54,933 research outputs found
Search Techniques for Multi-Objective Optimization of Mixed-Variable Systems Having Stochastic Responses
A method is proposed for solving stochastic multi-objective optimization problems. Such problems are typically encountered when one desires to optimize systems with multiple, often competing, objectives that do not have a closed form representation and must be estimated via simulation. A two-stage method is proposed that combines generalized pattern search/ranking and selection (GPS/R&S) and and Mesh Adaptive Direct Search (MADS) developed for single-objective stochastic problems with three multi-objective methods: interactive techniques for the specification of aspiration/reservation levels, scalarization functions, and multi-objective ranking and selection. This combination is devised specifically so as to keep the desirable convergence properties of GPS/R&S and MADS while extending application to the multi-objective case
Systems approaches and algorithms for discovery of combinatorial therapies
Effective therapy of complex diseases requires control of highly non-linear
complex networks that remain incompletely characterized. In particular, drug
intervention can be seen as control of signaling in cellular networks.
Identification of control parameters presents an extreme challenge due to the
combinatorial explosion of control possibilities in combination therapy and to
the incomplete knowledge of the systems biology of cells. In this review paper
we describe the main current and proposed approaches to the design of
combinatorial therapies, including the empirical methods used now by clinicians
and alternative approaches suggested recently by several authors. New
approaches for designing combinations arising from systems biology are
described. We discuss in special detail the design of algorithms that identify
optimal control parameters in cellular networks based on a quantitative
characterization of control landscapes, maximizing utilization of incomplete
knowledge of the state and structure of intracellular networks. The use of new
technology for high-throughput measurements is key to these new approaches to
combination therapy and essential for the characterization of control
landscapes and implementation of the algorithms. Combinatorial optimization in
medical therapy is also compared with the combinatorial optimization of
engineering and materials science and similarities and differences are
delineated.Comment: 25 page
A decomposition procedure based on approximate newton directions
The efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods, as well as to study the impact of different preconditioner choices
Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry
Convex optimization is a well-established research area with applications in
almost all fields. Over the decades, multiple approaches have been proposed to
solve convex programs. The development of interior-point methods allowed
solving a more general set of convex programs known as semi-definite programs
and second-order cone programs. However, it has been established that these
methods are excessively slow for high dimensions, i.e., they suffer from the
curse of dimensionality. On the other hand, optimization algorithms on manifold
have shown great ability in finding solutions to nonconvex problems in
reasonable time. This paper is interested in solving a subset of convex
optimization using a different approach. The main idea behind Riemannian
optimization is to view the constrained optimization problem as an
unconstrained one over a restricted search space. The paper introduces three
manifolds to solve convex programs under particular box constraints. The
manifolds, called the doubly stochastic, symmetric and the definite multinomial
manifolds, generalize the simplex also known as the multinomial manifold. The
proposed manifolds and algorithms are well-adapted to solving convex programs
in which the variable of interest is a multidimensional probability
distribution function. Theoretical analysis and simulation results testify the
efficiency of the proposed method over state of the art methods. In particular,
they reveal that the proposed framework outperforms conventional generic and
specialized solvers, especially in high dimensions
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