A nature recoil mechanism-based Octopus optimization algorithm for solving the global and constraint optimization from engineering structural design problems

Abstract Global and constraint optimization in engineering structural design problems often involves more complex types, which increases computational complexity. To address this challenge, this paper constructs an exploration mechanism inspired by the hunting behaviours of marine octopuses, along with an exploitation mechanism based on their mating behaviours. These mechanisms aim to balance convergence speed and solution accuracy using a specially designed stochastic regulatory factor. This paper develops a nature-swarm phenomenon-based search strategy and mathematical model, named the octopus optimization algorithm (OOA), by simulating processes of octopuses searching for potential prey, escaping natural predators, attacking prey, and mating behaviours. In addition, inspired by the water-spraying recoil and transient acceleration phenomenon, a recoil motion-based stochastic feedback mechanism is proposed by designing a unique recoil operator to achieve information exchange in different search spaces. To demonstrate the universal applicability of the proposed OOA algorithm, we qualitatively analysed swarm convergence and swarm search behaviours, population diversity, exploration and exploitation performance on 84 benchmarks covering unimodal, multi-modal, fixed-dimensional, and composite functions and quantitatively verified convergence, effectiveness, significance, robustness, population diversity, exploration and exploitation efficiency, progressive scalability, and parameter sensitivity on the CEC2017 suites with 10, 30, 50, and 100 dimensions. Moreover, OOA beats 12 highly cited competitors in terms of computational performance when solving different optimization problems. Based on the pairwise comparisons-based Wilcoxon test and multiple pairwise comparisons-based Friedman test, it indicates that compared to 12 state-of-the-art algorithms, OOA achieved a mean rank of 1.19 across 84 benchmarks. The non-parametric test significance results show OOA contains 981 positive signs out of 1008 comparisons (84 benchmarks), with an optimization efficiency of 97.3%. On the CEC2017 suites, the mean ranks across four dimensions were 1.22 with 10Dim, 1.0 with 30Dim, 1.0 with 50Dim, and 1.0 with 100Dim, respectively, all ranking first. The non-parametric test results indicate OOA contains 1427 positive signs out of 1440 comparisons (120 benchmarks), with a solution efficiency of 99.1%. Thus, the proposed OOA algorithm demonstrates statistically significant advantages in computational performance and scalability. OOA has achieved better results than competitors in eight engineering problems, showing superior computational efficiency and reliability. The source code of OOA is publicly accessible at https://ww2.mathworks.cn/matlabcentral/fileexchange/183324-recoil-mechanism-based-octopus-optimization-algorithm-ooa and https://github.com/kaiguangnxu/OOA.