PSA: A novel optimization algorithm based on survival rules of porcellio scaber

Bio-inspired algorithms such as neural network algorithms and genetic algorithms have received a significant amount of attention in both academic and engineering societies. In this paper, based on the observation of two major survival rules of a species of woodlice, i.e., porcellio scaber, we present an algorithm called the porcellio scaber algorithm (PSA) for solving general unconstrained optimization problems, including differentiable and non-differential ones as well as the case with local optima. Numerical results based on benchmark problems are presented to validate the efficacy of PSA.

💡 Research Summary

The paper introduces a new bio‑inspired optimization method called the Porcellio scaber Algorithm (PSA), which is derived from the observed survival behaviors of the woodlouse species Porcellio scaber. Two fundamental biological rules are identified: (1) aggregation, where individuals cluster at locations offering the most favorable environmental conditions, and (2) a propensity to explore novel environments when conditions are suboptimal. The authors translate these rules into a mathematical model that combines a deterministic pull toward the current best position in the population with a stochastic exploratory step.

The deterministic component is expressed as a weighted difference between an individual’s current position and the best‑fitness position among all individuals, scaled by a factor (1 − λ). The exploratory component is modeled as λ p τ, where τ is a random direction vector of the same dimensionality as the decision variables, and p is a normalized measure of the fitness improvement that would be obtained by moving a small step τ from the current position. The overall update rule for each individual i at iteration k is:
x_{k+1}^i = x_k^i − (1 − λ)(x_k^i − x*) − λ p τ,
where x* = arg min_j f(x_k^j) is the best current position. The parameter λ ∈ (0, 1) balances exploitation (aggregation) and exploration (novel‑environment search).

Algorithm 1 outlines the PSA procedure: initialize N agents randomly within the search domain, evaluate the objective function f(x) for each agent, and iteratively update positions using the rule above until a maximum number of steps (MaxStep) is reached or convergence criteria are satisfied. The algorithm is deliberately simple, requiring only the choice of λ, the distribution of τ (typically zero‑mean Gaussian with a small standard deviation), and the number of agents N.

To assess performance, the authors apply PSA to three benchmark problems that span a range of difficulty characteristics:

1. Michalewicz function (d = 2, m = 10) – a highly multimodal, differentiable function with many local minima. Using N = 20 agents, λ = 0.8, and 40 iterations, PSA converged to a solution near the known global minimum f* ≈ −1.801, demonstrating effective escape from local traps.

2. Goldstein‑Price function – a non‑convex, multimodal function with four local minima and a global minimum at x* =