With the rapid development of the economy, the disparity between supply and demand of resources is becoming increasingly prominent in engineering design. In this paper, an improved gray wolf optimization algorithm is proposed (IGWO) to optimize engineering design problems. First, a tent map is used to generate the initial location of the gray wolf population, which evenly distributes the gray wolf population and lays the foundation for a diversified global search process. Second, Gaussian mutation perturbation is used to perform various operations on the current optimal solution to avoid the algorithm falling into local optima. Finally, a cosine control factor is introduced to balance the global and local exploration capabilities of the algorithm and to improve the convergence speed. The IGWO algorithm is applied to four engineering optimization problems with different typical complexity, including a pressure vessel design, a tension spring design, a welding beam design and a three-truss design. The experimental results show that the IGWO algorithm is superior to other comparison algorithms in terms of optimal performance, solution stability, applicability and effectiveness; and can better solve the problem of resource waste in engineering design. The IGWO also optimizes 23 different types of function problems and uses Wilcoxon rank-sum test and Friedman test to verify the 23 test problems. The results show that the IGWO algorithm has higher convergence speed, convergence precision and robustness compared with other algorithms.

In this paper, an improved moth-flame optimization algorithm (IMFO) is presented to solve engineering problems. Two novel effective strategies composed of Lévy flight and dimension-by-dimension evaluation are synchronously introduced into the moth-flame optimization algorithm (MFO) to maintain a great global exploration ability and effective balance between the global and local search. The search strategy of Lévy flight is used as a regulator of the moth-position update mechanism of global search to maintain a good research population diversity and expand the algorithm’s global search capability, and the dimension-by-dimension evaluation mechanism is added, which can effectively improve the quality of the solution and balance the global search and local development capability. To substantiate the efficacy of the enhanced algorithm, the proposed algorithm is then tested on a set of 23 benchmark test functions. It is also used to solve four classical engineering design problems, with great progress. In terms of test functions, the experimental results and analysis show that the proposed method is effective and better than other well-known nature-inspired algorithms in terms of convergence speed and accuracy. Additionally, the results of the solution of the engineering problems demonstrate the merits of this algorithm in solving challenging problems with constrained and unknown search spaces.

This paper proposed an improved bat algorithm based on Lévy flights and adjustment factors (LAFBA). Dynamically decreasing inertia weight is added to the velocity update, which effectively balances the global and local search of the algorithm; the search strategy of Lévy flight is added to the position update, so that the algorithm maintains a good population diversity and the global search ability is improved; and the speed adjustment factor is added, which effectively improves the speed and accuracy of the algorithm. The proposed algorithm was then tested using 10 benchmark functions and 2 classical engineering design optimizations. The simulation results show that the LAFBA has stronger optimization performance and higher optimization efficiency than basic bat algorithm and other bio-inspired algorithms. Furthermore, the results of the real-world engineering problems demonstrate the superiority of LAFBA in solving challenging problems with constrained and unknown search spaces.

The firefly algorithm (FA) is proposed as a heuristic algorithm, inspired by natural phenomena. The FA has attracted a lot of attention due to its effectiveness in dealing with various global optimization problems. However, it could easily fall into a local optimal value or suffer from low accuracy when solving high-dimensional optimization problems. To improve the performance of the FA, this paper adds the self-adaptive logarithmic inertia weight to the updating formula of the FA, and proposes the introduction of a minimum attractiveness of a firefly, which greatly improves the convergence speed and balances the global exploration and local exploitation capabilities of FA. Additionally, a step-size decreasing factor is introduced to dynamically adjust the random step-size term. When the dimension of a search is high, the random step-size becomes very small. This strategy enables the FA to explore solution more accurately. This improved FA (LWFA) was evaluated with ten benchmark test functions under different dimensions (D = 10, 30, and 100) and with standard IEEE CEC 2010 benchmark functions. Simulation results show that the performance of improved FA is superior comparing to the standard FA and other algorithms, i.e., particle swarm optimization, the cuckoo search algorithm, the flower pollination algorithm, the sine cosine algorithm, and other modified FA. The LWFA also has high performance and optimal efficiency for a number of optimization problems.