Abstract Computational efficiency of metaheuristic optimization algorithms depends on appropriate balance between exploration and exploitation. An important concern in metaheuristic optimization is that there is no guarantee that new trial designs will always improve the current best record. In this regard, there not exist any metaheuristic algorithm inherently superior over all other methods. This study compares three advanced formulations of state-of-the-art metaheuristic optimization algorithms – Simulated Annealing (SA), Harmony Search (HS) and Big Bang-Big Crunch (BBBC) – including enhanced approximate line search and computationally cheap gradient evaluation strategies. The rationale behind the new formulations is to generate high quality trial designs lying on a properly chosen set of descent directions. This is done throughout the optimization process. Besides hybridizing the metaheuristic search engines of HS/BBBC/SA with gradient information and approximate line search, HS and BBBC are also hybridized with an enhanced 1-D probabilistic search derived from SA. All these enhancements allow to approach more quickly the region of design space hosting the global optimum. The new algorithms are tested in four weight minimization problems of skeletal structures and three mechanical/civil engineering design problems with up to 204 continuous/discrete variables and 20,070 nonlinear constraints. All test problems may contain multiple local minima. The optimization results and an extensive comparison with the literature clearly demonstrate the validity of the proposed approach which allows to significantly reduce the number of function evaluations/structural analyses with respect to the literature and improves robustness of metaheuristic search engines.

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三种新的混合元启发式算法用于结构优化问题的比较

摘要 元启发式优化算法的计算效率取决于探索和开发之间的适当平衡。元启发式优化中的一个重要问题是不能保证新的试验设计总能改善当前的最佳记录。在这方面，不存在任何本质上优于所有其他方法的元启发式算法。本研究比较了最先进的元启发式优化算法的三种高级公式——模拟退火 (SA)、和谐搜索 (HS) 和 Big Bang-Big Crunch (BBBC)——包括增强的近似线搜索和计算成本低的梯度评估策略. 新公式背后的基本原理是在一组正确选择的下降方向上生成高质量的试验设计。这是在整个优化过程中完成的。除了将 HS/BBBC/SA 的元启发式搜索引擎与梯度信息和近似线搜索混合之外，HS 和 BBBC 还与源自 SA 的增强的一维概率搜索混合。所有这些改进都允许更快地接近承载全局最优的设计空间区域。新算法在四个骨架结构的权重最小化问题和三个机械/土木工程设计问题中进行了测试，其中包含多达 204 个连续/离散变量和 20,070 个非线性约束。所有测试问题都可能包含多个局部最小值。