Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications

In recent years, numerous meta-heuristic algorithms based on swarm intelligence have been proposed and widely popularized. Although algorithms are designed by some specific behaviors of organisms, their heuristic paradigms and constructed modules are similar, resulting in algorithms still suffer from imbalance between exploration and exploitation for complex optimization problems. Combining mathematical properties with a stochastic search process in meta-heuristic algorithms contributes to breaking the traditional single/dual population-based evolutionary paradigm and facilitating individuals forward optimization. Taking this as motivation, this article proposes a novel mathematics-based meta-heuristic algorithm, named Triangulation Topology Aggregation Optimizer (TTAO), for solving continuous optimization and engineering applications. The core of the proposed algorithm is based on similar triangular topology in mathematics. The TTAO algorithm contains two strategies, i.e., the generic aggregation and the local aggregation, which contributes to iteratively constructing multiple similar triangular topological units to balance the exploration and exploitation. The former generates new vertexes through positive information exchange between different triangular topological units. And the latter constructs new units at promising locations according to the local optimum vertex of each unit. The performance of the TTAO algorithm is evaluated in comparison with some competitive algorithms on CEC2017 functions for different dimensions and 8 real-world engineering problems. Moreover, the Wilcoxon rank sum test is used to verify the effectiveness of the proposed algorithm. The experimental results show that the TTAO algorithm, compared with 10 competitors, obtains 23, 23, and 22 best average results for 29 CEC2017 functions on 30, 50 and 100 dimensions, and its Wilcoxon rank sum test scores still rank first on three different dimensional cases. And more numerical results verify the outstanding optimization performance of the TTAO algorithm effectively. Source codes of TTAO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/136029-triangulation-topology-aggregation-optimizer.