This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves (Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known test functions, and the results are verified by a comparative study with Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolution Strategy (ES). The results show that the GWO algorithm is able to provide very competitive results compared to these wellknown meta-heuristics. The paper also considers solving three classical engineering design problems (tension/compression spring, welded beam, and pressure vessel designs) and presents a real application of the proposed method in the field of optical engineering. The results of the classical engineering design problems and real application prove that the proposed algorithm is applicable to challenging problems with unknown search spaces.

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This paper proposes an optimisation algorithm called Grasshopper Optimisation Algorithm (GOA) and applies it to a challenging problem in structural optimisation. The proposed algorithm mathematically models and mimics the behaviour of grasshopper swarms in nature for solving optimisation problems. The GOA algorithm is first benchmarked on a set of test problems including CEC2005 to test and verify its performance qualitatively and quantitatively. It is then employed to find the optimal shape for a 52-bar truss, 3-bar truss, and cantilever beam to demonstrate its applicability. The results show that the proposed algorithm is able to provide superior results compared to well-known and recent algorithms in the literature. The results of the real applications also prove the merits of GOA in solving real problems with unknown search spaces.

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The Biogeography-Based Optimisation (BBO) algorithm is a novel evolutionary algorithm inspired by biogeography. Similarly to other evolutionary algorithms, entrapment in local optima and slow convergence speed are two probable problems it encounters in solving challenging real problems. Due to the novelty of this algorithm, however, there is little in the literature regarding alleviating these two problems. Chaotic maps are one of the best methods to improve the performance of evolutionary algorithms in terms of both local optima avoidance and convergence speed. In this study we utilise 10 chaotic maps to enhance the performance of the BBO algorithm. The chaotic maps are employed to define selection, emigration, and mutation probabilities. The proposed Chaotic BBO (CBBO) algorithms are benchmarked on 10 test functions. The results demonstrate that the chaotic maps (especially Gauss/mouse map) are able to significantly boost the performance of BBO. In addition the results show that the combination of chaotic selection and emigration operators results in the highest performance.