623,104 research outputs found
On Neighborhood Tree Search
We consider the neighborhood tree induced by alternating the use of different
neighborhood structures within a local search descent. We investigate the issue
of designing a search strategy operating at the neighborhood tree level by
exploring different paths of the tree in a heuristic way. We show that allowing
the search to 'backtrack' to a previously visited solution and resuming the
iterative variable neighborhood descent by 'pruning' the already explored
neighborhood branches leads to the design of effective and efficient search
heuristics. We describe this idea by discussing its basic design components
within a generic algorithmic scheme and we propose some simple and intuitive
strategies to guide the search when traversing the neighborhood tree. We
conduct a thorough experimental analysis of this approach by considering two
different problem domains, namely, the Total Weighted Tardiness Problem
(SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show
that independently of the considered domain, the approach is highly
competitive. In particular, we show that using different branching and
backtracking strategies when exploring the neighborhood tree allows us to
achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012
Quantum algorithm for tree size estimation, with applications to backtracking and 2-player games
We study quantum algorithms on search trees of unknown structure, in a model
where the tree can be discovered by local exploration. That is, we are given
the root of the tree and access to a black box which, given a vertex ,
outputs the children of .
We construct a quantum algorithm which, given such access to a search tree of
depth at most , estimates the size of the tree within a factor of in steps. More generally, the same algorithm can
be used to estimate size of directed acyclic graphs (DAGs) in a similar model.
We then show two applications of this result:
a) We show how to transform a classical backtracking search algorithm which
examines nodes of a search tree into an time
quantum algorithm, improving over an earlier quantum backtracking algorithm of
Montanaro (arXiv:1509.02374).
b) We give a quantum algorithm for evaluating AND-OR formulas in a model
where the formula can be discovered by local exploration (modeling position
trees in 2-player games). We show that, in this setting, formulas of size
and depth can be evaluated in quantum time . Thus,
the quantum speedup is essentially the same as in the case when the formula is
known in advance.Comment: Fixed some typo
The Unreasonable Success of Local Search: Geometric Optimization
What is the effectiveness of local search algorithms for geometric problems
in the plane? We prove that local search with neighborhoods of magnitude
is an approximation scheme for the following problems in the
Euclidian plane: TSP with random inputs, Steiner tree with random inputs,
facility location (with worst case inputs), and bicriteria -median (also
with worst case inputs). The randomness assumption is necessary for TSP
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Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
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