MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows
New ideas in optimization
A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows
INFORMS Journal on Computing
A cooperative parallel meta-heuristic for the vehicle routing problem with time windows
Computers and Operations Research
Multi-Objective Genetic Algorithms for Vehicle Routing Problem with Time Windows
Applied Intelligence
A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows
Computational Optimization and Applications
A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows
Transportation Science
Vehicle Routing Problem with Time Windows, Part II: Metaheuristics
Transportation Science
A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows
Computers and Operations Research
A multiobjectivization approach for vehicle routing problems
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows
Computers and Operations Research
A hybrid algorithm for vehicle routing problem with time windows
Expert Systems with Applications: An International Journal
DEMO: differential evolution for multiobjective optimization
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A powerful route minimization heuristic for the vehicle routing problem with time windows
Operations Research Letters
Computers and Operations Research
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This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.