Bombardier Beetle Optimizer (BBO)

• Bombardier Beetle Optimizer (BBO) is a bio-inspired metaheuristic that emulates the beetle's defense and escape strategies for efficient global optimization.
• It integrates stochastic exploration via a chemical spray mechanism with deterministic exploitation based on Newtonian lift to adjust candidate solutions dynamically.
• Empirical tests on the CEC 2017 benchmark reveal BBO's superior convergence speed and solution quality compared to several established metaheuristics.

The Bombardier Beetle Optimizer (BBO) is a novel bio-inspired metaheuristic optimization algorithm that emulates the unique defense and escape mechanisms of the bombardier beetle. Incorporating mathematically faithful analogues of interactions between beetles and predators, BBO merges exploration (stochastic chemical spray-based defense) with exploitation (Newtonian lift-driven escape) to drive search in complex, multimodal objective landscapes. The algorithm has demonstrated efficiency and competitiveness on challenging global optimization tasks, as validated using the CEC 2017 benchmark suite, outperforming established metaheuristics in convergence behavior and solution quality.

1. Biological Inspiration and Mechanistic Analogy

The core design of BBO draws on the bombardier beetle’s natural responses to predation. When threatened, the beetle stores hydroquinone and hydrogen peroxide in separate abdominal chambers; upon attack, these are mixed in a reaction chamber, catalyzed by enzymes (catalase and peroxidase), triggering an exothermic process that forcefully ejects hot vapor, oxygen, and irritating p-benzoquinones. BBO translates these elements into two algorithmic components:

• Defense Mechanism (Exploration): Modeled via intersection detection between candidate “beetle” and “predator” circles in the search space; triggering a stochastic chemical spray function upon overlap.
• Escape Mechanism (Exploitation): Captured through a lift-based “flight” modeled on Newton’s laws, enabling candidate solutions to dynamically adjust positions and escape potential local minima.

These mechanisms together allow dynamic shifts between global exploration and local exploitation in the optimization context.

2. Algorithm Structure

BBO operates in two principal phases, initialization and iterative search, which are structured as follows:

Initialization

Candidate solutions (“beetles”) are randomized within problem bounds using: $X_{i,d} = lba + r \times (uba - lba)$ where $r \sim U[0, 1]$, and $lba, uba$ denote variable bounds for dimension $d$.

Iterative Search

Each iteration for every candidate (indexed by $i$) performs:

• Defense:
  • Computes intersection area (circle overlap) with a predator.
  • Triggers a stochastic spray if overlap detected, introducing chaos and nonlinearity via:

  $$Spray = chaos \times 2.7^{iteration / Max\_Iteration}$$

  where “chaos” encompasses chaotic map randomization. - Updates position based on predator position, intersection area (CIA), and a chemical reaction factor (CR) combining constants and random perturbations:

  $$X_{i,d}^{new} = X_{i,d} + (SelectedPredator_{i,d} > CIA \times CR \times X_{i,d}^{Spray})$$

• Escape:
  • Applies lift-based model:

  $L = LC \times 0.5 \times \rho \times V^2 \times A$

  where $LC$ is lift coefficient, $\rho$ is air density, $V$ is relative wing velocity, and $A$ is effective area. - Updates position if the new solution yields improved objective function value.

The best candidate is tracked and updated iteratively. The complete pseudocode is encapsulated in Algorithm 1 from the source.

3. Mathematical Foundation

BBO’s principal mathematical constructs are summarized as follows:

Phenomenon	Equation and Role	Variables Involved
Initialization	$X_{i,d} = lba + r \times (uba - lba)$ (Eq. 29)	$r, lba, uba, i, d$
Circle Intersection	Area: $$A = r^2 \cos^{-1}\left(E_1\right) + R^2 \cos^{-1}\left(E_2\right) - 0.5 \sqrt{F}$$ (Eq. 30)	$r, R, d$, with $E_1, E_2, F$ as per Eq. (30)
Spray Factor	$$Spray = chaos \times 2.7^{Iteration/Max\_Iteration}$$ (Eq. 33)	chaos, Iteration, Max_Iteration
Defense Update	$$X_{i,d}^{new} = X_{i,d} + (SelectedPredator_{i,d} > CIA \times CR \times X_{i,d}^{Spray})$$ (Eq. 31)	see above
Escape (Lift)	$L = LC \times 0.5 \times \rho \times V^2 \times A$ (Eq. 34)	$LC, \rho, V, A$

These components effectuate a balance between global search (scattering candidates in response to “threats”) and local search (exploiting promising regions).

4. Benchmarking and Comparative Performance

BBO’s efficacy was empirically established on the CEC 2017 suite (23 test functions), with benchmarking against six established metaheuristics: Chernobyl Disaster Optimizer (CDO), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Bermuda Triangle Optimizer (BTO), Sperm Swarm Optimization (SSO), and Gravitational Search Algorithm (GSA).

Summary of empirical results:

• Attained the exact optimal value on 20/23 benchmark functions, including rugged and noisy landscapes.
• Exhibited superior convergence rates as measured by mean, standard deviation, and best fitness.
• Outperformed all compared methods in mean rank (total mean rank of 3.9), with convergence curves showing faster attainment of global minima.
• Demonstrated stability and robustness on complex multimodal search spaces.

This performance positions BBO as highly competitive for diverse optimization domains requiring both exploration and exploitation.

5. Potential Applications

BBO’s exploration-exploitation dynamics and resilience to local minima suggest applicability across a spectrum of optimization problems, including:

• Engineering and biomedical optimization with multimodal characteristics.
• Wireless Sensor Networks (WSNs) and Radio Networks (RNs), addressing deployment, coverage, and interference minimization tasks.
• Underwater sensor network design, accommodating challenges of signal propagation and attenuation.
• Other real-world NP-hard domains such as power dispatch, communications, and robotic path planning, where rugged fitness landscapes and noise are salient.

This suggests BBO is particularly suited for problems characterized by high-dimensionality, ruggedness, and nonconvexity.

6. Implications, Limitations, and Future Work

BBO’s demonstrated performance, especially its capability to avoid premature convergence and rapidly attain global optima, implies strong potential as an alternative to conventional metaheuristics in time-sensitive or high-stakes applications. Possible future directions explicitly noted include:

• Hybridization with other metaheuristics to further enhance robustness or adaptivity.
• Refinement of chaotic spray components to tune the exploration/exploitation balance.
• Adaptation for dynamic or multi-objective optimization scenarios.
• Further parameter sensitivity analysis to characterize algorithmic stability.

A plausible implication is that BBO may catalyze new research into bio-inspired optimization, particularly those leveraging sophisticated animal defense or escape behaviors as stochastic operators.

7. Conclusion

The Bombardier Beetle Optimizer (BBO) introduces a rigorous bio-inspired framework for global optimization, mathematically codifying aspects of chemical defense and aerodynamic escape. Its performance on recognized benchmarks against leading metaheuristics confirms its speed and solution quality. Ongoing extensions, including hybrid and domain-tailored variants, are anticipated to broaden applicability and efficacy in both theoretical and applied optimization research (Shehadeh et al., 19 Oct 2025).