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A newly hybrid nature inspired algorithm called HPSOGWO is presented with the combination of Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO). The main idea is to improve the ability of exploitation in Particle Swarm Optimization with the ability of exploration in Grey Wolf Optimizer to produce both variants' strength. Some unimodal, multimodal, and fixeddimension multimodal test functions are used to check the solution quality and performance of HPSOGWO variant. The numerical and statistical solutions show that the hybrid variant outperforms significantly the PSO and GWO variants in terms of solution quality, solution stability, convergence speed, and ability to find the global optimum.

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The bio-inspired optimization techniques have obtained great attention in recent years due to its robustness, simplicity and efficiency to solve complex optimization problems. The firefly Optimization (FA or FFA) algorithm is an optimization method with these features. The algorithm is inspired by the flashing behavior of fireflies. In the algorithm, randomly generated solutions will be considered as fireflies, and brightness is assigned depending on their performance on the objective function. The algorithm is analyzed on basis of performance and success rate using five standard benchmark functions by which guidelines of parameter selection are derived. The tradeoff between exploration and exploitation is illustrated and discussed.

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Particle swarm optimization (PSO) is one of the most famous swarm-based optimization techniques inspired by nature. Due to its properties of flexibility and easy implementation, there is an enormous increase in the popularity of this nature-inspired technique. Particle swarm optimization (PSO) has gained prompt attention from every field of researchers. Since its origin in 1995 till now, researchers have improved the original Particle swarm optimization (PSO) in varying ways. They have derived new versions of it, such as the published theoretical studies on various parameters of PSO, proposed many variants of the algorithm and numerous other advances. In the present paper, an overview of the PSO algorithm is presented. On the one hand, the basic concepts and parameters of PSO are explained, on the other hand, various advances in relation to PSO, including its modifications, extensions, hybridization, theoretical analysis, are included.

This paper presents a modified butterfly optimization algorithm (MBOA) for solving mechanical design optimization problems. The modification is focused on an additional intensive exploitation phase which provides more chance to solutions to improve itself. The performance of the proposed algorithm is validated on fifteen benchmark test functions and three engineering design problems which have different natures of objective functions, constraints and decision variables. The experimental results are analyzed in comparison with those reported in the literature. The results indicate that the MBOA provides very competitive results in comparison with other existing optimization algorithms.