Daniel Guimarans

Rich Vehicle Routing Problem: Survey

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.

Combining biased randomization with iterated local search for solving the multidepot vehicle routing problem

This paper proposes a hybrid approach for solving the multidepot vehicle routing problem (MDVRP) with a limited number of identical vehicles per depot. Our approach, which only uses a few parameters, combines “biased randomization”—use of nonsymmetric probability distributions to generate randomness—with the iterated local search (ILS) metaheuristic. Two biased-randomized processes are employed at different stages of the ILS framework in order to (a) assign customers to depots following a randomized priority criterion—this allows for fast generation of alternative allocation maps and (b) improving routing solutions associated with a “promising” allocation map—this is done by randomizing the classical savings heuristic. These biased-randomized processes rely on the use of the geometric probability distribution, which is characterized by a single and bounded parameter. Being an approach with few parameters, our algorithm does not require troublesome fine-tuning processes, which tend to be time consuming. Using standard benchmarks, the computational experiments show the efficiency of the proposed algorithm. Despite its hybrid nature, our approach is relatively easy to implement and can be parallelized in a very natural way, which makes it an interesting alternative for practical applications of the MDVRP.

A Biased-Randomised Large Neighbourhood Search for the two-dimensional Vehicle Routing Problem with Backhauls

The two-dimensional loading vehicle routing problem with clustered backhauls (2L-VRPB) is a realistic extension of the classical vehicle routing problem where both delivery and pickup demands are composed of non-stackable items. Despite the fact that the 2L-VRPB can be frequently found in real-life transportation activities, it has not been analysed so far in the literature. This paper presents a hybrid algorithm that integrates biased-randomised versions of vehicle routing and packing heuristics within a Large Neighbourhood Search metaheuristic framework. The use of biased randomisation techniques allows to better guide the local search process. The proposed approach for solving the 2L-VRPB is tested on an extensive set of instances, which have been adapted from existing benchmarks for the two-dimensional loading vehicle routing problem (2L-VRP). Additionally, when no backhauls are considered our algorithm is able to find new best solutions for several 2L-VRP benchmark instances with sequential oriented loading, both with and without items rotation.

Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem

This paper presents an original hybrid approach to solve the Capacitated Vehicle Routing Problem (CVRP). The approach combines a Probabilistic Algorithm with Constraint Programming (CP) and Lagrangian Relaxation (LR). After introducing the CVRP and reviewing the existing literature on the topic, the paper proposes an approach based on a probabilistic Variable Neighbourhood Search (VNS) algorithm. Given a CVRP instance, this algorithm uses a randomized version of the classical Clarke and Wright Savings constructive heuristic to generate a starting solution. This starting solution is then improved through a local search process which combines: (a) LR to optimise each individual route, and (b) CP to quickly verify the feasibility of new proposed solutions. The efficiency of our approach is analysed after testing some well-known CVRP benchmarks. Benefits of our hybrid approach over already existing approaches are also discussed. In particular, the potential flexibility of our methodology is highlighted.

A Methodology Combining Optimization and Simulation for Real Applications of the Stochastic Aircraft Recovery Problem

The Aircraft Recovery Problem appears when external events cause disruptions in a flight schedule. Thus in order to minimize the losses caused by the externalities, aircrafts must be reallocated (rescheduled) in the best possible way. The aim of this paper is to develop a suitable methodology that combines optimization techniques with a simulation approach to tackle the so-called Stochastic Aircraft Recovery Problem. The approach solves the problem through the rescheduling of the flight plan using delays, swaps, and cancellations. The main objective of the optimization model is to restore as much as possible the original flight schedule, minimizing the total delay and the number of cancelled flights. By applying simulation techniques, the robustness of the given solution is assessed. The proposed methodology is applied on a medium-sized scenario based on real data provided by a commercial airline. The obtained results show that the methodology described in the paper is capable of producing a feasible and robust solution for this problem.

Solving Vehicle Routing Problems Using Constraint Programming and Lagrangean Relaxation in a Metaheuristics Framework

This paper presents a methodology based on the Variable Neighbourhood Search metaheuristic, applied to the Capacitated Vehicle Routing Problem. The presented approach uses Constraint Programming and Lagrangean Relaxation methods in order to improve algorithm’s efficiency. The complete problem is decomposed into two separated subproblems, to which the mentioned techniques are applied to obtain a complete solution. With this decomposition, the methodology provides a quick initial feasible solution which is rapidly improved by metaheuristics’ iterative process. Constraint Programming and Lagrangean Relaxation are also embedded within this structure to ensure constraints satisfaction and to reduce the calculation burden. By means of the proposed methodology, promising results have been obtained. Remarkable results presented in this paper include a new best-known solution for a rarely solved 200-customers test instance, as well as a better alternative solution for another benchmark problem.

A simheuristic approach for the two-dimensional vehicle routing problem with stochastic travel times

Abstract The two-dimensional vehicle routing problem (2L-VRP) is a realistic extension of the classical vehicle routing problem in which customers’ demands are composed by sets of non-stackable items. Examples can be found in real-life applications such as the transportation of furniture or industrial machinery. Often, it is necessary to consider stochastic travel times due to traffic conditions or customers availability. However, there is a lack of works discussing stochastic versions of the 2L-VRP. This paper offers a model of the 2L-VRP with stochastic travel times that also includes penalty costs generated by overtime. To solve this stochastic and non-smooth version of the 2L-VRP, a hybrid simheuristic algorithm is proposed. Our approach combines Monte Carlo simulation, an iterated local search framework, and biased-randomised routing and packing heuristics. Our algorithm is tested on an extensive benchmark, which extends the deterministic one for the 2L-VRP with unrestricted and non-oriented loading.

ACO and CP Working Together to Build a Flexible Tool for the VRP

In this paper a flexible hybrid methodology, combining Ant Colony Optimisation (ACO) and Constraint Programming (CP), is presented for solving Vehicle Routing Problems (VRP). The stress of this methodology is on the word ‘flexible’: It gives reasonably good results to changing problems without high solution redesign efforts. Thus a different problem with a new set of constraints and objectives requires no changes to the search algorithm. The search part (driven by ACO) and the model of the problem (included in the CP part) are separated to take advantage of their best attributes. This separation makes the application of the framework to different problems much simpler. To assess the feasibility of our approach, we have used it to solve different instances of the VRP family. These instances are built by combining different sets of constraints. The results obtained are promising but show that the methodology needs deeper communication between ACO and CP to improve its performance.