**3.5 Level-set method (LSM)**

Allaire et al. [122] applied LSM with enabling local mesh modifications. Chen and Chen [123] considered geometric uncertainty and related problems. Van Dijk et al. [124] used uses a direct steepest-descent update of the design variables in a LSM. Dunning and Alicia Kim [125] developed a third dimension for 2D problems to adjust new hole positions and to prevent violations with boundaries. Emmendoerfer and Fancello [126] minimized mass under stress constraints using an augmented Lagrangian approach. Gomes et al. [127] interested in the reduction of the design space dimension by the help of a GUI. Guo et al. [128] used LSM in stress-related topology optimization problems. Otomori et al. applied LSM to the design of electromagnetic cloaks using a ferrite material [129] and a light-scattering layer for solar cell applications [130]. Guo et al. [131] developed a local and explicit feature control scheme. James et al. [132] used isoparametric finite element, and James and Martins [133] used a body-fitted, nonuniform finite element mesh to overcome irregular shape problems. Jang et al. [134] considered geometric uncertainties in the production of microsystems. Lim et al. [135] applied to magnetic actuator design problems. Liu et al. [136] adopted extended finite element method (XFEM) with unified structural optimization model help to cover the topology, shape, and sizing optimization at the same time. Luo et al. [137] combined meshless Galerkin method with LSM. Makhija and Maute [138] applied a generalized Heaviside enrichment strategy with XFEM formulation. Mohamadian and Shojaee [139] combined binary level-set method and Merriman-Bence-Osher scheme. Otomori et al. [140] used LSM in the design of negative permeability dielectric metamaterials. Shojaee and Mohammadian [141] combined piecewise constant level-set (PCLS) method with a MBO scheme. Shu et al. [142] used LSM to minimize frequency response which results in the reduction in the vibration of structure. Shu et al. [143] used LSM in the design of coupled structural-acoustic system with a focus on interior noise reduction. Suresh and Takalloozadeh [144] used LSM considering stress constraints. Xia et al. [145] used LSM to maximize the simple or repeated first eigenvalue of structure vibration. Xia et al. [146] built a strict 0–1 model considering stress to be minimized. Xia et al. [147] optimized both structure and support using traction free and Dirichlet boundaries separately. Yamasaki et al. [148] proposed a method combined application of boundary element mesh with LSM. Zhu and Zhang [149] used LSM without re-initialization for the optimization of compliant mechanisms. Zhu et al. [150] combined projection Lagrangian method with piecewise constant level-set functions to manage the optimization for elliptic boundary value problems. Zhu et al. [151] used LSM to optimize hinge-free compliant mechanisms with multiple outputs. Zhu and Zhang [152] developed an accelerated level-set evolution algorithm by adding an extra energy function to be able to optimize the distributed compliant mechanisms. Zhu et al. [153] developed a new LSM to manage multiobjective optimization of hinge-free compliant mechanisms.

### **3.6 Meshless methods**

Lin et al. [154] generated a method mimicking leaf venation and using element-free Galerkin method to design heat conduction channels. Wang and Luo [155] proposed a meshless Galerkin level-set method using compactly supported radial basis functions to construct the meshless shape functions. Cui et al. [156] proposed a new method based on SIMP and using EFG method for multi-material optimization problems. Zhao [157] developed a new approach based on Pareto frontier solutions using EFG method. He et al. [158] combined density variable approach with EFG to optimize geometrically nonlinear structures. Evgrafov [159] proposed a method based on SIMP combined with Petrov-Galerkin methods based on minimizing the squared residual. Khan et al. [160] used EFG with LSM and also implemented sensitivity analysis. Gong et al. [161] developed a new method, particle moving, based on EFG considering density gradient and combined it with SIMP. Hur et al. [162] used a Spline-based meshfree method where nonuniform rational B-spline functions are used to smooth trimmed boundaries. Ren et al. [163] used a method combination of EFG and SIMP to design a two-material micro-compliant mechanism under stress constraints. Zhang et al. [164] applied a combined method of SIMP and direct coupling method of FE and EFG methods to decrease computational cost of meshless methods. Ai and Gao [165] integrated a parametric level-set method with a meshless method based on compactly supported radial basis functions. Wang et al. [166] applied EFG to the design of large displacement compliant mechanisms having geometrical nonlinearity. Yang et al. [167] applied EFG to the design of continuum structures under displacement constraints. Kefal et al. [38] combined BESO with a new meshless method peridynamics. Zheng et al. [168] used a combination of SIMP and EFG to optimize free vibrating continuum structures. Zhang et al. [169] used a directly coupled FE and EFG to optimize nonlinear hyperelastic structures. Luo et al. [36] used dual-level point-wise density approximation with EFG. Wu et al. [170] improved EFG by adding moving least squares approximation. Zheng et al. [171] used EFG to optimize geometrically nonlinear continuum structures. Zhao [172] combined BESO with EFG.
