Multi-objectivising the Quadratic Assignment Problem by Means of an Elementary Landscape Decomposition

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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