Hypervolume (HV) has become one of the most popular indicators to assess the quality of Pareto front approximations. However, the best algorithm for computing these values has a computational complexity of O(Nk/3polyl...
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Hypervolume (HV) has become one of the most popular indicators to assess the quality of Pareto front approximations. However, the best algorithm for computing these values has a computational complexity of O(Nk/3polylog(N)) for N candidate solutions and k objectives. In this study, we propose a regression-based approach to learn new mathematical expressions to approximate the HV value and improve at the same time their computational efficiency. In particular, Genetic Programming is used as the modeling technique, because it can produce compact and efficient symbolic models. To evaluate this approach, we exhaustively measure the deviation of the new models against the real HV values using the DTLZ and WFG benchmark suites. We also test the new models using them as a guiding mechanism within the indicator-based algorithm SMS-EMOA. The results are very consistent and promising since the new models report very low errors and a high correlation for problems with 3, 4, and 5 objectives. What is more striking is the execution time achieved by these models, which in a direct comparison against standard HV calculation achieved extremely high speedups of close to 100X for a single front and over 1000X for all the HV contributions in a population, speedups reach over 10X in full runs of SMS-EMOA compared with the standard Monte Carlo approximations of the HV, particularly for large population sizes. Finally, the evolved models generalize across multiple complex problems, using only two problems to train the problems from the DTLZ benchmark and performing efficiently and effectively on all remaining DTLZ and WFG benchmark problems. (C) 2022 Elsevier B.V. All rights reserved.
Lot streaming is the most widely used technique to facilitate overlapping of successive operations. Inspired by real-world scenarios, this paper studies a multi-objective hybrid flowshop scheduling problem with consis...
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Lot streaming is the most widely used technique to facilitate overlapping of successive operations. Inspired by real-world scenarios, this paper studies a multi-objective hybrid flowshop scheduling problem with consistent sublots, aiming to simultaneously optimize two conflicting objectives: the makespan and total number of sublots. Considering the setup and transportation operations, a multi-objective mixed integer programming model is developed and the trade-off between the two objectives is evaluated. Because of the NP-hard property of the addressed problem, metaheuristics are suggested. It is well known that the performance of metaheuristics is highly dependent on the setting of algorithmic parameters, referred to as numerical and categorical parameters. However, the traditional design process might be biased by previous experience. To eliminate these issues, an automated algorithmdesign (AAD) methodology is introduced to conceive a multi-objective evolutionary algorithm (MOEA) in a promising framework. The AAD enables designing the algorithm by automatically determining parameters and their combinations with minimal user intervention. With regard to the problem-specific characteristics and the employed algorithm framework, for the categorical parameters, including decomposition, solution encoding and decoding, solution initialization and neighborhood structures, several operators are designed specifically. Along with the numerical parameters, these categorical parameters are determined and combined using the designed iterated racing procedure. Comprehensive computational results demonstrate that the automated MOEA outperforms other state-of-the-art MOEAs for the addressed problem. (c) 2021 Elsevier B.V. All rights reserved.
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