Pareto Shortest Paths is Often Feasible in Practice

Müller‐Hannemann, Matthias; Weihe, Karsten

doi:10.1007/3-540-44688-5_15

Cited by 55 publications

(37 citation statements)

References 10 publications

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“…The complexity of the problem is much higher if you take connections, vehicle types, transfer times, or traffic days into account. It is therefore feasible to perform a shortest-path computation to find tighter lower bounds [29]. More precisely, you run Dijkstra's algorithm on a condensed graph: The nodes of this graph are the stations (or stops) and an edge between two stations exists iff there is a non-stop connection.…”

Section: Goal-directed Search or A *mentioning

confidence: 99%

Speed-Up Techniques for Shortest-Path Computations

Wagner

Willhalm

Stacs 2007

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Abstract. During the last years, several speed-up techniques for Dijkstra's algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speed-up techniques can be realized to take advantage from different strategies.

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Section: Goal-directed Search or A *mentioning

confidence: 99%

Speed-Up Techniques for Shortest-Path Computations

Wagner

Willhalm

Stacs 2007

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“…Thus, they constitute interesting trade-offs. Pareto optimization is used widely in combinatorial optimization; see [2][3][4] for recent applications. It is often employed, albeit in a heuristic fashion, with genetic algorithms.…”

Section: Introductionmentioning

confidence: 99%

Integrating Pareto Optimization into Dynamic Programming

2016

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Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1) We introduce the operation of a "Pareto algebra product" in the dynamic programming framework of Bellman's GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman's GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2) We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman's GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch.

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“…Otherwise, it is too costly and it does not provide enough guidance to the decision maker. While, in many applications, it has been observed that the Pareto set is indeed usually small (see, e.g., [15] for an experimental study of the multiobjective shortest path problem), one can, for almost every problem with more than one objective function, find instances with an exponential number of Pareto-optimal solutions (see, e.g., [10]). …”

Section: Introductionmentioning

confidence: 99%

Improved Smoothed Analysis of Multiobjective Optimization

Brunsch

Röglin

2015

J. ACM

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We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the last decade. We consider problems in which d linear and one arbitrary objective function are to be optimized over a set S ⊆ {0, 1} n of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to O(n 2d φ d ), where φ denotes the perturbation parameter. Additionally, we show that for any constant c the c th moment of the smoothed number of Pareto-optimal solutions is bounded by O((n 2d φ d ) c ). This improves the previously best known bounds significantly.Furthermore, we address the criticism that the perturbations in smoothed analysis destroy the zero-structure of problems by showing that the smoothed number of Pareto-optimal solutions remains polynomially bounded even for zero-preserving perturbations. This broadens the class of problems captured by smoothed analysis and it has consequences for non-linear objective functions. One corollary of our result is that the smoothed number of Pareto-optimal solutions is polynomially bounded for polynomial objective functions. Our results also extend to integer optimization problems.

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Pareto Shortest Paths is Often Feasible in Practice

Cited by 55 publications

References 10 publications

Speed-Up Techniques for Shortest-Path Computations

Speed-Up Techniques for Shortest-Path Computations

Integrating Pareto Optimization into Dynamic Programming

Improved Smoothed Analysis of Multiobjective Optimization

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