2,291 research outputs found
Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues
Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm
inspired by the convergence mechanism to the center of potential generated
within a single well of a spatially co-located double-delta well setup. It
mimics the wave nature of candidate positions in solution spaces and draws upon
quantum mechanical interpretations much like other quantum-inspired
computational intelligence paradigms. In this work, we introduce a Chebyshev
map driven chaotic perturbation in the optimization phase of the algorithm to
diversify weights placed on contemporary and historical, socially-optimal
agents' solutions. We follow this up with a characterization of solution
quality on a suite of 23 single-objective functions and carry out a comparative
analysis with eight other related nature-inspired approaches. By comparing
solution quality and successful runs over dynamic solution ranges, insights
about the nature of convergence are obtained. A two-tailed t-test establishes
the statistical significance of the solution data whereas Cohen's d and Hedge's
g values provide a measure of effect sizes. We trace the trajectory of the
fittest pseudo-agent over all function evaluations to comment on the dynamics
of the system and prove that the proposed algorithm is theoretically globally
convergent under the assumptions adopted for proofs of other closely-related
random search algorithms.Comment: 27 pages, 4 figures, 19 table
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d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response
Identifying optimal designs for generalized linear models with a binary response can be a challengingtask, especially when there are both discrete and continuous independent factors in the model. Theoreticalresults rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions.In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particleswarm optimization, to find a variety of D-optimal approximate and exact designs for experiments withdiscrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficientlyfind locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigaterobustness properties of the d-QPSO algorithm-generated designs to variousmodel assumptions andprovide real applications to design a bio-plastics odor removal experiment, an electronic static experiment,and a 10-factor car refueling experiment. Supplementary materials for the article are available online
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