الگوریتم جستجوی گرانشی چند شتاب برای بهینه سازی اندازه سازه های خرپا Accelerated multi-gravitational search algorithm for size optimization of truss structures

1 Introduction Over the course of billions of years of evolutionary history, nature has heuristically (i.e. experimentally, especially by trial and error) developed a diverse and remarkably-ingenious set of dynamic and robust strategies that have endowed creatures and organisms with optimum yet sustainably-resilient adaptability to their in-flux environments. The last few decades saw significant research efforts that were devoted to understanding these strategies and exploring their applicability to solve complex engineering problems (e.g. see [1]). These efforts coupled with those driven by other inspirations (e.g. musical improvisation [2]) led to the development of several optimization techniques knows as optimization metaheuristics that in turn made previouslyunimaginable advances in structural optimization possible. The prefix meta-, meaning more developed/higher level, indicates that, in contrast to heuristic techniques, metaheuristics are problem-independent and versatile, making them suitable for various kinds of problems. In addition, compared to now-traditional gradient-based optimization techniques, the stochastic mechanism of metaheuristics allows them to effectively explore and exploit a vast search space enclosed by highly-nonlinear and discontinuous constraints without requiring gradient information and explicit formulations for the objective function and constraints [3]. It is not within the scope of the present study to detail the history of metaheuristics. However, a brief review of the most prominent metaheuristic optimization techniques is given below, and the interested reader is referred to, e.g., Sorensen et al. [4] for a portrait of the evolution of optimization metaheuristics. The phenomenal growth in the field of optimization metaheuristics has been taking place in a series of stages with divisions usually spaced out over several years. While the first use of heuristics by humans can be traced back to prehistoric times when they employed the strategies learned from determining the trajectory of a stone to hit a bear toward hitting a mammoth with a spear, the modern application of heuristics took place in the late 1950s and early 1960s when the advent of computer enabled researchers to develop and use algorithms to study the phenomenon of natural evolution. One of the first methods to receive recognition was the so-called evolution strategy, where the better of a solution and its mutated version is used as the parent for the next round of mutation [5]. Another method was evolutionary programming, where solutions are represented as finite-state machines that change from one state to another in response to a mutation operator [6].