769 research outputs found
Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows
We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature
Workload Equity in Vehicle Routing Problems: A Survey and Analysis
Over the past two decades, equity aspects have been considered in a growing
number of models and methods for vehicle routing problems (VRPs). Equity
concerns most often relate to fairly allocating workloads and to balancing the
utilization of resources, and many practical applications have been reported in
the literature. However, there has been only limited discussion about how
workload equity should be modeled in VRPs, and various measures for optimizing
such objectives have been proposed and implemented without a critical
evaluation of their respective merits and consequences.
This article addresses this gap with an analysis of classical and alternative
equity functions for biobjective VRP models. In our survey, we review and
categorize the existing literature on equitable VRPs. In the analysis, we
identify a set of axiomatic properties that an ideal equity measure should
satisfy, collect six common measures, and point out important connections
between their properties and those of the resulting Pareto-optimal solutions.
To gauge the extent of these implications, we also conduct a numerical study on
small biobjective VRP instances solvable to optimality. Our study reveals two
undesirable consequences when optimizing equity with nonmonotonic functions:
Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all
tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent,
i.e. composed of tours whose workloads are all equal to or longer than those of
other Pareto-optimal solutions. We show that the extent of these phenomena
should not be underestimated. The results of our biobjective analysis are valid
also for weighted sum, constraint-based, or single-objective models. Based on
this analysis, we conclude that monotonic equity functions are more appropriate
for certain types of VRP models, and suggest promising avenues for further
research.Comment: Accepted Manuscrip
Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System
The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an
extension of the well-known Vehicle Routing Problem (VRP), which takes into
account the dynamic nature of the problem. This aspect requires the vehicle
routes to be updated in an ongoing manner as new customer requests arrive in
the system and must be incorporated into an evolving schedule during the
working day. Besides the vehicle capacity constraint involved in the classical
VRP, DVRPTW considers in addition time windows, which are able to better
capture real-world situations. Despite this, so far, few studies have focused
on tackling this problem of greater practical importance. To this end, this
study devises for the resolution of DVRPTW, an ant colony optimization based
algorithm, which resorts to a joint solution construction mechanism, able to
construct in parallel the vehicle routes. This method is coupled with a local
search procedure, aimed to further improve the solutions built by ants, and
with an insertion heuristics, which tries to reduce the number of vehicles used
to service the available customers. The experiments indicate that the proposed
algorithm is competitive and effective, and on DVRPTW instances with a higher
dynamicity level, it is able to yield better results compared to existing
ant-based approaches.Comment: 10 pages, 2 figure
Deep Policy Dynamic Programming for Vehicle Routing Problems
Routing problems are a class of combinatorial problems with many practical
applications. Recently, end-to-end deep learning methods have been proposed to
learn approximate solution heuristics for such problems. In contrast, classical
dynamic programming (DP) algorithms guarantee optimal solutions, but scale
badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP),
which aims to combine the strengths of learned neural heuristics with those of
DP algorithms. DPDP prioritizes and restricts the DP state space using a policy
derived from a deep neural network, which is trained to predict edges from
example solutions. We evaluate our framework on the travelling salesman problem
(TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and
show that the neural policy improves the performance of (restricted) DP
algorithms, making them competitive to strong alternatives such as LKH, while
also outperforming most other 'neural approaches' for solving TSPs, VRPs and
TSPTWs with 100 nodes.Comment: 21 page
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Centralized versus market-based approaches to mobile task allocation problem: State-of-the-art
Centralized approach has been adopted for finding solutions to resource allocation problems (RAPs) in many real-life applications. On the other hand, market-based approach has been proposed as an alternative to solve the problem due to recent advancement in ICT technologies. In spite of the existence of some efforts to review the pros and cons of each approach in RAPs, the studies cannot be directly applied to specific problem domains like mobile task allocation problem which is characterised with high level of uncertainty on the availability of resources (workers). This paper aims to review existing studies on task allocation problems(TAPs) focusing on those two approaches and their comparison and identify major issues that need to be resolved for comparing the two approaches in mobile task allocation problems. Mobile Task Allocation Problem (MTAP) is defined and its problematic structures are explained in relation with task allocation to mobile workers. Solutions produced by each approach to some applications and variations of MTAP are also discussed and compared. Finally, some future research directions are identified in order to compare both approaches in function of uncertainty emerging from the mobile nature of the MTAP
A dynamic programming approach to multi-objective time-dependent capacitated single vehicle routing problems with time windows
A single vehicle performs several tours to serve a set of geographically dis- persed customers. The vehicle has a finite capacity and is only available for a limited amount of time. Moreover, tours' duration is restricted (e.g. due to quality or security issues). Because of road congestion, travel times are time-dependent: depending on the departure time at a customer, a different travel time is incurred. Furthermore, all customers need to get delivered in their specicified time windows. Contrary to most of the literature, we con- sider a multi-objective cost function: simultaneously minimizing the total time traveled including waiting times at customers due to time windows, and maximizing the total demand fulfilled. Efficient dynamic programming algorithms are developed to compute the Pareto set of routes, assuming a specific structure for time windows and travel time profiles
The stochastic vehicle routing problem : a literature review, part II : solution methods
Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio
Efficient neighborhood evaluations for the vehicle routing problem with multiple time windows
In the vehicle routing problem with multiple time windows (VRPMTW), a single time window must be selected for each customer from the multiple time windows provided. Compared with classical vehicle routing problems with only a single time window per customer, multiple time windows increase the complexity of the routing problem. To minimize the duration of any given route, we present an exact polynomial time algorithm to efficiently determine the optimal start time for servicing each customer. The proposed algorithm has a reduced worst-case and average complexity than existing exact algorithms. Furthermore, the proposed exact algorithm can be used to efficiently evaluate neighborhood operations during a local search resulting in significant acceleration. To examine the benefits of exact neighborhood evaluations and to solve the VRPMTW, the proposed algorithm is embedded in a simple metaheuristic framework generating numerous new best known solutions at competitive computation times
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