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Abstract Functionally graded beams (FGBs) have been studied extensively in literature to predict their static stability and dynamic behavior. In typical FGBs, each of material variation has significant influence on overall beams’ strength. This research utilized single and multi-objective optimization approaches to optimize the volume fraction distribution in the Timoshenko FGBs in order to maximize the fundamental frequency while minimizing mass and axial stresses. The FGBs with different ratios of material properties are considered. Several metaheuristic optimization techniques are utilized to address single and multi-objective problems. For validating purpose, computational optimization results are compared with those available in the literature. [ABSTRACT FROM AUTHOR]

In this article, a model of a T-shaped fin, consisting of a set of ordinary differential equations (ODEs), is considered. The purpose of this article is to numerically solve ODE systems of a T-shaped fin (there is no reported exact and analytical solution) using an alternative approach. Utilizing a base approximation function, some mathematical principles and metaheuristics, an approximate solution very close to the existing numerical solution was found. The weighted residual function is used as an objective function along with its constraints, such as boundary and initial values. For the sake of comparison, a generational distance metric is used to evaluate the obtained results compared with the existing results in the literature. The approximate solution found by the applied approach demonstrates its efficiency and performance compared with the existing numerical approach. [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]

Harmony Search (HS) is a music-inspired optimization algorithm for solving complex optimization problems that imitate the musical improvisational process. This paper reviews the potential of applying the HS algorithm in three countries, China, South Korea, and Japan. The applications represent several disciplines in fields of study such as computer science, mathematics, electrical/electronic, mechanical, chemical, civil, and industrial engineering. We anticipate an increasing number of HS applications from these countries in near future. [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]

Public transportation can have an efficient role ingainingtraveler satisfaction while decreasing operation costs through establishing an integrated public transit system. The main objective of this research is to propose an integrated multimodal transit model to design the best combination of both railway and feeder bus mode transit systems, while minimizing total cost. In this paper, we have proposed a strategy for designing transit networks that provide multimodal services at each stop, and for consecutively assigning optimum demand to the different feeder modes. Optimum transit networks have been achieved using single and multi-objective approaches via metaheuristic optimization algorithms, such as simulated annealing, genetic algorithms, and the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The used input data and study area were based on the real transit network of Petaling Jaya, located in Kuala Lumpur, Malaysia. Numerical results of the presented model, containing the statistical results, the optimum demand ratio, optimal solution, convergence rate, and comparisons among best solutions have been discussed in detail. [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]

Water Cycle Algorithm (WCA) is a nature-inspired population-based metaheuristic algorithm, which has been successfully applied to solve a wide range of benchmarks and real-world optimization problems. In this paper, an extended version of WCA, namely Gradient-based Water Cycle Algorithm (GWCA) with evaporation rate, is introduced to enhance the performance of the standard WCA by incorporating a local optimization operator so-called gradient-based approach. The idea of GWCA is underlined using the concept of moving (flowing) individuals along the steepest direction slope under a certain criterion. In order to demonstrate parameters influence on the performance of GWCA, an extensive sensitivity analysis is also carried out. To verify the performance of the GWCA, twelve well-known benchmark functions are adopted from the literature in the experiments. Both value-based and ranked-based methods are conducted to compare the performance of reported algorithms on the whole test suite. To this reason, the mean best and standard deviation of the results are provided and the Friedman test is utilized to determine average ranking of the algorithms based on their performances in each experiment. Corresponding results indicate that the proposed GWCA has outstanding performance in comparison with some state-of-art optimization algorithms. Finally, the chaos suppression problem using backstepping control as a real case study was adopted to confirm the efficiency of GWCA. The experimental results demonstrate the feasibility and efficiency of the proposed GWCA. [ABSTRACT FROM AUTHOR]

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms. [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]

This paper presents a modified version of the water cycle algorithm (WCA). The fundamental concepts and ideas which underlie the WCA are inspired based on the observation of water cycle process and how rivers and streams flow to the sea. New concept of evaporation rate for different rivers and streams is defined so called evaporation rate based WCA (ER-WCA), which offers improvement in search. Furthermore, the evaporation condition is also applied for streams that directly flow to sea based on the new approach. The ER-WCA shows a better balance between exploration and exploitation phases compared to the standard WCA. It is shown that the ER-WCA offers high potential in finding all global optima of multimodal and benchmark functions. The WCA and ER-WCA are tested using several multimodal benchmark functions and the obtained optimization results show that in most cases the ER-WCA converges to the global solution faster and offers more accurate results than the WCA and other considered optimizers. Based on the performance of ER-WCA on a number of well-known benchmark functions, the efficiency of the proposed method with respect to the number of function evaluations (computational effort) and accuracy of function value are represented. [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]

In recent years, many researchers have utilized metaheuristic optimization algorithms along with fuzzy logic theory in their studies for various purposes. The harmony search (HS) algorithm is one of the metaheuristic optimization algorithms that is widely employed in different studies along with fuzzy logic (FL) theory. FL theory is a mathematical approach to expressing uncertainty by applying the conceptualization of fuzziness in a system. This review paper presents an extensive review of published papers based on the combination of HS and FL systems. In this regard, the functional characteristics of models obtained from integration of FL and HS have been reported in various articles, and the performance of each study is investigated. The basic concept of the FL approach and its derived models are introduced to familiarize readers with the principal mechanisms of FL models. Moreover, appropriate descriptions of the primary classifications acquired from the coexistence of FL and HS methods for specific purposes are reviewed. The results show that the high efficiency of HS to improve the exploration of FL in achieving the optimal solution on the one hand, and the capability of fuzzy inference systems to provide more flexible and dynamic adaptation of the HS parameters based on human perception on the other hand, can be a powerful combination for solving optimization problems. This review paper is believed to be a useful resource for students, engineers, and professionals. [ABSTRACT FROM AUTHOR]

This paper represents a hybrid Firefly and Self-Regulating Particle Swarm Optimization (FSRPSO) algorithm to solve optimal Combined Heat and Power Economic Dispatch (CHPED) problem. Valve point effect on fuel cost function of pure generation units, electrical power losses in transmission systems and feasible operating zones are taken into account in the CHPED problem. The CHPED refers to minimize total costs of fuel for electricity and heat generation supply to load demand. The proposed FSRPSO attempts to determine the start of the local search process properly by checking the previous global best. Thus, the FSRPSO is able to exploit strong points of both Firefly Algorithm (FA) and SRPSO mechanisms in order to balance between exploration and exploitation phases. Besides, for the sake of validation the proposed hybrid method, the FSRPSO is examined on 21 well-known benchmarks, and also a real engineering case i.e., two power systems for evaluating its performance compared with the SRPSO, FA, PSO, and other state-of-the-art algorithms. The obtained optimization results show that the proposed FSRPSO provides fast, mature and reliable optimum solutions and outperform other compared algorithms in diverse categories of benchmarks along with the studied CHPED problem. • A novel hybrid algorithm named as FSRPSO is introduced to solve CHPED problem. • In the FSRPSO, some intelligent capabilities is used to achieve the optimal solution. • The FSRPSO is validated by 21 benchmarks and small and large scale power systems. • The FSRPSO illustrates competitive results over SRPSO, FA and other optimizers. [ABSTRACT FROM AUTHOR]

In recent years, both sustainability and optimization concepts have become inseparable developing topics with diverse concepts, elements, and aspects. The principal goal of optimization is to improve the overall sustainability including the environmental sustainability, social sustainability, economic sustainability, and energy resources sustainability through satisfying the objective functions. Therefore, applying optimization algorithms and methods to achieve the sustainable development have significant importance. This paper represents a considerable review on the employed optimization methodologies to sustainability and the sustainable development including sustainable energy, sustainable buildings, and sustainable environment. Since energy optimization is one of the major necessities of sustainability, sustainable development is investigated from the energy perspective. In addition, the concept, definitions, and elements of the sustainability and optimization have been presented, and the review of the optimization metaheuristic algorithms used in recent published articles related to sustainability and sustainable development was carried out. Thus, it is believed that this paper can be appropriate, beneficial, and practical for students, academic researchers, engineers, and other professionals. [ABSTRACT FROM AUTHOR]