The vehicle routing problem
A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows
Transportation Science
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization
INFORMS Journal on Computing
Formulations and exact algorithms for the vehicle routing problem with time windows
Computers and Operations Research
Handbook of Parametric and Nonparametric Statistical Procedures
Handbook of Parametric and Nonparametric Statistical Procedures
A population-based local search for solving a bi-objective vehicle routing problem
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
An effective memetic algorithm for the cumulative capacitated vehicle routing problem
Computers and Operations Research
An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows
Computers and Operations Research
Improved dynamic lexicographic ordering for multi-objective optimisation
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
Enhancements of NSGA II and its application to the vehicle routing problem with route balancing
EA'05 Proceedings of the 7th international conference on Artificial Evolution
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
AbYSS: Adapting Scatter Search to Multiobjective Optimization
IEEE Transactions on Evolutionary Computation
An NSGA-II algorithm for the green vehicle routing problem
EvoCOP'12 Proceedings of the 12th European conference on Evolutionary Computation in Combinatorial Optimization
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This work is motivated by a real problem posed to the authors by a company in Tenerife, Spain. Given a fleet of vehicles, daily routes have to be designed in order to minimize the total traveled distance while balancing the workload of drivers. This balance has been defined in relation to the length of the routes, regarding to the required time. A bi-objective mixed-integer linear model for the problem is proposed and a solution approach, based on the scatter search metaheuristic, is developed. An extensive computational experience is carried out, using benchmark instances with 25, 50 and 100 customers, to test several components of the proposed method. Comparisons with the exact Pareto fronts for instances up to 25 customers show that the proposed methods obtain good approximations. For comparison purposes, an NSGA-II algorithm has also been implemented. Results obtained on a real case instance are also discussed. In this case, the solution provided by the method proposed in this paper improves the solution implemented by the company.