tiny, tough insect: the Bombardier Beetle.

The Inspiration: The Beetle's Superpower

The Bombardier Beetle is famous for one thing: its defense mechanism. When a predator (like a frog or a bird) gets too close, the beetle doesn't just run; it fights back.

Inside its belly, the beetle stores two harmless chemicals. But when threatened, it mixes them in a special chamber. This creates a violent, boiling chemical reaction that shoots a hot, toxic spray out of its rear end at the predator. It's like a tiny, living flamethrower.

The beetle also has a second trick: if the predator is too close, it calculates the distance and flies away to safety.

How the Computer Algorithm Works

The authors took these two beetle behaviors and turned them into math rules for a computer program. Here is how the "Bombardier Beetle Optimizer" solves problems:

1. The "Chemical Spray" (Exploration)
Imagine a group of beetles (solutions) wandering around a dark room. If a beetle gets too close to a "predator" (a bad solution or a trap), it triggers its defense.

In the math: The computer calculates the distance between a current solution and a "predator." If they are too close, the beetle "sprays" a toxic cloud.
The Analogy: Think of this spray as a chaotic explosion that pushes the beetle in a new, random direction. It forces the beetle to jump out of a small, boring dip in the ground and land somewhere completely new. This helps the computer avoid getting stuck in "fake" low points and keeps it exploring the whole map.

2. The "Escape Flight" (Exploitation)
If the beetle is safe but needs to find the best spot, it uses its wings.

In the math: The computer uses physics equations (specifically Newton's laws of motion and lift) to calculate how the beetle should fly.
The Analogy: This is like the beetle gliding smoothly toward the deepest, most promising valley it has seen so far. It refines its position, getting closer and closer to the perfect answer without jumping around wildly.

The Test: Who Wins the Race?

To see if this new beetle strategy was any good, the authors put it in a race against six other famous algorithms:

Chernobyl Disaster Optimizer (CDO): Based on nuclear radiation.
Bermuda Triangle Optimizer (BTO): Based on ships vanishing in a mysterious triangle.
Grey Wolf Optimizer (GWO): Based on wolf hunting packs.
Particle Swarm Optimization (PSO): Based on birds flocking.
Sperm Swarm Optimization (SSO): Based on sperm swimming to an egg.
Gravitational Search Algorithm (GSA): Based on gravity pulling objects together.

They tested all of them on 23 different math puzzles (known as the CEC 2017 benchmarks). These puzzles range from simple hills to extremely rugged, noisy, and confusing landscapes.

The Results: The Beetle Takes the Crown

The paper claims that the Bombardier Beetle Optimizer (BBO) was the clear winner.

Speed: The beetle algorithm found the best answers faster than the others.
Accuracy: It found the "true" bottom of the valleys more often, especially in the hardest, most confusing puzzles where the other algorithms got stuck.
Consistency: If you ran the test 10 times, the beetle algorithm gave the best results almost every time, whereas the others were more hit-or-miss.

In the final scoreboard (called "Mean Rank"), the Beetle came in 1st place. The Chernobyl optimizer came in 2nd, and the Bermuda Triangle optimizer came in 3rd. The others trailed behind.

The Conclusion

The authors conclude that by copying the Bombardier Beetle's ability to blast away from danger (to explore new areas) and fly precisely to safety (to refine the answer), they created a superior tool for solving complex math problems.

They suggest that while this new tool is excellent at solving these specific math puzzles, it should be tested on real-world problems in the future, such as improving radio networks or wireless sensors. However, for now, the paper simply proves that the beetle strategy is the most efficient way to navigate the math maze among the competitors they tested.

Technical Summary: Bombardier Beetle Optimizer (BBO)

Problem Statement

Real-world optimization problems, such as those found in wireless sensor networks, biomedical engineering, and general engineering design, often present significant challenges due to complex geometries containing numerous local minima. Traditional optimization methods frequently struggle to escape these local optima, resulting in slow convergence rates or suboptimal solutions. While existing metaheuristic algorithms—categorized into physical-based, swarm-based, evolutionary, and manmade classes—offer various advantages, they still face limitations such as premature convergence, slow exploration, and difficulties in balancing exploration and exploitation strategies. To address these deficiencies, this paper proposes a novel bio-inspired algorithm designed to enhance global optimization performance.

Methodology

The proposed Bombardier Beetle Optimizer (BBO) is a bio-inspired metaheuristic algorithm modeled after the defense and escape mechanisms of the Bombardier Beetle (Carabidae family). The algorithm simulates two primary biological behaviors:

1. Defense Mechanism (Exploration)

The core of the BBO's exploration strategy mimics the beetle's ability to eject a hot, toxic chemical spray when threatened by a predator.

Chemical Reaction: The model incorporates the beetle's internal reaction chamber where Hydroquinone and Hydrogen peroxide react via catalase and peroxidase enzymes. This exothermic reaction produces a spray exceeding 100°C, consisting of water vapor, oxygen, and irritating p-benzoquinones.
Geometric Simulation: The algorithm models the interaction between the beetle and a predator as two intersecting circles. The "spray" is triggered when the predator's area intersects or overlaps with the beetle's area.
Mathematical Formulation: The intersection area ( $A$ ) is calculated using a specific geometric equation involving the radii of the beetle and predator and the distance between their centers. The new position of the beetle is updated based on this intersection area, a chemical reaction factor (incorporating temperature, oxygen, and irritant values), and a chaotic spreading function. This mechanism is designed to disperse the population across the search space, aiding in the avoidance of local optima.

2. Escape Mechanism (Exploitation)

The second phase simulates the beetle's ability to calculate the distance from a predator and fly away.

Aerodynamic Lift: This behavior is modeled using Newton's laws of motion and an empirical lift equation for flapping flight ( $L = LC \times 0.5 \times \rho \times V^2 \times A$ ).
Position Update: The algorithm calculates an upward reactive force (lift) to determine a new position, allowing the beetle to move away from the threat (local minima) toward better solutions. This phase focuses on refining the search and exploiting promising regions.

Algorithm Execution

The BBO initializes a population of beetles within the problem's search space bounds. In each iteration, the algorithm alternates between the defense mechanism (exploration) and the escape mechanism (exploitation). The population is updated based on the objective function values, retaining the best solutions found. The process continues until the maximum number of iterations is reached.

Key Contributions

Novel Algorithm: The introduction of the Bombardier Beetle Optimizer (BBO), a new metaheuristic inspired by the specific chemical defense and escape behaviors of the Bombardier Beetle.
Hybrid Mechanism: The integration of a chemical reaction-based spray model (for exploration) and an aerodynamic lift model (for exploitation) to balance the search process.
Comprehensive Evaluation: A rigorous comparative study against six established metaheuristic algorithms: Chernobyl Disaster Optimizer (CDO), Sperm Swarm Optimization (SSO), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), Bermuda Triangle Optimizer (BTO), and Grey Wolf Optimizer (GWO).

Experimental Results

The performance of BBO was evaluated using the CEC 2017 test bed suite, comprising 23 benchmark functions (including unimodal, multimodal, and hybrid functions). The experiments were conducted in MATLAB R2023a with 30 independent runs per algorithm, each running for 1,000 iterations.

Performance Metrics: The algorithms were compared based on Best Fitness (optimal value), Mean ( $\mu$ ), Standard Deviation ( $\sigma$ ), and Mean Rank.
Quantitative Outcomes:
- BBO achieved the lowest total mean rank (3.9) among all tested algorithms, significantly outperforming CDO (8.65), SSO (9.51), GSA (12.06), PSO (9.9), BTO (8.9), and GWO (9.61).
- BBO obtained the best fitness values for 20 out of the 23 benchmark functions (F1–F8, F10, F11, F13–F18, F21–F23).
- In terms of convergence, BBO demonstrated superior speed and accuracy in reaching global minima, particularly in "rugged and noisy" problems (F1–F4) and functions with narrow domains.
Comparative Analysis: While other algorithms showed strength in specific subsets (e.g., CDO and BTO performed well on certain unimodal functions), BBO consistently provided more stable results with lower standard deviations across the majority of the test suite.

Significance and Claims

The paper claims that the Bombardier Beetle Optimizer is a highly efficient and feasible alternative for global optimization problems. The authors assert that BBO's unique combination of a chemically inspired defense mechanism and a physics-based escape mechanism allows it to effectively balance exploration and exploitation.

The study concludes that BBO outperforms the compared algorithms (PSO, SSO, GSA, GWO, BTO, and CDO) in terms of convergence rate and solution quality, particularly for complex, rugged, and noisy search spaces. The authors suggest that while the current results are promising based on CEC 2017 benchmarks, future work should validate the algorithm's efficacy on real-world applications, specifically citing Wireless Sensor Networks (WSN) for minimizing attenuation and interference, and Radio Networks (RN) for maximizing signal propagation. The paper maintains a modest tone regarding these future applications, noting that the test suites used have limitations and that further tuning may be required for specific real-world scenarios.