IEEE transactions on very large scale integration (VLSI) systems

Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multistage problems with continuous recourse. This paper takes a step toward extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust binary programs by their corresponding K-adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K-adaptability problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations for stylized instances o...

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K-Adaptability in Two-Stage Robust Binary Programming

Distributionally robust facility location problem under decision-dependent stochastic demand

We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed framework includes two-stage decision dependent distributionally robust stochastic programming as a special case. Decision dependent generalizations of five types of ambiguity sets are considered. These sets are based on bounds on moments, covariance matrix, Wasserstein metric, Phi-divergence and Kolmogorov–Smirnov test. For the finite support case, we use linear, conic or Lagrangian duality to give reformulations of these models with a finite number of constraints. Reformulations are also given for the continuous support case for moment, covariance, Wasserstein and Kolmogorov–Smirnov based models. These reformulations allow solutions of such problems using global optimization techniques within the framework of a cutting surface algorithm. The importance of decision dependence in the ambiguity set is demonstrated with the help of a numerical example modeling simultaneous determination of order quantity and selling price for a newsvendor problem.

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Distributionally robust optimization with decision dependent ambiguity sets

The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes a step towards generalizing robust linear optimization to problems with decision-dependent uncertainties. In general settings, we show these problems to be NP-complete. To alleviate the computational inefficiencies, we introduce a class of uncertainty sets whose size depends on binary decisions. We propose reformulations that improve upon alternative standard linearization techniques. To illustrate the advantages of this framework, a shortest path problem is discussed, where the uncertain arc lengths are affected by decisions. Beyond the modeling and performance advantages, the proposed notion of proactive uncertainty control also mitigates over conservatism of current robust optimization approaches.

Optimization under Decision-Dependent Uncertainty

The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general-purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and size. In particular, hardware components offering high speed tend to accommodate only few code segments. The goal of software partitioning is to find an assignment of code segments to execution locations that minimizes the overall program run time and respects the size constraints. In this paper we demonstrate that an additional speedup is obtained if we allow code segments to be instantiated on more than one location. We further show that the program run time not only depends on the execution frequency of the code segments but also on their execution order if there are multiply instantiated code segments. Unlike frequency information, however, sequence information is not available at the time when the software partition is selected. This motivates us to formulate the software-partitioning problem as a robust optimization problem with decision-dependent uncertainty. We transform this problem to a mixed-integer linear program of moderate size and report on promising numerical results.

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Robust Software Partitioning with Multiple Instantiation

This paper introduces the 3SP Design Space Exploration System. 3SP automatically quantifies acceleration opportunities for programs across a wide range of heterogeneous architectures to allow designers to identify promising implementation platforms before investing in a particular hardware/ software codesign. 3SP uses a novel program execution model to integrate comprehensive hardware characteristics including clock speed, number of execution units, issue rates, bandwidths and latencies with software program execution, parallelism, control and data flow measurements to estimate codesign performance for evaluating opportunities for hardware acceleration.

Simon A. Spacey

Papers

Robust Software Partitioning with Multiple Instantiation

Rapid Design Space visualisation through hardware/software partitioning

Parallel partitioning for distributed systems using sequential assignment

Improving communication latency with the write-only architecture