💻 computer science

GeoSSA: Geometric Sparrow Search Algorithm for UAV Path Planning and Engineering Design Optimization

This paper proposes the Geometric Sparrow Search Algorithm (GeoSSA), which enhances the original SSA through geometric initialization and improved update strategies to achieve superior global optimization performance, stability, and robustness in benchmark testing, UAV path planning, and engineering design problems.

Original authors: Junhao Wei, Wenxuan Zhu, Qingyang Xu, Yanxiao Li, Yifu Zhao, Zikun Li, Ran Zhang, Yanzhao Gu, Jinhong Song, Yapeng Wang, Zhiwen Wang, Ngai Cheong, Sio-Kei Im, Xu Yang

Published 2026-01-28

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Junhao Wei, Wenxuan Zhu, Qingyang Xu, Yanxiao Li, Yifu Zhao, Zikun Li, Ran Zhang, Yanzhao Gu, Jinhong Song, Yapeng Wang, Zhiwen Wang, Ngai Cheong, Sio-Kei Im, Xu Yang

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

Imagine you are trying to find the absolute best route for a delivery drone to fly through a busy city, or you are trying to design a machine part that is strong but uses the least amount of material possible. These are "optimization problems." You have millions of possible answers, but only one is the perfect "Goldilocks" solution—not too long, not too short, just right.

For decades, scientists have used "metaheuristic algorithms" to solve these puzzles. Think of these algorithms as a team of explorers sent into a dark, foggy forest to find the highest peak (the best solution).

The Original Team: The Sparrows

One popular explorer team is called the Sparrow Search Algorithm (SSA). It mimics a flock of sparrows looking for food.

Producers: A few brave birds that lead the way, searching for food in wide areas.
Scroungers: The rest of the flock that follows the leaders, hoping to find food near them.
Edge Sparrows: Birds on the outside of the flock that watch for predators (dangers) and move to safety.

The Problem: The original team has a flaw. Sometimes the birds get too comfortable in one spot, thinking they found the best food, only to realize later they were stuck in a small valley while a huge mountain peak was right next to them. They get "stuck" too early (premature convergence) and miss the real best answer.

The New Team: GeoSSA (The Geometric Sparrows)

The authors of this paper, a team from Macao Polytechnic University and others, decided to upgrade the flock. They created GeoSSA (Geometric Sparrow Search Algorithm). They didn't just tweak the rules; they gave the birds three superpowers to make them smarter explorers.

1. The "Perfect Map" Start (Good Nodes Set Initialization)

The Old Way: When the original flock started, they were placed randomly, like throwing darts blindfolded onto a map. This often meant too many birds landed in the same spot (clumping) while huge areas of the map were left empty.
The GeoSSA Upgrade: Instead of random throwing, they used a "Good Nodes Set." Imagine laying out a grid of tiles so perfectly that every single inch of the map is covered evenly, with no gaps and no clumps.

Why it helps: The birds start with a perfect view of the whole forest, ensuring they don't miss any potential "food sources" right from the beginning.

2. The "Sine-Cosine" Leap (Enhanced Producer Update)

The Old Way: The leader birds (Producers) moved using simple, predictable steps. If they were close to a good spot, they just took small steps forward. If they were far, they might jump, but the jump wasn't very smart.
The GeoSSA Upgrade: The leaders now use a mix of Sine and Cosine functions (mathematical waves) to decide how to move.

The Analogy: Imagine the leader bird doesn't just walk in a straight line. Instead, it dances in a wave pattern. Sometimes the wave tells it to take a giant, sweeping leap to a totally new part of the forest (exploration). Other times, the wave tells it to take tiny, careful steps to polish a good spot (exploitation).
Why it helps: This prevents the birds from getting stuck in a local valley. They can make big, strategic jumps to find the real highest peak.

3. The "Triangular Walk" Safety Net (Enhanced Edge Update)

The Old Way: The birds on the edge of the flock (who are most vulnerable) moved in simple, straight lines to escape danger. This was too rigid.
The GeoSSA Upgrade: These birds now use a "Triangular Walk."

The Analogy: Instead of running in a straight line away from a predator, imagine a bird running in a triangle shape. It moves forward, then angles sharply left, then angles right. This creates a zig-zag path that is much harder to predict and allows the bird to explore the immediate area more thoroughly before settling down.
Why it helps: It adds a layer of randomness and flexibility, helping the flock escape tricky traps (local optima) that would have caught the original birds.

Putting It to the Test

The researchers put this new "Super Flock" through three major trials:

The Math Gym (Benchmark Functions): They tested the algorithm on 23 different complex math puzzles.
- Result: GeoSSA won almost every time. It found the best answers faster and more consistently than the original Sparrows and other famous explorer teams (like Wolf Optimizers or Ant Colony algorithms). It had a "Win Rate" of 95.65%.
The Drone Race (UAV Path Planning): They asked the algorithms to plan a 3D flight path for a drone to fly from Point A to Point B while avoiding obstacles.
- Result: GeoSSA drew the smoothest, shortest, and safest path. Other algorithms sometimes crashed into walls or took very long, winding routes. GeoSSA's path was stable and reliable.
The Engineering Workshop: They used the algorithm to solve four real-world engineering design problems:
- Designing a Corrugated Bulkhead (a strong wall for chemical tanks).
- Designing a Piston Lever (a part for pumps).
- Designing a Reactor Network (for chemical plants).
- Designing an Industrial Refrigeration System.
- Result: In all four cases, GeoSSA found the most efficient designs (using less material or energy) and did so with the most consistency. It didn't just get lucky once; it got the best result every single time it ran the test.

The Bottom Line

The paper claims that by giving the Sparrow Search Algorithm a better starting map, smarter movement rules for its leaders, and a more flexible escape strategy for its edge members, they created a tool that is significantly better at solving complex puzzles.

Whether it's guiding a drone through a city or designing a machine part, GeoSSA is presented as a more reliable, faster, and smarter way to find the "perfect" solution among millions of possibilities. It doesn't just guess; it explores the whole forest systematically and knows exactly when to take a giant leap and when to take a careful step.

Technical Summary: Geometric Sparrow Search Algorithm (GeoSSA) for UAV Path Planning and Engineering Design Optimization

Problem Statement
The Sparrow Search Algorithm (SSA), a population-based metaheuristic inspired by the foraging and anti-predation behaviors of sparrows, is known for its simple structure and ease of implementation. However, the original SSA suffers from an insufficient balance between exploration (global search) and exploitation (local search). This imbalance often leads to premature convergence, slow optimization progress, and a tendency to get trapped in local optima, particularly when addressing high-dimensional, complex, and multimodal optimization problems. These limitations hinder its effectiveness in critical real-world applications such as 3D Unmanned Aerial Vehicle (UAV) path planning and complex engineering design optimization, where robust global search capabilities and high solution stability are required.

Methodology
To address these deficiencies, the authors propose the Geometric Sparrow Search Algorithm (GeoSSA). This enhanced algorithm integrates three specific strategies to improve the original SSA's performance:

Good Nodes Set Initialization: Replacing the traditional pseudo-random number initialization, GeoSSA utilizes the "Good Nodes Set" method (based on Hua Luogeng's number theory). This approach generates a population with a more uniform spatial distribution across the search space, effectively preventing population clustering and ensuring broader coverage during the initial exploration phase. This method is noted for maintaining uniformity even in high-dimensional spaces.
Sine-Cosine Enhanced Producer Position Update: The update mechanism for "producers" (the individuals with the best fitness) is modified to incorporate sine and cosine functions. A decision logic based on the alarm value ( $R_2$ ) determines whether to use sine or cosine functions to control the position update. Additionally, an adaptive inertia weight based on a sigmoid function is introduced. This strategy enhances global search diversity, allowing producers to make wider jumps in the solution space to escape local optima while maintaining a balance between exploration and exploitation.
Triangular Walk Enhanced Edge Sparrow Position Update: For "edge sparrows" (individuals with poorer fitness), the algorithm introduces a Triangular Walk mechanism. This involves a dynamic adjustment factor and a random disturbance mechanism based on trigonometric functions. This strategy increases the randomness of the position update process, breaking the limitation of single-direction perturbations and enhancing the algorithm's ability to escape local optima while improving local search accuracy in later stages.

Key Contributions

Algorithmic Innovation: The development of GeoSSA, which synergistically combines geometric initialization, sine-cosine dynamics, and triangular walk perturbations to address the specific weaknesses of the original SSA.
Comprehensive Validation: The paper conducts a rigorous evaluation of GeoSSA through:
- Ablation Studies: Demonstrating the individual contribution of each proposed strategy.
- Qualitative Analysis: Analyzing search history, exploration-exploitation ratios, and population diversity on 23 standard benchmark functions.
- Comparative Experiments: Benchmarking GeoSSA against state-of-the-art algorithms (AROA, WOA, IWOA, MWOA, IPSO, ISSA) and the original SSA.
Practical Application: The successful application of GeoSSA to two distinct real-world domains:
- 3D UAV Path Planning: Optimizing flight paths to minimize length and height variance while avoiding obstacles and satisfying dynamic constraints.
- Engineering Design Optimization: Solving four complex constrained problems: Corrugated Bulkhead design, Piston Lever design, Reactor Network design, and Industrial Refrigeration System design.

Results
Experimental results indicate that GeoSSA achieves superior performance compared to the compared algorithms:

Benchmark Functions: On 23 benchmark functions, GeoSSA achieved the best or near-best average fitness and standard deviation. It secured the top rank in Friedman tests with an average rank of 1.9514 and an Overall Effectiveness (OE) of 95.65%. Wilcoxon signed-rank tests confirmed statistically significant improvements over most competitors.
UAV Path Planning: In 3D path planning tasks, GeoSSA demonstrated the highest stability (lowest standard deviation of 0.95654) and produced the shortest, smoothest paths with effective obstacle avoidance, outperforming algorithms like IWOA, which suffered from extreme instability.
Engineering Design: In all four engineering design problems, GeoSSA consistently attained the highest solution accuracy (lowest average fitness) and the strongest stability (lowest standard deviation), often reaching theoretical optimal or near-optimal values where other algorithms struggled with convergence or constraint satisfaction.

Significance and Claims
The paper claims that GeoSSA provides an efficient and reliable solution framework for complex optimization problems. By effectively balancing global exploration and local exploitation, GeoSSA overcomes the premature convergence and stagnation issues inherent in the original SSA. The authors assert that the algorithm exhibits strong robustness and generalization ability, making it suitable not only for standard benchmark testing but also for practical engineering applications characterized by high dimensionality, nonlinearity, and complex constraints. The study concludes that GeoSSA represents a significant advancement in metaheuristic optimization, offering a versatile tool for tackling challenging tasks in UAV navigation and engineering design.