Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Optimasi Biaya Distribusi pada HFVRP Menggunakan Algoritma Particle Swarm Optimization

Distribution systems play a significant role in logistics operations. For the companies with consumer goods products this even more important as consumer goods production has fairly cheap price compared to the distribution cost that must be spent by the company. In addition, increased fuel costs have urged the company to be more efficient in planning and schedule the transportation routes. This paper presents the application of the Particle Swarm Optimization (PSO) algorithm to minimize the travel distance and total cost of a Heterogeneous Fleet Vehicle Routing Problem (HFVRP). Experimental results from its application to a real-world case study are presented. The model in this research is the HFVRP where vehicles have different capacities, variable costs, and fixed costs. PSO algorithm was applied because of the high number of customers served, and therefore the exact methods may not be sufficient. PSO parameter setting which produced the optimum result was with the number of swarms 50, C1 1,5, and C2 2 determined through the design of the experiment. The results of computation show that using PSO can minimize the total traveled distance with an average savings of 51.55% and minimize total cost with an average savings of 44.92% from the existing vehicle routes operated by the company.Distribution systems play a significant role in logistics operations. For the companies with consumer goods products this even more important as consumer goods production has fairly cheap price compared to the distribution cost that must be spent by the company. In addition, increased fuel costs have urged the company to be more efficient in planning and schedule the transportation routes. This paper presents the application of the Particle Swarm Optimization (PSO) algorithm to minimize the travel distance and total cost of a Heterogeneous Fleet Vehicle Routing Problem (HFVRP). Experimental results from its application to a real-world case study are presented. The model in this research is the HFVRP where vehicles have different capacities, variable costs, and fixed costs. PSO algorithm was applied because of the high number of customers served, and therefore the exact methods may not be sufficient. PSO parameter setting which produced the optimum result was with the number of swarms 50, C1 1,5, and C2 2 determined through the design of the experiment. The results of computation show that using PSO can minimize the total traveled distance with an average savings of 51.55% and minimize total cost with an average savings of 44.92% from the existing vehicle routes operated by the company

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments

A Discrete and Improved Bat Algorithm for solving a medical goods distribution problem with pharmacological waste collection

The work presented in this paper is focused on the resolution of a real-world drugs distribution problem with pharmacological waste collection. With the aim of properly meeting all the real-world restrictions that comprise this complex problem, we have modeled it as a multi-attribute or rich vehicle routing problem (RVRP). The problem has been modeled as a Clustered Vehicle Routing Problem with Pickups and Deliveries, Asymmetric Variable Costs, Forbidden Roads and Cost Constraints. To the best of authors knowledge, this is the first time that such a RVRP problem is tackled in the literature. For this reason, a benchmark composed of 24 datasets, from 60 to 1000 customers, has also been designed. For the developing of this benchmark, we have used real geographical positions located in Bizkaia, Spain. Furthermore, for the proper dealing of the proposed RVRP, we have developed a Discrete and Improved Bat Algorithm (DaIBA). The main feature of this adaptation is the use of the well-known Hamming Distance to calculate the differences between the bats. An effective improvement has been also contemplated for the proposed DaIBA, which consists on the existence of two different neighborhood structures, which are explored depending on the bat's distance regarding the best individual of the swarm. For the experimentation, we have compared the performance of our presented DaIBA with three additional approaches: an evolutionary algorithm, an evolutionary simulated annealing and a firefly algorithm. Additionally, with the intention of obtaining rigorous conclusions, two different statistical tests have been conducted: the Friedman's non-parametric test and the Holm's post-hoc test. Furthermore, an additional experimentation has been performed in terms of convergence. Finally, the obtained outcomes conclude that the proposed DaIBA is a promising technique for addressing the designed problem

Investigating the Vehicle Routing Problem with Simultaneous Pickup and Delivery in Multi-Product Distribution: An Optimization Approach

This study addresses a method to solve the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD), which carries multi-products in multiple compartments within a single-vehicle. The unique characteristics of the study is on the route determination of the vehicle from the depot to customers because not only does it consider the vehicle’s capacity but also the compartment capacity of each product as a limitation We calculate the set of instances using two customer grouping methods namely smallest maximum load (SML) and largest maximum load (LML). The solution obtained by the cheapest insertion method can be improved by the Tabu Search algorithm. Finally, the computational result is reported from the test instance