98 research outputs found
Constraint Programming models for the parallel drone scheduling vehicle routing problem
Drones are currently seen as a viable way for improving the distribution of
parcels in urban and rural environments, while working in coordination with
traditional vehicles like trucks. In this paper we consider the parallel drone
scheduling vehicle routing problem, where the service of a set of customers
requiring a delivery is split between a fleet of trucks and a fleet of drones.
We consider two variations of the problem. In the first one the problem is more
theoretical, and the target is the minimization of the time required to
complete the service and have all the vehicles back to the depot. In the second
variant more realistic constraints involving operating costs, capacity
limitation and workload balance, are considered, and the target is to minimize
the total operational costs. We propose several constraint programming models
to deal with the two problems. An experimental champaign on the instances
previously adopted in the literature is presented to validate the new solving
methods. The results show that on top of being a viable way to solve problems
to optimality, the models can also be used to derive effective heuristic
solutions and high-quality lower bounds for the optimal cost, if the execution
is interrupted after its natural end
Parallel drone scheduling vehicle routing problems with collective drones
We study last-mile delivery problems where trucks and drones collaborate to
deliver goods to final customers. In particular, we focus on problem settings
where either a single truck or a fleet with several homogeneous trucks work in
parallel to drones, and drones have the capability of collaborating for
delivering missions. This cooperative behaviour of the drones, which are able
to connect to each other and work together for some delivery tasks, enhance
their potential, since connected drone has increased lifting capabilities and
can fly at higher speed, overcoming the main limitations of the setting where
the drones can only work independently.
In this work, we contribute a Constraint Programming model and a valid
inequality for the version of the problem with one truck, namely the
\emph{Parallel Drone Scheduling Traveling Salesman Problem with Collective
Drones} and we introduce for the first time the variant with multiple trucks,
called the \emph{Parallel Drone Scheduling Vehicle Routing Problem with
Collective Drones}. For the latter variant, we propose two Constraint
Programming models and a Mixed Integer Linear Programming model.
An extensive experimental campaign leads to state-of-the-art results for the
problem with one truck and some understanding of the presented models'
behaviour on the version with multiple trucks. Some insights about future
research are finally discussed
Combinatorial Benders’ Cuts for the Strip Packing Problem
We study the strip packing problem, in which a set of two-dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height, with the aim of minimizing the height used. The problem is important because it models a large number of real-world applications, including cutting operations where stocks of materials such as paper or wood come in large rolls and have to be cut with minimum waste, scheduling problems in which tasks require a contiguous subset of identical resources, and container loading problems arising in the transportation of items that cannot be stacked one over the other.
The strip packing problem has been attacked in the literature with several heuristic and exact algorithms, nevertheless, benchmark instances of small size remain unsolved to proven optimality since many years. In
this paper we propose a new exact method, that solves a large number of the open benchmark instances within a limited computational effort. Our method is based on a Benders’ decomposition, in which in the master we cut items into unit-width slices and pack them contiguously in the strip, and in the slave we attempt to reconstruct the rectangular items by fixing the vertical positions of their unit-width slices. If the slave proves that the reconstruction of the items is not possible, then a cut is added to the master, and the algorithm is re-iterated. We show that both the master and the slave are strongly NP-hard problems, and solve them with tailored pre-processing, lower and upper bounding techniques, and exact algorithms. We also propose several new
techniques to improve the standard Benders’ cuts, using the so-called combinatorial Benders’ cuts, and an
additional lifting procedure. Extensive computational tests show that the proposed algorithm provides a
substantial breakthrough with respect to previously published algorithms
Mathematical models and decomposition methods for the multiple knapsack problem
We consider the multiple knapsack problem, that calls for the optimal assignment of a set of items, each having a profit and a weight, to a set of knapsacks, each having a maximum capacity. The problem has relevant managerial implications and is known to be very difficult to solve in practice for instances of realistic size. We review the main results from the literature, including a classical mathematical model and a number of improvement techniques. We then present two new pseudo-polynomial formulations, together with specifically tailored decomposition algorithms to tackle the practical difficulty of the problem. Extensive computational experiments show the effectiveness of the proposed approaches
Precedence-Constrained Arborescences
The minimum-cost arborescence problem is a well-studied problem in the area
of graph theory, with known polynomial-time algorithms for solving it. Previous
literature introduced new variations on the original problem with different
objective function and/or constraints. Recently, the Precedence-Constrained
Minimum-Cost Arborescence problem was proposed, in which precedence constraints
are enforced on pairs of vertices. These constraints prevent the formation of
directed paths that violate precedence relationships along the tree. We show
that this problem is NP-hard, and we introduce a new scalable mixed integer
linear programming model for it. With respect to the previous models, the newly
proposed model performs substantially better. This work also introduces a new
variation on the minimum-cost arborescence problem with precedence constraints.
We show that this new variation is also NP-hard, and we propose several mixed
integer linear programming models for formulating the problem
The single-finger keyboard layout problem
The problem of designing new keyboards layouts able to improve the typing speed of an average message has been widely considered in the literature of the Ergonomics domain. Empirical tests with users and simple optimization criteria have been used to propose new solutions. On the contrary, very few papers in Operations Research have addressed this optimization problem. In this paper we firstly resume the most relevant problems in keyboard design, enlightening the related Ergonomics aspects. Then we concentrate on keyboards that must be used witha single finger or stylus, like that of Portable Data Assistant, Smartphones and other small devices.We show that the underlying optimization problem is a generalization of the well known Quadratic Assignment Problem (QAP). We recall some of the most effective metaheuristic algorithms for QAP and we propose some non trivial extensions to the keyboard design problem. We compare the new algorithms through computational experiments with instances obtained from word lists of the English, French, Italian and Spanish languages. We provide on the web benchmark instances for each language and the best solutions we obtained
An Adaptive Iterated Local Search for the Mixed Capacitated General Routing Problem
We study the mixed capacitated general routing problem (MCGRP) in which a fleet of capacitated vehicles has to serve a set of requests by traversing a mixed weighted graph. The requests may be located on nodes, edges, and arcs. The problem has theoretical interest because it is a generalization of the capacitated vehicle routing problem (CVRP), the capacitated arc routing problem (CARP), and the general routing problem. It is also of great practical interest since it is often a more accurate model for real-world cases than its widely studied specializations, particularly for so-called street routing applications. Examples are urban waste collection, snow removal, and newspaper delivery. We propose a new iterated local search metaheuristic for the problem that also includes vital mechanisms from adaptive large neighborhood search combined with further intensification through local search. The method utilizes selected, tailored, and novel local search and large neighborhood search operators, as well as a new local search strategy. Computational experiments show that the proposed metaheuristic is highly effective on five published benchmarks for the MCGRP. The metaheuristic yields excellent results also on seven standard CARP data sets, and good results on four well-known CVRP benchmarks, including improvement of the best known upper bound for one instance
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