Cuckoo search via Lévy flights for the capacitated vehicle routing problem

Abstract

For this paper, we explored the implementation of the cuckoo search algorithm applied to the capacitated vehicle routing problem. The cuckoo search algorithm was implemented with Lévy flights with the 2-opt and doublebridge operations, and with 500 iterations for each run. The algorithm was tested on the problem instances from the Augerat benchmark dataset. The algorithm did not perform well on the problem instances, save for a select few on which the algorithm achieved the close to near-optimal result and one on which the algorithm achieved the optimal result. Increasing the number of iterations for each run of the algorithm on the two large-scale problem instances led to obtaining solutions closer to the optimal solution compared to the ones obtained with fewer number iterations. This gives an idea that the larger the problem instance becomes, the slower the algorithm converges to the optimal solution. Several other factors may also have contributed to the overall performance of the algorithm. Regardless of its performance, the algorithm was able to obtain routes that satisfied the constraints of the capacitated vehicle routing problem. The potential of the cuckoo search algorithm in solving combinatorial problems is demonstrated in this study in which the performance of the algorithm on routing problems was explored.

Parallel computation framework for optimizing trailer routes in bulk transportation

“…Presented several heuristic approaches as well as techniques to determine a lower bound and underestimate of the optimal solution Ceselli et al (2009) Heterogeneous Deterministic Proposed a column generation based algorithm in which they compute a daily plan for vehicles that depart from various depots and must visit a set of customers to deliver certain goods Choi and Tcha (2007) Heterogeneous Deterministic Developed an integrated column generation and dynamic programming based schema approach to generate tight bounds on the optimal solution Afshar-Bakeshloo et al (2016) HeterogeneousDeterministic Developed a mixed integer linear programming (MILP) model which efficiently uses piecewise linear functions (PLFs) to linearize a nonlinear fuzzy interval in order to incorporate customer satisfaction into other linear objectives Woensel et al (2003) Homogeneous Stochastic Developed a heuristic approach that combines the ant colony optimization algorithm with congestion component that was modeled using a queuing approach to traffic flows Jula et al (2006) Homogeneous Stochastic Proposed a solution approach that uses a dynamic programming based approximate solution method to find the best route with minimum expected cost Tas et al (2013) Homogeneous Stochastic Solved a problem that considers both transportation costs and service costs by a Tabu search algorithm. Further improvements have been made by using a post-optimization method Errico et al (2016) Homogeneous Stochastic Solved the problem using a two-stage recourse model with priori optimization Unlike dispatch decisions with pickups and deliveries under deterministic travel times (DellAmico et al 2006;Bianchessi and Righini 2007;Qu and Bard 2014;Kır et al 2017;Santillan et al 2018), stochastic transit times (Li et al 2010;Tavakkoli-Moghaddam et al 2012;Lei et al 2012;Yan et al 2013;Errico et al 2013) create additional complexity. Woensel et al (2003) develop a heuristic approach to solve a vehicle routing problem with stochastic travel times due to potential traffic congestion.…”

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Multiverse Optimization Algorithm Based on Lévy Flight Improvement for Multithreshold Color Image Segmentation

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