Optimum Cost Design Research Articles

An innovative simulation algorithm for optimising the cost of communal water supply systems using EPANET

In this work, the EPANET software is used to parametrize the design, simulate and optimise the overall cost of building and running a reliable, sustainable and efficient communal Water Supply System. Considering a model community of forty houses with an average of six occupants per home, the developed optimization algorithm using the simulated annealing heuristics approach minimizes the total cost of continuous water distribution to the community through a system of pipe network in a way that satisfies the critical hydraulic rules and constraints for efficient water distribution. Thus, the controlled variables of the simulated system include volumetric flow, velocity and head loss. To realize the desired goal, the prototyped communal water distribution system was first simulated by water free fall i.e., only gravity feed under a peak demand flow condition. This facilitated the identification and localization of head-loss zones. Subsequently, virtual pump stations of various capacities were optimally introduced as boosters at identified nodal points to overcome critical head losses. The response of the system to varying capacities of the booster pumps was then used to analyse and determine the optimum capacity of the pump. Simulation outcome showed that the optimum least cost design for a sixtyyear system’s life cycle is achieved by using a combination of gravity and 5 hp (3.73 kW) pump with optimum pipe diameter ranging from 60 - 150mm.

Optimum cost design of facade scaffoldings

Optimum cost design of facade scaffoldings

Optimum Cost Design of Reinforced Concrete Beams Using Artificial Bee Colony Algorithm

Optimum Cost Design of Reinforced Concrete Beams Using Artificial Bee Colony Algorithm

Modified Harmony Search Algorithm-Based Optimization for Eco-Friendly Reinforced Concrete Frames

Cost and CO2 are two factors in the optimum design of structures. This study proposes a modified harmony search methodology for optimization of reinforced concrete beams with minimum CO2 emissions. The optimum design was developed in detail by considering all possible combinations of variable loads, including dynamic force resulting from earthquake motion. Moreover, time-history analyses were performed, and requirements of the ACI-318 building code were considered in the reinforced concrete design. The results show that the optimum design based on CO2 emission minimization is greatly different from the optimum cost design results. According to these results, using recycled members provides a sustainable design.

Adaptive-Hybrid Harmony Search Algorithm for Multi-Constrained Optimum Eco-Design of Reinforced Concrete Retaining Walls

In the optimum design of reinforced concrete (RC) structural members, the robustness of the employed method is important as well as solving the optimization problem. In some cases where the algorithm parameters are defined as non-effective values, local-optimum solutions may prevail over the existing global optimum results. Any metaheuristic algorithm can be effective to solve the optimization problem but must give the same results for several runs. Due to the randomization nature of these algorithms, the performance may vary with respect to time. The essential and novel work done in this study is the comparative investigation of 10 different metaheuristic algorithms and two modifications of harmony search (HS) algorithm on the optimum cost design of RC retaining walls constrained with geotechnical and structural state limits. The employed algorithms include classical ones (genetic algorithm (GA), differential evaluation (DE), and particle swarm optimization (PSO)), proved ones on structural engineering applications (harmony search, artificial bee colony, firefly algorithm), and recent algorithms (teaching–learning-based optimization (TLBO), flower pollination algorithm (FPA), grey wolf optimization, Jaya algorithm (JA)). The modifications of HS include adaptive HS (AHS) concerning the automatic change of algorithm parameters and hybridization of AHS with JA that is developed for the investigated problem. According to the numerical investigations, recent algorithms such as TLBO, FPA, and JA are generally the best at finding the optimum values with less deviation than the others. The adaptive-hybrid HS proposed in this study is also competitive with these algorithms, while it can reach the best solution by using a lower population number which can lead to timesaving in the optimization process. By the minimization of material used in construction via best optimization, sustainable structures that support multiple types of constraints are provided.

Comparative study of optimum cost design of reinforced concrete retaining wall via metaheuristics

Design engineers may find various options of metaheuristic method in optimization of their problems. Because of the randomization nature of metaheuristic methods, solutions may trap to non-optimum solutions which are just optimums in a limited part of the selected range of the design variables. Generally, metaheuristics use several options to prevent this situation, but the same optimization process may solve different performances in every run of the process. Due to that, a comparative study by using ten different algorithms was done in this study. The optimization problem is the cost minimization of an L-shaped reinforced concrete (RC) retaining wall. The evaluation is done by conducting 30 multiple cycles of optimization, and comparing minimum cost, average cost and standard deviation values.

Effects of cost optimised grid configuration on earthing system performance: a comparative assessment

This study presents the comparative analysis of earthing grid configurations to determine the optimum design in terms of safety parameters and cost for 66/11 kV substation. For different grid configurations, a fixed earthing area of 9000 m2 was considered. Rectangular, triangular, L-shaped and T-shaped grids buried in two-layer soil model were considered for this study. Three methods, i.e. ANSI/IEEE standard 80-2000, finite element method and genetic algorithm, were used to design the grids. All safety constraints as mentioned in the IEEE standard were followed for designing the earthing grid. A new mathematical cost function (CF) was proposed for designing an effective and economic L-shaped, T-shaped and triangular earthing systems. The CFs used in this study include grid depth, dimensions of earthing rod and horizontal conductor, number of rods and conductors, revetment and excavation area. The economic earthing grid obtained through the proposed method reduces the total cost related to grid materials, installation and excavation. Analysis also showed that the rectangular grid showed preferred results in terms of safety parameters while the triangular grid showed optimum cost design for the earthing system under study. Good agreements were found with the rectangular earthing grid in comparison with triangular, T-shape and L-shape configurations.

Design of Reinforced Concrete Deep Beams using Particle Swarm Optimization Technique

Researches available in literature interrelating neural networks to civil engineering design problems, especially for beep beams, are very rare. Therefore, an optimization algorithm is developed and verified in this study and coded using MATLAB functions to determine the optimum cost design of reinforced concrete deep beams. ACI 318-14 code method is used benefiting from iterative particle swarm optimization technique due to its efficiency and reliability. Minimizing total cost is used as the objective function in terms of four decision variables. Self-adaptive penalty function technique is used to handle constraints for each of the 300 randomly selected particles, and in each of the 50 total iterations followed for each one of four suggested deep beam design case studies. Performing all iterations is used as a stopping criteria for the developed algorithm. Comparative studies are made to show the effect of concrete compressive strength, live load scheme, and length of deep beam, on the optimum total cost and the corresponding decision variables. Results presented in the form of graphs and tables show that the loading condition has a significant effect on the total cost of deep beams. The cost increase is accompanied by deep beam length increase, height increase, longitudinal reinforcement area increase and vertical shear reinforcement area decrease. The calculated optimum cost is noticed for beam DB1, which is 1255 US$, with 1.29 m beam height, 0.01445 m2 vertical shear reinforcement, 0.00914 m2 horizontal shear reinforcement and 0.00238 m2 main longitudinal reinforcement. The results show a relatively less difference in total cost between all the four beams at 4 m length compared to 8 m length. Also, a relatively mild increase in total cost is happened for beams DB3 and DB4 as the height increases, especially above 1.7 m height. As the main longitudinal reinforcement increases, cost of DB4 is affected more significantly than others, and as the vertical shear reinforcement increases, DB4 curve shows a relatively low degradation in cost.

Optimum design of reinforced earth walls using evolutionary optimization algorithms

This study addresses the optimum cost design of mechanically stabilized earth (MSE) using geosynthetics. The design process of MSEs is mathematically programmed based on an objective function depending on the length of reinforcements and vertical distance of reinforced layers. Design restrictions control the final design to be valid in terms of constraints. The aim is to explore the efficiency of evolutionary-based algorithms in dealing with MSE optimization problem along with automating the minimum cost design of MSE walls. To this end, three evolutionary algorithms, differential evolution (DE), evolution strategy, and biogeography-based optimization algorithm (BBO), are tackled to solve this problem. Comprehensive computational simulations confirm the impact of different effective parameters variation on the final design. Finally, the BBO algorithm performed the best, while DE recorded the most unsatisfactory results.

Material Price Enfluence on the Optimum Design of Different Structural Members

This study presents the application of Genetic Algorithms (GAs) for the optimum cost design of reinforced concrete beams and columns based on the standard specifications of the American Concrete Institute (ACI 318-11). The produced optimization procedure satisfies the strength, serviceability, ductility, durability, and other constraints related to good design and detailing practice. While most of the approaches reported in this field have considered steel reinforcement only or cross-sectional dimensions of the members as design variables and for the flexural aspect in general, the dimensions and reinforcing steel in this study were introduced as design variables, considering the axial, flexural, shear, and torsion effects on the members. The aim of this study is to find the effect of material’s price on the optimum cost of beams and columns according to the local market using the GAs, by limiting the design procedure with many constraints that control the optimum design variables to a certain limits. It was found that the Genetic Algorithms is a sufficient method for finding the optimum solution smoothly and flawless with many complicated constraints. Also, increasing the applied torsion on a beam section with a constant cost ratio r will increase the optimum cost by about 3.8%.

Optimum design of RC shallow tunnels in earthquake zones using artificial bee colony and genetic algorithms

The main purpose of this study is to perform optimum cost design of cut and cover RC shallow tunnels using Artificial bee colony and genetic algorithms. For this purpose, mathematical expressions of objective function, design variables and constraints for the design of cut and cover RC shallow tunnels were determined. By using these expressions, optimum cost design of the Trabzon Kalekapisi junction underpass tunnel was carried out by using the cited algorithms. The results obtained from the algorithms were compared with the results obtained from traditional design and remarkable saving from the cost of the tunnel was achieved.

Optimum Cost Design of Reinforced Concrete Retaining Walls Using Hybrid Firefly Algorithm

This paper develops a novel optimization method namely hybrid firefly algorithm with harmony search technique (IFA-HS), to obtain the optimal cost of the reinforced concrete retaining walls satisfying the stability criteria. The hybrid IFA-HS is utilized to find the economical design adhering to provisions of ACI 318-05. Also Coulomb lateral earth pressure theory is used to derive the lateral total thrust on the wall. Some design examples are tested using the new method. The results carried out on these examples confirm the validity of the proposed algorithm. The IFA-HS method can be considered as an improvement of the recently developed firefly algorithm. The improvements include the utilizing of a memory that contains some information extracted online during the search, adding of pitch adjustment operation in harmony search serving as mutation operator during the process of the firefly updating, and modifying the movement phase of firefly algorithm. The detailed implementation procedure for this improved meta-heuristic method is also described.

Optimum Cost Design of Reinforced Concrete Columns Using Genetic Algorithms

The aim of this study is finding the optimum cost design of reinforced concrete columns with all loading conditions (axially, uniaxially and biaxially loaded) using the Genetic Algorithms GAs. Many design constraints were used to cover all the reliable design results, such as limiting the cross sectional dimensions, limiting the reinforcement ratio and even the behavior of the optimally designed sections. Each of the designed columns was handled by the GAs solver according to its loading condition specifications. The load contour method was used to design the biaxial sections with the adjustment of the plastic centroid. A long column constraint was introduced to limit the design procedure with the short columns only. The optimum results were compared with other published works, and a reduction in design cost of the biaxially loaded columns of about 26 % was achieved using the GAs design method while a small percent in the cost reduction ( 1 – 3 % ) was achieved for the uniaxially designed sections, while 50% was the cost savings in the axially loaded columns. It was proved that the genetic algorithm is capable for designing optimum columns sections despite the complex constraints that control the designing procedure

A chaotic imperialist competitive algorithm for optimum cost design of cantilever retaining walls

This paper develops a model to obtain the optimum cost of the cantilever retaining walls having different cases of backfill satisfying the stability criteria, according to the height and properties of earth that the wall is required to support. Chaotic Imperialist Competitive Algorithm (CICA) is utilized to find the economical sections as the output after minimizing the cost for sections adhering to provisions of ACI 318-05. The CICA, one of the recently developed meta-heuristic algorithms utilizes imperialism and imperialistic competition process combined with chaos theory as a source of inspiration. Cost design problem of cantilever retaining walls is tested using the new method and the results are compared to those of other algorithms. In addition, a detailed sensitivity analysis for selected design variables, parameters and related safety factors will be presented.

Optimum cost design of RC columns using artificial bee colony algorithm

Optimum cost design of columns subjected to axial force and uniaxial bending moment is presented in this paper. In the formulation of the optimum design problem, the height and width of the column, diameter and number of reinforcement bars are treated as design variables. The design constraints are implemented according to ACI 318-08 and studies in the literature. The objective function is taken as the cost of unit length of the column consisting the cost of concrete, steel, and shuttering. The solution of the design problem is obtained using the artificial bee colony algorithm which is one of the recent additions to metaheuristic techniques. The Artificial Bee Colony Algorithm is imitated the foraging behaviors of bee swarms. In application of this algorithm to the constraint problem, Deb's constraint handling method is used. Obtained results showed that the optimum value of numerical example is nearly same with the existing values in the literature.

Optimum cost design of reinforced concrete continuous beams using Genetic Algorithms

This paper presents the application of genetic algorithms (GA) for the optimum cost design of reinforced concrete continuous beams based on the standard specifications of the American Concrete Institute. The produced optimum design satisfies the strength, serviceability, ductility, durability, and other constraints related to good design and detailing practice. While most of the approaches reported in the literature consider steel reinforcement and cross-sectional dimensions of beam as design variables of the flexural aspect only, the dimensions and reinforcing steel in this research were introduced as design variables, considering the flexural, shear, and torsion effects on the beam. The constant parameters specified prior to the solution of the optimization problem included the number of bays, lengths of span, support conditions, loads, material properties, and unit costs. The forces, moments, and deformations needed in the GA constraints were determined from the analysis. The beam dimensions were corrected to the nearest 25 mm, and the areas of the longitudinal and transverse steel obtained from the design were converted into the least weight detailing of steel reinforcements. This conversion was achieved by generating a database of reinforcement templates containing different available reinforcement bar diameters in a pre-specified pattern, satisfying the user-specified bar rules and other bar spacing requirements. The optimum design results were compared with those in the available literature. Upon the illustration of an example problem and the presentation of results, the proposed optimum design model is concluded to yield rational, reliable, economic, and practical designs.

Charged System Search Algorithm for the Optimum Cost Design of Reinforced Concrete Cantilever Retaining Walls

In this paper, optimal design of reinforced concrete cantilever retaining walls is performed under static loads utilizing the charged system search (CSS) method. This design is based on ACI 318-05, and optimization is on the basis of cost function of materials used in retaining walls and their constructions. This function is minimized while satisfying the design constraints. Performance of the CSS algorithm is compared to that of the improved harmony search algorithm. Four examples are optimized and their convergence curves are compared.

Optimum design of a reinforced concrete beam using artificial bee colony algorithm

Optimum cost design of a simply supported reinforced concrete beam is presented in this paper. In the formulation of the optimum design problem, the height and width of the beam, and reinforcement steel area are treated as design variables. The design constraints are implemented according to ACI 318-08 and studies in the literature. The objective function is taken as the cost of unit length of the beam consisting the cost of concrete, steel and shuttering. The solution of the design problem is obtained using the artificial bee colony algorithm which is one of the recent additions to metaheuristic techniques. The artificial bee colony algorithm is imitated the foraging behaviors of bee swarms. In application of this algorithm to the constraint problem, Deb\'s constraint handling method is used. Obtained results showed that the optimum value of numerical example is nearly same with the existing values in the literature.

Optimum cost design of controlled cable stayed footbridges

Traditionally, structures and control devices are designed separately. Here an integrated approach is proposed and applied to find the least cost solution of a passive and active cable stayed footbridge. The optimization process reduces simultaneously cost, stress, acceleration and displacement. By using an entropy-based procedure a Pareto solution is obtained by unconstrained scalar function minimization and an efficient polynomial convergence algorithm is employed. The designed controller is compared with an active linear quadratic regulator (LQR). Numerical simulations show that both passive and active optimum designs are efficient, with different geometry, mass distribution and cost (22% higher in the passive design).

Heuristic Approach for Optimum Cost and Layout Design of 3D Reinforced Concrete Frames

AbstractThis paper presents a new methodology for cost optimization of the preliminary layout design of three-dimensional (3D) reinforced concrete (RC) frames. This approach is capable of being easily employed for the optimal layout design of a realistic large RC structure that accounts for constraints imposed by design standards. The new approach considers modeling, structural analysis, concrete member design, and discrete optimization together with data on the cost of systems and materials. The methodology is comprised of two parts. First, using the cross-sectional action effects as design variables, a heuristic cost function is presented as an alternative to traditional cost functions for layout optimization of RC structures. Using the presented cost function, a structural optimization problem is formulated for column layout design of 3D RC frames. Then, an ant system algorithm, a discrete method, is proposed to solve the cost optimization problem. Two comparative design examples are included to demons...