Cost Optimization of Cantilever Retaining Wall Using Flower Pollination Algorithm

Abstract

The flower pollination algorithm is nature-inspired in which it mimics the pollination process of the flowers. In this study, the cost of the cantilever retaining wall is optimized, which includes the cost of concrete and the cost of reinforcement steel. The eight design variables define the geometry of the RC wall. The external stability and structural stability are considered as constraints. Overturning, sliding, eccentricity, and bearing are considered external constraints. The structural stability constraints are shear and moment failure of toe slab, heel slab, and stem. The fitness function is developed using a static exterior penalty. The study found that the FPA outperforms the non-dominated sorting genetic algorithm (NSGA-Ⅱ) in this design problem without violating any constraints. An analysis of sensitivity is carried out for the angle of internal friction of backfill soil and the angle of backfill slope. Results show that the total cost rapidly increases after 5 m height of backfill but significantly decreases with the internal friction angle of backfill increases. For backfill heights from 6 to 10 m, the change in cost is significant after the value of the inclination angle of 15°.

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

“…Eccentricity As discussed earlier, due to large overturning moments, uplift can be generated at heel. To mitigate this, pressure at heel must not be negative and an additional check for eccentricity (e can be applied as done by various studies [17,20,21,39,41,43,47,49,54,63,68,71,80,83,88,93,101]. Generally it is defined as in equation ( 14); it should not be greater than one-sixth of the total base width (B.…”

“…Apart from that, comparisons with GA and PSO were drawn which showed that FPA outperforms GA and PSO in terms of variability. Kayabekir et al [75], Mevada et al [88], and Temür [99] also utilized FPA and evidence its capabilities and effectiveness. Yücel et al [97] produced a hybridized algorithm by combining the metaheuristic technique of FPA with a machine learning technique called artificial neural network (ANN).…”

“…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.…”