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Further Commentary on the Sooty Tern Optimization Algorithm and Tunicate Swarm Algorithm

Ngaiming Kwok

TL;DR

This work builds on Kudela's critique to identify the probabilistic origins of zero-bias in STOA and TSA. It shows that exponentiation, trigonometric transforms, and divisions involving random numbers distort search-space sampling away from uniformity, biasing updates toward zero. By analyzing core update rules and correcting key formulations (e.g., $\rho=\exp(-\theta)$ and division-based steps), the authors illustrate the resulting PDFs and demonstrate the practical impact on exploration. The results underscore the need to simplify BNIOA designs and ensure uniform-space exploration to preserve optimization performance across nonzero optima.

Abstract

In the article (Kudela, 2022), experimental demonstrations indicated that two Bio-/Nature inspired optimization algorithms (BNIOAs), Sooty Tern Optimization Algorithm (STOA) and Tunicate Swarm Algorithm (TSA), exhibit a zero-bias, leading to the conclusion that the claims made in the original papers were overstated. In this work, we extend the analysis by investigating the source of this bias from a probabilistic perspective. Our findings suggest that operations involving exponentiation, trigonometric functions, and divisions between random numbers are the primary causes of design flaws. These operations result in probability density distributions with a noticeable shift toward zero. Therefore, the application of these two algorithms should be approached with due caution.

Further Commentary on the Sooty Tern Optimization Algorithm and Tunicate Swarm Algorithm

TL;DR

This work builds on Kudela's critique to identify the probabilistic origins of zero-bias in STOA and TSA. It shows that exponentiation, trigonometric transforms, and divisions involving random numbers distort search-space sampling away from uniformity, biasing updates toward zero. By analyzing core update rules and correcting key formulations (e.g., and division-based steps), the authors illustrate the resulting PDFs and demonstrate the practical impact on exploration. The results underscore the need to simplify BNIOA designs and ensure uniform-space exploration to preserve optimization performance across nonzero optima.

Abstract

In the article (Kudela, 2022), experimental demonstrations indicated that two Bio-/Nature inspired optimization algorithms (BNIOAs), Sooty Tern Optimization Algorithm (STOA) and Tunicate Swarm Algorithm (TSA), exhibit a zero-bias, leading to the conclusion that the claims made in the original papers were overstated. In this work, we extend the analysis by investigating the source of this bias from a probabilistic perspective. Our findings suggest that operations involving exponentiation, trigonometric functions, and divisions between random numbers are the primary causes of design flaws. These operations result in probability density distributions with a noticeable shift toward zero. Therefore, the application of these two algorithms should be approached with due caution.

Paper Structure

This paper contains 22 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Necessity of Uniform Distribution
  3. Concerned Algorithms
  4. STOA
  5. Exploration:
  6. Collision avoidance:
  7. Convergence to the best-so-far agent:
  8. Update step-size:
  9. Exploitation:
  10. TSA
  11. Avoiding Conflicts:
  12. Movement Towards Best-So-Far:
  13. Remaining Around Best-So-Far:
  14. Swarm Behavior:
  15. Design Flaws and Zero-Bias
  16. ...and 7 more sections

Figures (2)

  • Figure 1: PDF of the intermediate STOA stages. (a) convergence to best-so-far, (b)sine and cosin terms in Eq. \ref{['eq:STOA trajectory']}, (c) exploitation stage, (d) updated agent position.
  • Figure 2: PDF of the intermediate TSA stages. (a) movement factor $\mathbf a$, (b) movement towards best-so-far, (c) remain around best-so-far, (d) swarm behavior.