Sine Cosine Algorithm with Multigroup and Multistrategy for Solving CVRP

Abstract

Sine Cosine Algorithm (SCA) has been proved to be superior to some existing traditional optimization algorithms owing to its unique optimization principle. However, there are still disadvantages such as low solution accuracy and poor global search ability. Aiming at the shortcomings of the sine cosine algorithm, a multigroup multistrategy SCA algorithm (MMSCA) is proposed in this paper. e algorithm executes multiple populations in parallel, and each population executes a different optimization strategy. Information is exchanged among populations through intergenerational communication. Using 19 different types of test functions, the optimization performance of the algorithm is tested. Numerical experimental results show that the performance of the MMSCA algorithm is better than that of the original SCA algorithm, and it also has some advantages over other intelligent algorithms. At last, it is applied to solving the capacitated vehicle routing problem (CVRP) in transportation. e algorithm can get better results, and the practicability and feasibility of the algorithm are also proved. [29,30], bat algorithm (BA) [31,32], symbiotic organism search algorithm (SOS) [33,34], and QUATRE [35][36][37].At present, there are so many optimization algorithms, which can solve some complex optimization problems well. Why do we need so many optimization algorithms? As demonstrated by the No Free Lunch (NFL) [38] proposed by Wolpert and Macready, no single optimization algorithm is applicable to all problems. Inspired by this, a new intelligent optimization algorithm was proposed by Australian scholar Mirjalili in 2016, which is called Sine Cosine Algorithm (SCA) [39]. e SCA algorithm iterates through the properties of the sine and cosine functions to achieve optimization. It has fewer parameter settings, is easy to implement, and has a strong optimization ability. It has been proved that it is better than PSO algorithm, genetic algorithm (GA), and firefly algorithm (FA) in convergence with accuracy and speed [39].With the rapid development of software and hardware, parallel computing has become a form of high-performance computing. In evolutionary computing, parallelism often represents the iterative updating of multiple populations at the same time. e advantage of this method is to ensure population diversity, to further improve the search ability and performance of the algorithm. Especially when solving complex optimization problems, parallelizing the algorithm is an effective way to improve the efficiency and accuracy of the algorithm. At present, many existing algorithms have successfully applied the parallel mechanism, such as parallel PSO [40], parallel ACO [41], and parallel QUATRE [42]. Inspired by this, this paper introduces the multigroup and multistrategy optimization mechanism to further improve the SCA algorithm. It is called MMSCA. When the algorithm is solved, multiple populations execute in parallel, and each population adopts different updating strategies. By comparing the results of test functions, MMSCA is be...

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“…When the proposed method is compared with contemporary algorithms it has been found that the method performs exceptionally well, which proofs the effectiveness of the method. Qingyong Yang et al [57] proposed the multigroup multistrategy SCA algorithm (MMSCA) for capacitated vehicle routing problem (CVRP). The numerical experimental results proofs the efficacy of the proposed method.…”

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“…QUATRE is an excellent algorithm which improved the drawback of DE that did not achieve equilibrium search in search space without prior knowledge and moveover, it generalized the crossover operation of DE from vector to matrix. In algorithms based on physical or mathematical models, Simulated Annealing (SA) [38], [39] originates from the principle of solid annealing; Gravitational Search Algorithm (GSA) [40], [41] mainly uses the law of gravitation between two objects to guide the motion optimization of each particle to search for the optimal solution; Sine Cosine Algorithm (SCA) [42], [43] is achieved by iteration of sine and cosine functions.…”

Compact Sine Cosine Algorithm with Multigroup and Multistrategy for Dispatching System of Public Transit Vehicles

“…Sine Cosine Algorithm with Multigroup and Multistrategy (MMSCA) is an improved SCA algorithm [24]. MMSCA divides the population into groups and uses different update strategies in different groups.…”

“…In the best strategy, the best individual in all populations is still the solution target. e SCA and the improved SCA algorithms [24][25][26] are used in many different fields to solve different problems. For example, the SCA algorithm can solve the economic and emission dispatch problem [27,28], a design damping controller [29], and a system for battery charging [30], predict wind speed [31], reconfigure the power distribution network [32], segment image [33], and control the load frequency of power system [34].…”