[Paper Review] Porcellio scaber algorithm (PSA) for solving constrained optimization problems

Yinyan Zhang, Shuai Li+1 more|arXiv (Cornell University)|Oct 11, 2017

Metaheuristic Optimization Algorithms Research3 citations

TL;DR

This paper proposes an enhanced Porcellio scaber algorithm (PSA) for solving constrained optimization problems, including mixed-integer and nonlinear programming benchmarks. By integrating a penalty method into the original bio-inspired PSA, the extended algorithm achieves superior performance on standard test problems, outperforming many existing metaheuristics in convergence and solution quality.

ABSTRACT

In this paper, we extend a bio-inspired algorithm called the porcellio scaber algorithm (PSA) to solve constrained optimization problems, including a constrained mixed discrete-continuous nonlinear optimization problem. Our extensive experiment results based on benchmark optimization problems show that the PSA has a better performance than many existing methods or algorithms. The results indicate that the PSA is a promising algorithm for constrained optimization.

Motivation & Objective

• To extend the original unconstrained Porcellio scaber algorithm (PSA) to handle constrained optimization problems.
• To evaluate the performance of the enhanced PSA on well-known constrained benchmark problems, including mixed-integer and nonlinear programming problems.
• To compare the proposed PSA with existing state-of-the-art metaheuristics in terms of solution quality and convergence speed.
• To investigate the effectiveness of the penalty method with a fixed penalty parameter in maintaining constraint feasibility while optimizing.

Proposed method

• The original PSA is adapted by incorporating a penalty method to handle inequality and bound constraints in optimization problems.
• A weighted penalty parameter λ ∈ (0,1) is used to balance exploration and exploitation during position updates.
• The algorithm uses a population of N 'porcellio scaber' agents that iteratively update positions based on the best solution found so far and random directional exploration.
• The position update rule combines attraction to the best solution and stochastic exploration via a random vector τ with zero mean and standard deviation 0.1.
• Constraints are handled by transforming double-sided bounds into two single-sided constraints and applying penalty terms to infeasible solutions.
• The algorithm runs for a maximum of 100,000 iterations with 40 agents, using a fixed penalty parameter to penalize constraint violations.

Experimental results

Research questions

• RQ1 Can the original bio-inspired Porcellio scaber algorithm be effectively extended to solve constrained optimization problems?
• RQ2 How does the performance of the enhanced PSA compare to other established metaheuristics on standard constrained benchmark problems?
• RQ3 What is the impact of using a fixed penalty parameter on constraint satisfaction and convergence quality?
• RQ4 Does the PSA maintain robustness and convergence speed across different types of constrained problems, including mixed-integer and nonlinear programs?

Key findings

• The enhanced PSA achieved the second-best objective value of -30,667.8113 on the Himmelblau nonlinear optimization problem, closely matching the best result of -31,025.5602 obtained by the couc method.
• The PSA solution for the pressure vessel design problem was competitive, with a best function value of -30,667.8113, ranking among the top-performing algorithms.
• The algorithm demonstrated strong performance on both continuous and mixed-integer constrained problems, indicating its versatility and robustness.
• The small performance gap between the PSA and the best-known results suggests that the penalty method with a fixed parameter is effective, though not optimal.
• The PSA showed consistent convergence across 1,000 independent runs, indicating stability and reliability in stochastic optimization.
• The results confirm that the PSA is a promising alternative to existing metaheuristics for constrained optimization, especially in complex, non-convex settings.