Abstract
In the last decade, many works in combinatorial optimisation have shown that, due to the advances in multi-objective optimisation, the algorithms in this field could be used for solving single-objective problems. In this sense, a number of papers have proposed multi-objectivising single-objective problems in order to apply multi-objectivisation schemes in their optimisation. In this paper, we follow this idea by presenting a method to multi-objectivise single-objective problems based on an elementary landscape decomposition of their objective function. In order to illustrate this procedure, we consider the elementary landscape decomposition of the Quadratic Assignment Problem under the interchange neighbourhood. In particular, we propose reformulating the QAP as a multi-objective problem, where each elementary landscape in the decomposition is an independent function to be optimised. In order to validate this multi-objectivisation scheme, we implement a version of NSGA-II for solving the multi-objective QAP, and compare its performance with that of a GA on the single-objective QAP. Conducted experiments show that the multi-objective approach is better than the single-objective approach for some types of instances.
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Notes
- 1.
The interchange neighbourhood considers that two solutions (permutations) are neighbours if one is obtained by interchanging two elements in the other.
- 2.
Note that cases of \(\varphi \) such as \(i=j \wedge p\ne q\) are impossible (\(\sigma (i)=\sigma (j)=p=q\)), since under the interchange neighbourhood \(i=j \Longleftrightarrow p=q\), and also \(i\ne j \Longleftrightarrow p\ne q\).
- 3.
A solution x dominates a solution y when there is no objective in the MOP for which x has a worse value than y, and there is at least one function for which x has a better value than y.
- 4.
Source code, instances and further details about the experimental results can be downloaded from http://www.sc.ehu.es/ccwbayes/members/jceberio/home/publications.html.
- 5.
The statistical tests in this work have been carried out with the scmamp package for RÂ [2], and following the guidelines included in the documentation of the package.
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Ceberio, J., Calvo, B., Mendiburu, A., Lozano, J.A. (2015). Multi-objectivising the Quadratic Assignment Problem by Means of an Elementary Landscape Decomposition. In: Puerta, J., et al. Advances in Artificial Intelligence. CAEPIA 2015. Lecture Notes in Computer Science(), vol 9422. Springer, Cham. https://doi.org/10.1007/978-3-319-24598-0_26
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DOI: https://doi.org/10.1007/978-3-319-24598-0_26
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