Simultaneous solution of Lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem

Muhandiramge, Ranga; Boland, Natashia

doi:10.1002/net.20292

Cited by 22 publications

(30 citation statements)

References 20 publications

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“…Several solution approaches have been defined for solving to optimality the RCSPP. The main strategies are based on dynamic-programming (Beasley and Christofides, 1989;Mehlhorn and Ziegelmann 2000;Dumitrescu and Boland, 2003), path ranking (Santos et al, 2007;Di Puglia Pugliese and Guerriero, 2013a) and branch and bound (Carlyle et al, 2008;Muhandiramge and Boland, 2009) procedures. When negative cost cycles are present, elementary requirements must be explicitly introduced.…”

Section: State Of the Artmentioning

confidence: 99%

Solution approaches for determining user-oriented paths on dynamic networks

Pugliese

Guerriero

2015

IJSCIM

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This paper addresses the time dependent multi-objective constrained shortest path problem. Solving the problem aims at providing the user a Pareto-optimal solution associated with an efficient path. The solution process takes into account information given by the user in order to obtain a path, satisfying his/her requirements. For the first time, more than two criteria are considered and the reference point methodology is used to define the aggregation function. In addition, knapsack-like constraints are introduced in the formulation in order to model budget restrictions. Dynamic-programming-based algorithms are devised and tested on randomly generated networks and on real life instances derived from US city maps. The computational results underline that the proposed algorithms are able to solve the problem in a reasonable amount of time. This is a good result since the problem considered contains features of three NP-hard problems: the multi-objective, the constrained and the time dependent shortest path problems.

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Section: State Of the Artmentioning

confidence: 99%

Solution approaches for determining user-oriented paths on dynamic networks

Pugliese

Guerriero

2015

IJSCIM

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“…In our implementation of the META-BASIC algorithm, we use the method described in [13] to solve the WCSPPs. One of our enhancements, discussed in later sections, utilises the fact that this method provides increasing lower bounds on the costs throughout the processing, which is not necessarily a feature of all WCSPP methods.…”

Section: Basic Algorithmmentioning

confidence: 99%

“…One of our enhancements, discussed in later sections, utilises the fact that this method provides increasing lower bounds on the costs throughout the processing, which is not necessarily a feature of all WCSPP methods. In later sections, we also make use of the ability of the method of [13] to use upper bounds to remove arcs and so speed up computation.…”

Section: Basic Algorithmmentioning

confidence: 99%

“…However significant work has highlighted the utility of preprocessing procedures, and the use of Lagrangian relaxation, enumeration, kth-shortest paths, and combinations of these ideas to achieve substantial computational improvements. The most recent sequence of work combines preprocessing and Lagrangian relaxation with label-setting [7], interleaves Lagrangian relaxation and preprocessing, combined with enumeration [13], and culminates with Carlyle et al [4], which integrates Lagrangian relaxation, enumeration and preprocessing for problems with one or more weight constraints, to find -optimal solutions with controllable . The latter also includes a broader overview of methods for WCSPP.…”

Section: Introductionmentioning

confidence: 99%

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Solving shortest path problems with a weight constraint and replenishment arcs

Smith¹,

Boland²,

Waterer³

2012

Computers & Operations Research

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This paper tackles a generalization of the weight constrained shortest path problem in a directed network (WCSPP) in which replenishment arcs, that reset the accumulated weight along the path to zero, appear in the network. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests, and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we introduce the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We provide the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications.

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“…The problem of finding a minimum cost path in the network from a to b is now a standard network shortest path problem, which is easily solvable, with techniques such as Dijkstra's algorithm [6] or the A * algorithm [11], to give globally optimal solutions. Problems with the additional Euclidean length constraint take the form of a Weight-Constrained Shortest Path Problem in a network, (WCSPP), which is also now very well solved for practical purposes, for example, using the recent approaches of Dumitrescu and Boland [7], Carlyle and Wood [3] or Muhandiramge and Boland [17]. In either case, solving the network shortest path problem provides a feasible solution to the continuous problem, and so yields an upper bound on its value.…”

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confidence: 99%

Convergent Network Approximation for the Continuous Euclidean Length Constrained Minimum Cost Path Problem

Muhandiramge¹,

Boland²,

Wang³

2009

SIAM J. Optim.

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Abstract. In many path planning situations we would like to find a path of constrained Euclidean length in R 2 that minimises a line integral. We call this the Continuous Length-Constrained Minimum Cost Path Problem (C-LCMCPP). Generally, this will be a non-convex optimization problem, for which continuous approaches only ensure locally optimal solutions. However, network discretisations yield weight constrained network shortest path problems (WCSPPs), which can in practice be solved to global optimality, even for large networks; we can readily find a globally optimal solution to an approximation of the C-LCMCPP. Solutions to these WCSPPs yield feasible solutions and hence upper bounds. We show how networks can be constructed, and a WCSPP in these networks formulated, so that the solutions provide lower bounds on the global optimum of the continuous problem. We give a general convergence scheme for our network discretisations and use it to prove that both the upper and lower bounds so generated converge to the global optimum of the C-LCMCPP, as the network discretisation is refined. Our approach provides a computable lower bound formula (of course the upper bounds are readily computable). We give computational results showing the lower bound formula in practice, and compare the effectiveness of our network construction technique with that of standard grid-based approaches in generating good quality solutions. We find that for the same computational effort, we are able to find better quality solutions, particularly when the length-constraint is tighter.

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Simultaneous solution of Lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem

Cited by 22 publications

References 20 publications

Solution approaches for determining user-oriented paths on dynamic networks

Solution approaches for determining user-oriented paths on dynamic networks

Solving shortest path problems with a weight constraint and replenishment arcs

Convergent Network Approximation for the Continuous Euclidean Length Constrained Minimum Cost Path Problem

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