Abstract
A multi-objective optimization problem (MOP) involves simultaneous minimization or maximization of more than one conflicting objectives. Such problems are commonly encountered in a number of domains, such as engineering, finance, operations research, etc. In the recent years, algorithms based on decomposition have shown commendable success in solving MOPs. In particular they have been helpful in overcoming the limitation of Pareto-dominance based ranking when the number of objectives is large. Decomposition based evolutionary algorithms divide an MOP into a number of simpler sub-problems and solve them simultaneously in a cooperative manner. In order to define the sub-problems, a reference point is needed to construct reference vectors in the objective space to guide the corresponding sub-populations. However, the effect of the choice of this reference point has been scarcely studied in literature. Most of the existing works simply construct the reference point using the minimum objective values in the current nondominated population. Some of the recent studies have gone beyond and suggested the use of optimistic, pessimistic or dynamic reference point specification. In this study, we first qualitatively examine the implications of using different strategies to construct the reference points. Thereafter, we suggest an alternative method which relies on identifying promising reference points rather than specifying them. In the proposed approach, each objective is individually minimized in order to estimate a point close to the true ideal point to identify such reference points. Some initial results and analysis are presented to demonstrate the potential benefits and limitations of the approach. Overall, the approach demonstrates promising results but needs further development for achieving more significant improvements in solving MOPs.
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Notes
- 1.
Without loss of generality, all objectives are considered to be minimized in this study.
- 2.
The performance using \(\mathbf {z}^R=\mathbf {z}^I\) is reported to be marginally inferior to \(\varepsilon =1\) for L-WFG and \(\varepsilon =5\) for K-WFG in [19]. There is a possibility that this minor variation could have resulted due to finite population size, stochastic nature of the search, as well as the nature of the HV metric itself (i.e. a higher HV doesn’t necessarily always imply better distribution).
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Acknowledgements
The first author would like to acknowledge the Australian Bicentennial Fellowship from the Menzies Centre, Kings College London, which supported his research visit to the University of Birmingham for this work, where the second author holds a concurrent position. The work was also partially supported by Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284) and NSFC (Grant No. 61329302).
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Singh, H.K., Yao, X. (2017). Improvement of Reference Points for Decomposition Based Multi-objective Evolutionary Algorithms. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_24
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