63,531 research outputs found
New Techniques and Algorithms for Multiobjective and Lexicographic Goal-Based Shortest Path Problems
Shortest Path Problems (SPP) are one of the most extensively studied problems in the fields of Artificial Intelligence (AI) and Operations Research (OR). It consists in finding the shortest path between two given nodes in a graph such that the sum of the weights of its constituent arcs is minimized. However, real life problems frequently involve the consideration of multiple, and often conflicting, criteria. When multiple objectives must be simultaneously optimized, the concept of a single optimal solution is no longer valid. Instead, a set of efficient or Pareto-optimal solutions define the optimal trade-off between the objectives under consideration.
The Multicriteria Search Problem (MSP), or Multiobjective Shortest Path Problem, is the natural extension to the SPP when more than one criterion are considered. The MSP is computationally harder than the single objective one. The number of label expansions can grow exponentially with solution depth, even for the two objective case. However, with the assumption of bounded integer costs and a fixed number of objectives the problem becomes tractable for polynomially sized graphs. A wide variety of practical application in different fields can be identified for the MSP, like robot path planning, hazardous material transportation, route planning, optimization of public transportation, QoS in networks, or routing in multimedia networks.
Goal programming is one of the most successful Multicriteria Decision Making (MCDM) techniques used in Multicriteria Optimization. In this thesis we explore one of its variants in the MSP. Thus, we aim to solve the Multicriteria Search Problem with lexicographic goal-based preferences. To do so, we build on previous work on algorithm NAMOA*, a successful extension of the A* algorithm to the multiobjective case. More precisely, we provide a new algorithm called LEXGO*, an exact label-setting algorithm that returns the subset of Pareto-optimal paths that satisfy a set of lexicographic goals, or the subset that minimizes deviation from goals if these cannot be fully satisfied. Moreover, LEXGO* is proved to be admissible and expands only a subset of the labels expanded by an optimal algorithm like NAMOA*, which performs a full Multiobjective Search.
Since time rather than memory is the limiting factor in the performance of multicriteria search algorithms, we also propose a new technique called t-discarding to speed up dominance checks in the process of discarding new alternatives during the search. The application of t-discarding to the algorithms studied previously, NAMOA* and LEXGO*, leads to the introduction of two new time-efficient algorithms named NAMOA*dr and LEXGO*dr , respectively.
All the algorithmic alternatives are tested in two scenarios, random grids and realistic road maps problems. The experimental evaluation shows the effectiveness of LEXGO* in both benchmarks, as well as the dramatic reductions of time requirements experienced by the t-discarding versions of the algorithms, with respect to the ones with traditional pruning
An evaluation of best compromise search in graphs
This work evaluates two different approaches for multicriteria graph
search problems using compromise preferences. This approach focuses search on
a single solution that represents a balanced tradeoff between objectives, rather
than on the whole set of Pareto optimal solutions. We review the main concepts
underlying compromise preferences, and two main approaches proposed for their
solution in heuristic graph problems: naive Pareto search (NAMOA
), and a k-shortest-path approach (kA
). The performance of both approaches is evaluated
on sets of standard bicriterion road map problems. The experiments reveal that
the k-shortest-path approach looses effectiveness in favor of naive Pareto search
as graph size increases. The reasons for this behavior are analyzed and discussedPartially funded by P07-TIC-03018, Cons. Innovación, Ciencia y
Empresa (Junta AndalucÃa), and Univ. Málaga, Campus Excel. Int. AndalucÃa Tec
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Energy management in communication networks: a journey through modelling and optimization glasses
The widespread proliferation of Internet and wireless applications has
produced a significant increase of ICT energy footprint. As a response, in the
last five years, significant efforts have been undertaken to include
energy-awareness into network management. Several green networking frameworks
have been proposed by carefully managing the network routing and the power
state of network devices.
Even though approaches proposed differ based on network technologies and
sleep modes of nodes and interfaces, they all aim at tailoring the active
network resources to the varying traffic needs in order to minimize energy
consumption. From a modeling point of view, this has several commonalities with
classical network design and routing problems, even if with different
objectives and in a dynamic context.
With most researchers focused on addressing the complex and crucial
technological aspects of green networking schemes, there has been so far little
attention on understanding the modeling similarities and differences of
proposed solutions. This paper fills the gap surveying the literature with
optimization modeling glasses, following a tutorial approach that guides
through the different components of the models with a unified symbolism. A
detailed classification of the previous work based on the modeling issues
included is also proposed
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