A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy

TLDR: This work has tackled a real-world newspaper distribution problem with recycling policy as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP), which is the first study of such a problem in the literature.

Abstract: A real-world newspaper distribution problem with recycling policy is tackled in this work. To meet all the complex restrictions contained in such a problem, it has been modeled as a rich vehicle routing problem, which can be more specifically considered as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP). This is the first study of such a problem in the literature. For this reason, a benchmark composed by 15 instances has been also proposed. In the design of this benchmark, real geographical positions have been used, located in the province of Bizkaia, Spain. For the proper treatment of this AC-VRP-SPDVCFP, a discrete firefly algorithm (DFA) has been developed. This application is the first application of the firefly algorithm to any rich vehicle routing problem. To prove that the proposed DFA is a promising technique, its performance has been compared with two other well-known techniques: an evolutionary algorithm and an evolutionary simulated annealing. Our results have shown that the DFA has outperformed these two classic meta-heuristics.

Figures

Table 2 Parametrization of the EA and ESA for the proposed AC-VRP-SPDVCFP, where −sup∆f is the difference in the objective function of the best and the worse individuals of the initial population, and p=0.95.

Table 3 Small study about the population size on the DFA

Fig. 1 Possible AC-VRP-SPDVCFP instance composed by 14 nodes, and one feasible solution. Gray paths represent forbidden arcs.

Table 1 Summary of the benchmark proposed for the ACVRP-SPDVCFP. Forbidden paths depicts the number of forbidden arcs in each cluster.

Fig. 2 Geographical locations of the depot, customers and clusters around the province of Bizkaia. Source: Open Street Maps, via uMap, accessed Sept 2015.

Table 6 Average rankings returned by the Friedman’s nonparametric test for DFA, ESA and EA.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy" ?

A real-world newspaper distribution problem with recycling policy is tackled in this work. This is the first study of such a problem in the literature. To prove that the proposed DFA is a promising technique, its performance has been compared with two other well-known techniques: an evolutionary algorithm and an evolutionary simulated annealing. 

Q2. What are the future works mentioned in the paper "A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy" ?

As for future work, it is intended to extend the application of the DFA to other complex real-world situations, related to transportation and logistics. Various improvements will be investigate so as to see if the results shown in this work for the AC-VRP-SPDVCFP can be improved. 

Q3. What is the critical point in a 2 distribution with 2 degrees of freedom?

Taking into account that the confidence interval has been stated at the 99% confidence level, the critical point in a χ2 distribution with 2 degrees of freedom is 9.21. 

Q4. What is the definition of the ACVRP-SPDVCFP?

the ACVRP-SPDVCFP is a minimization problem, in which the fireflies with a lower objective function value are the most attractive ones. 

Q5. What is the philosophy of the proposed AC-VRP-SPDVCFP?

With the above assumptions and simplifications, the proposed AC-VRP-SPDVCFP is an R-VRP, whose objective is to find a set of r routes, trying to minimize the total cost of the complete solution, and taking into account the two different kinds of nodes, respecting the restrictions of the clusters and vehicles capacities (Q) and not traveling through any forbidden path. 

Q6. What is the simplest way to describe the AC-VRP-SPDVCFP?

The presented AC-VRP-SPDVCFP can be defined on a complete graph G = (V,A) where V = {v0, v1, . . . , vn} is the set of vertices which represent the nodes of the system. 

Q7. How is the attractiveness of a firefly determined?

First of all, the attractiveness of a firefly is determined by its light intensity, and it can be calculated using this formula:β(r) = β0e −γr2 (20) 

Q8. How can the authors conclude that DFA is better than ESA and EA?

Analyzing this data, and taking into account that all the p-values are lower than 0.05, it can be concluded that DFA is significantly better than ESA and EA at a 95% confidence level. 

Q9. What is the significance of the DFA post-hoc test?

To evaluate the statistical significance of the better performance of DFA, the Holm’s post-hoc test has been conducted using DFA as control algorithm. 

Q10. What is the example of a hybrid genetic algorithm?

In [23], for example, a hybrid genetic algorithm is presented for solving a large class of vehicle routing problems with time-windows.