الگوریتم بهینه سازی کلونی مورچه های اصلاح شده برای بهینه سازی توپولوژی پویا

A modified ant colony optimization (MACO) algorithm implementing a new definition of pheromone and a new cooperation mechanism between ants is presented in this paper. The sensitivity of structural response to the presence of each element included in the finite element (FE) model is evaluated. The study aims to improve the suitability and computational efficiency of the ant colony optimization algorithm in dynamic topology optimization problems. The natural frequencies of the structure must be maximized yet satisfying a constraint on the final volume. Optimization results obtained in three test cases indicate that MACO is more efficient and robust than standard ACO in solving dynamic topology optimization problems.

The ant colony optimization (ACO) algorithm is a metaheuristic search method for global optimization. ACO was initially proposed by Dorigo [1] to find the optimal path in a graph. ACO mimics the behavior of ants seeking a path between their colony and a food source. This optimization technique was successfully applied to many engineering problems including structural optimization [2], [3] and [4]. Topology optimization of structures underwent tremendous development after the introduction of the homogenization method [5]. In addition, ad hoc optimization algorithms such as evolutionary structural optimization (ESO) [6] and [7], performance-based optimization (PBO) [8] and [9], and level set theory [10] and [11] were successfully applied to topology optimization problems. The homogenization method divides the design space in an infinite number of microscale holes and optimal topology is obtained by solving a material distribution problem. However, it may yield an undesirable structure with infinitesimal pores in the materials that make the structure not realizable practically [12]. The rationale of ESO and PBO is to remove gradually from the structure, the “inefficient” elements hosting very low stress that hence do not contribute much to the overall response of the structure: such an operation is governed by the sensitivity number. Convergence behavior of PBO depends on the performance of the structure. Bidirectional ESO (BESO) [13] was developed to improve the capability of adding or removing elements. However, the computational efficiency of BESO depends on the previous positions of the elements as well as on the area/volume of the element predefined by the meshing operation. Topology optimization can be performed with metaheuristic algorithms that mimic natural phenomena and physical processes. Applications of genetic algorithms (GA) [14] and simulated annealing (SA) [15] to topology optimization problems were reviewed in the paper written by Luh and Lin [16]. Also, ant colony optimization was utilized in topology optimization problems [16] and [17]. For example, Luh and Lin [16] used the element transition rule instead of node transition rule and connectivity analysis, pheromone updating rule and multiple-colony memories. Kaveh et al. [17] developed a topology optimization technique to find the stiffest structure with a certain amount of material; the search criterion was based on the contribution of each element to strain energy. It was found that ACO can handle the topology optimization problem as an on-off discrete optimization. However, there are not many other examples of applying ACO to topology optimization problems documented in literature. Although dynamic topology optimization with respect to natural frequencies is of fundamental importance in aerospace and automotive engineering, the number of papers published on this subject is limited in comparison with the available literature on static problems. For example, the homogenization method [18] and [19] and modified SIMP (Solid Isotropic Microstructure with Penalization) with a discontinuous function [20], [21] and [22] were successfully used to solve eigenvalue problems in topology design of vibrating structures. In this study, a modified ant colony optimization (MACO) algorithm is developed in order to improve computational efficiency and suitability of ACO in topology optimization problems dealing with natural frequencies. An important improvement with respect to classical ACO is the definition of a continuous variable, the element contribution significance (ECS), which serves to evaluate the effective contribution to structural response deriving from the presence of each element. A mesh independent filtering scheme [23] is adopted to prevent the formation of checkerboard patterns in the optimization process. Optimal designs are compared with those obtained with standard ACO and soft-kill BESO in order to assess the applicability and the efficiency of the proposed MACO algorithm in dynamic problems.

This paper presented a modified ant colony optimization algorithm (MACO) for dynamic topology optimization of 2D structures. MACO implemented a novel ant colony optimization formulation where the concept of ant position is reformulated in terms of the sensitivity of structural response to the presence of each element. This effect is evaluated by introducing the ECS parameter. Numerical tests demonstrated that MACO is a robust and stable metaheuristic algorithm highly suited for topology optimization in dynamic problems where the objective is to maximize natural frequencies. In particular, the proposed algorithm was absolutely superior over standard ant colony optimization and very competitive with bilinear evolutionary structural optimization algorithms in terms of convergence rate. The natural frequencies corresponding to the designs optimized by MACO are higher than those obtained by ACO, and almost the same or even slightly higher than for BESO. However, further research will be required in order to improve the convergence speed of MACO that was much faster than ACO but sometimes considerably slower than BESO. Natural frequencies optimized by MACO were greater than those found by standard ACO but sometimes slightly smaller than those found by BESO.