Hybrid modified ant system with sweep algorithm and path relinking for the capacitated vehicle routing problem

Abstract

Vehicle routing problem is a widely researched combinatorial optimization problem. We developed a hybrid of three strategies—a modified ant system, a sweep algorithm, and a path relinking—for solving a capacitated vehicle routing optimization problem, a vehicle routing problem with a capacity constraint. A sweep algorithm was used to generate initial solutions and assign customers to vehicles, followed by a modified ant system to generate new generations of good solutions. Path relinking was used for building a better solution (candidate) from a pair of guiding and initial solutions. Finally, a local search method—swap, insert, reverse and greedy search operations—was used to prevent solutions from getting trapped in a local minimum. Performance of the proposed algorithm was evaluated on three datasets from CVRPLIB. Our proposed method was at least competitive to state-of-the-art algorithms in terms of the total route lengths. It even surpassed the best-known solution in the P-n55-k8 instance. Our findings can lower the transportation cost by reducing the travelling distance and efficiently utilizing the vehicle capacity.

A novel hybrid jellyfish algorithm for minimizing fuel consumption capacitated vehicle routing problem

“…There are four constraints of this FCCVRP problem. Constraints to keep the load from exceeding the vehicle's capacity (9) and (10). The constraint that ensures that the start and end trips are at the distribution center is (11).…”

“…Transportation activities have contributed to an increase in pollution [6]. Thus, logistics policies in the supply chain sector must consider environmental effects [7]- [9] and economic aspects [10]. According to Fameli and Assimakopoulos [11], fuel consumption in transportation activities is critical for pollution control.…”

Multi-target Rural Vehicle Route Planning Model with Satisfaction Evaluation

“…The individual of the parental population is set as h 1 , h 2 • • • h N . All the individuals in the parental population are arranged from the largest to the smallest according to the relative fitness Z w , that is, Z s (1)…”

“…Additionally, most of the vehicle routing problems are solved by heuristic algorithms [11]. There is hybrid strategy algorithm combined with scanning algorithm, ant colony algorithm and path reconnect algorithm [1] and particle swarm algorithm with dynamic weights [9] to solve the vehicle path optimization problem.…”

A global satisfaction degree method for fuzzy capacitated vehicle routing problems

“…Uncertain CVRPs have been addressed in different ways: Men, Jiang & Xu [7] solved a CVRP for transportation of hazardous materials with interval Type–2 fuzzy numbers, chance constrained programming and simulated annealing; Ewbank et al [8] solved a fuzzy demands assignment problem using neural networks; Helal et al [9] has solved a stochastic CVRP using a two–step method which combines a chance–constrained model and a stochastic model with recourse and Mańdziuk & Świechowski [10] solved a dynamic CVRP with random traffic jams using probabilistic upper bounds and decision trees to compare against ant-colony, tabu and evolutionary algorithms; Hannan et al [11] used PSO algorithms to solid waste collection problems with uncertain transportation costs and environmental impact; Pekel & Kara [12] solved location routing problems with fuzzy demands and deterministic travel times using fuzzy chance constrained programming models; Wang et al [13] solved a two-echelon CVRP with uncertain demands using genetic algorithms. M Shan–Huen [14] solved a multi-compartment capacitated location routing problem with stochastic demands and multiple–products using tabu search; Beraldi et al [15] solved CVRPs with stochastic demands using a probabilistic formulation involving a predefined reliability degree and Thammano & Rungwachira [16] solved complex CVRPs by efficiently generating initial solutions via a sweep method evolved with ant colony algorithms to then be debugged/relinked using local search methods.…”