410,096 research outputs found
Optimization with multivariate conditional value-at-risk constraints
For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice.
As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to
finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the
proposed solution methods
Optimization with multivariate conditional value-at-risk constraints
For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice.
As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to
finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the
proposed solution methods
Combined Machine Learning Techniques for Decision Making Support in Medicine
Computational intelligent support for decision making is becoming increasingly popular and essential among medical professionals. Also, with the modern medical devices being capable to communicate with ICT, created models can easily find practical translation into software. Machine learning solutions for medicine range from the robust but opaque paradigms of support vector machines and neural networks to the also performant, yet more comprehensible, decision trees and rule-based models. So how can such different techniques be combined such that the professional obtains the whole spectrum of their particular advantages? The presented approaches have been conceived for various medical problems, while permanently bearing in mind the balance between good accuracy and understandable interpretation of the decision in order to truly establish a trustworthy ‘artificial’ second opinion for the medical expert.Universidad de Málaga. Campus de Excelencia Internacional Andlaucía Tech
Dynamic remapping of parallel computations with varying resource demands
A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming
Despite methodological advances for modeling decision problems under
uncertainty, faithfully representing endogenous uncertainty still proves
challenging, both in terms of modeling capabilities and computational
requirements. A novel framework called Decision Programming provides an
approach for solving such decision problems using off-the-shelf mathematical
optimization solvers. This is made possible by using influence diagrams to
represent a given decision problem, which is then formulated as a mixed-integer
linear programming problem.
In this paper, we focus on the type of endogenous uncertainty that received
less attention in the introduction of Decision Programming: conditionally
observed information. Multi-stage stochastic programming (MSSP) models use
conditional non-anticipativity constraints (C-NACs) to represent such
uncertainties, and we show how such constraints can be incorporated into
Decision Programming models. This allows us to consider the two main types of
endogenous uncertainty simultaneously, namely decision-dependent information
structure and decision-dependent probability distribution. Additionally, we
present a decomposition approach that provides significant computational
savings and also enables considering continuous decision variables in certain
parts of the problem, whereas the original formulation was restricted to
discrete variables only.
The extended framework is illustrated with two example problems. The first
considers an illustrative multiperiod game and the second is a large-scale
cost-benefit problem regarding climate change mitigation. Neither of these
example problems could be solved with existing frameworks.Comment: 26 pages, 10 figure
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