966 research outputs found
Meta-heuristic combining prior online and offline information for the quadratic assignment problem
The construction of promising solutions for NP-hard combinatorial optimization problems (COPs) in meta-heuristics is usually based on three types of information, namely a priori information, a posteriori information learned from visited solutions during the search procedure, and online information collected in the solution construction process. Prior information reflects our domain knowledge about the COPs. Extensive domain knowledge can surely make the search effective, yet it is not always available. Posterior information could guide the meta-heuristics to globally explore promising search areas, but it lacks local guidance capability. On the contrary, online information can capture local structures, and its application can help exploit the search space. In this paper, we studied the effects of using this information on metaheuristic's algorithmic performances for the COPs. The study was illustrated by a set of heuristic algorithms developed for the quadratic assignment problem. We first proposed an improved scheme to extract online local information, then developed a unified framework under which all types of information can be combined readily. Finally, we studied the benefits of the three types of information to meta-heuristics. Conclusions were drawn from the comprehensive study, which can be used as principles to guide the design of effective meta-heuristic in the future
On quadratic Siegel disks with a class of unbounded type rotation numbers
In this paper we explore a class of quadratic polynomials having Siegel disks
with unbounded type rotation numbers. We prove that any boundary point of
Siegel disks of these polynomials is a Lebesgue density point of their
filled-in Julia sets, which generalizes the corresponding result of McMullen
for bounded type rotation numbers. As an application, this result can help us
construct more quadratic Julia sets with positive area. Moreover, we also
explore the canonical candidate model for quasiconformal surgery of quadratic
polynomials with Siegel disks. We prove that for any irrational rotation
number, any boundary point of ``Siegel disk'' of the canonical candidate model
is a Lebesgue density point of its ``filled-in Julia set'', in particular the
critical point is a measurable deep point of the ``filled-in Julia set''.Comment: 45 pages, 4 figure
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