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Highlights • An improved discrete water cycle algorithm is presented for the TSP and ATSP. • This version includes inclination feature, enhancing exploration and exploitation. • 33 datasets of the TSP/ATSP have been used for the experimentation. • Results have been compared with six different techniques. • Friedman's and Holm's post hoc statistical tests have been conducted. Abstract The water cycle algorithm (WCA) is a nature-inspired meta-heuristic recently contributed to the community in 2012, which finds its motivation in the natural surface runoff phase in water cycle process and on how streams and rivers flow into the sea. This method has been so far successfully applied to many engineering applications, spread over a wide variety of application fields. In this paper an enhanced discrete version of the WCA (coined as DWCA) is proposed for solving the Symmetric and Asymmetric Traveling Salesman Problem. Aimed at proving that the developed approach is a promising approximation method for solving this family of optimization problems, the designed solver has been tested over 33 problem datasets, comparing the obtained outcomes with the ones got by six different algorithmic counterparts from the related literature: genetic algorithm, island-based genetic algorithm, evolutionary simulated annealing, bat algorithm, firefly algorithm and imperialist competitive algorithm. Furthermore, the statistical significance of the performance gaps found in this benchmark is validated based on the results from non-parametric tests, not only in terms of optimality but also in regards to convergence speed. We conclude that the proposed DWCA approach outperforms – with statistical significance – any other optimization technique in the benchmark in terms of both computation metrics. [ABSTRACT FROM AUTHOR]

This paper studies a large-scale urban traffic light scheduling problem (LUTLSP). A centralized model is developed to describe the LUTLSP, where each outgoing flow rate is described as a nonlinear mixed logical switching function over the source link’s density, the destination link’s density and capacity, and the driver’s potential psychological response to the past traffic light signals. The objective is to minimize the total network-wise delay time of all vehicles in a time window. Three metaheuristic optimization algorithms, named as Jaya algorithm, harmony search (HS) and water cycle algorithm (WCA) are implemented to solve the LUTLSP. Since we adopt a discrete-time formulation of LUTLSP, we firstly develop a discrete version of Jaya and WCA. Secondly, some improvement strategies are proposed to speed up the convergence of applied optimizers. Thirdly, a feature based search operator is utilized to improve the search performance of reported optimization methods. Finally, experiments are carried out based on the real traffic data in Singapore. The HS, WCA, Jaya, and their variants are evaluated by solving 11 cases of traffic networks. The comparisons and discussions verify that the considered metaheuristic optimization methods can effectively solve the LUTLSP considerably surpassing the existing traffic light control strategy. [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]

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]

This paper presents the applications of the mine blast algorithm (MBA) and the water cycle algorithm (WCA), in addition to an improved version of MBA for weight minimization of truss structures including discrete sizing variables. The MBA mimics the explosion of landmines, while the WCA is inspired by the observation of water cycle process. An improved version of MBA (IMBA), is also presented. The efficiency of the three optimization algorithms is tested using classical benchmark discrete truss design problems. Optimization results show that MBA, IMBA, and WCA offer a good degree of competitiveness against other state-of-the-art metaheuristic techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new optimization technique called water cycle algorithm (WCA) which is applied to a number of constrained optimization and engineering design problems. The fundamental concepts and ideas which underlie the proposed method is inspired from nature and based on the observation of water cycle process and how rivers and streams flow to the sea in the real world. A comparative study has been carried out to show the effectiveness of the WCA over other well-known optimizers in terms of computational effort (measures as number of function evaluations) and function value (accuracy) in this paper. [Copyright &y& Elsevier]