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Optimal design of large-scale structures is a rather difficult task and the computational efficiency of the currently available methods needs to be improved. In view of this, the paper presents a modified Charged System Search (CSS) algorithm. The new methodology is based on the combination of CSS and Particle Swarm Optimizer. In addition, in order to improve optimization search, the sequence of tasks entailed by the optimization process is changed so that the updating of the design variables can directly be performed after each movement. In this way, the new method acts as a single-agent algorithm while preserving the positive characteristics of its original multi-agent formulation.

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The Charged System Search (CSS) is combined to chaos to solve mathematical global optimization problems. The CSS is a recently developed meta-heuristic optimization technique inspired by the governing laws of physics and mechanics. The present study introduces chaos into the CSS in order to increase its global search mobility for a better global optimization. Nine chaos-based CSS (CCSS) methods are developed, and then for each variant, the performance of ten different chaotic maps is investigated to identify the most powerful variant. A comparison of these variants and the standard CSS demonstrates the superiority and suitability of the selected variants for the benchmark mathematical optimization problems.

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In this paper, an efficient optimization algorithm is proposed based on Particle Swarm Optimization (PSO) and Simulated Annealing (SA) to optimize truss structures. The proposed algorithm utilizes the PSO for finding high fitness regions in the search space and the SA is used to perform further investigation in these regions. This strategy helps to use of information obtained by swarm in an optimal manner and to direct the agents toward the best regions, resulting in possible reduction of the number of particles. To show the computational advantages of the new PSO-SA method, some benchmark numerical examples are studied. The PSO-SA algorithm converges to better or at least the same solutions, while the number of structural analyses is significantly reduced

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The Big Bang-Big Crunch (BB–BC) method is a relatively new meta-heuristic algorithm which inspired by one of the theories of the evolution of universe. In the BB–BC optimization algorithm, firstly random points are produced in the Big Bang phase then these points are shrunk to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. In this paper, the BB–BC algorithm is presented for optimal cost design of water distribution systems and employed to optimize different types of hydraulic networks with discrete variables. The results demonstrate the efficiency of the proposed method compared to other algorithms.

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Over the past few years, swarm intelligence based optimization techniques such as ant colony optimization and particle swarm optimization have received considerable attention from engineering researchers. These algorithms have been used in the solution of various structural optimization problems where the main goal is to minimize the weight of structures while satisfying all design requirements imposed by design codes. In this paper, artificial bee colony algorithm (ABC) is utilized to optimize different skeletal structures. The results of the ABC are compared with the results of other optimization algorithms from the literature to show the efficiency of this technique for structural design problems.

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Chaos is embedded to the he Charged System Search (CSS) to solve practical optimization problems. To improve the ability of global search, different chaotic maps are introduced and three chaotic-CSS methods are developed. A comparison of these variants and the standard CSS demonstrates the superiority and suitability of the selected variants for practical civil optimization problems.

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A charged system search algorithm (CSS) is applied to the optimal cost design of water distribution networks. This algorithm is inspired by the Coulomb and Gauss’s laws of electrostatics in physics. The CSS utilizes a number of charged particles which influence each other based on their fitness values and their separation distances considering the governing law of Coulomb. The well-known benchmark instances, Hanoi network, double Hanoi network, and New York City tunnel problem, are utilized as the case studies to evaluate the optimization performance of CSS. Comparison of the results of the CSS with some other meta-heuristic algorithms indicates the performance of the new algorithm.

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Tunnel structures are known as expensive infrastructures and determining optimum designs of these structures can play a great role in minimizing their cost. The formulation of optimum design of industrial tunnel sections as an optimization is considered in this paper and then the enhanced charged system search, as a recently developed meta-heuristic approach, has been applied to solve the problem. The results and comparisons based on numerical examples show the efficiency of the optimization algorithm.

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Deterring the optimum design of large-scale structures is a difficult task. Great number of design variables, largeness of the search space and controlling great number of design constraints are major preventive factors in performing optimum design of large-scale truss structures in a reasonable time. Meta-heuristic algorithms are known as one of the useful tools to deal with these problems. This paper presents an improved bat algorithm for optimizing large-scale structures. The capability of the algorithm is examined by comparing the resulting design parameters and structural weight with those of other methods from literature.

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This paper utilizes recent optimization algorithm called Ant Lion Optimizer (ALO) for optimal design of skeletal structures. The ALO is based on the hunting mechanism of Antlions in nature. The random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are main steps for this algorithm. The new algorithm is examined by designing three truss and frame design optimization problems and its performance is further compared with various classical and advanced algorithms.

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This paper presents an efficient optimization procedure to find the optimal shapes of double curvature  arch  dams  considering  fluid–structure  interaction  subject  to  earthquake  loading. The optimization is carried out using a combination of the magnetic charged system search, big bang-big crunch algorithm and artificial neural network methods. Performing the finite element  analysis  during  the  optimization  process  is  time  consuming.  Back  propagation neural  network  is  utilized  to  reduce  the  computational  burden.  A  real-world  arch  dam  is considered as a numerical example to demonstrate the efficiency of the proposed method. The numerical results reveal the computational advantages of the new method for optimal 
design of arch dams.

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For optimization of real-world arch dams, it is unavoidable to consider two or more conflicting objectives. This paper employs two multi-objective differential evolution algorithms (MoDE) in combination of a parallel working MATLAB-APDL code to obtain a set of Pareto solutions for optimal shape of arch dams. Full dam-reservoir interaction subjected to seismic loading is considered. A benchmark arch dam is then examined as the numerical example. The numerical results are compared to show the performance of the MoDE methods.

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This paper utilizes the Colliding Bodies of Optimization (CBO), Enhanced Colliding Bodies of Optimization (ECBO) and Vibrating Particles System (VPS) algorithms to optimize the reservoir system operation. CBO is based on physics equations governing the one-dimensional collisions between bodies, with each agent solution being considered as an object or body with mass and ECBO utilizes memory to save some historically best solutions and uses a random procedure to escape from local optima. VPS is based on simulating free vibration of single degree of freedom systems with viscous damping. To evaluate the performance of these three recent population-based meta-heuristic algorithms, they are applied to one of the most complex and challenging issues related to water resource management, called reservoir operation optimization problems. Hypothetical 4 and 10-reservoir systems are studied to demonstrate the effectiveness and robustness of the algorithms. The aim is on discovering the optimum mix of releases, which will lead to maximum benefit generation throughout the system. Comparative results show the successful performance of the VPS algorithm in comparison to the CBO and its enhanced version.

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Water distribution networks are one of the important and costly infrastructures of cities and many meta-heuristic algorithms in standard or hybrid forms were used for optimizing water distribution networks. These algorithms require a large amount of computational cost. Therefore, the converging speed of algorithms toward the optimization goal is as important as the goal itself. In this paper, a new method is developed by linking the charged system search algorithm and firefly algorithm for optimizing water distribution networks. For evaluating the proposed method, some popular benchmark examples are considered. Simulation results demonstrate the efficiency of the proposed algorithm compared to others.

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In this article, an Advanced Charged System Search (ACSS) algorithm is applied for the optimum design of steel structures. ACSS uses the idea of Opposition-based Learning and Levy flight to enhance the optimization abilities of the standard CSS. It also utilizes the information of the position of each charged particle in the subsequent search process to increase the convergence speed. The objective function is to find a minimum weight by choosing suitable sections subjected to strength and displacement requirements specified by the American Institute of Steel Construction (AISC) standard subject to the loads defined by Load Resistance Factor Design (LRFD). To show the performance of the ACSS, four steel structures with different number of elements are optimized. The results, efficiency, and accuracy of the ACSS algorithm are compared to other meta-heuristic algorithms. The results show the superiority of the ACSS compared to the other considered algorithms.

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In this work, a new hybrid Symbiotic Organisms Search (SOS) algorithm introduced to design and optimize spatial and planar structures under structural constraints. The SOS algorithm is inspired by the interactive behavior between organisms to propagate in nature. But one of the disadvantages of the SOS algorithm is that due to its vast search space and a large number of organisms, it may trap in a local optimum. To fix this problem Harmony search (HS) algorithm, which has a high exploration and high exploitation, is applied as a complement to the SOS algorithm. The weight of the structures' elements is the objective function which minimized under displacement and stress constraints using finite element analysis. To prove the high capabilities of the new algorithm several spatial and planar benchmark truss structures, designed and optimized and the results have been compared with those of other researchers. The results show that the new algorithm has performed better in both exploitation and exploration than other meta-heuristic and mathematics methods.

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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.