Partial branch and bound algorithm for improved data association in multiframe processing

This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

The problem of data association remains central in multitarget, multisensor, and multiplatform tracking. Lagrangian relaxation methods have been shown to yield near optimal answers in real-time. The necessity of improvement in the quality of these solutions warrants a continuing interest in these methods. A partial branch-and-bound technique along with adequate branching and ordering rules are developed. Lagrangian relaxation is used as a branching method and as a method to calculate the lower bound for subproblems. The result shows that the branch-and-bound framework greatly improves the solutions in less time than relaxation alone.

This paper presents an application of combined Lagrangian relaxation (LR) method and particle swarm optimization (PSO) technique for the Unit Commitment (UC) problem. This hybrid technique uses LR as the main algorithm. The LR method provides a fast solution, but it may suffer from numerical convergence and solution quality problem. The proposed algorithm uses PSO to update the Lagrangian multipliers and improve the performance of LR method. In this paper, ramp rate limit is also considered besides taking minimum up time and minimum down time of thermal units. The proposed method is implemented for solving two examples of UC test problems. The study results have shown that the approach developed is feasible and efficient.

The AC-DC hybrid microgrid is a credible evolution path for the microgrid. State estimation in complex distribution network is a significant foundation for the safe operation. In AC-DC hybrid microgrid, centralised state estimation algorithms have quite a few deficiencies such as large communication capacity and privacy protection. In response to these obstacles, this paper proposed a novel distributed state estimation algorithm. First, a three-stage state estimation model was established for AC-DC hybrid microgrid, in which the second stage is a nonlinear transform for the linearisation of the nonlinear state estimation progress so that the first and third stage can solve the linear state estimation problem. Furthermore, the Lagrangian relaxation method was ultilised for the distributed problem solution. In the proposed algorithm, AC subsystems and DC subsystems respectively execute state estimation through local information, and the overall consistency of the system state estimation can be eventually achieved according to the transfer iteration of the boundary information. The computational efficiency and convergence of the proposed method was ensured owing to the combination of bilinear theory and Lagrangian relaxation. Simulation results indicate that the proposed method can achieve its goal and be superior to existing method in efficiency.

This paper deals with the configuration of a wireless network with the aim of minimizing the overall cost of both operation and network installation. The trade-off between the operation cost and the installation cost is the key consideration when designing cellular telecommunication networks, and can save costs and improve the performance of the network. In this paper, we propose an integrated framework for selecting Mobile Switching Center (MSC) among the candidate MSCs and assigning Base Stations (BSs) to the selected MSCs with the objective function of minimizing the cost of MSC setup, BS to MSC cabling, as well as the cost of handover. Capacity constraint for the selected MSC is also considered in the problem. The problem is expressed in an integer programming model and the Lagrangian relaxation method is proposed to solve the problem by dualizing some constraints. The Lagrangian relaxed problem is decomposed into subproblems that can be resolved optimally. The Lagrangian heuristic algorithm is suggested to find feasible solutions to the original problem. Computational experiments are performed to test the effectiveness and efficiency of the proposed heuristic algorithm. In the experiments, Lagrangian bounds on the optimal solution are used to show the effectiveness of the algorithm. The results of the proposed algorithm are also compared with those of some conventional meta-heuristics, Tabu search (TS) and Genetic algorithm (GA). The computational experiments show that the performance of the proposed heuristics is satisfactory in both the speed and the quality of the solution generated.

The focus of this paper is to present the results of our investigation and evaluation of various shared-memory parallelizations of the data association problem in multitarget tracking. The multitarget tracking algorithm developed was for a sparse air traffic surveillance problem, and is based on an Interacting Multiple Model (IMM) state estimator embedded into the (2D) assignment framework. The IMM estimator imposes a computational burden in terms of both space and time complexity, since more than one filter model is used to calculate state estimates, covariances, and likelihood functions. In fact, contrary to conventional wisdom, for sparse multitarget tracking problems, we show that the assignment (or data association) problem is not the major computational bottleneck. Instead, the interface to the assignment problem, namely, computing the rather numerous gating tests and IMM state estimates, covariance calculations, and likelihood function evaluations (used as cost coefficients in the assignment problem), is the major source of the workload. Using a measurement database based on two FAA air traffic control radars, we show that a coarse-grained (dynamic) parallelization across the numerous tracks found in a multitarget tracking problem is robust, scalable, and demonstrates superior computational performance to previously proposed fine-grained (static) parallelizations within the IMM.

Recently we proposed a new Mixed-Integer Linear Programming formulation for the Multi-Target Tracking (MTT) problem and used a standard optimization solver to demonstrate its viability [1]. Subsequently, we provided Graphics Processing Unit (GPU) accelerated algorithms for the underlying Multidimensional Assignment Problem (MAP) with decomposable costs or triplet costs using a Lagrangian Relaxation (LR) framework. Here, we present a Dual-Ascent algorithm that provides monotonically increasing lower bounds and converges in a fraction of iterations required for a subgradient scheme. This approach can handle a large number of targets for many time steps with massive parallelism and computational efficiency. The dual-ascent framework decomposes the MAP into a set of Linear Assignment Problems (LAPs) for adjacent time-steps, which can be solved in parallel using the GPU-accelerated method of [2], [3]. The overall dual-ascent algorithm is able to efficiently solve problems with 100 targets and 100 time-frames with high accuracy. We demonstrate the applicability of our new algorithm to MTT by including realistic issues of missed detections and false alarms. Computational results demonstrate the robustness of the algorithm with good MMEP and ITCP scores and solution times for the larger problems in less than 6 seconds.

This study has focused on the UELB problem that aims at leveling the traffic load of a communication link in an information network by determining the path of a flow that minimizes the maximum load factor of the link. The UELB problem has been proved to be NP-hard, and an approximate solution method using the LP relaxation has been proposed to verify the results. This paper proposes another algorithm using the Lagrangian relaxation method in order to objectively evaluate the accuracy of the approximate solutions obtained so far. We have conducted comparison experiments with the exact solution. The results showed that the proposed algorithm gradually improves the accuracy of the solution as the number of calculations of the subgradient method is increased. In addition, it was found that when Lagrangian relaxation is performed, it is better to apply LP relaxation at the same time. Conducting the relaxation at the same time will lead to a reduction in computation time.

An LP-based algorithm for the data association problem in multitarget tracking

Application of Lagrangian relaxation to computer network control

Lagrangian Relaxation Technique for Solving Scheduling Problems by Decomposition of Timed Petri Nets

Dynamic economic dispatch (DED) over multiple time periods is a large-scale coupled spatial-temporal optimization problem. Therefore, the Lagrangian relaxation method has been widely used to split the large-scale optimization problem with coupled structure into several small sub-problems. In order to bring robustness for updating the dual multipliers and yielding convergence without strong assumptions, the augmented Lagrangian relaxation method is introduced in this paper. However, the added penalty term in an augmented Lagrangian function is non-separable, which leads to the difficulty in achieving full decomposition for parallel computation. To address this problem, a diagonal quadratic approximation method is employed to yield an approximated block separation of the non-separable penalty term. Furthermore, the ramp rate constraints are relaxed in this paper, so that the DED model is decomposed into several single-period economic dispatch models that can be efficiently handled in parallel, called the parallel augmented Lagrangian relaxation method. Particularly, the proposed relaxation strategy has a high separability feature which theoretically leads to sound convergence property. Numerical results on the IEEE 118-bus and a practical Polish 2383-bus test system over a different number of time periods show the effectiveness of the proposed method. In addition, the proposed method can be extended to other coupled spatial-temporal scheduling problems in power systems, such as energy storage dispatch.

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

Tracking and fusion using multiple sensors

This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of view (FOV). Besides, each camera might receive noisy measurements. To overcome these problems, this paper proposes a novel multi-target square-root cubature information weighted consensus filter (MTSCF), which reduces the effect of clutter or spurious measurements using joint probabilistic data association (JPDA) and proper weights on the information matrix and information vector. The simulation results show that the proposed algorithm can efficiently track multiple targets in camera networks and is obviously better in terms of accuracy and stability than conventional multi-target tracking algorithms.