Weight Reduction of a Speed Reducer using Modified Particle Swarm Optimization and Shuffled Frog Leaping Algorithm

Objectives

• Identify the minimal cost function evaluation for the given constraints
• Identify the optimal combination of algorithm specific parameters (in this case - 𝜔, c₁, c₂) for the problem

Problem Diagram

Results

• The cost function evaluation obtained using modified PSO and SFLA were 8.1790% lower than the result obtained using the Taguchi method by Ku et al. (1998), 1.1619% (Crude Monte-Carlo method) and 13.41% (Stray Process) lower than that obtained by Jan Golinski (1970), and around 11% lower than results obtained by other researchers.
• Optimal parameter combinations:
  • PSO: 𝜔 = 0.5, c₁ = 1.5 and c₂ = 1.5, for a population size of 30
  • SFLA: 𝜔 = 1, c₁ = 2 and c₂ = 0.5, for a population size of 150 (15 memeplexes with 10 frogs each)
• Modified SFLA generally takes lesser number of convergence iterations (CI) on average as compared to modified PSO.
• The average run time (RT) for the same number of iterations (1000) is greater for modified SFLA.

Tools Used

• MATLAB - A programming and numeric computing platform
  • To implement PSO and SFLA algorithms
• Python - A high-level, general-purpose programming language
  • To statistically analyse project results
  • NumPy - A fundamental package for scientific computing in Python
  • Matplotlib - A comprehensive library for creating static, animated, and interactive visualizations in Python
  • Pandas - a fast, powerful, flexible and easy to use open source data analysis and manipulation tool
  • Seaborn - a Python data visualization library based on matplotlib

Other Resources Used

• Optimization Test Problems - For benchmark functions

References

• Ku, K. J., Rao, S. S., & Chen, L. (1998). Taguchi-aided search method for design optimization of engineering systems. Engineering Optimization, 30(1), 1–23. https://doi.org/10.1080/03052159808941235
• Jan Golinski. (1970). Optimal synthesis problems solved by means of nonlinear programming and random methods. Journal of Mechanisms, 5(3), 287–309. https://doi.org/10.1016/0022-2569(70)90064-9
• Heris, M. K. (2015). Shuffled Frog Leaping Algorithm in MATLAB. Yarpiz. https://yarpiz.com/71/ypea109-shuffled-frog-leaping-algorithm
• Heris, M. K. (2016). Particle Swarm Optimization (PSO) in MATLAB - Video Tutorial. Yarpiz. https://yarpiz.com/440/ytea101-particle-swarm-optimization-pso-in-matlab-video-tutorial
• Kotecha, P. (2020, March 11). Lec 22 : Constraint-Handling in Metaheuristic Techniques - YouTube. NPTEL IIT Guwahati