Iterated Local Search and Column Generation to solve Arc-Routing as a permutation set-covering problem

Daniel Porumbel, Gilles Goncalves, Hamid Allaoui and Tienté Hsu

European Journal of Operational Research, 2017, vol. 256, issue 2, 349-367

Abstract: We propose a method that combines Column Generation (CG) and Iterated Local Search (ILS) to solve the Capacitated Arc-Routing Problem (CARP). One of the goals is to integrate into the ILS (some of) the duality information that underpins the CG paradigm. The CARP is expressed in a space of permutations and sub-permutations (sequences, routes) of the set of required edges. For this, the ILS uses an exact decoder that maps any permutation s to a list of sequences (routes) of minimum cost servicing all edges in the order s(1), s(2), s(3), etc. This permutation space is explored both by an ILS process and a CG process that run in parallel and that communicate by exchanging sequences. The first use of the CG paradigm in ILS is the following: all sequences discovered by CG are sent to the ILS process that can inject them into the current ILS solution. The second application of CG in ILS is a “CG improver” operator that acts on the current ILS solution, so as to (try to) improve it by running several CG iterations. The first half of the paper describes the method in a general framework based on sequences, permutations and set covering. The second part is devoted to more specialized Arc-Routing techniques. For instance, the CG convergence could be accelerated by factors of tens or even hundreds by exploiting two ideas in the Dynamic Programming (DP) pricing: (i) avoid as much as possible to traverse edges without service, and (ii) record only non-dominated DP states using a fast-access data structure mixing an array and a red-black tree. Regarding the ILS, we show that the permutation-level search can be substantially improved if the exact decoder is reinforced by a deterministic post-decoder acting on explicit routes. The general results are competitive (reducing the best-known gap of five instances) and certain ideas could be potentially useful for other set-covering or permutation problems.

Keywords: Column Generation; Iterated Local Search; Arc routing (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:256:y:2017:i:2:p:349-367

DOI: 10.1016/j.ejor.2016.06.055

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