# Topology Optimisation Using MPBILs and Multi-Grid Ground Element
## 6 Conclusions  
The purposes of this work are the demonstration of the performance comparison of an original MPBIL and their performance enhancement, and the MG approach for multi-objective structural topology optimization problems, respectively. Among the performance enhancements of MPBIL, OMPBIL outperforms other techniques. It promotes the opposition-based concept, which can improve  
Figure 7: Topologies of MOP4: (**a**) OMPBIL with multi-grid; and (**b**) MPBIL without multi-grid. the search performance of MPBIL. The use of MPBILs in combination with the MG approach is well capable of solving multi-objective structural topology optimization. The resulting topologies obtained from using OMPBIL are close to those obtained from the classical gradient-based approach. The new design strategy is a procedure for structural topology optimization, which uses multiple ground element resolutions, so the MG approach is more efficient than using single-resolution ground elements in the sense that the suitable grid resolution is automatically detected and used in one optimization run. These conclusions are very similar those obtained in our previous work [3]. In addition, the use of the MG approach combined with ground element filtering for alleviating checkerboards is effective. In future work, the proposed method is extended to solve topology optimization with uncertainty. The authors are grateful for the financial support provided by the Thailand Research Fund (MRG6080148), Chiangrai College, and King Mongkut's Institute of Technology Ladkrabang, and are grateful to [PERSON], who took the time to proofread this manuscript. [PERSON]. * [PERSON] et al. (2007) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A new implementation of population based incremental learning method for optimizations in electromagnetic. _IEEE Trans. Magn._**2007**, _43_, 1601-1604. [CrossRef]
* [PERSON] and [PERSON] (2013) [PERSON]; [PERSON] New conceptual design of aeroelastic wing structures by multi-objective optimization. _Eng. Optim._**2013**, _45_, 107-122. [CrossRef]
* [PERSON] et al. (2013) [PERSON]; [PERSON]; [PERSON] Aircraft morphing wing design by using partial topology optimization. _Struct. Multidiscip. Optim._**2013**, _48_, 1109-1128. [CrossRef]
* [PERSON] and [PERSON] (2006) [PERSON]; [PERSON] [PERSON] Performance enhancement of evolutionary search for topology optimization. _Finite Elem. Anal. Des._**2006**, _42_, 547-566. [CrossRef]
* [PERSON] and [PERSON] (2008) [PERSON]; [PERSON] Structural topology optimization using simulated annealing with multiresolution design variables. _Finite Elem. Anal. Des._**2008**, _44_, 738-747. [CrossRef]
* [PERSON] and [PERSON] (2016) [PERSON]; [PERSON] A derivative-free level-set method for topology optimization. _Finite Elem. Anal. Des._**2016**, _120_, 41-56. [CrossRef]
* [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] Evolutionary and GPU computing for topology optimization of structures. _Swarm Evol.Comput._**2017**, _35_, 1-13. [CrossRef]
* [PERSON] (2017) [PERSON] [PERSON] Commentson\"Evolutionary and GPU computing for topology optimization of structures\". _Swarm Evol. Comput._**2017**, _35_, 111-113. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Multi-objective topologyoptimization of multi-component continuum structures via a Kriging interpolated level set approach. _Struct. Multidiscip. Optim._**2015**, _51_, 733-748. [CrossRef]
* [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON] Optimal design of material microstructure for maximizing damping dissipation velocity of piezoelectric composite beam. _Int. J. Mech. Sci._**2017**, _128-129_, 527-540. * [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] An improved fast plane wave expansion method for topology optimization of phononic crystals. _Int. J. Mech. Sci._**2017**, _120_, 171-181. [CrossRef]
* [PERSON] et al.