Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems

• WCA concepts are inspired by nature and based on water cycle process.
• New concepts of evaporation rate for rivers and streams are applied in the ER-WCA.
• Variable evaporation rate is utilized in the ER-WCA to evaporate the water adaptively.
• ER-WCA forces new generated streams to search near sea using the concept of variance.
• ER-WCA outperforms or equals other methods in terms of function evaluations and solution quality.

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.

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