1,028 research outputs found
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
A novel multi-objective evolutionary algorithm based on space partitioning
To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks
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
The Hybridization of Branch and Bound with Metaheuristics for Nonconvex Multiobjective Optimization
A hybrid framework combining the branch and bound method with multiobjective
evolutionary algorithms is proposed for nonconvex multiobjective optimization.
The hybridization exploits the complementary character of the two optimization
strategies. A multiobjective evolutionary algorithm is intended for inducing
tight lower and upper bounds during the branch and bound procedure. Tight
bounds such as the ones derived in this way can reduce the number of
subproblems that have to be solved. The branch and bound method guarantees the
global convergence of the framework and improves the search capability of the
multiobjective evolutionary algorithm. An implementation of the hybrid
framework considering NSGA-II and MOEA/D-DE as multiobjective evolutionary
algorithms is presented. Numerical experiments verify the hybrid algorithms
benefit from synergy of the branch and bound method and multiobjective
evolutionary algorithms
Multi-Objective Particle Swarm Optimisation Methods
Copyright Ā© 2004 University of ExeterThis study compares a number of selection regimes for the choosing of global best (gbest) and personal best (pbest) for swarm members in multi-objective particle swarm optimisation (MOPSO).
Two distinct gbest selection techniques are shown to exist in the literature, those that do not restrict the selection of archive members and those with `distance' based gbest selection techniques. Theoretical justification for both of these approaches is discussed, in terms of the two types of search that these methods promote, and the potential problem of particle clumping in MOPSO is described. The popular pbest selection methods in the literature are also compared, and the ffect of the recently introduced turbulence term is viewed in terms of the additional search it promotes, across all parameter combinations. In light of the discussion, new avenues of MOPSO research are highlighted.Department of Computer Science, University of Exete
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