A Benders decomposition based framework for solving cable trench problems

Abstract

In this work, we present an algorithmic framework based on Benders decomposition for the Capacitated p-Cable Trench Problem with Covering. We show that our approach can be applied to most variants of the Cable Trench Problem (CTP) that have been considered in the literature. The proposed algorithm is augmented with a stabilization procedure to accelerate the convergence of the cut loop and with a primal heuristic to derive high-quality primal solutions. Three different variants of the CTP are considered in a computational study which compares the Benders approach with two compact integer linear programming formulations that are solved with CPLEX. The obtained results show that the proposed algorithm significantly outperforms the two compact models and that it can be used to tackle significantly larger instances than previously considered algorithms based on Lagrangean relaxation.

Uma Abordagem Exata E Meta-Heurísticas Para O P-Cable Trench Problem With Covering

“…Nos trabalhos de Marianov et al (2015) e Calik et al (2016), o pCTPC foi modelado como um problema de programação linear inteira. Na formulação foi inserido o vértice 0 em , assim como todas arestas, (0, ) ∀ ∈ , inseridas em .…”

“…Aplicação do pCTPC. Adaptada de Calik et al (2016) O pCTPC é uma variação do Cable Trench Problem (CTP), em que todos os nós são considerados como servidores e devem estar conectados, através de uma conexão dedicada, a um único nó primário da rede, sendo os demais secundários (Vasko et al 2002). Dentre as aplicações destes problemas e suas variantes pode-se citar o planejamento de redes cabeadas e sem fio e reconstrução de vascularização em imagens de tomografia computadorizada (Vasko et al 2015).…”

“…Neste trabalho é apresentada uma formulação em programação linear inteira adaptada de outros trabalhos da literatura (Marianov et al 2015, Calik et al 2016) para o pCTPC e são propostas três abordagens para tratá-lo, sendo a solução exata utilizando o resolvedor de programação linear inteira GUROBI e a duas heurísticas, uma delas baseadas no Biased random-key genetic algorithm e outra no Variable neighborhood search.…”

The electric location-routing problem with heterogeneous fleet: Formulation and Benders decomposition approach

“…There are several applications in the literature where flow based formulations with capacity constraints are successfully solved using a Benders decomposition approach. These include the hub location-routing problem studied by de Camargo et al (2013) and network design problems by Fortz and Poss (2009), Botton et al (2013), andCalik et al (2017). See also other relevant Benders decomposition applications for the location of EV recharging stations in car sharing systems (Ç alık and Fortz, 2019), under probabilistic travel range (Lee and Han, 2017), and with plug-in hybrid EVs (Arslan and Karaşan, 2016); in the survey by Costa (2005) for fixed-charge network design problems; and in the book by Birge and Louveaux (2011) for stochastic programming problems.…”

Modeling the capacitated p-cable trench problem with facility costs

“…The demand nodes, however, connect through a wireless system and need to be located in the covering area of at least one server node. The capacitated p-cable trench problem with covering (C p-CTPC), addressed by Calik et al (2016), incorporates customers' demands and capacity constraints to the primary and secondary servers. To enable a joint network design for different network operators, Schwarze (2015) extends the CTP to multiple cable types.…”