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In this paper, an efficient multi-objective model is proposed to solve time-cost trade off problem considering cash flows. The proposed multi-objective meta-heuristic is based on Ant colony optimization and is called Non Dominated Archiving Ant Colony Optimization (NAACO). The significant feature of this work is consideration of uncertainties in time, cost and more importantly interest rate. A fuzzy approach is adopted to account for uncertainties. Mathematics of cash-flow analysis in a fuzzy environment is described. A case study is done using the proposed approach

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This paper presents an improved multi-objective group search optimizer (IMGSO) that is based on Pareto theory that is designed to handle multi-objective optimization problems. The optimizer includes improvements in three areas: the transition-feasible region is used to address constraints, the Dealer’s Principle is used to construct the non-dominated set, and the producer is updated using a tabu search and a crowded distance operator. Two objective optimization problems, the minimum weight and maximum fundamental frequency, of four truss structures were optimized using the IMGSO. The results show that IMGSO rapidly generates the non-dominated set and is able to handle constraints. The Pareto front of the solutions from IMGSO is clearly dominant and has good diversity.

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The main aim of the present paper is to propose efficient multi-objective optimization algorithms (MOOAs) to tackle truss structure optimization problems. The proposed meta-heuristic algorithms are based on the firefly algorithm (FA) and bat algorithm (BA), which have been recently developed for single-objective optimization. In order to produce a well distributed Pareto front, some improvements are implemented on the basic algorithms. The proposed MOOAs are examined for three truss optimization problems, and the results are compared to those of some other well-known methods. The numerical results demonstrate that the proposed MOOAs possess better computational performance compared to the other algorithms.

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This paper presents a Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) for the optimal operation of a complex multipurpose and multi-reservoir system. Firstly, MOEA/D decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems and optimizes them simultaneously. It uses information of its several neighboring sub-problems for optimizing each sub-problem. This simple procedure makes MOEA/D have lower computational complexity compared with non-dominated sorting genetic algorithm II (NSGA-II). The algorithm (MOEA/D) is compared with the Genetic Algorithm (NSGA-II) using a set of common test problems and the real-world Zohre reservoir system in southern Iran. The objectives of the case study include water supply of minimum flow and agriculture demands over a long-term simulation period. Experimental results have demonstrated that MOEA/D can improve system performance to reduce the effect of drought compared with NSGA-II superiority. Therefore, MOEA/D is highly competitive and recommended to solve multi-objective optimization problems for water resources planning and management.

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The interbasin water transfer is a remedy to mitigate the negative issues of water shortage in arid and semi-arid regions. In  a water transfer project  the receiving basin always  benefits while, the sending basin may suffer. In this study, the project of interbasin water transfer from Dez water resources system in south-west of Iran to the central part of the contrary is 
investigated during a drought period. To this end, a multi-objective optimization model is developed  based  on  the  Non  Dominated  Sorting  Genetic  Algorithm  (NSGA-II).  The optimum trade-off between the water supply benefits into and out of the Dez River basin as well  as  energy  production  is  derived.  Formulating  the  problem  as  a  multi-objective 
optimization provides a better insight into the gains and losses of a water transfer project. Analyzing the case study, revealed that to reach an acceptable level of reliability for meeting the water demands it is no longer possible to generate hydropower energy with high levels of reliability. 

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The most recent approaches of multi-objective optimization constitute application of meta-heuristic algorithms for which, parameter tuning is still a challenge. The present work hybridizes swarm intelligence with fuzzy operators to extend crisp values of the main control parameters into especial fuzzy sets that are constructed based on a number of prescribed facts. Such parameter-less particle swarm optimization is employed as the core of a multi-objective optimization framework with a repository to save Pareto solutions. The proposed method is tested on a variety of benchmark functions and structural sizing examples. Results show that it can provide Pareto front by lower computational time in competition with some other popular multi-objective algorithms.

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This research presents a novel design approach to achieve an optimal structure established upon multiple objective functions by simultaneous utilization of the Enhanced Time Evolutionary Optimization method and Fuzzy Logic (FLETEO). For this purpose, at first, modeling of the structure design problem in this space is performed using fuzzy logic concepts. Thus, a new problem creates with functions and constraints regarding the design in fuzzy space as well as membership functions corresponded to every single of them. Then, the problem is solved by means of the Enhanced Time Evolutionary Optimization method (ETEO), eventually, based on the acquired results, the values of optimal design variables are obtained in the main problem. In the current paper, to validate the proposed approach and evaluate its performance, the optimal design of several standard structures has been carried out. Comparing the acquired results and previous ones is an indication of the high power of the proposed method in finding the best possible design with high convergence speed and deprived of contravening the constraints governing the problems.

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In this paper, a procedure has been introduced to the multi-objective optimal design of semi-active tuned mass dampers (SATMDs) with variable stiffness for nonlinear structures considering soil-structure interaction under multiple earthquakes. Three bi-objective optimization problems have been defined by considering the mean of maximum inter-story drift as safety criterion of structural components, absolute acceleration as the criterion of occupants’ convenience, and safety of non-structural acceleration sensitive components, as well as SATMD relative displacement as the cost criterion of the control device. The parameters of the weighting matrices of the instantaneous optimal control algorithm and the maximum and minimum level of variable stiffness of the semi-active device have been considered as design variables. An improved version of the non-dominated sorting genetic algorithm (NSGA-II), has been employed to solve the optimization problems and figure out the set of Pareto optimal solutions. SATMDs with different mass ratios have been designed for an eight-story shear type building with bilinear elasto-plastic stiffness model where the soil-structure interaction has been incorporated by Cone model with three degrees of freedom for the soil. Results show the capability and simplicity of the proposed procedure to design SATMDs considering multiple performance criteria. It is observed that this procedure can offer a wide range of optimal solutions throughout the Pareto front which can be chosen by the designer based on desired performance and application of the structure.

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Parallel Cellular Automata (PCA) previously has been employed for optimizing bi-objective reservoir operation, where one release is used to meet both objectives. However, if a single release can only be used for one objective, meaning two separate sets of releases are needed, the method is not applicable anymore. In this paper, Multi-Step Parallel Cellular Automata (MSPCA) has been developed for bi-objective optimization of single-reservoir systems’ operation. To this end, a novel cellular automata formulation is proposed for such problems so that PCA’s incapability when dealing with them will be overcome. In order to determine all releases throughout the operation period, in each iteration – unlike PCA – two updates take place so as to calculate releases individually. Since a bi-objective problem in Dez reservoir (in southern Iran) has been solved by PCA in earlier works, the same data is used here. The results are given for a 60-months operation period, and to evaluate this method, the results of Non-Dominated Sorting Genetic Algorithm (NSGAII) is also given for the same problem. The comparison shows MSPCA, beside remarkable reduction in computational costs, gives up solutions with higher quality as well.

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This paper introduces a reliability-based multi-objective design method for spatial truss structures. A multi-objective optimization problem has been defined considering three conflicting objective functions including truss weight, nodal deflection, and failure probability of the entire truss structure with design variables of cross sectional area of the truss members. The failure probability of the entire truss system has been determined considering the truss structure as a series system. To this end, the uncertainties of the applied load and the resistance of the truss members have been accounted by generating a set of 50 random numbers. The limitations of members' allowable have been defined as constraints. To explain the methodology, a 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the game theory concept and genetic algorithm (GA). The results show effectiveness and simplicity of the proposed method which can provide Pareto optimal solution. These optimal solutions can provide both safety and reliability for the truss structure.
 

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In this study, the response of semi-actively controlled structures is investigated, with a focus on the effects of magneto-rheological (MR) damper distribution on the seismic response of structures such as drift and acceleration. The proposed model is closed loop, and the structure's response is used to determine the optimal MR damper voltage. A Fuzzy logic controller (FLC) is employed to calculate the optimum voltage of MR dampers. Drifts and velocities of the structure’s stories are used as FLC inputs. The FLC parameters and the distribution of MR dampers across stories are determined using the NSGA-II, when the structure is subjected to the El-Centro earthquake, so as to minimize the peak inter-story drift ratio and peak acceleration simultaneously. The efficiency of the proposed approach is illustrated through a twenty-story nonlinear benchmark structure. Non-dominated solutions are obtained to minimize the inter-story drift and acceleration of structures and Pareto front produced. Then, the non-dominated solutions are used to control the seismic response of the benchmark structure, which was subjected to the Northridge, Kobe, and Hachinohe earthquake records. In the numerical example the maximum drift and acceleration decrease by about 36.3% and 15%, respectively, in the El-Centro earthquake. The results also demonstrate that the proposed controller is more efficient in reducing drift than reducing acceleration.
 

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In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the natural frequencies and mode shapes. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO algorithms consist of Colliding Bodies Optimization (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.

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Optimization has become increasingly significant and applicable in resolving numerous engineering challenges, particularly in the structural engineering field. As computer science has advanced, various population-based optimization algorithms have been developed to address these challenges. These methods are favored by most researchers because of the difficulty of calculations in classical optimization methods and achieving ideal solutions in a shorter time in metaheuristic technique methods. Recently, there has been a growing interest in optimizing truss structures. This interest stems from the widespread utilization of truss structures, which are known for their uncomplicated design and quick analysis process. In this paper, the weight of the truss, the cross-sectional area of the members as discrete variables, and the coordinates of the truss nodes as continuous variables are optimized using the HGPG algorithm, which is a combination of three metaheuristic algorithms, including the Gravity Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Gray Wolf Optimization (GWO). The presented formulation aims to improve the weaknesses of these methods while preserving their strengths. In this research, 15, 18, 25, and 47-member trusses were utilized to show the efficiency of the HGPG method, so the weight of these examples was optimized while their constraints such as stress limitations, displacement constraints, and Euler buckling were considered. The proposed HGPG algorithm operates in discrete and continuous modes to optimize the size and geometric configuration of truss structures, allowing for comprehensive structural optimization. The numerical results show the suitable performance of this process.

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Structural optimization plays a critical role in improving the efficiency, cost-effectiveness, and sustainability of engineering designs. This paper presents a comparative study of single-objective and multi-objective optimization in the structural design process. Single-objective problems focus on optimizing just one objective, such as minimizing weight or cost, while other important aspects are treated as constraints like deflections and strength requirements. Multi-objective optimization addresses multiple conflicting objectives, such as balancing cost, with displacement treated as a secondary objective and strength requirements defined as constraints within the given limits. Both optimization approaches are carried out using Chaos Game Optimization (CGO). While single-objective optimization produces a definitive optimal solution that can be used directly in the final design, multi-objective optimization results in a set of trade-off solutions (Pareto front), requiring a decision-making process based on design codes and practical criteria to select the most appropriate design. Through a real-world case study, this research will assess the performance of both optimization strategies, providing insights into their suitability for modern structural engineering challenges.