Tree-Seed Algorithm Applications in Continuous Optimization

The Tree-Seed Algorithm (TSA) is a bioinspired metaheuristic designed for continuous optimisation, modelling each candidate solution as a tree that generates seeds to explore the search space. Its interplay between population diversity, convergence speed and avoidance of local optima makes it well suited to engineering design, energy management and resource allocation. Recent advances have focused on adaptive strategies and hybridisation with pattern search, quantum-inspired operators and velocity-driven mechanisms, yielding faster convergence and enhanced global search capabilities. Practical applications span filter parameter tuning, battery modelling, reservoir production and constrained engineering design, illustrating TSA’s versatility and growing maturity as a solver for complex continuous problems.

Research from Nature Portfolio

Recent studies have proposed a multi-strategy improved TSA (PDSTSA) combining global pattern search, dimension permutation and an elimination update mechanism. The global pattern search enhances detection of promising regions, dimension permutation preserves population diversity through random mutation of individual dimensions, and the elimination update discards inferior trees during mid-to-late iterations. Evaluation on numerical test functions demonstrates that PDSTSA surpasses several representative metaheuristics in both accuracy and convergence speed. An engineering application to constrained optimisation problems further confirms its practicality and superiority in achieving precise and reliable outcomes across complex continuous landscapes.

Research from all publishers

One study introduced an improved TSA for designing tenth-order Butterworth and Bessel filters, integrating opposition-based learning to enhance exploration and convergence. The enhanced algorithm achieved superior parameter tuning and predictive accuracy compared with basic TSA and other heuristics, demonstrating its applicability to high-order filter design. A further advance incorporated water-cycling and quantum rotation-gate mechanisms into TSA to balance exploration and exploitation, leading to faster convergence on benchmark functions and improved performance in reservoir production optimisation. Another variant, DTSA, adopted a PSO-inspired seed-generation mechanism with velocity-driven updates and an adaptive count-based strategy to prevent premature convergence. Validated on standard benchmarks and constrained engineering scenarios, DTSA delivered higher stability, diversity and solution quality than previous TSA variants and established metaheuristics.

Tree-Seed Algorithm Applications in Continuous Optimization publication trend

The graph below shows the total number of articles in tree-seed algorithm applications in continuous optimization across all publications each year (not limited to Nature Index journals).

Technical terms

Tree-Seed Algorithm (TSA): A plant-inspired metaheuristic in which each tree represents a solution and seeds represent new candidate solutions generated to explore the search space.

Metaheuristic algorithm: A high-level, problem-independent framework that guides search heuristics to identify near-optimal solutions across complex domains.

Exploration and exploitation: The dual phases of search in metaheuristics; exploration seeks diverse regions of the solution space while exploitation refines solutions around promising areas.

Opposition-Based Learning (OBL): A strategy that concurrently evaluates a solution and its opposite to accelerate convergence and enhance diversity.

Particle Swarm Optimization (PSO): A population-based metaheuristic inspired by the collective movement of bird flocks, where particles update positions based on personal and global best solutions.

References

1. Optimization of Butterworth and Bessel Filter Parameters with Improved Tree-Seed Algorithm. Biomimetics (2023).
2. A multi-strategy improved tree–seed algorithm for numerical optimization and engineering optimization problems. Scientific Reports (2023).
3. Parameter Identification of Equivalent Circuit Models for Li-ion Batteries Based on Tree Seeds Algorithm. IOP Conference Series Earth and Environmental Science (2017).
4. An Enhanced Tree-Seed Algorithm for Function Optimization and Production Optimization. Biomimetics (2024).
5. DTSA: Dynamic Tree-Seed Algorithm with Velocity-Driven Seed Generation and Count-Based Adaptive Strategies. Symmetry (2024).