Table 1.

Main approaches for solving VRPs.

Algorithms			Remarks
The exact algorithms	Branch and bound method [4,5]		The Efficiency depends on the depth of the branch and bound tree.
	Set segmentation method [6,7]		Hard to determine the minimum cost for each solutions.
	Dynamic programming method [8,9]		Effective to limited-size problems, hard to consider the concrete demands such as time windows.
	Integer programming algorithm [10,11]		High precision, time consuming, complex.
The heuristic algorithms	The traditional heuristic algorithms	Savings algorithm [12,13]	Computes rapidly, hard to get the optimal solution.
		Sweep algorithm [14,15]	Suitable to the same number of customers for each route with few routes.
		Two-phase algorithm [16,17]	Hard to get the optimal solution.
	The meta-heuristic algorithms	Tabu search algorithm [18,19,20]	Has the good ability of local search, but is time consuming, and depends on the initial solution.
		Genetic algorithm [13,21]	Has the good ability of global search, computes rapidly, hard to obtain the global optimal solution.
		Iterated local search [22,23]	Has the strength of fast convergence rate and low computational complexity.
		Simulated annealing algorithm [24,25]	Slow convergence rates, carefully chosen tunable parameters.
		Variable neighborhood Search [26,27]	Is suitable for large and complex optimization problems with constraints.
		Ant colony algorithm [28,29,30]	Has good positive feedback mechanism, but is time consuming and prone to stagnation.
		Neural network algorithm [31,32]	Computes rapidly, has slow convergence and can easily be trapped in a local optimum
		Artificial bee colony algorithm [30,33]	Achieves a fast convergence speed, is associated with the piecewise linear cost approximation.
		Particle swarm optimization [34,35,36]	Is robust and has fast searching speed, brings easily premature convergence.
		Hybrid algorithm [2,8,12,20,28,37,38]	Is simple with fast optimizing speed and less calculation.