14,784 research outputs found
Hybridizing Non-dominated Sorting Algorithms: Divide-and-Conquer Meets Best Order Sort
Many production-grade algorithms benefit from combining an asymptotically
efficient algorithm for solving big problem instances, by splitting them into
smaller ones, and an asymptotically inefficient algorithm with a very small
implementation constant for solving small subproblems. A well-known example is
stable sorting, where mergesort is often combined with insertion sort to
achieve a constant but noticeable speed-up.
We apply this idea to non-dominated sorting. Namely, we combine the
divide-and-conquer algorithm, which has the currently best known asymptotic
runtime of , with the Best Order Sort algorithm, which
has the runtime of but demonstrates the best practical performance
out of quadratic algorithms.
Empirical evaluation shows that the hybrid's running time is typically not
worse than of both original algorithms, while for large numbers of points it
outperforms them by at least 20%. For smaller numbers of objectives, the
speedup can be as large as four times.Comment: A two-page abstract of this paper will appear in the proceedings
companion of the 2017 Genetic and Evolutionary Computation Conference (GECCO
2017
ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem
In this paper we propose a new method called ND-Tree-based update (or shortly
ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online
update of a Pareto archive composed of mutually non-dominated points. It uses a
new ND-Tree data structure in which each node represents a subset of points
contained in a hyperrectangle defined by its local approximate ideal and nadir
points. By building subsets containing points located close in the objective
space and using basic properties of the local ideal and nadir points we can
efficiently avoid searching many branches in the tree. ND-Tree may be used in
multiobjective evolutionary algorithms and other multiobjective metaheuristics
to update an archive of potentially non-dominated points. We prove that the
proposed algorithm has sub-linear time complexity under mild assumptions. We
experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front
methods using artificial and realistic benchmarks with up to 10 objectives and
show that with this new method substantial reduction of the number of point
comparisons and computational time can be obtained. Furthermore, we apply the
method to the non-dominated sorting problem showing that it is highly
competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table
Improved dynamical particle swarm optimization method for structural dynamics
A methodology to the multiobjective structural design of buildings based on an improved particle swarm optimization algorithm is presented, which has proved to be very efficient and robust in nonlinear problems and when the optimization objectives are in conflict. In particular, the behaviour of the particle swarm optimization (PSO) classical algorithm is improved by dynamically adding autoadaptive mechanisms that enhance the exploration/exploitation trade-off and diversity of the proposed algorithm, avoiding getting trapped in local minima. A novel integrated optimization system was developed, called DI-PSO, to solve this problem which is able to control and even improve the structural behaviour under seismic excitations. In order to demonstrate the effectiveness of the proposed approach, the methodology is tested against some benchmark problems. Then a 3-story-building model is optimized under different objective cases, concluding that the improved multiobjective optimization methodology using DI-PSO is more efficient as compared with those designs obtained using single optimization.Peer ReviewedPostprint (published version
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