The vehicle routing problem

A literature review on the vehicle routing problem with multiple depots

The Vehicle Routing Problem (VRP) is a well-known research line in the optimization research community. Its different basic variants have been widely explored in the literature. Even though it has been studied for years, the research around it is still very active. The new tendency is mainly focused on applying this study case to real-life problems. Due to this trend, the Rich VRP arises: combining multiple constraints for tackling realistic problems. Nowadays, some studies have considered specific combinations of real-life constraints to define the emerging Rich VRP scopes. This work surveys the state of the art in the field, summarizing problem combinations, constraints defined, and approaches found.

Rich Vehicle Routing Problem: Survey

Thirty years of heterogeneous vehicle routing

https://repository.tudelft.nl/islandora/object/uuid%3A94f169c4-78ce-465e-9833-880ab57965ef/datastream/OBJ/download

Emergency medical services and beyond

We present a branch-and-cut-and-price algorithm for the exact solution of a variation of the vehicle routing problem with time windows in which the transportation fleet is made by vehicles with different capacities and fixed costs, based at different depots. We illustrate different pricing and cutting techniques and we present an experimental evaluation of their combinations. Computational results are reported on the use of the algorithm both for exact optimization and as a heuristic method.

A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows

The two-dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem is \({{\mathcal{NP}}}\) -hard and arises from applications in logistics and transportation. We present a set covering formulation of the 2LSPP suitable for a column generation approach, where each column corresponds to a feasible combination of items inserted into the same level. For the exact optimization of the 2LSPP we present a branch-and-price algorithm, in which the pricing problem is a penalized knapsack problem. Computational results are reported for benchmark instances with some hundreds items.

http://air.unimi.it/bitstream/2434/5783/2/2lspp.pdf

A branch-and-price algorithm for the two-dimensional level strip packing problem

Modularity maximization is extensively used to detect communities in complex networks. It has been shown, however, that this method suffers from a resolution limit: Small communities may be undetectable in the presence of larger ones even if they are very dense. To alleviate this defect, various modifications of the modularity function have been proposed as well as multiresolution methods. In this paper we systematically study a simple model (proposed by Pons and Latapy [Theor. Comput. Sci. 412, 892 (2011)] and similar to the parametric model of Reichardt and Bornholdt [Phys. Rev. E 74, 016110 (2006)]) with a single parameter α that balances the fraction of within community edges and the expected fraction of edges according to the configuration model. An exact algorithm is proposed to find optimal solutions for all values of α as well as the corresponding successive intervals of α values for which they are optimal. This algorithm relies upon a routine for exact modularity maximization and is limited to moderate size instances. An agglomerative hierarchical heuristic is therefore proposed to address parametric modularity detection in large networks. At each iteration the smallest value of α for which it is worthwhile to merge two communities of the current partition is found. Then merging is performed and the data are updated accordingly. An implementation is proposed with the same time and space complexity as the well-known Clauset-Newman-Moore (CNM) heuristic [Phys. Rev. E 70, 066111 (2004)]. Experimental results on artificial and real world problems show that (i) communities are detected by both exact and heuristic methods for all values of the parameter α; (ii) the dendrogram summarizing the results of the heuristic method provides a useful tool for substantive analysis, as illustrated particularly on a Les Miserables data set; (iii) the difference between the parametric modularity values given by the exact method and those given by the heuristic is moderate; (iv) the heuristic version of the proposed parametric method, viewed as a modularity maximization tool, gives better results than the CNM heuristic for large instances.

Algorithm for parametric community detection in networks.

In this paper we consider a variation of the bin packing problem in which bins of different types have different costs and capacities. Furthermore, each bin has to be filled at least to a certain level, which depends on its type. We present a set partitioning formulation and an exact optimization algorithm which exploits column generation and specialized heuristics. We compare our algorithm with the general purpose solver ILOG CPLEX, running on two compact ILP formulations and we report on experimental results on instances we have generated from data-sets for the variable size bin packing problem.

Andrea Bettinelli

Papers

A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows

A branch-and-price algorithm for the two-dimensional level strip packing problem

Algorithm for parametric community detection in networks.

A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint

A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint.