Abstract
Populations of multipopulation genetic algorithms (MPGAs) parallely evolve with some interaction mechanisms. Previous studies have shown that the interaction structures can impact on the performance of MPGAs to some extent. This paper introduces the concept of complex networks such as ring-shaped networks and small-world networks to study how interaction structures and their parameters influence the MPGAs, where subpopulations are regarded as nodes and their interaction or migration of elites between subpopulations as edges. After solving the flexible job-shop scheduling problem (FJSP) by MPGAs with different parameters of interaction structures, simulation results were measured by criteria, such as success rate and average optimal value. The analysis reveals that (1) the smaller the average path length (APL) of the network is, the higher the propagation rate will be; (2) the performance of MPGAs increased first and then decreased along with the decrease of APL, indicating that, for better performance, the networks should have a proper APL, which can be adjusted by changing the structural parameters of networks; and (3) because the edge number of small-world networks remains unchanged with different rewiring possibilities of edges, the change in performance indicates that the MPGA can be improved by a more proper interaction structure of subpopulations as other conditions remain unchanged.
Highlights
IntroductionTo maintain population diversity (enhancing the search diversity) and avoid premature convergence, a multipopulation genetic algorithm (MPGA) [4] is one feasible method where subpopulations are generated and individuals migrate periodically among them
Genetic algorithm (GA) [1], an original metaheuristic, is easy to fall into local optima when employed to solve resource-constrained project scheduling problems [2] such as flexible job-shop schedule problems (FJSPs) due to the complexity of searched space and high dimensions [3].To maintain population diversity and avoid premature convergence, a multipopulation genetic algorithm (MPGA) [4] is one feasible method where subpopulations are generated and individuals migrate periodically among them
With the accumulation of advantageous genes through the operators of MPGA, the difference between individuals becomes small. erefore, if the propagation rate of advantageous genes is larger, the difference between these elites will be smaller. us, we introduce the Hamming distance index (HDI) to evaluate the difference between elite individuals. e HDI is calculated as follows [24]: HDI
Summary
To maintain population diversity (enhancing the search diversity) and avoid premature convergence, a multipopulation genetic algorithm (MPGA) [4] is one feasible method where subpopulations are generated and individuals migrate periodically among them. In the evolutionary process, when intra-subpopulation evolution pushes individuals towards different local optima, migration can introduce new genes into the subpopulations [5]. To more effectively research on the performance with different interaction structures between subpopulations, we can consider subpopulations as nodes and their interaction or migration of elites between subpopulations as edges so that MPGA can be regarded as complex networks. But not identically, Du et al [7] proposed the networked evolutionary algorithm where nodes represent information process units, i.e., individuals, and connections denote information transmission links. Payne et al [8] shed light on dynamic population structures, wherein edges are dynamically rewired according to the genotypic or phenotypic properties of individuals or according to the success of prior
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