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Considered as cost-efficient, reliable and aesthetic alternatives to the conventional retaining structures, Mechanically Stabilized Earth Walls (MSEWs) have been increasingly used in civil engineering practice over the previous decades. The design of these structures is conventionally based on engineering guidelines, requiring the use of trial and error approaches to determine the design variables. Therefore, the quality and cost effectiveness of the design is limited with the effort, intuition, and experience of the engineer while the process transpires to be time-consuming, both of which can be solved by developing automated approaches. In order to address these issues, the present study introduces a novel framework to optimize the (i) reinforcement type, (ii) length, and (iii) layout of MSEWs for minimum cost, integrating metaheuristic optimization algorithms in compliance with the Federal Highway Administration guidelines. The framework is conjoined with optimization algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Differential Evolution (DE) and tested with a set of benchmark design problems that incorporate various types of MSEWs with different heights. The results are comparatively evaluated to assess the most effective optimization algorithm and validated using a well-known MSEW analysis and design software. The outcomes indicate that the proposed framework, implemented with a powerful optimization algorithm, can effectively produce the optimum design in a matter of seconds. In this sense, DE algorithm is proposed based on the improved results over GA, PSO, and ABC.

This paper introduces a new algorithm named Elitist Stepped Distribution Algorithm (ESDA), which is inspired from the existing Cross Entropy Method (CEM) through the modification of elite sample based normal distribution used in CEM. Considering the natural behavior of normal distribution, ESDA is proposed to enhance the drawbacks of CEM through improving the efficiency in both exploration and exploitation processes when applying for complex function optimization problems. In ESDA, the elite sample percent defined in CEM is separated into two parts: (1) elite sample percent to calculate the mean value, and (2) elite sample percent to calculate standard deviation of normal distribution to construct an applicable balance between exploration and exploitation ability of the algorithm at a reasonable convergence speed. The elite sample percent parameter for the mean guides the algorithm to focus more on the better solutions and therefore improves the exploitation ability, whereas the elite sample percent parameter for the standard deviation controls the length of standard deviation to handle the exploration process more effectively. Performance of ESDA is investigated using unconstrained benchmark problems and compared with CEM, Simple Genetic Algorithm and Particle Swarm Optimization. The comparisons on unimodal and multi-modal functions confirm the efficiency of the algorithm in both exploration and exploitation process. In addition, the performance of ESDA is tested using constrained engineering problems commonly used in literature by comparing its performance with the other ones statistically. The results on engineering problems also prove that ESDA is perfectly applicable in real-world applications.