Stochastic paint optimizer: theory and application in civil engineering
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ORIGINAL ARTICLE
Stochastic paint optimizer: theory and application in civil engineering Ali Kaveh1 · Siamak Talatahari2 · Nima Khodadadi1 Received: 5 July 2020 / Accepted: 15 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This paper presents an art-inspired optimization algorithm, which is called Stochastic Paint Optimizer (SPO). The SPO is a population-based optimizer inspired by the art of painting and the beauty of colors plays the main role in this algorithm. The SPO, as an optimization algorithm, simulates the search space as a painting canvas and applies a different color combination for finding the best color. Four simple color combination rules without the need for any internal parameter provide a good exploration and exploitation for the SPO. The performance of the algorithm is evaluated by twenty-three mathematical well-known benchmark functions, and the results are verified by a comparative study with recent well-studied algorithms. In addition, a set of IEEE Congress of Evolutionary Computation benchmark test functions (CEC-C06 2019) are utilized. On the other hand, the Wilcoxon test, as a non-parametric statistical test, is used to determine the significance of the results. Finally, to prove the practicability of the SPO, this algorithm is applied to four different structural design problems, known as challenging problems in civil engineering. The results of all these problems indicate that the SPO algorithm is able to provide very competitive results compared to the other algorithms. Keywords Stochastic paint optimizer · Metaheuristic algorithm · Optimization
1 Introduction For optimization problems, two major methods, containing mathematical and metaheuristic algorithms, are developed and applied; However, using mathematical algorithms is difficult and time-consuming for solving many optimization problems. Furthermore, they require a good starting point to successful converge to the optimum result, otherwise, they may be trapped in a local optimum. On the other hand, metaheuristic methods are often nature-inspired techniques that are able to explore the entire search space and exploit a final good result. Within an affordable computational time, they can find optimal or near-optimal solutions to the tough and even NP-hard problems. Unlike mathematical methods, they are very flexible and simple, making them popular among both researchers and practitioners [1]. Meta-heuristics, which are among the most promising and successful * Ali Kaveh [email protected] 1
School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
Department of Civil Engineering, University of Tabriz, Tabriz, Iran
2
techniques [2], represent a family of approximate optimization techniques that have gained a lot of popularity in the past two decades. As aforementioned, these techniques rely on the rules observed in nature. The origins of inspiration can be divided into three classes: i. Evolutionary Algorithms (EAs): The theories are based on bio
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