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

Racionalização e optimização de infra-estruturas militares face aos novos sistemas de armas

A actual situação estratégica mundial, conceptualizada em documentação de referência nacional e da Aliança Atlântica, não só compromete Portugal a efectuar missões em qualquer parte do globo como coloca especial ênfase na execução de operações militares de apoio e de operações combinadas e conjuntas de forças-tarefa (CJTF)1, com a finalidade de responderem às necessidades da Nação Portuguesa enquanto entidade política interveniente na cena internacional. Para o efeito, foram aprovados programas de modernização das Forças Armadas (FFAA), com o intuito de criar e de as dotar de capacidades ou valências militares indispensáveis à satisfação das variadíssimas missões que venham a ser superiormente determinadas ou, que a nossa parceria internacional assim o determine. A Lei da Defesa Nacional e das Forças Armadas (LDNFA), no seu artigo 26º, prevê que as despesas militares a efectuar pelo Estado, no reequipamento das FFAA e nas infra-estruturas de defesa, devem ser objecto de planeamento a médio prazo, mediante Leis de Programação Militar (LPM). Estes normativos legais deram corpo e estabeleceram linhas orientadoras para a consecução dos programas de investimento, materializados através da introdução de novos sistemas de armas, armamento e, na adequação e construção de novas infra-estruturas. Pese embora, as diversas vicissitudes que têm norteado a implementação desses programas de investimento, crê-se que a componente das infra-estruturas não tem merecido a atenção desejável, donde o presente trabalho, vise, analisar os procedimentos conducentes ao planeamento e programação desses programas, a adequabilidade das infra-estruturas aos programas introduzidos e, em comparação com as limitações remanescentes, apresentar soluções correctivas que conduzam à racionalização e optimização das infra-estruturas militares face aos novos sistemas de armas, ao mesmo tempo que se criam melhorias das condições de vivência, actividade e dignidade de quem serve nas FFAA. Abstract: The present strategic world situation, based on national and in the Atlantic Alliance documentation of reference, compromises Portugal to perform missions anywhere on globe wide as well as puts special emphasis on military missions of support and in Combined Joint Task Forces (CJTF), with the purpose of answering to the needs of Portuguese Nation as a political intervenient entity in the international scene. To do so, there have been approved modernization programs for the Armed Forces, with the intention of creating capabilities or military unities, considered crucial to satisfy several missions that may be determined from superior levels or, because of our international partnership. The National Defence Law of the Armed Forces, in the article 26º, makes reference to the military expenditure for equipment and defence infrastructure, which must be subject in a medium term planning, through Military Program Laws. These legal mechanisms have made structure and guidance for the execution of these investment programs, through the acquisition of new armed systems, ammunition systems and by the construction of new and big infrastructure repairs. Even so, some delays have occurred in the implementation of these investments programs and, it is believed that the infrastructure component has not had the disable attention, as all the other matters that make part of the armed system. Because of that, the aim of this study is to analyse the planning procedures, the suitability already done in the fixed installations for supporting the new armed systems and, by comparison with the remaining deficiencies, to introduce corrective actions in order to make available the optimization and rationalization of the infrastructures and, at same time, creating better conditions in terms of quality and comfort, to those who serves in the Armed Forces

Impact Fees in Pennsylvania

This article focuses on impact fees as authorized by Pennsylvania law. It examines legislatively authorized impact fees under the municipalities planning code and, through examination of Pennsylvania case law, addresses the question of whether impact fees may be impliedly authorized pursuant to the police power or other planning and zoning powers of the municipality. Finally, the article analyzes the standard a municipality must meet in order to justify the charging of transportation impact fees under the recently-enacted transportation impact fee legislation, and compares the standard to a more rigorous one employed by a handful of other states

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

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

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

Distributed Primal Decomposition for Large-Scale MILPs

This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints and a linear coupling constraint involving all the decision variables. A key, challenging feature of the considered set-up is that some components of the decision variables must assume integer values. The addressed MILPs are NP-hard, nonconvex and large-scale. Moreover, several additional challenges arise in a distributed framework due to the coupling constraint, so that feasible solutions with guaranteed suboptimality bounds are of interest. We propose a fully distributed algorithm based on a primal decomposition approach and an appropriate tightening of the coupling constraint. The algorithm is guaranteed to provide feasible solutions in finite time. Moreover, asymptotic and finite-time suboptimality bounds are established for the computed solution. Montecarlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm

ChoiRbot: A ROS 2 Toolbox for Cooperative Robotics

In this letter, we introduce ChoiRbot, a toolbox for distributed cooperative robotics based on the novel Robot Operating System (ROS) 2. ChoiRbot provides a fully-functional toolset to execute complex distributed multi-robot tasks, either in simulation or experimentally, with a particular focus on networks of heterogeneous robots without a central coordinator. Thanks to its modular structure, ChoiRbot allows for a highly straight implementation of optimization-based distributed control schemes, such as distributed optimal control, model predictive control, task assignment, in which local computation and communication with neighboring robots are alternated. To this end, the toolbox provides functionalities for the solution of distributed optimization problems. The package can be also used to implement distributed feedback laws that do not need optimization features but do require the exchange of information among robots. The potential of the toolbox is illustrated with simulations and experiments on distributed robotics scenarios with mobile ground robots. The ChoiRbot toolbox is available at https://github.com/OPT4SMART/choirbot