A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

Abstract

In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

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“…Therefore, the firefly algorithm formulation is based on three ideal rules as follows: the equation of the firefly movement is given in Eq. ( 18) [27,28] and it represents the movement of a firefly 𝑖 to another, more attractive firefly 𝑗, Eq. ( 19) [27,28] describes a firefly's attractiveness, and Eq.…”

“…( 18) [27,28] and it represents the movement of a firefly 𝑖 to another, more attractive firefly 𝑗, Eq. ( 19) [27,28] describes a firefly's attractiveness, and Eq. ( 20) [27,28] calculates the distance between firefly 𝑖 and firefly 𝑗.…”

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