8 research outputs found
Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming
We study mixed-integer programming (MIP) relaxation techniques for the
solution of non-convex mixed-integer quadratically constrained quadratic
programs (MIQCQPs). We present two MIP relaxation methods for non-convex
continuous variable products that enhance existing approaches. One is based on
a separable reformulation, while the other extends the well-known MIP
relaxation normalized multiparametric disaggregation technique (NMDT). In
addition, we introduce a logarithmic MIP relaxation for univariate quadratic
terms, called sawtooth relaxation, based on [4]. We combine the latter with the
separable reformulation to derive MIP relaxations of MIQCQPs. We provide a
comprehensive theoretical analysis of these techniques, and perform a broad
computational study to demonstrate the effectiveness of the enhanced MIP
relaxations in terms producing tight dual bounds for MIQCQP
Data-driven Distributionally Robust Optimization over Time
Stochastic Optimization (SO) is a classical approach for optimization under
uncertainty that typically requires knowledge about the probability
distribution of uncertain parameters. As the latter is often unknown,
Distributionally Robust Optimization (DRO) provides a strong alternative that
determines the best guaranteed solution over a set of distributions (ambiguity
set). In this work, we present an approach for DRO over time that uses online
learning and scenario observations arriving as a data stream to learn more
about the uncertainty. Our robust solutions adapt over time and reduce the cost
of protection with shrinking ambiguity. For various kinds of ambiguity sets,
the robust solutions converge to the SO solution. Our algorithm achieves the
optimization and learning goals without solving the DRO problem exactly at any
step. We also provide a regret bound for the quality of the online strategy
which converges at a rate of , where is the
number of iterations. Furthermore, we illustrate the effectiveness of our
procedure by numerical experiments on mixed-integer optimization instances from
popular benchmark libraries and give practical examples stemming from
telecommunications and routing. Our algorithm is able to solve the DRO over
time problem significantly faster than standard reformulations
Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences
The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & NemĂ©sio 2007; Donegan 2008, 2009; NemĂ©sio 2009aâb; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported
by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on
18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based
researchers who signed it in the short time span from 20 September to 6 October 2016
Solving network design problems via decomposition, aggregation and approximation
Andreas BĂ€rmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time. Contents Decomposition for Multi-Period Network Design Solving Network Design Problems via Aggregation Approximate Second-Order Cone Robust Optimization Target Groups Researchers, teachers and students in mathematical optimization and operations research Network planners in the field of logistics and beyond < About the Author Dr. Andreas BĂ€rmann is currently working as a postdoctoral researcher at the Friedrich-Alexander-UniversitĂ€t Erlangen-NĂŒrnberg (FAU) at the chair of Economics, Discrete Optimization and Mathematics. His research is focussed on mathematical optimization, especially the optimization of logistic processes
Improving Quantum Computation by Optimized Qubit Routing
In this work we propose a high-quality decomposition approach for qubit
routing by swap insertion. This optimization problem arises in the context of
compiling quantum algorithms onto specific quantum hardware. Our approach
decomposes the routing problem into an allocation subproblem and a set of token
swapping problems. This allows us to tackle the allocation part and the token
swapping part separately. Extracting the allocation part from the qubit routing
model of Nannicini et al. (arXiv:2106.06446), we formulate the allocation
subproblem as a binary program. Herein, we employ a cost function that is a
lower bound on the overall routing problem objective. We strengthen the linear
relaxation by novel valid inequalities. For the token swapping part we develop
an exact branch-and-bound algorithm. In this context, we improve upon known
lower bounds on the token swapping problem. Furthermore, we enhance an existing
approximation algorithm. We present numerical results for the integrated
allocation and token swapping problem. Obtained solutions may not be globally
optimal due to the decomposition and the usage of an approximation algorithm.
However, the solutions are obtained fast and are typically close to optimal. In
addition, there is a significant reduction in the number of gates and output
circuit depth when compared to state-of-the-art heuristics. Reducing these
figures is crucial for minimizing noise when running quantum algorithms on
near-term hardware. As a consequence, using the novel decomposition approach
leads to compiled algorithms with improved quality. Indeed, when compiled with
the novel routing procedure and executed on real hardware, our experimental
results for quantum approximate optimization algorithms show an significant
increase in solution quality in comparison to standard routing methods.Comment: Replaced undefined variable c_ij in model, Removed inconsitency
between text and table