94,310 research outputs found
Different Decomposition Strategies to Solve Stochastic Hydrothermal Unit Commitment Problems
Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a broad range technique that leads to many different decomposition schemes. The LR supplies a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). This problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units
Comparing Spatial and Scenario Decomposition for Stochastic Hydrothermal Unit Commitment Problems
Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, that are iteratively solved to produce useful information. One such approach is the Lagrangian Relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for Stochastic Hydrothermal Unit Commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units
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On evolution of relatively large combinational logic circuits
Evolvable hardware (EHW) (Yao and Higuchi, 1999) is a technique introduced to automatically design circuits where the circuit configuration is carried out by evolutionary algorithms. One of the main difficulties in using EHW to solve real-world problems is the scalability. Until now, several strategies have been proposed to avoid this problem, but none of them completely tackle the issue. In this paper three different methods for evolving the most complex circuits have been tested for their scalability. These methods are bi-directional incremental evolution (SO-BIE); generalised disjunction decomposition (GD-BIE) and evolutionary strategies (ES) with dynamic mutation rate. In order to achieve the generalised conclusions the chosen approaches were tested using multipliers, traditionally used in EHW, but also logic circuits taken from MCNC (Yang, 1991) benchmark library and randomly generated circuits. The analysis of the approaches demonstrated that PLA-based ES is capable of evolving logic circuits of up to 12 inputs. The use of SO-BIE allows the generation of fully functional circuits of 14 inputs and GD-BIE is estimated to be able to evolve circuits of 21 inputs
Biases in human behavior
The paper shows that biases in individual’s decision-making may result from the process of mental editing by which subjects produce a “representation” of the decision problem. During this process, individuals make systematic use of default classifications in order to reduce the short-term memory load and the complexity of symbolic manipulation. The result is the construction of an imperfect mental representation of the problem that nevertheless has the advantage of being simple, and yielding “satisficing” decisions. The imperfection origins in a trade-off that exists between the simplicity of representation of a strategy and his efficiency. To obtain simplicity, the strategy’s rules have to be memorized and represented with some degree of abstraction, that allow to drastically reduce their number. Raising the level of abstraction with which a strategy’s rule is represented, means to extend the domain of validity of the rule beyond the field in which the rule has been experimented, and may therefore induce to include unintentionally domains in which the rule is inefficient. Therefore the rise of errors in the mental representation of a problem may be the "natural" effect of the categorization and the identification of the building blocks of a strategy. The biases may be persistent and give rise to lock-in effect, in which individuals remain trapped in sub-optimal strategies, as it is proved by experimental results on stability of sub-optimal strategies in games like Target The Two. To understand why sub-optimal strategies, that embody errors, are locally stable, i.e. cannot be improved by small changes in the rules, it is considered Kauffman’ NK model, because, among other properties, it shows that if there are interdependencies among the rules of a system, than the system admits many sub-optimal solutions that are locally stable, i.e. cannot be improved by simple mutations. But the fitness function in NK model is a random one, while in our context it is more reasonable to define the fitness of a strategy as efficiency of the program. If we introduce this kind of fitness, then the stability properties of the NK model do not hold any longer: the paper shows that while the elementary statements of a strategy are interdependent, it is possible to achieve an optimal configuration of the strategy via mutations and in consequence the sub-optimal solutions are not locally stable under mutations. The paper therefore provides a different explanation of the existence and stability of suboptimal strategies, based on the difficulty to redefine the sub-problems that constitute the building blocks of the problem’s representation
Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems
This paper deals with the definition and optimization of augmentation spaces
for faster convergence of the conjugate gradient method in the resolution of
sequences of linear systems. Using advanced convergence results from the
literature, we present a procedure based on a selection of relevant
approximations of the eigenspaces for extracting, selecting and reusing
information from the Krylov subspaces generated by previous solutions in order
to accelerate the current iteration. Assessments of the method are proposed in
the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24
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Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress
This paper deals with the parallel simulation of delamination problems at the
meso-scale by means of multi-scale methods, the aim being the Virtual
Delamination Testing of Composite parts. In the non-linear context, Domain
Decomposition Methods are mainly used as a solver for the tangent problem to be
solved at each iteration of a Newton-Raphson algorithm. In case of strongly
nonlinear and heterogeneous problems, this procedure may lead to severe
difficulties. The paper focuses on methods to circumvent these problems, which
can now be expressed using a relatively general framework, even though the
different ingredients of the strategy have emerged separately. We rely here on
the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix,
2001). The method proposed in this paper introduces three additional features:
(i) the adaptation of the macro-basis to situations where classical
homogenization does not provide a good preconditioner, (ii) the use of
non-linear relocalization to decrease the number of global problems to be
solved in the case of unevenly distributed non-linearities, (iii) the
adaptation of the approximation of the local Schur complement which governs the
convergence of the proposed iterative technique. Computations of delamination
and delamination-buckling interaction with contact on potentially large
delaminated areas are used to illustrate those aspects
Decomposition Strategies for Constructive Preference Elicitation
We tackle the problem of constructive preference elicitation, that is the
problem of learning user preferences over very large decision problems,
involving a combinatorial space of possible outcomes. In this setting, the
suggested configuration is synthesized on-the-fly by solving a constrained
optimization problem, while the preferences are learned itera tively by
interacting with the user. Previous work has shown that Coactive Learning is a
suitable method for learning user preferences in constructive scenarios. In
Coactive Learning the user provides feedback to the algorithm in the form of an
improvement to a suggested configuration. When the problem involves many
decision variables and constraints, this type of interaction poses a
significant cognitive burden on the user. We propose a decomposition technique
for large preference-based decision problems relying exclusively on inference
and feedback over partial configurations. This has the clear advantage of
drastically reducing the user cognitive load. Additionally, part-wise inference
can be (up to exponentially) less computationally demanding than inference over
full configurations. We discuss the theoretical implications of working with
parts and present promising empirical results on one synthetic and two
realistic constructive problems.Comment: Accepted at the Thirty-Second AAAI Conference on Artificial
Intelligence (AAAI-18
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