Abstract
Moth–flame optimization (MFO) is a prominent swarm intelligence algorithm that demonstrates sufficient efficiency in tackling various optimization tasks. However, MFO cannot provide competitive results for complex optimization problems. The algorithm sinks into the local optimum due to the rapid dropping of population diversity and poor exploration. Hence, in this article, a migration-based moth–flame optimization (M-MFO) algorithm is proposed to address the mentioned issues. In M-MFO, the main focus is on improving the position of unlucky moths by migrating them stochastically in the early iterations using a random migration (RM) operator, maintaining the solution diversification by storing new qualified solutions separately in a guiding archive, and, finally, exploiting around the positions saved in the guiding archive using a guided migration (GM) operator. The dimensionally aware switch between these two operators guarantees the convergence of the population toward the promising zones. The proposed M-MFO was evaluated on the CEC 2018 benchmark suite on dimension 30 and compared against seven well-known variants of MFO, including LMFO, WCMFO, CMFO, CLSGMFO, LGCMFO, SMFO, and ODSFMFO. Then, the top four latest high-performing variants were considered for the main experiments with different dimensions, 30, 50, and 100. The experimental evaluations proved that the M-MFO provides sufficient exploration ability and population diversity maintenance by employing migration strategy and guiding archive. In addition, the statistical results analyzed by the Friedman test proved that the M-MFO demonstrates competitive performance compared to the contender algorithms used in the experiments.
Highlights
The moth–flame optimization (MFO) is applicable for solving real-world problems and many improvements have been developed, it has been observed that the MFO and its variants hereditarily suffer from poor exploration and loss of population diversity before the near-optimal solution is met, which leads the algorithm toward local optima trapping and premature convergence
To converge the algorithm and provide more exploitation, the number of flames decreases in the course of iterations based on Equation (5), where t determines the current number of iterations, while N and Max iterations (MaxIt) demonstrate the total number of flames and the maximum number of iterations, respectively
This study proposes a migration-based moth–flame optimization (M-MFO) algorithm, which is a hybridization of the MFO algorithm and the crossover operator introduced in the genetic algorithm (GA)
Summary
Optimization techniques have been developed widely to solve complex problems that emerged in different fields of science, such as engineering [1,2,3,4,5,6,7,8,9], clustering [10,11,12,13,14,15,16,17,18], feature selection [19,20,21,22,23,24,25,26,27,28], and task scheduling [29,30,31,32]. Metaheuristic algorithms mostly employ stochastic techniques to solve optimization problems by exploring the search space to promote population diversity in the early iterations. The MFO is applicable for solving real-world problems and many improvements have been developed, it has been observed that the MFO and its variants hereditarily suffer from poor exploration and loss of population diversity before the near-optimal solution is met, which leads the algorithm toward local optima trapping and premature convergence. The experimental results revealed that the migration strategy enhances the exploration ability and maintains the population diversity to avoid local optimum by stochastically migrating the worst individuals across the search space in the first iterations and exploiting promising areas discovered by the RM operator in the iterations.
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