Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  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.
['Daniel Cosmin Porumbel', 'Gilles Goncalves', 'Hamid Allaoui', 'Tiente Hsu']
I am writing a research paper on a idea Iterated Local Search and Column Generation to solve Arc-Routing as a permutation set-covering problem
[{"from": "human", "value": "I am writing a research paper on a idea Iterated Local Search and Column Generation to solve Arc-Routing as a permutation set-covering problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 \u201cCG improver\u201d 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,  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."}]