Meta-heuristic search algorithms in truss optimization: Research on stability and complexity analyses

Although they are among the most researched real world engineering design problems, it is encountered with significant problems in the optimization of structural truss bar problems (TPs). The main reasons for these problems are (i) the studies on the optimization of TPs being carried out with different experimental settings, (ii) the competitor algorithms used in the optimization process being insufficient, and (iii) the stability analysis and computational complexity information of the algorithms are not investigated. It is designed a simulation environment with defined standards and a benchmarking suite consisting of nine TPs of three different types in order to eliminate these problems. It is found optimum solutions for all problems in the benchmark suite and it is introduced feasible solutions for the first time. According to the statistical analysis results, among the seventy-seven competing algorithms, the best ten algorithms showed competitive performance in the optimization of TPs are LSHADE-EpSin, LSHADE-CnEpSin, SHADE, LSHADE, GSK, FDB-AGDE, MPA, LRFDB-COA and BES. According to the results of the stability analysis carried out on feasible solutions, it has been determined the algorithms with the best success rate for planar type; LSHADE, LSHADE-CnEpSin, LSHADE-EpSin and GSK with 100% success rate, LSHADE-CnEpSin, LSHADE-EpSin, LSHADE and SHADE for Space type with 100% success rate, and LSHADE-EpSin with 69% success rate for frequency constrained type. When the performances of the algorithms are evaluated regardless of the problem type, LSHADE-EpSin has been the most stable algorithm with an overall success rate of 90% on the TPs. Click here for the simulation environment containing the source codes of the ten competitive algorithms and the TP benchmark suite proposed in the article: https://www.mathworks.com/matlabcentral/fileexchange/131668-structural-truss-problems-benchmark-suite.