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In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. This paper aims to contribute to this endeavor by examining the impact of solution initialization methods on the performance of a hybrid algorithm applied to the set union knapsack problem (SUKP). Three distinct solution initialization methods, random, greedy, and weighted, have been proposed and evaluated. These have been integrated within a sine cosine algorithm employing k-means as a binarization procedure. Through testing on medium- and large-sized SUKP instances, the study reveals that the solution initialization strategy influences the algorithm's performance, with the weighted method consistently outperforming the other two. Additionally, the obtained results were benchmarked against various metaheuristics that have previously solved SUKP, showing favorable performance in this comparison. [ABSTRACT FROM AUTHOR]

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA. [ABSTRACT FROM AUTHOR]

Many metaheuristic approaches are inherently stochastic. In order to compare such methods, statistical tests are needed. However, choosing an appropriate test is not trivial, given that each test has some assumptions about the distribution of the underlying data that must be true before it can be used. Permutation tests (P-Tests) are statistical tests with minimal number of assumptions. These tests are simple, intuitive and nonparametric. In this paper, we argue researchers in the field of metaheuristics to adopt P-Tests to compare their algorithms. We define two statistic tests and then present an algorithm that uses them to compute the p-value. The proposed process is used to compare 5 metaheuristic algorithms on 10 benchmark functions. The resulting p-values are compared with the p-values of two widely used statistical tests. The results show that the proposed P-test is generally consistent with the classical tests, but more conservative in few cases. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA's robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

For process control in engineering applications, the fewer the coding lines of optimization algorithms, the more applications there are. Therefore, this work develops a new straightforward metaheuristic optimization algorithm named the propagation search algorithm (PSA), stirred by the wave propagation of the voltage and current along long transmission lines. The mathematical models of the voltage and current are utilized in modeling the PSA, where the voltage and current are the search agents. The propagation constant of the transmission line is the control parameter for the exploitation and exploration of the PSA. After that, the robustness of the PSA is verified using 23 famous testing functions. The statistical tests, comprising mean, standard deviation, and p-values, for 20 independent optimization experiments are utilized to confirm the robustness of the PSA to find the best result and the significant difference between the outcomes of the PSA and those of the compared algorithms. Finally, the proposed PSA is applied to find the optimum design parameters of four engineering design problems, including a three-bar truss, compression spring, pressure vessel, and welded beam. The outcomes show that the PSA converges to the best solutions very quickly, which can be applied to those applications that require a fast response. [ABSTRACT FROM AUTHOR]

Currently, industry is undergoing an exponential increase in binary-based combinatorial problems. In this regard, metaheuristics have been a common trend in the field in order to design approaches to successfully solve them. Thus, a well-known strategy includes the employment of continuous swarm-based algorithms transformed to perform in binary environments. In this work, we propose a hybrid approach that contains discrete smartly adapted population-based strategies to efficiently tackle binary-based problems. The proposed approach employs a reinforcement learning technique, known as SARSA (State–Action–Reward–State–Action), in order to utilize knowledge based on the run time. In order to test the viability and competitiveness of our proposal, we compare discrete state-of-the-art algorithms smartly assisted by SARSA. Finally, we illustrate interesting results where the proposed hybrid outperforms other approaches, thus, providing a novel option to tackle these types of problems in industry. [ABSTRACT FROM AUTHOR]