Monitored convergence curve: a new framework for metaheuristic structural optimization algorithms

Metaheuristic optimization algorithms, by nature, depend on random processes, and therefore, performing numerous algorithm runs is inevitable to locate a reasonably good solution. Although executing the algorithms for small-size or trivial structural optimization problems could be computationally affordable, when dealing with challenging optimization problems, there is almost no chance of performing numerous independent runs of metaheuristics in a timely manner. This difficulty is basically due to the limitations in computational technologies as well as the excessive computational cost of such problems. In such cases that the number of independent runs is limited to a small number, each optimization run becomes highly valuable and, therefore, the stability of results becomes much more significant. In the present study, it is attempted to monitor the convergence curve of each succeeding run of the algorithm with respect to the information obtained in the previous runs. An easy-to-implement yet efficient framework is proposed for metaheuristic structural optimization algorithms where every succeeding run is monitored at certain intervals named as solution monitoring period. The solution monitoring period is selected such that, at each run, on the one hand, the algorithm could explore the search space to improve the solution quality, and on the other hand, the algorithm is occasionally forced to return to the previously visited more promising solutions if it is not able to improve the solution after a certain number of iterations. The numerical experiments using challenging test instances with up to 354 design variables indicate that, in general, the proposed approach helps to improve the solution quality as well as the robustness or stability of results in metaheuristic structural optimization.