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In order to develop the dynamic effectiveness of the structures such as trusses, the application of optimisation methods plays a significant role in improving the shape and size of elements. However, conjoining two heterogeneous variables, nodal coordinates and cross-sectional elements, makes a challenging optimisation problem that is nonlinear, multimodal, large-scale with dynamic constraints. To handle these challenges, evolutionary and swarm optimisation algorithms can be robust and practical tools and show great potential to solve such complex problems. This paper proposed a comparative truss optimisation framework to solve two large-scale structures, including 314-bar and 260-bar trusses. The proposed framework consists of twelve state-of-the-art bio-inspired algorithms. The experimental results show that the marine predators algorithm (MPA) performed best compared with other algorithms in terms of convergence speed and the quality of the proposed designs of the trusses. [ABSTRACT FROM AUTHOR]

Internationally, there are heightened demands for efficient public transportation systems due to high population growth rates in urban areas and their associated increased trip demands within and across city boundaries. An ideal and sustainable public transportation system should satisfy its passengers while minimizing operation costs that are often associated with energy consumptions. One such cost-effective approach is establishing an integrated public transit system. A transit system generally includes a set of bus routes and rail lines connected by transfer stations. The main objective of this research is to propose a sustainable and integrated transit establishment model to design an optimal bus transit system in combination with an existing railway system dealing with both fixed and variable demands while satisfying multiple objectives. Moreover, this paper finds an optimum set of transit routes that corresponds to chosen tradeoffs between user cost, operator cost and, notably, unsatisfied demand cost. Optimal transit networks have been achieved using single and multi-objective approaches via metaheuristic optimization algorithms including the genetic algorithm and the non-dominated sorting genetic algorithm II (NSGA-II). The study area is chosen as Daejeon City, South Korea for its strategic location. Compared with existing transit networks, the proposed approach shows significant improvements in terms of costs. In addition, the proposed approach can provide an efficient methodology for finding alternative alignments of existing transit systems for decision makers. [ABSTRACT FROM AUTHOR]

In recent years, significant attentions have been devoted to design of metaheuristic optimization algorithms in order to solve optimization problems. Metaheuristic optimizers are methods which are inspired by observing the phenomena occurring in nature. In this paper, a comprehensive and exhaustive review has been carried out on water cycle algorithm (WCA) and its applications in a wide variety of study fields. The WCA is one of the novel metaheuristic optimization algorithms which is inspired by water cycle process in nature and how streams and rivers flow into the sea. Good exploitation and exploration capabilities have made the WCA a good alternative for solving large-scale optimization problems. Due to its capabilities and strengths, the WCA has been utilized in many and various majors including mechanical engineering, electrical and electronic engineering, civil engineering, industrial engineering, water resources and hydropower engineering, computer engineering, mathematics, and so forth. A variety of articles based on WCA have been published in different international journals such as Elsevier, Springer, IEEE Transactions, Wiley, Taylor & Francis, and in the proceedings of international conferences as well, since 2012 to the present. Thus, it is highly believed that this paper can be appropriate, beneficial and practical for students, academic researchers, professionals, and engineers. Also, it can be an innovative and comprehensive reference for subsequent academic papers and books relevant to the WCA, optimization methods, and metaheuristic optimization algorithms. [ABSTRACT FROM AUTHOR]

Water cycle algorithm (WCA) is a population-based metaheuristic algorithm, inspired by the water cycle process and movement of rivers and streams towards sea. The WCA shows good performance in both exploration and exploitation phases. Further, the relationship between improvised exploitation and each parameter under asymmetric interval is derived and an iterative convergence of WCA is proved theoretically. In this paper, CEC'15 computationally expensive benchmark problems (i.e., 15 problems) have been considered for efficiency measurement of WCA accompanied with other optimisers. Also, a new discretisation strategy for the WCA has been proposed and applied along with other optimisers for solving combinatorial Internet shopping optimisation problem. By applying complexity analysis, it shows that using the WCA intricacy from dimension 10–30 is increased for almost three times. Proposing a unique discretisation approach along with providing iterative convergence proof can be considered as novelty of this research. By observing the attained numerical results, the WCA could find the minimum average error of CEC'15 in 12 and 8 out of 15 cases for dimensions 10 and 30, respectively. Experimental optimisation results for a wide range computationally expensive problems reveal the effectiveness and advantage of WCA for solving both continuous and discrete optimisation problems. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A dynamic optimization model Neural Network Algorithm (NNA) is proposed. • NNA is inspired by the structure of ANNs and biological nervous systems. • NNA is a parallel associated memory-based sequential-batch learning optimizer. • Convergence proof has been carried out for a random initial population. • NNA outperformed reported metaheuristic methods obtaining better quality solutions. Abstract In this research, a new metaheuristic optimization algorithm, inspired by biological nervous systems and artificial neural networks (ANNs) is proposed for solving complex optimization problems. The proposed method, named as neural network algorithm (NNA), is developed based on the unique structure of ANNs. The NNA benefits from complicated structure of the ANNs and its operators in order to generate new candidate solutions. In terms of convergence proof, the relationship between improvised exploitation and each parameter under asymmetric interval is derived and an iterative convergence of NNA is proved theoretically. In this paper, the NNA with its interconnected computing unit is examined for 21 well-known unconstrained benchmarks with dimensions 50–200 for evaluating its performance compared with the state-of-the-art algorithms and recent optimization methods. Besides, several constrained engineering design problems have been investigated to validate the efficiency of NNA for searching in feasible region in constrained optimization problems. Being an algorithm without any effort for fine tuning initial parameters and statistically superior can distinguish the NNA over other reported optimizers. It can be concluded that, the ANNs and its particular structure can be successfully utilized and modeled as metaheuristic optimization method for handling optimization problems. [ABSTRACT FROM AUTHOR]

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs. [ABSTRACT FROM AUTHOR]

One of the serious concerns in network design is creating an efficient and appropriate network capable of efficiently migrating the passenger's mode of transportation from private to public. The main goal of this study is to present an improved model for combining the feeder bus network design system and the railway transit system while minimizing total cost. In this study, the imperialist competitive algorithm (ICA) and the water cycle algorithm (WCA) were employed to optimize feeder bus and railway services. The case study and input data were based on a real transit network in Petaling Jaya, Kuala Lumpur, Malaysia. Numerical results for the proposed model, including the optimal solution, statistical optimization results and the convergence rate, as well as comparisons are discussed in detail. [ABSTRACT FROM AUTHOR]

Nowadays, many passengers use transit systems to reach their destinations; however, the growing concern for public transit is its inability to shift passenger's mode from private to public transportation. By designing a well-integrated public transit system and improving the cost-effectiveness network, the public transport could play a crucial role in passenger satisfaction and reducing the operating cost. The main target of this paper is to present a new mathematical programming model and design an efficient transit system to increase the efficiency of integrated public transit services through the development of feeder bus services and coordination of major transportation services with the aim of minimizing the costs. In this study, optimized transit services and coordinated schedules are developed using metaheuristic algorithms such as genetic algorithm, particle swarm optimization, and imperialist competitive algorithm. The data used and the coordination were obtained from a case study widely provided in the literature. Finally, obtained numerical results of the proposed model including optimal solution, statistical optimization results, and the convergence rate, and comparisons are discussed in detail using tables and figures. [ABSTRACT FROM AUTHOR]

In this paper, the water cycle algorithm (WCA), a recently developed metaheuristic method is proposed for solving multi-objective optimization problems (MOPs). The fundamental concept of the WCA is inspired by the observation of water cycle process, and movement of rivers and streams to the sea in the real world. Several benchmark functions have been used to evaluate the performance of the WCA optimizer for the MOPs. The obtained optimization results based on the considered test functions and comparisons with other well-known methods illustrate and clarify the robustness and efficiency of the WCA and its exploratory capability for solving the MOPs. [ABSTRACT FROM AUTHOR]

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. Approximate approaches have been utilized when obtaining analytical (exact) solutions requires substantial computational effort and often is not an attainable task. Hence, the importance of approximation methods, particularly, metaheuristic algorithms are understood. In this paper, a novel approach is suggested for solving engineering ordinary differential equations (ODEs). With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic methods, ODEs can be represented as an optimization problem. The target is to minimize the weighted residual function (error function) of the ODEs. The boundary and initial values of ODEs are considered as constraints for the optimization model. Generational distance and inverted generational distance metrics are used for evaluation and assessment of the approximate solutions versus the exact (numerical) solutions. Longitudinal fins having rectangular, trapezoidal, and concave parabolic profiles are considered as studied ODEs. The optimization task is carried out using three different optimizers, including the genetic algorithm, the particle swarm optimization, and the harmony search. The approximate solutions obtained are compared with the differential transformation method (DTM) and exact (numerical) solutions. The optimization results obtained show that the suggested approach can be successfully applied for approximate solving of engineering ODEs. Providing acceptable accuracy of the proposed technique is considered as its important advantage against other approximate methods and may be an alternative approach for approximate solving of ODEs. [ABSTRACT FROM AUTHOR]

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. In this paper, a general approach is suggested to solve a wide variety of linear and nonlinear ordinary differential equations (ODEs) that are independent of their forms, orders, and given conditions. With the aid of certain fundamental concepts of mathematics, Fourier series expansion and metaheuristic methods, ODEs can be represented as an optimization problem. The target is to minimize the weighted residual function (cost function) of the ODEs. To this end, two different approaches, unit weight function and least square weight function, are examined in order to determine the appropriate method. The boundary and initial values of ODEs are considered as constraints for the optimization model. Generational distance metric is used for evaluation and assessment of the approximate solutions versus the exact solutions. Six ODEs and four mechanical problems are approximately solved and compared with their exact solutions. The optimization task is carried out using different optimizers including the particle swarm optimization, the cuckoo search, and the water cycle algorithm. The optimization results obtained show that metaheuristic algorithms can be successfully applied for approximate solving of different types of ODEs. The suggested least square weight function is slightly superior over the unit weight function in terms of accuracy and statistical results for approximate solving of ODEs. [ABSTRACT FROM AUTHOR]

In this paper, a metaheuristic optimizer, the multi-objective water cycle algorithm (MOWCA), is presented for solving constrained multi-objective problems. The MOWCA is based on emulation of the water cycle process in nature. In this study, a set of non-dominated solutions obtained by the proposed algorithm is kept in an archive to be used to display the exploratory capability of the MOWCA as compared to other efficient methods in the literature. Moreover, to make a comprehensive assessment about the robustness and efficiency of the proposed algorithm, the obtained optimization results are also compared with other widely used optimizers for constrained and engineering design problems. The comparisons are carried out using tabular, descriptive, and graphical presentations. [ABSTRACT FROM AUTHOR]

Injectable calcium phosphate cements have been introduced as adjuncts to internal fixation for treating selected fractures. These cements harden without producing much heat, develop compressive strength, and are remodeled slowly in vivo. The main purpose of the cement is to fill voids in metaphyseal bone, thereby reducing the need for bone graft. However, such cements may also improve the holding strength around metal devices in osteoporotic bone. This paper presents the optimum mechanical behavior of calcium phosphate cement/hydroxyl group functionalized multi-walled carbon nanotubes/bovine serum albumin (CPC/MWCNT-OH/BSA) composites in terms of compressive strength using well-known metaheuristic optimizers. The process parameters studied were wt% of MWCNT-OH (0.2-0.5 wt%) and wt% of BSA (5-15 wt%). The obtained results from metaheuristic algorithms were compared with the results from the response surface methodology (RSM) in the literature. The results obtained from metaheuristic algorithms outperformed the results given by the RSM in terms of less error percentage and high compressive strength. [ABSTRACT FROM AUTHOR]

Engineering benchmark problems with specific characteristics have been used to compare the performance and reliability of metaheuristic algorithms, and water distribution system design benchmarks are also widely used. However, only a few benchmark design problems have been considered in the research community. Due to the limited set of previous benchmarks, it is challenging to identify the algorithm with the best performance and the highest reliability among a group of algorithms. Therefore, in this study, a new water distribution system design benchmark problem generation method is proposed considering problem size and complexity modifications of a reference benchmark. The water distribution system design benchmark problems are used for performance and reliability comparison among several reported metaheuristic optimization algorithms. The optimal design results are able to quantify the performance and reliability of the compared algorithms which shows each metaheuristic algorithm has its own strengths and weaknesses. Finally, using the proposed method in this study, guidelines are derived for selecting an appropriate metaheuristic algorithm for water distribution system design. [ABSTRACT FROM AUTHOR]