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Scaling-up many-objective combinatorial optimization with Cartesian products of scalarization functions

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Abstract

The trade-off between the exploration of large size neighborhoods and the exploitation of Pareto fronts with high cardinality is a challenging task for the metaheuristics for many-objective combinatorial optimization problems. Cartesian products of scalarization functions, or simpler, Cartesian scalarization, is a novel technique that simplifies the search by reducing the number of objectives using sets of scalarization functions. Cartesian scalarization is an alternative to scalarization functions that scales up the local search for many-objective spaces. We introduce a method that automatically generates Cartesian scalarization functions; we use combinatorics to analyze the properties of Cartesian scalarization functions. Cartesian scalarization local search (CsLs) uses a set of Cartesian scalarization functions to generate a quality Pareto local front. We show that CsLs is a well-defined local search algorithm that converges to a Pareto local solution set in finite time. Cartesian scalarization outperforms other Pareto and scalarization local search methods on many-objective combinatorial optimization instances.

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  1. Artificial Intelligence Lab, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Mădălina M. Drugan

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  1. Mădălina M. Drugan
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Drugan, M.M. Scaling-up many-objective combinatorial optimization with Cartesian products of scalarization functions. J Heuristics 24, 135–172 (2018). https://doi.org/10.1007/s10732-017-9361-x

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