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

Domain Decomposition for Stochastic Optimal Control

This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high polynomial degree to capture local phenomena. To improve the scalability of the method to problems of interest, a domain decomposition scheme is presented. By using local approximations, lower degree polynomials become sufficient, and both local and global properties of the value function are captured. The domain of the problem is split into a non-overlapping partition, with added constraints ensuring $C^1$ continuity. The Alternating Direction Method of Multipliers (ADMM) is used to optimize over each domain in parallel and ensure convergence on the boundaries of the partitions. This results in improved conditioning of the problem and allows for much larger and more complex problems to be addressed with improved performance.Comment: 8 pages. Accepted to CDC 201

Scenario-Game ADMM: A Parallelized Scenario-Based Solver for Stochastic Noncooperative Games

Decision making in multi-agent games can be extremely challenging, particularly under uncertainty. In this work, we propose a new sample-based approximation to a class of stochastic, general-sum, pure Nash games, where each player has an expected-value objective and a set of chance constraints. This new approximation scheme inherits the accuracy of objective approximation from the established sample average approximation (SAA) method and enjoys a feasibility guarantee derived from the scenario optimization literature. We characterize the sample complexity of this new game-theoretic approximation scheme, and observe that high accuracy usually requires a large number of samples, which results in a large number of sampled constraints. To accommodate this, we decompose the approximated game into a set of smaller games with few constraints for each sampled scenario, and propose a decentralized, consensus ADMM algorithm to efficiently compute a generalized Nash equilibrium of the approximated game. We prove the convergence of our algorithm and empirically demonstrate superior performance relative to a recent baseline

A REVIEW OF APPLICATIONS OF MULTIPLE - CRITERIA DECISION-MAKING TECHNIQUES TO FISHERIES

Management of public resources, such as fisheries, is a complex task. Society, in general, has a number of goals that it hopes to achieve from the use of public resources. These include conservation, economic, and social objectives. However, these objectives often conflict, due to the varying opinions of the many stakeholders. It would appear that the techniques available in the field of multiple-criteria decision-making (MCDM) are well suited to the analysis and determination of fisheries management regimes. However, to date, relatively few publications exist using such MCDM methods compared to other applicational fields, such as forestry, agriculture, and finance. This paper reviews MCDM applied to fishery management by providing an overview of the research published to date. Conclusions are drawn regarding the success and applicability of these techniques to analyzing fisheries management problems.Resource /Energy Economics and Policy,

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss their implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots

Network Target Coordination for Design Optimization of Decomposed Systems

A complex engineered system is often decomposed into a number of different subsystems that interact on one another and together produce results not obtainable by the subsystems alone. Effective coordination of the interdependencies shared among these subsystems is critical to fulfill the stakeholder expectations and technical requirements of the original system. The past research has shown that various coordination methods obtain different solution accuracies and exhibit different computational efficiencies when solving a decomposed system. Addressing these coordination decisions may lead to improved complex system design. This dissertation studies coordination methods through two types of decomposition structures, hierarchical, and nonhierarchical. For coordinating hierarchically decomposed systems, linear and proximal cutting plane methods are applied based on augmented Lagrangian relaxation and analytical target cascading (ATC). Three nonconvex, nonlinear design problems are used to verify the numerical performance of the proposed coordination method and the obtained results are compared to traditional update schemes of subgradient-based algorithm. The results suggest that the cutting plane methods can significantly improve the solution accuracy and computational efficiency of the hierarchically decomposed systems. In addition, a biobjective optimization method is also used to capture optimality and feasibility. The numerical performance of the biobjective algorithm is verified by solving an analytical mass allocation problem. For coordinating nonhierarchically decomposed complex systems, network target coordination (NTC) is developed by modeling the distributed subsystems as different agents in a network. To realize parallel computing of the subsystems, NTC via a consensus alternating direction method of multipliers is applied to eliminate the use of the master problem, which is required by most distributed coordination methods. In NTC, the consensus is computed using a locally update scheme, providing the potential to realize an asynchronous solution process. The numerical performance of NTC is verified using a geometrical programming problem and two engineering problems

Motion Planning and Feedback Control of Simulated Robots in Multi-Contact Scenarios

Diese Dissertation präsentiert eine optimale steuerungsbasierte Architektur für die Bewegungsplanung und Rückkopplungssteuerung simulierter Roboter in Multikontaktszenarien. Bewegungsplanung und -steuerung sind grundlegende Bausteine für die Erstellung wirklich autonomer Roboter. Während in diesen Bereichen enorme Fortschritte für Manipulatoren mit festem Sockel und Radrobotern in den letzten Jahren erzielt wurden, besteht das Problem der Bewegungsplanung und -steuerung für Roboter mit Armen und Beinen immer noch ein ungelöstes Problem, das die Notwendigkeit effizienterer und robusterer Algorithmen belegt. In diesem Zusammenhang wird in dieser Dissertation eine Architektur vorgeschlagen, mit der zwei Hauptherausforderungen angegangen werden sollen, nämlich die effiziente Planung von Kontaktsequenzen und Ganzkörperbewegungen für Floating-Base-Roboter sowie deren erfolgreiche Ausführung mit Rückkopplungsregelungsstrategien, die Umgebungsunsicherheiten bewältigen könne