Modified Rat Swarm Optimizer (MRSO) for Global Optimization

Adaptive metaheuristic (MRSO) that improves the Rat Swarm Optimizer's exploration-exploitation balance for global optimization.

The Modified Rat Swarm Optimizer (MRSO) is a population-based, nature-inspired metaheuristic for continuous global optimization. MRSO extends the original Rat Swarm Optimizer (RSO) — inspired by the social chasing and fighting behaviour of rats — by reformulating RSO's single, static exploration/exploitation coefficient into a three-term adaptive coefficient. This directly addresses RSO's main known weaknesses: a tendency to converge prematurely, difficulty maintaining the exploration/exploitation balance, and susceptibility to local optima in multimodal and fixed-dimension multimodal problems.

How MRSO works

Every rat (candidate solution) is moved each iteration by a single, unified chasing-and-fighting update rather than a hard switch between separate exploration and exploitation rules. The balance between global search and local refinement is governed continuously by an adaptive coefficient built from three terms:

• F1 = R - l·(R/MaxIter) — linearly shrinks with iteration count.
• F2 = 1 - it·(1/MaxIter) — a second, independent linear decay.
• F3 = 2·rand - 1·rand — a stochastic sign/scale term.

The product of these three terms (the modified coefficient) produces large, exploratory jumps early in the run and progressively tightens the search around the best-known rat as iterations proceed, giving MRSO a richer, less easily-saturated exploration/exploitation balance than the original RSO.

Key features

• Adaptive, three-term coefficient replacing RSO's single static formula — the core enhancement over standard RSO.
• Simple, low-overhead update rule — no gradients or problem-specific tuning required.
• Convergence-curve output for immediate visualization.

Validated in the associated publication against:

• The classical 23-function benchmark suite, where MRSO outperformed the original RSO in six out of nine multimodal functions and all seven fixed-dimension multimodal functions.
• The CEC 2019 benchmark suite (10 functions), where MRSO outperformed RSO in six out of ten functions.
• Seven real-world constrained engineering design problems (including welded beam, pressure vessel, and gear train design), where MRSO consistently delivered better average results than RSO.
• Comparative evaluation against eight recent and well-known algorithms (SCA, MRA, LCA, CSA, TSA, DOA, EHO, WSO), outperforming each on six of 23 classical and four of 10 CEC-2019 benchmark functions, with significance confirmed by the Wilcoxon rank-sum and Friedman mean-rank tests.