998 research outputs found
The Kalai-Smorodinski solution for many-objective Bayesian optimization
An ongoing aim of research in multiobjective Bayesian optimization is to
extend its applicability to a large number of objectives. While coping with a
limited budget of evaluations, recovering the set of optimal compromise
solutions generally requires numerous observations and is less interpretable
since this set tends to grow larger with the number of objectives. We thus
propose to focus on a specific solution originating from game theory, the
Kalai-Smorodinsky solution, which possesses attractive properties. In
particular, it ensures equal marginal gains over all objectives. We further
make it insensitive to a monotonic transformation of the objectives by
considering the objectives in the copula space. A novel tailored algorithm is
proposed to search for the solution, in the form of a Bayesian optimization
algorithm: sequential sampling decisions are made based on acquisition
functions that derive from an instrumental Gaussian process prior. Our approach
is tested on four problems with respectively four, six, eight, and nine
objectives. The method is available in the Rpackage GPGame available on CRAN at
https://cran.r-project.org/package=GPGame
Generalized decomposition and cross entropy methods for many-objective optimization
Decomposition-based algorithms for multi-objective
optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized
decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms â convergence to the PF, evenly distributed Pareto
optimal solutions and coverage of the entire front â to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables
the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs
Phase transition in protocols minimizing work fluctuations
For two canonical examples of driven mesoscopic systems - a
harmonically-trapped Brownian particle and a quantum dot - we numerically
determine the finite-time protocols that optimize the compromise between the
standard deviation and the mean of the dissipated work. In the case of the
oscillator, we observe a collection of protocols that smoothly trade-off
between average work and its fluctuations. However, for the quantum dot, we
find that as we shift the weight of our optimization objective from average
work to work standard deviation, there is an analog of a first-order phase
transition in protocol space: two distinct protocols exchange global optimality
with mixed protocols akin to phase coexistence. As a result, the two types of
protocols possess qualitatively different properties and remain distinct even
in the infinite duration limit: optimal-work-fluctuation protocols never
coalesce with the minimal work protocols, which therefore never become
quasistatic.Comment: 6 pages, 6 figures + SI as ancillary fil
Multiobjective genetic algorithm strategies for electricity production from generation IV nuclear technology
Development of a technico-economic optimization strategy of cogeneration systems of electricity/hydrogen, consists in finding an optimal efficiency of the generating cycle and heat delivery system, maximizing the energy production and minimizing the production costs. The first part of the paper is related to the development of a multiobjective optimization library (MULTIGEN) to tackle all types of problems arising from cogeneration. After a literature review for identifying the most efficient methods, the MULTIGEN library is described, and the innovative points are listed. A new stopping criterion, based on the stagnation of the Pareto front, may lead to significant decrease of computational times, particularly in the case of problems involving only integer variables. Two practical examples are presented in the last section. The former is devoted to a bicriteria optimization of both exergy destruction and total cost of the plant, for a generating cycle coupled with a Very High Temperature Reactor (VHTR). The second example consists in designing the heat exchanger of the generating turbomachine. Three criteria are optimized: the exchange surface, the exergy destruction and the number of exchange modules
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