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32
A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty
 Operations Research
, 1993
"... In recent years new insights and algorithms have been obtained for the classical, deterministic, vehicle routing problem as well as for natural stochastic and dynamic variations of it. These new developments are based on theoretical analysis, combine probabilistic and combinatorial modelling and ..."
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Cited by 44 (0 self)
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In recent years new insights and algorithms have been obtained for the classical, deterministic, vehicle routing problem as well as for natural stochastic and dynamic variations of it. These new developments are based on theoretical analysis, combine probabilistic and combinatorial modelling and lead to (1) new algorithms that produce near optimal solutions and (2) a deeper understanding of uncertainty issues in vehicle routing. In this paper we survey these new developments with an emphasis on the insights gained and on the algorithms proposed. Research supported in part by ONR contract N0001490J1649, NSF contracts DDM8922712, DDM9014751, and by a Presidential Young Investigator award DDM9158118 with matching funds from Draper Laboratory. y Sloan School of Management, MIT, Cambridge, MA 02139. z Dept. of Industrial Engineering and Operations Research, Columbia University, NY, NY, 10027 and Department of Operations Research and Management Sciences, Northwestern Universi...
An ant colony optimization approach to the probabilistic traveling salesman problem
 Proceedings of the 7th International Conference on Parallel Problem Solving from Nature (PPSN VII
, 2002
"... Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem where each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a random subset of customers in the same ..."
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Cited by 22 (10 self)
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Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem where each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a random subset of customers in the same order as they appear in the a priori tour. We address the question of whether and in which context an a priori tour found by a TSP heuristic can also be a good solution for the PTSP. We answer this question by testing the relative performance of two ant colony optimization algorithms, Ant Colony System (ACS) introduced by Dorigo and Gambardella for the TSP, and a variant of it (pACS) which aims to minimize the PTSP objective function. We show in which probability configuration of customers pACS and ACS are promising algorithms for the PTSP. 1
Exploiting knowledge about future demands for realtime vehicle dispatching
 Transportation Science
"... doi 10.1287/trsc.1050.0114 ..."
Computational approaches to stochastic vehicle routing problems
 Transport. Sci
, 1995
"... We develop and test several heuristics for two wellknown vehicle routing problems which have stochastic demand: the probabilistic traveling salesman problem (PTSP) and the probabilistic vehicle routing problem (PVRP). The goal in these problems is to obtain optimal a priori tours, that is, tours wh ..."
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Cited by 13 (1 self)
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We develop and test several heuristics for two wellknown vehicle routing problems which have stochastic demand: the probabilistic traveling salesman problem (PTSP) and the probabilistic vehicle routing problem (PVRP). The goal in these problems is to obtain optimal a priori tours, that is, tours which are designed before demands are known. We develop a number of heuristics which lead to such solutions, examine the quality of these solutions, and perform computational experiments against alternative strategies of reoptimization, which we are able to compute using sampling techniques. Based on extensive testing we conclude that our heuristics are very close in terms of performance compared with reoptimization strategies and can be used by a practitioner.
Solving the homogeneous probabilistic travelling salesman problem by the ACO metaheuristic
 Ant Algorithms, 3rd International Workshop, ANTS 2002, volume 2463 of LNCS
, 2002
"... Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem in which each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a random subset of customers in the sa ..."
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Cited by 12 (9 self)
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Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem in which each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a random subset of customers in the same order as they appear in the a priori tour. We propose an ant based a priori tour construction heuristic, the probabilistic Ant Colony System (pACS), which is derived from ACS, a similar heuristic previously designed for the TSP problem. We show that pACS finds better solutions than other tour construction heuristics for a wide range of homogeneous customer probabilities. We also show that for high customers probabilities ACS solutions are better than pACS solutions. 1
Estimationbased local search for stochastic combinatorial optimization
 IRIDIA, Université Libre de Bruxelles
, 2007
"... informs doi 10.1287/ijoc.1080.0276 ..."
Metaheuristics for the vehicle routing problem with stochastic demands
 PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON PARALLEL PROBLEM SOLVING FROM NATURE (PPSN VIII), VOLUME 3242 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... In the vehicle routing problem with stochastic demands a vehicle has to serve a set of customers whose exact demand is known only upon arrival at the customer’s location. The objective is to find a permutation of the customers (an a priori tour) that minimizes the expected distance traveled by the v ..."
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Cited by 7 (3 self)
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In the vehicle routing problem with stochastic demands a vehicle has to serve a set of customers whose exact demand is known only upon arrival at the customer’s location. The objective is to find a permutation of the customers (an a priori tour) that minimizes the expected distance traveled by the vehicle. Since the objective function is computationally demanding, effective approximations of it could improve the algorithms’ performance. For the problem under study, we show that a good choice is using the length of the a priori tour as a fast approximation of the objective, to be used in the local search of the several metaheuristics analyzed. We also show that for the instances tested, our metaheuristics find better solutions with respect to a known effective heuristic and with respect to solving the problem as two related deterministic problems.
The ACO/FRACE algorithm for combinatorial optimization under uncertainty
 Metaheuristics  Progress in Complex Systems Optimization. Operations Research/Computer Science Interfaces Series
, 2006
"... Abstract The paper introduces ACO/FRace, an algorithm for tackling combinatorial optimization problems under uncertainty. The algorithm is based on ant colony optimization and on FRace. The latter is a general method for the comparison of a number of candidates and for the selection of the best on ..."
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Cited by 6 (4 self)
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Abstract The paper introduces ACO/FRace, an algorithm for tackling combinatorial optimization problems under uncertainty. The algorithm is based on ant colony optimization and on FRace. The latter is a general method for the comparison of a number of candidates and for the selection of the best one according to a given criterion. Some experimental results on the probabilistic traveling salesman problem are presented.
Algorithms for the universal and a priori tsp
 Oper. Res. Lett
, 2008
"... We present two simple results for generalizations of the traveling salesman problem (TSP): For the universal TSP, we show that one can compute a tour that is universally optimal whenever the input is a tree metric. A (randomized) O(log n)approximation algorithm for the a priori TSP follows as a cor ..."
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Cited by 6 (0 self)
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We present two simple results for generalizations of the traveling salesman problem (TSP): For the universal TSP, we show that one can compute a tour that is universally optimal whenever the input is a tree metric. A (randomized) O(log n)approximation algorithm for the a priori TSP follows as a corollary.
Analysis of Probabilistic Combinatorial Optimization Problems in Euclidean Spaces
, 1993
"... Probabilistic combinatorial optimization problems are generalized versions of deterministic combinatorial optimization problems with explicit inclusion of probabilistic elements in the problem definitions. Based on the probabilistic traveling salesman problem (PTSP) and on the probabilistic minimum ..."
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Cited by 6 (3 self)
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Probabilistic combinatorial optimization problems are generalized versions of deterministic combinatorial optimization problems with explicit inclusion of probabilistic elements in the problem definitions. Based on the probabilistic traveling salesman problem (PTSP) and on the probabilistic minimum spanning tree problem (PMSTP), the objective of this paper is to give a rigorous treatment of the probabilistic analysis of these problems in the plane. More specifically we present general finitesize bounds and limit theorems for the objective functions of the PTSP and PMSTP. We also discuss the practical implications of these results and indicate some open problems. Appeared in MATHEMATICS OF OPERATIONS RESEARCH, 18, 5171 (1993) 1 Introduction During the last decade combinatorial optimization has undoubtedly been one of the fastest growing and most exciting areas in the field of discrete mathematics. Needless to say, the related scientific literature has been expanding at a very r...