2,008 research outputs found
Tight Bound for Sum of Heterogeneous Random Variables: Application to Chance Constrained Programming
We study a tight Bennett-type concentration inequality for sums of
heterogeneous and independent variables, defined as a one-dimensional
minimization. We show that this refinement, which outperforms the standard
known bounds, remains computationally tractable: we develop a polynomial-time
algorithm to compute confidence bounds, proved to terminate with an
epsilon-solution. From the proposed inequality, we deduce tight
distributionally robust bounds to Chance-Constrained Programming problems. To
illustrate the efficiency of our approach, we consider two use cases. First, we
study the chance-constrained binary knapsack problem and highlight the
efficiency of our cutting-plane approach by obtaining stronger solution than
classical inequalities (such as Chebyshev-Cantelli or Hoeffding). Second, we
deal with the Support Vector Machine problem, where the convex conservative
approximation we obtain improves the robustness of the separation hyperplane,
while staying computationally tractable
Complexity results and exact algorithms for robust knapsack problems.
This paper studies the robust knapsack problem, for which solutions are, up to a certain point, immune to data uncertainty. We complement the works found in the literature where uncertainty affects only the profits or only the weights of the items by studying the complexity and approximation of the general setting with uncertainty regarding both the profits and the weights, for three different objective functions. Furthermore, we develop a scenario-relaxation algorithm for solving the general problem and present computational results.Knapsack problem; Robustness; Scenario-relaxation algorithm; NP-hard; Approximation;
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
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