Multi-objective optimization of retaining wall using genetic algorithm

Abstract

The paper investigates the possibility of applying the genetic algorithm NSGA-II to optimize a reinforced concrete retaining wall embedded in saturated silty sand. Multi-objective constrained optimization was performed to minimize the cost, while maximizing the overdesign factors (ODF) against sliding, overturning, and soil bearing resistance. For a given change in ground elevation of 5.0 m, the width of the foundation and the embedment depth were optimized. Comparing the algorithm's performance in the cases of two-objective and three objective optimizations showed that the number of objectives significantly affects its convergence rate. It was also found that the verification of the wall against the sliding yields a lower ODF value than verifications against overturning and soil bearing capacity. Because of that, it is possible to exclude them from the definition of optimization problem. The application of the NSGA-II algorithm has been demonstrated to be an effective tool for determining the set of optimal retaining wall designs.

Design Optimization of Reinforced Concrete Cantilever Retaining Walls: A State‐of‐the‐Art Review

“…e cost of concrete can be expanded to include the cost of formwork, transportation, labor, vibration, Earth removal, and cost of backfill as done by Naeem [22], Villalba et al [27], Al Sebai et al [31], Ceranic et al [34], Yepes et al [37], Camp and Akin [42], Sable and Patil [45], Kaveh et al [47], Talatahari and Sheikholeslami [51], Kaveh and Farhoudi [56], Temür and Bekdas [58], Mohammad and Ahmed [67], Moayyeri et al [69], Konstandakopoulou et al [76], Mergos and Mantoglou [77], Tousi et al [90], and Dodigović et al [94]. e cost of varying concrete and steel strength can also be used for optimization as done by Villalba et al [27], Yepes et al [37], Kaveh et al [47], Kalateh-Ahani and Sarani [68], Konstandakopoulou et al [76], Tousi et al [90], and Shakeel et al [100].…”

“…is value can be then set as objective to be optimized. e multiobjective optimization is still a developing concept and has been applied by Purohit [21], Kaveh et al [47], Khajehzadeh et al [49], Rahbari [23], Rahbari et al [64], Kalateh-Ahani and Sarani [68], Kayabekir et al [75], Ravichandran et al [84], Uray et al [92], Dodigović et al [94], and Tutus ¸et al [95]. e study of Kayabekir et al [75] has also attempted to vary the cost of concrete and steel to study their effects on optimization with respect to economical and sustainable design.…”

“…e problem can be modeled to maximize safety factors to ensure a safe design in high seismicity prone regions (Purohit [21] and Dodigović et al [94]) or to minimize to indirectly create an economical design (Uray and Tan [30] and Uray et al [92]). However, one of the first studies to investigate this objective was Dembicki and Chi [18].…”

“…e crossover ensures intermixing of 16 Advances in Civil Engineering [94], and Uray et al [102]). e above studies prove the effectiveness of GA in providing optimized results; however, it is seen that modern algorithms perform slightly better in terms of percentage of optimization and significantly better in terms of rate of convergence.…”

“…Optimization can be applied through multiple programming software; however, due to their complexities civil engineers often choose simpler programming languages such as MATLAB (Schmied and Karlsson [24], Pei and Xia [28], Al Sebai et al [31], Srivastavaa et al [32], Babu and Basha [36], Khajehzadeh et al [38], Khajehzadeh and Eslami [43], Sable and Patil [44], Sable and Patil [45], Kaveh and Behnam [46], Kaveh et al [47], Khajehzadeh et al [49], Gandomi et al [52], Kaveh and Mahdavi [53], Gandomi et al [61], Öztürk and Türkeli [70], Uray et al [71], Kalemci et al [78], Kayabekir [79], Kashani et al [82], Mevada et al [88], Uray et al [92], Tutus ¸et al [95], Khajehzadeh et al [101], and Khajehzadeh et al [103]), Fortran (Villalba et al [27] and Ukritchon et al [65]), C#.NET (Linh et al [93]), Python (Dodigović et al [94]), and C++ (Dagdeviren and Kaymak [72]). Studies have also tried to combine analysis software such as ABAQUS, ANSYS, PLAXIS 2D, and GeoSlope (Rahbari [23], Papazafeiropoulos et al [29], Uray and Tan [30], Rahbari et al [64], and Ravichandran et al [84]) with optimization.…”