46,842 research outputs found

    Parallel competing algorithms in global optimization

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    Specialized techniques are needed to solve global optimization problems, due to the existence of multiple local optima or numerical noise in the objective function. The complexity of the problem is aggravated when discontinuities and constraints are present, or when evaluation of the objective function is computationally expensive. The global (minimization) programming problem is defined as finding the variable set for which the objective function obtains not only a local minimum, but also the smallest value, the global minimum. From a mathematical point of view, the global programming problem is essentially unsolvable, due to a lack of mathematical conditions characterizing the global optimum. In this study, the unconstrained global programming problem is addressed using a number of novel heuristic approaches. Firstly, a probabilistic global stopping criterion is presented for multi-start algorithms. This rule, denoted the unified Bayesian stopping criterion, is based on the single mild assumption that the probability of convergence to the global minimum is comparable to the probability of convergence to any other local minimum. This rule was previously presented for use in combination with a specific global optimization algorithm, and is now shown to be effective when used in a general multi-start approach. The suitability of the unified Bayesian stopping criterion is demonstrated for a number of algorithms using standard test functions. Secondly, multi-start global optimization algorithms based on multiple local searches, combined with the unified Bayesian stopping criterion, are presented. Numerical results reveal that these simple multi-start algorithms outperform a number of leading contenders. Thirdly, parallelization of the sequential multi-start algorithms is shown to effectively reduce the apparent computational time associated with solving expensive global programming problems. Fourthly, two algorithms simulating natural phenomena are implemented, namely the relatively new particle swarm optimization method and the well-known genetic algorithm. For the current implementations, numerical results indicate that the computational effort associated with these methods is comparable. Fifthly, the observation that no single global optimization algorithm can consistently outperform any other algorithm when a large set of problems is considered, leads to the development of a parallel competing algorithm infrastructure. In this infrastructure different algorithms, ranging from deterministic to stochastic, compete simultaneously for a contribution to the unified Bayesian global stopping criterion. This is an important step towards facilitating an infrastructure that is suitable for a range of problems in different classes. In the sixth place, the constrained global programming problems is addressed using constrained algorithms in the parallel competing algorithm infrastructure. The developed methods are extensively tested using standard test functions, for both serial and parallel implementations. An optimization procedure is also presented to solve the slope stability problem faced in civil engineering. This new procedure determines the factor of safety of slopes using a global optimization approach.Dissertation (MSc)--University of Pretoria, 2000.Mechanical and Aeronautical EngineeringMScUnrestricte

    First-principles molecular structure search with a genetic algorithm

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    The identification of low-energy conformers for a given molecule is a fundamental problem in computational chemistry and cheminformatics. We assess here a conformer search that employs a genetic algorithm for sampling the low-energy segment of the conformation space of molecules. The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers to prevent repeated evaluations of very similar solutions. The aim of the search is not only to find the global minimum, but to predict all conformers within an energy window above the global minimum. The performance of the search strategy is: (i) evaluated for a reference data set extracted from a database with amino acid dipeptide conformers obtained by an extensive combined force field and first-principles search and (ii) compared to the performance of a systematic search and a random conformer generator for the example of a drug-like ligand with 43 atoms, 8 rotatable bonds and 1 cis/trans bond

    Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

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    The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

    An Overview of Approaches to Modernize Quantum Annealing Using Local Searches

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    I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which is now obsolete. Hence, I explore strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms, and additionally should be less sensitive to problem mis-specification then the traditional quantum annealing algorithm.Comment: In Proceedings PC 2016, arXiv:1606.06513. An extended version of this contribution will appear on arXiv soon which will describe more detailed algorithms, comment more on robustness to problem mis-specification, comment on thermal sampling applications, and discuss applications on real device
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