An adaptive CP method for TSP solving

M. Sellmann showed that CP-based Lagrangian relaxation gave good results but the interactions between the two techniques were quite dicult to understand. There are two main reasons for this: the best multipliers do not lead to the best ltering and each ltering disrupts the Lagrangian multiplier problem (LMP) to be solved. As the resolution of the TSP in CP is mainly based on a Lagrangian relaxation, we propose to study in detail these interactions for this particular problem. This article experimentally conrms the above statements and shows that it is very dicult to establish any relationship between ltering and the method used to solve the LMP in practice. Thus, it seems very dicult to select a priori the best method suited for a given instance. We propose to use a multi-armed bandit algorithm to nd the best possible method to use. The experimental results show the advantages of our approach

Modeling of RFID-Enabled Real-Time Manufacturing Execution System in Mixed-Model Assembly Lines

To quickly respond to the diverse product demands, mixed-model assembly lines are well adopted in discrete manufacturing industries. Besides the complexity in material distribution, mixed-model assembly involves a variety of components, different process plans and fast production changes, which greatly increase the difficulty for agile production management. Aiming at breaking through the bottlenecks in existing production management, a novel RFID-enabled manufacturing execution system (MES), which is featured with real-time and wireless information interaction capability, is proposed to identify various manufacturing objects including WIPs, tools, and operators, etc., and to trace their movements throughout the production processes. However, being subject to the constraints in terms of safety stock, machine assignment, setup, and scheduling requirements, the optimization of RFID-enabled MES model for production planning and scheduling issues is a NP-hard problem. A new heuristical generalized Lagrangian decomposition approach has been proposed for model optimization, which decomposes the model into three subproblems: computation of optimal configuration of RFID senor networks, optimization of production planning subjected to machine setup cost and safety stock constraints, and optimization of scheduling for minimized overtime. RFID signal processing methods that could solve unreliable, redundant, and missing tag events are also described in detail. The model validity is discussed through algorithm analysis and verified through numerical simulation. The proposed design scheme has important reference value for the applications of RFID in multiple manufacturing fields, and also lays a vital research foundation to leverage digital and networked manufacturing system towards intelligence

Integrating concepts from constraint programming and operations research algorithms

von Torsten FahlePaderborn, Univ., Diss., 200

Convex Identifcation of Stable Dynamical Systems

This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems

Using the ℓ1-norm for Image-based tomographic reconstruction

This paper introduces an ℓ1-norm model based on Total Variation Minimization for tomographic reconstruction. The reconstructions produced by the proposed model are more accurate than those obtained with classical reconstruction models based on the ℓ2-norm. This model can be linearized and solved by linear programming techniques. Furthermore, the complementary slackness conditions can be exploited to reduce the dimension of the resulting formulation by removing unnecessary variables and constraints. Since the efficacy of the reduced formulation strongly depends on the quality of the dual-multipliers used when applying the reduction method, Lagrangian relaxation is used to obtain near-optimal multipliers. This allows solving larger instances in an efficient way

Privacy-Preserving Decentralized Optimization and Event Localization

This dissertation considers decentralized optimization and its applications. On the one hand, we address privacy preservation for decentralized optimization, where N agents cooperatively minimize the sum of N convex functions private to these individual agents. In most existing decentralized optimization approaches, participating agents exchange and disclose states explicitly, which may not be desirable when the states contain sensitive information of individual agents. The problem is more acute when adversaries exist which try to steal information from other participating agents. To address this issue, we first propose two privacy-preserving decentralized optimization approaches based on ADMM (alternating direction method of multipliers) and subgradient method, respectively, by leveraging partially homomorphic cryptography. To our knowledge, this is the first time that cryptographic techniques are incorporated in a fully decentralized setting to enable privacy preservation in decentralized optimization in the absence of any third party or aggregator. To facilitate the incorporation of encryption in a fully decentralized manner, we also introduce a new ADMM which allows time-varying penalty matrices and rigorously prove that it has a convergence rate of O(1/t). However, given that encryption-based algorithms unavoidably bring about extra computational and communication overhead in real-time optimization [61], we then propose another novel privacy solution for decentralized optimization based on function decomposition and ADMM which enables privacy without incurring large communication/computational overhead. On the other hand, we address the application of decentralized optimization to the event localization problem, which plays a fundamental role in many wireless sensor network applications such as environmental monitoring, homeland security, medical treatment, and health care. The event localization problem is essentially a non-convex and non-smooth problem. We address such a problem in two ways. First, a completely decentralized solution based on augmented Lagrangian methods and ADMM is proposed to solve the non-smooth and non-convex problem directly, rather than using conventional convex relaxation techniques. However, this algorithm requires the target event to be within the convex hull of the deployed sensors. To address this issue, we propose another two scalable distributed algorithms based on ADMM and convex relaxation, which do not require the target event to be within the convex hull of the deployed sensors. Simulation results confirm effectiveness of the proposed algorithms