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Evolutionary computation including swarm intelligence is a population-based search method inspired by biological phenomena. Based on such population-based search methods, many researchers contribute to developing optimization and adaptation algorithms in these years. Conventional evolutionary algorithms focus on providing an actual solution for a single optimization task. Researchers use these algorithms to handle the multi-objective optimization problems where the Pareto optimal set is approximated by the population or the archived candidates. In recent years, taking advantage of parallel processing ability in population-based search, evolutionary multitask optimization or evolutionary multitasking has been proposed (Ong & Gupta 2016). This is a novel area of evolutionary computation that is different problems are handled separately in a single population. Then, for processing multiple optimization problems, multifactorial optimization has been presented as a method in which each constitutive task would affect the evolution of a single population (Gupta et al., 2016). As an actual multifactorial optimization framework that is inspired by the bio-cultural models of multifactorial inheritance, a multifactorial evolutionary algorithm (MFEA) is developed (Ong & Gupta 2016). In MFEA, a skill factor is used to assign a preferred task for each individual of the population.
On the other hand, swarm intelligence is one of the popular metaheuristics for optimization problems. A wide variety of swarm models are developed such as particle swarm optimization (PSO) (Kennedy & Eberhart, 1995), Firefly algorithm (FA) (Yang, 2009), Cuckoo search (Yang & Deb, 2009) and so on. These models have some common properties and inherent characteristics. Besides, making hybridization of suitable selected swarm models is also one way for processing optimization problems effectively. There are some related researches about the hybridization presented in recent years. With different strategies such as fixed numbers of particles and fireflies (Xiao & Hatanaka, 2016), model selection (Aydilek, 2018; Xiao & Hatanaka, 2020), it shows that the hybridization can provide different kinds of improvement ways for optimization problems.
The motivation for this research is to contribute an application of a hybrid swarm to multifactorial optimization. Multifactorial optimization works to make one individual searches in a unified space and let it be evaluated for multiple minimization problems. By applying swarm intelligence to multifactorial optimization, it expects that the automatic search swarm is able to process multiple optimization tasks simultaneously. This paper proposes a multifactorial PSO-FA hybrid algorithm (MFHA). The PSO-FA hybrid swarm utilizes a model selection mechanism with an event-driven trigger based on whether the personal best information is updated (Xiao & Hatanaka, 2020). In the proposed multifactorial swarm intelligence mechanism, it utilizes a skill factor to help the task assignment of individuals, which means the population can explore different tasks at the same time. For a multifactorial swarm, it is important to suitably assign a task to each individual in the population. This assignment is usually based on a skill factor that indicates the preferred task to each individual based on the pre-evaluated ranking and is exchanged by a crossover in the evolutionary algorithm. However, there is no explicit information exchange mechanism such as a crossover in the swarm intelligence model. Thus a skill factor reassignment method is also introduced in this paper. The hybrid swarm is expected to contribute to adjusting the population for well processing multiple tasks by a combination of a model selection mechanism and skill factor reassignment. By testing the multifactorial PSO (MFPSO) and the multifactorial PSO-FA hybrid algorithm on the benchmark multifactorial optimization problem, then comparing them with each other to show how the hybrid swarm performs better than PSO for the multifactorial optimization problem.