A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.Comment: 57th IEEE Conference on Decision and Contro

A Distributed Mixed-Integer Framework to Stochastic Optimal Microgrid Control

This paper deals with distributed control of microgrids composed of storages, generators, renewable energy sources, critical and controllable loads. We consider a stochastic formulation of the optimal control problem associated to the microgrid that appropriately takes into account the unpredictable nature of the power generated by renewables. The resulting problem is a Mixed-Integer Linear Program and is NP-hard and nonconvex. Moreover, the peculiarity of the considered framework is that no central unit can be used to perform the optimization, but rather the units must cooperate with each other by means of neighboring communication. To solve the problem, we resort to a distributed methodology based on a primal decomposition approach. The resulting algorithm is able to compute high-quality feasible solutions to a two-stage stochastic optimization problem, for which we also provide a theoretical upper bound on the constraint violation. Finally, a Monte Carlo numerical computation on a scenario with a large number of devices shows the efficacy of the proposed distributed control approach. The numerical experiments are performed on realistic scenarios obtained from Generative Adversarial Networks trained an open-source historical dataset of the EU

Multi-Robot Pickup and Delivery via Distributed Resource Allocation

In this article, we consider a large-scale instance of the classical pickup-and-delivery vehicle routing problem that must be solved by a network of mobile cooperating robots. Robots must self-coordinate and self-allocate a set of pickup/delivery tasks while minimizing a given cost figure. This results in a large, challenging mixed-integer linear problem that must be cooperatively solved without a central coordinator. We propose a distributed algorithm based on a primal decomposition approach that provides a feasible solution to the problem in finite time. An interesting feature of the proposed scheme is that each robot computes only its own block of solution, thereby preserving privacy of sensible information. The algorithm also exhibits attractive scalability properties that guarantee solvability of the problem even in large networks. To the best of our knowledge, this is the first attempt to provide a scalable distributed solution to the problem. The algorithm is first tested through Gazebo simulations on a ROS 2 platform, highlighting the effectiveness of the proposed solution. Finally, experiments on a real testbed with a team of ground and aerial robots are provided

A Distributed Primal Decomposition Scheme for Nonconvex Optimization

In this paper, we deal with large-scale nonconvex optimization problems, typically arising in distributed nonlinear optimal control, that must be solved by agents in a network. Each agent is equipped with a local cost function, depending only on a local variable. The variables must satisfy private nonconvex constraints and global coupling constraints. We propose a distributed algorithm for the fast computation of a feasible solution of the nonconvex problem in finite time, through a distributed primal decomposition framework. The method exploits the solution of a convexified version of the problem, with restricted coupling constraints, to compute a feasible solution of the original problem. Numerical computations corroborate the results. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved

Epidermal Growth Factor Receptor Intron-1 Polymorphism Predicts Gefitinib Outcome in Advanced Non-small Cell Lung Cancer

IntroductionEpidermal growth factor receptor (EGFR) gene intron 1 contains a polymorphic single sequence dinucleotide repeat (CA)n whose length has been found to inversely correlate with transcriptional activity. This study was designed to assess the role of (CA)n polymorphism in predicting the outcome of gefitinib treatment in advanced non-small cell lung cancer (NSCLC).MethodsBlood and tumor tissue from 58 patients with advanced NSCLC submitted to gefitinib were collected. EGFR intron 1 gene polymorphism, along with EGFR gene mutation, gene copy number and immunohistochemistry expression were determined. Moreover, a panel of lung cancer cell lines characterized for EGFR intron 1 polymorphism was also studied.ResultsEGFR intron 1 polymorphism showed a statistically significant correlation with the gefitinib response (response rate 25 versus 0%, for patients with a (CA)16 and with a (CA)else genotype, respectively; p = 0.044). Patients with a (CA)16 genotype had a longer survival compared with those with a (CA)else genotype (11.4 versus 4.8 months, respectively; p = 0.037). In addition, cell lines lacking the (CA)16 allele showed a statistically significant higher IC50 compared with cell lines bearing at least one (CA)16 allele (p = 0.003).ConclusionsThis study supports a potential role of EGFR intron 1 polymorphism in predicting the outcome of gefitinib treatment in advanced NSCLC

Induction of immune response after SARS-CoV-2 mRNA BNT162b2 vaccination in healthcare workers

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