Results 1  10
of
14
A priori optimization
 Operations Research
, 1990
"... Algorithm for cardinalityconstrained quadratic ..."
RealTime Multivehicle Truckload Pickup and Delivery Problems
 Transportation Science
, 2004
"... In this paper we formally introduce a generic realtime multivehicle truckload pickup and delivery problem. The problem includes the consideration of various costs associated with trucks ’ empty travel distances, jobs ’ delayed completion times, and job rejections. Although very simple, the proble ..."
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Cited by 21 (2 self)
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In this paper we formally introduce a generic realtime multivehicle truckload pickup and delivery problem. The problem includes the consideration of various costs associated with trucks ’ empty travel distances, jobs ’ delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a realworld trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously over time. We propose a mixed integer programming formulation for the offline version of the problem. We then consider and compare five rolling horizon strategies for the realtime version. Two of the policies are based on a repeated reoptimization of various instances of the offline problem, while the others use simpler local (heuristic) rules. One of the reoptimization strategies is new while the other strategies have recently been tested for similar realtime fleet management problems. The comparison of the policies is done under a general simulation framework. The analysis is systematic and consider varying traffic intensities, varying degrees of advance information, and varying degrees of flexibility for job rejection decisions. The new reoptimization policy is shown to systematically outperform the others under all these conditions.
A Tabu Search Algorithm for solving ChanceConstrained Programs
"... Solution of real world problems have to deal with some uncertainties. This is particularly true for the planning of services whose requests are unknown a priori. Several approaches for solving stochastic problems are reported in the literature. Metaheuristics seem to be a powerful tool for computing ..."
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Cited by 3 (0 self)
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Solution of real world problems have to deal with some uncertainties. This is particularly true for the planning of services whose requests are unknown a priori. Several approaches for solving stochastic problems are reported in the literature. Metaheuristics seem to be a powerful tool for computing good and robust solutions. However, the efficiency of algorithms based on Local Search, such as Tabu Search, suffers from the complexity of evaluating the objective function after each move. In this paper, we propose a Tabu Search algorithm which exploits simulation approach to solve chanceconstrained programs. We prove its efficiency reporting the results of extensive computational experiments. Categories and Subject Descriptors: G.1.6 [Numerical Analysis]: Optimization—Stochastic programming; G.3 [Probability and Statistics]: —Statistical computing; G.4 [Mathematical Software]: —Algorithm design and analysis
A SetPartitioningBased Model for the Stochastic Vehicle Routing Problem
, 2006
"... The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are m ..."
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Cited by 2 (0 self)
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The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are modeled as random variables. In this paper, we present a setpartitioningbased modeling framework for the VRP with stochastic demands (VRPSD). The framework can be adapted easily for routing problems with randomness in other problem elements, such as random customers and random travel times. We formulate the VRPSD as a twostage stochastic program and introduce an extended recourse strategy in which vehicles are allowed to serve additional customers from failed routes prior to returning to the depot or to serve customers from failed routes on a new route after returning to the depot. Computational experiments show that route plans generated using the new recourse function perform quite well, especially for problems with few customers per route, where cost savings of roughly 5 % are possible. 1
The Stochastic Vehicle Routing Problem for Minimum Unmet Demand
"... Summary. In this paper, we are interested in routing vehicles to minimize unmet demand with uncertain demand and travel time parameters. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An i ..."
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Summary. In this paper, we are interested in routing vehicles to minimize unmet demand with uncertain demand and travel time parameters. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An important application is the distribution of medical supplies to respond to largescale emergencies, such as natural disasters or terrorist attacks. We present a chance constrained formulation of the problem that is equivalent to a deterministic problem with modified demand and travel time parameters, under mild assumptions on the distribution of stochastic parameters; and relate it with a robust optimization approach. A tabu heuristic is proposed to solve this MIP and simulations are conducted to evaluate the quality of routes generated from both deterministic and chance constrained formulations. We observe that chance constrained routes can reduce the unmet demand by around 2%6 % for moderately tight deadline and total supply constraints. 1
Implementation Effort and Performance A Comparison of Custom and OutoftheBox Metaheuristics on the Vehicle Routing Problem with Stochastic Demand
"... Abstract. In practical applications, one can take advantage of metaheuristics in different ways: To simplify, we can say that metaheuristics can be either used outofthebox or a custom version can be developed. The former way requires a rather low effort, and in general allows to obtain fairly goo ..."
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Abstract. In practical applications, one can take advantage of metaheuristics in different ways: To simplify, we can say that metaheuristics can be either used outofthebox or a custom version can be developed. The former way requires a rather low effort, and in general allows to obtain fairly good results. The latter implies a larger investment in the design, implementation, and finetuning, and can often produce stateoftheart results. Unfortunately, most of the research works proposing an empirical analysis of metaheuristics do not even try to quantify the development effort devoted to the algorithms under consideration. In other words, they do not make clear whether they considered outofthebox or custom implementations of the metaheuristics under analysis. The lack of this information seriously undermines the generality and utility of these works. The aim of the paper is to stress that results obtained with outofthebox implementations cannot be always generalized to custom ones, and vice versa. As a case study, we focus on the vehicle routing problem with stochastic demand and on five among the most successful metaheuristics—namely, tabu search, simulated annealing, genetic algorithm, iterated local search, and ant colony optimization. We show that the relative performance of these algorithms strongly varies whether one considers outofthebox implementations or custom ones, in which the parameters are accurately finetuned. 1
Solving the Vehicle Routing Problem with Stochastic Demands via Hybrid Genetic AlgorithmTabu Search
"... Abstract: This study considers a version of the stochastic vehicle routing problem where customer demands are random variables with known probability distribution. A new scheme based on a hybrid GA and Tabu Search heuristic is proposed for this problem under a priori approach with preventive restock ..."
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Abstract: This study considers a version of the stochastic vehicle routing problem where customer demands are random variables with known probability distribution. A new scheme based on a hybrid GA and Tabu Search heuristic is proposed for this problem under a priori approach with preventive restocking. The relative performance of the proposed HGATS is compared to each GA and TS alone, on a set of randomly generated problems following some discrete probability distributions. The problem data are inspired by real case of VRPSD in waste collection. Results from the experiment show the advantages of the proposed algorithm that are its robustness and better solution qualities resulted.
Ecole Nationale des Ponis et Chaussees. Noisy Le Grand
, 1988
"... Consider a complete graph G = (K, E) in which each node is present with probability p,. We are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the s ..."
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Consider a complete graph G = (K, E) in which each node is present with probability p,. We are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization, under which the combinatorial optimization problem is solved optimally for every instance. We consider four problems: the traveling salesman problem (TSP), the minimum spanning tree, vehicle routing, and traveling salesman facility location. We discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance. We characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worstcase guarantees. Finally, we use the TSP as an example to find practical solutions based on ideas of local optimality. This paper is concerned with a specific family of combinatorial optitnization problems whose common characteristic is the explicit inclusion of probabilistic elements in the problem defmitions, as we will explain. For this reason, we shall refer to them
The probabilistic vehicle routing problem
"... The probabilistic vehicle routing problem (PVRP) is a natural probabilistic variation of the classical vehicle routing problem (VRP), in which demands are probabilistic. The goal is to determine an a priori route of minimal expected total length, which corresponds to the expected total length of the ..."
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The probabilistic vehicle routing problem (PVRP) is a natural probabilistic variation of the classical vehicle routing problem (VRP), in which demands are probabilistic. The goal is to determine an a priori route of minimal expected total length, which corresponds to the expected total length of the route plus the expected value of the extra distance that might be required because demand on the route may occasionally exceed the capacity of the vehicle and force it to go back to the depot before continuing on its route. In this paper we analyze the PVRP using a variety of theoretical approaches. We find closedform expressions and algorithms to compute the expected length of an a priori route under various probabilistic assumptions. Based on these expressions we find upper and lower bounds for the PVRP and the VRP reoptimization strategy, in which we find the optimal route at every instance. We propose heuristics and analyze their worstcase performance. Moreover, we perform probabilistic analysis for the case that customer locations are random in the unit square and succeed in proving some sharp asymptotic theorems for the PVRP and the VRP reoptimization strategy, in which we find the optimal route at every instance. We further propose some asymptotically optimal algorithms. It is quite surprising to find that the PVRP and the strategy of reoptimization are asymptotically equivalent in terms of performance. Our results suggest that the PVRP is a strong and useful alternative to the strategy of reoptimization in capacitated routing problems. Key words:Probabilistic vehicle routing problem, reoptimization strategy, probabilistic analysis, worstcase analysis of heuristics. 2
Accessed: 06/06/2011 09:04
, 1988
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