Slime Mould Algorithms for Global Optimization Problems

Slime mould algorithms (SMAs) are population-based metaheuristic methods inspired by the foraging behaviour of the Physarum polycephalum, a true slime mould known for its ability to form efficient transport networks. By modelling the oscillatory propagation of plasmodial veins and the dynamic allocation of nutrient flux, SMAs iteratively adjust the positions of candidate solutions to explore and exploit the search space. Their inherent capacity for distributed exploration, rapid convergence and adaptability has positioned SMAs as a versatile tool for tackling continuous and discrete global optimisation challenges. Key strengths of the approach include robust performance on multimodal landscapes and flexibility for hybridisation with other strategies such as chaotic maps, distribution-based mutations and sampling criteria from simulated annealing. Practical applications span engineering design, resource scheduling, network coverage, robotics path planning and combinatorial problems. Ongoing research efforts focus on enhancing the balance between exploration and exploitation, avoiding premature convergence, and scaling to high-dimensional or constrained scenarios through adaptive parameter control and hybrid operators.

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Recent work has advanced the classic SMA by integrating dominant swarm concepts and adaptive distribution-based mutations. One approach introduces an adaptive t-distribution mutation alongside a dominant-swarm mechanism that accelerates convergence while maintaining diversity. Tested on benchmark suites and an inverse kinematics problem for a seven-degree-of-freedom robotic manipulator, this variant achieved superior global search capability and solution quality compared with the original SMA and several contemporary metaheuristics. A second line of investigation hybridises SMA with chaotic maps and differential evolution. Chaotic sequences initialise the population to enhance ergodicity and avoid clustering, while crossover and mutation operators from differential evolution are fused with slime mould update rules. Evaluations on standard test functions demonstrate that this hybrid exhibits marked improvements in escaping local optima, convergence speed and stability across diverse real-world optimisation tasks. More recently, an SMA variant combining Cauchy mutation and simulated annealing principles has been applied to continuous and discrete challenges, including capacitated vehicle routing. By perturbing elite solutions with Cauchy-distributed jumps and accepting inferior moves under a Metropolis criterion, this algorithm expands its exploration horizon and mitigates stagnation. Empirical results highlight competitive performance in obtaining high-quality solutions and maintaining search diversity over extended runs.

Slime Mould Algorithms for Global Optimization Problems publication trend

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Technical terms

Metaheuristic algorithm: A high-level problem-independent strategy guiding subordinate heuristics to explore complex search spaces efficiently.

Exploration and exploitation: Dual phases of search wherein exploration seeks new regions of the solution space, and exploitation refines known promising regions.

Chaotic map: A deterministic sequence generator with ergodic properties used to diversify initial populations or perturb search trajectories.

Cauchy mutation: A heavy-tailed random perturbation strategy that introduces long jumps to overcome local optima.

Simulated annealing: An optimisation technique that probabilistically accepts worse solutions at early stages to escape local minima, with decreasing acceptance over time.

Levy flight: A random walk characterised by occasional large steps drawn from a Lévy distribution, used to enhance global search capability.

References

1. DTSMA: Dominant Swarm with Adaptive T-distribution Mutation-based Slime Mould Algorithm. Mathematical Biosciences and Engineering (2022).
2. Improved Slime Mould Algorithm Hybridizing Chaotic Maps and Differential Evolution Strategy for Global Optimization. IEEE Access (2022).
3. Improved slime mould algorithm based on hybrid strategy optimization of Cauchy mutation and simulated annealing. PLOS ONE (2023).