634 research outputs found
A fast and reliable hybrid algorithm for numerical nonlinear global optimization
PreprintHighly nonlinear and ill-conditioned numerical optimization problems take their toll on the convergence of existing resolution methods. Stochastic methods such as Evolutionary Algorithms carry out an efficient exploration of the searchspace at low cost, but get often trapped in local minima and do not prove the optimality of the solution. Deterministic methods such as Interval Branch and Bound algorithms guarantee bounds on the solution, yet struggle to converge within a reasonable time on high-dimensional problems. The contribution of this paper is a hybrid algorithm in which a Differential Evolution algorithm and an Interval Branch and Contract algorithm cooperate. Bounds and solutions are exchanged through shared memory to accelerate the proof of optimality. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate the efficiency of this algorithm on two currently unsolved problems: first by presenting new certified optimal results for the Michalewicz function for up to 75 dimensions and then by proving that the putative minimum of Lennard-Jones clusters of 5 atoms is optimal
Simple and Adaptive Particle Swarms
The substantial advances that have been made to both the theoretical and practical aspects of particle
swarm optimization over the past 10 years have taken it far beyond its original intent as a biological
swarm simulation. This thesis details and explains these advances in the context of what has been
achieved to this point, as well as what has yet to be understood or solidified within the research community.
Taking into account the state of the modern field, a standardized PSO algorithm is defined for
benchmarking and comparative purposes both within the work, and for the community as a whole.
This standard is refined and simplified over several iterations into a form that does away with potentially
undesirable properties of the standard algorithm while retaining equivalent or superior performance
on the common set of benchmarks. This refinement, referred to as a discrete recombinant swarm (PSODRS)
requires only a single user-defined parameter in the positional update equation, and uses minimal
additive stochasticity, rather than the multiplicative stochasticity inherent in the standard PSO. After a
mathematical analysis of the PSO-DRS algorithm, an adaptive framework is developed and rigorously
tested, demonstrating the effects of the tunable particle- and swarm-level parameters. This adaptability
shows practical benefit by broadening the range of problems which the PSO-DRS algorithm is wellsuited
to optimize
A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation
A software platform for global optimisation, called PaGMO, has been developed
within the Advanced Concepts Team (ACT) at the European Space Agency, and was
recently released as an open-source project. PaGMO is built to tackle
high-dimensional global optimisation problems, and it has been successfully
used to find solutions to real-life engineering problems among which the
preliminary design of interplanetary spacecraft trajectories - both chemical
(including multiple flybys and deep-space maneuvers) and low-thrust (limited,
at the moment, to single phase trajectories), the inverse design of
nano-structured radiators and the design of non-reactive controllers for
planetary rovers. Featuring an arsenal of global and local optimisation
algorithms (including genetic algorithms, differential evolution, simulated
annealing, particle swarm optimisation, compass search, improved harmony
search, and various interfaces to libraries for local optimisation such as
SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs
an object-oriented architecture providing a clean and easily-extensible
optimisation framework. Adoption of multi-threaded programming ensures the
efficient exploitation of modern multi-core architectures and allows for a
straightforward implementation of the island model paradigm, in which multiple
populations of candidate solutions asynchronously exchange information in order
to speed-up and improve the optimisation process. In addition to the C++
interface, PaGMO's capabilities are exposed to the high-level language Python,
so that it is possible to easily use PaGMO in an interactive session and take
advantage of the numerous scientific Python libraries available.Comment: To be presented at 'ICATT 2010: International Conference on
Astrodynamics Tools and Techniques
Analysis of some global optimization algorithms for space trajectory design
In this paper, we analyze the performance of some global search algorithms on a number of space trajectory design problems. A rigorous testing procedure is introduced to measure the ability of an algorithm to identify the set of ÂČ-optimal solutions. From the analysis of the test results, a novel algorithm is derived. The development of the novel algorithm starts from the redefinition of some evolutionary heuristics in the form of a discrete dynamical system. The convergence properties of this discrete dynamical system are used to derive a hybrid evolutionary algorithm that displays very good performance on the particular class of problems presented in this paper
Derivative-free hybrid methods in global optimization and their applications
In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.Doctor of Philosoph
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