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From Genetic Variation to Probabilistic Modeling
Genetic algorithms ⦓GAs) [53, 83] are stochastic optimization methods inspired by natural evolution and genetics. Over the last few decades, GAs have...
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Hierarchical Bayesian Optimization Algorithm
The previous chapter has discussed how hierarchy can be used to reduce problem complexity in black-box optimization. Additionally, the chapter has...
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The Challenge of Hierarchical Difficulty
Thus far, we have examined the Bayesian optimization algorithm (BOA), empirical results of its application to several problems of bounded difficulty,...
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Hierarchical BOA in the Real World
The last chapter designed hBOA, which was shown to provide scalable solution for hierarchical traps. Since hierarchical traps were designed to test...
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Bayesian Optimization Algorithm
The previous chapter argued that using probabilistic models with multivariate interactions is a powerful approach to solving problems of bounded...
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Probabilistic Model-Building Genetic Algorithms
The previous chapter showed that variation operators in genetic and evolutionary algorithms can be replaced by learning a probabilistic model of...
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Scalability Analysis
The empirical results of the last chapter were tantalizing. Easy and hard problems were automatically solved without user intervention in polynomial...
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Summary and Conclusions
The purpose of this chapter is to provide a summary of main contributions of this work and outline important conclusions.
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Implicit–explicit two–step peer methods with RK stability for implicit part
We develop a new family of implicit–explicit (IMEX) schemes appropriate for dealing with the systems of differential equations including two...
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Combinatorial refinement on circulant graphs
The combinatorial refinement techniques have proven to be an efficient approach to isomorphism testing for particular classes of graphs. If the...
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An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems
In this paper, we develop a novel higher-order compact finite difference scheme for solving systems of Lane-Emden-Fowler type equations. Our method...
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A robust second-order low-rank BUG integrator based on the midpoint rule
Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly model order reduction for prohibitively large matrix...
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Sublinear Algorithms in T-Interval Dynamic Networks
We consider standard T - interval dynamic networks , under the synchronous timing model and the broadcast CONGEST model. In a T - interval dynamic network ,...
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Unconditional energy stability and maximum principle preserving scheme for the Allen-Cahn equation
In this paper, we propose a novel fully implicit numerical scheme that satisfies both nonlinear energy stability and maximum principle for the space...
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Systematizing modeler experience (MX) in model-driven engineering success stories
Modeling is often associated with complex and heavy tooling, leading to a negative perception among practitioners. However, alternative paradigms,...
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Weak convergence of tamed exponential integrators for stochastic differential equations
We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers...
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Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative
This article provides an effective numerical approach using the fractional integral operational matrix method for a fractional Legendre wavelet to...
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Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes
The present article aims to design and analyze efficient first-order strong schemes for a generalized Aït-Sahalia type model arising in mathematical...
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Error analysis of a high-order fully discrete method for two-dimensional time-fractional convection-diffusion equations exhibiting weak initial singularity
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD)...
