Abstract
Moth search (MS) algorithm, originally proposed to solve continuous optimization problems, is a novel bio-inspired metaheuristic algorithm. At present, there seems to be little concern about using MS to solve discrete optimization problems. One of the most common and efficient ways to discretize MS is to use a transfer function, which is in charge of mapping a continuous search space to a discrete search space. In this paper, twelve transfer functions divided into three families, S-shaped (named S1, S2, S3, and S4), V-shaped (named V1, V2, V3, and V4), and other shapes (named O1, O2, O3, and O4), are combined with MS, and then twelve discrete versions MS algorithms are proposed for solving set-union knapsack problem (SUKP). Three groups of fifteen SUKP instances are employed to evaluate the importance of these transfer functions. The results show that O4 is the best transfer function when combined with MS to solve SUKP. Meanwhile, the importance of the transfer function in terms of improving the quality of solutions and convergence rate is demonstrated as well.
Highlights
The knapsack problem (KP) [1] is still considered as one of the most challenging and interesting classical combinatorial optimization problems, because it is non-deterministic polynomial hard problem and has many important applications in reality
Comparative studies were conducted among binary artificial bee colony algorithm (BABC), A-set-union knapsack problem (SUKP), and binary differential evolution (DE) [8]
The basic Moth search (MS) algorithm was initially proposed for continuous optimization problems, while SUKP belongs to a discrete optimization problem with constraints
Summary
The knapsack problem (KP) [1] is still considered as one of the most challenging and interesting classical combinatorial optimization problems, because it is non-deterministic polynomial hard problem and has many important applications in reality. A-SUKP has to face the inevitable problem, that is, how to compromise between achieving a high-quality solution and exponential runtime He et al [5] presented a binary artificial bee colony algorithm (BABC) to solve SUKP and comparative studies were conducted among BABC, A-SUKP, and binary differential evolution (DE) [8]. Ozsoydan et al [9] proposed a swarm intelligence-based algorithm for the SUKP and designed an effective mutation procedure This method does not require transfer functions, it lacks generality. Direct discretization is usually achieved by modifying the evolutionary operator of the original algorithm to solve a particular discrete problem. Many discrete versions of swarm intelligence algorithms using transfer functions have been proposed to solve various optimization problems. We draw conclusions and suggest some directions for future research
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