Relaxed Problem Research Articles

Distributed Multirobot Task Assignment via Consensus ADMM

In this article, we present a distributed algorithm to solve a class of multirobot task assignment problems. We formulate task assignment as a mathematical optimization and solve for optimal solutions with a variant of the consensus alternating direction method of multipliers (C-ADMM). We provide C-ADMM-based algorithms for both the primal and dual problem formulations and show the advantages of each form depending on the problem specifics. In our algorithm, each robot solves a series of local optimization problems and communicates the results to its local neighbors, ultimately converging to an optimal task assignment in problems with linear objective functions and an optimal solution of the relaxed problem in convex problems. While many other distributed algorithms require a central station for their implementation, in our algorithm, each robot only communicates with its one-hop neighbors. In linear task assignment problems, our algorithm converges to the optimal task assignment, unlike many other distributed algorithms for this problem, which yield suboptimal solutions. We demonstrate our algorithms in task assignment problems over a variety of communication network topologies, where we show that our inexact dual algorithm is at least 60% faster than other distributed algorithms, which produce an optimal task assignment. In addition, our dual algorithm attains a 69% speedup in computation time compared to a notable distributed variant of the Hungarian method (Chopra et al., 2017). We also apply our algorithm to a multi-unmanned-aerial-vehicle persistent surveillance problem, showing its suitability for problems involving periodic task assignments.

Convergences for robust bilevel polynomial programmes with applications

In this paper, we consider a bilevel polynomial optimization problem, where the constraint functions of both the upper-level and lower-level problems involve uncertain parameters. We employ the deterministic robust optimization approach to examine the bilevel polynomial optimization problem under data uncertainties by providing lower bound approximations and convergences of sum-of-squares (SOS) relaxations for the robust bilevel polynomial optimization problem. More precisely, we show that under the convexity of the lower-level problem and either the boundedness of the feasible set or the coercivity of the objective function, the global optimal values of SOS relaxation problems are lower bounds of the global optimal value of the robust bilevel polynomial problem and they converge to this global optimal value when the degrees of SOS polynomials in the relaxation problems tend to infinity. Moreover, an application to an electric vehicle charging scheduling problem with renewable energy sources demonstrates that using the proposed SOS relaxation schemes, we obtain more stable optimal values than applying a direct solution approach as the SOS relaxations are capable of solving these models involving data uncertainties in dynamic charging price and weather conditions.

Correntropy based model predictive controller with multi-constraints for robust path trajectory tracking of self-driving vehicle

Self-driving vehicles must be equipped with path tracking capability to enable automatic and accurate identification of the reference path. Model Predictive Controller (MPC) is an optimal control method that has received considerable attention for path tracking, attributed to its ability to handle control problems with multiple constraints. However, if the data acquired for determining the reference path is contaminated by non-Gaussian noise and outliers, the tracking performance of MPC would degrades significantly. To this end, Correntropy-based MPC (CMPC) is proposed in this paper to address the issue. Different from the conventional MPC model, the objective of CMPC is constructed using the robust metric Maximum Correntropy Criterion (MCC) to transform the optimization problem of MPC to a non-concave problem with multiple constraints, which is then solved by the Block Coordinate Update (BCU) framework. To find the solution efficiently, the linear inequality constraints of CMPC are relaxed as a penalty term. Furthermore, an iterative algorithm based on Fenchel Conjugate (FC) and the BCU framework is proposed to solve the relaxed optimization problem. It is shown that both objective sequential convergence and iterate sequence convergence are satisfied by the proposed algorithm. Simulation results generated by CarSim show that the proposed CMPC has better performance than conventional MPC in path tracking when noise and outliers exist.

Multiple Sources Restoration for Soft Open Points in Distribution Networks With a Two-Stage Accelerated Algorithm

Soft open points (SOPs) connected to distribution networks are instrumental in improving operational performance during outage periods, such as power supply reliability and power quality, and they have not been sufficiently studied. To fully harness the potential benefits of SOPs, a multiple-source distribution service restoration (DSR) strategy considering SOPs is proposed in this paper. The power outputs of distributed energy resources (DERs) and SOP flexibility are exploited to enhance the load restoration level and mitigate voltage deviations over a time horizon. Additionally, to cope with uncertainties, the chance-constrained method is adopted by the proposed strategy to allow intermittent renewable resources to participate in DSR. DSR is formulated as a mixed-integer linear programming (MILP) problem with many integer variables, making it very challenging to solve. To reduce the computational complexity, a two-stage accelerated algorithm (TSAA) is proposed. This allows us to solve a relaxed MILP problem in the first stage to decide the radial topology. An accelerated MILP problem is solved in the second stage to determine the load status as well as the outputs of the DERs and SOPs. Case studies on an IEEE 33-bus distribution network illustrate the effectiveness of the proposed DSR strategy and the feasibility of TSAA in reducing the computation time.

Multi-source coordinated stochastic restoration for SOP in distribution networks with a two-stage algorithm

After suffering from a grid blackout, distributed energy resources (DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s resilience. In this study, a multi-source coordinated load restoration strategy was investigated for a distribution network with soft open points (SOPs). Here, the flexible regulation ability of the SOPs is fully utilized to improve the load restoration level while mitigating voltage deviations. Owing to the uncertainty, a scenario-based stochastic optimization approach was employed, and the load restoration problem was formulated as a mixed-integer nonlinear programming model. A computationally efficient solution algorithm was developed for the model using convex relaxation and linearization methods. The algorithm is organized into a two-stage structure, in which the energy storage system is dispatched in the first stage by solving a relaxed convex problem. In the second stage, an integer programming problem is calculated to acquire the outputs of both SOPs and power resources. A numerical test was conducted on both IEEE 33-bus and IEEE 123-bus systems to validate the effectiveness of the proposed strategy.

A stabilizing benders decomposition method for the accessibility-oriented charging station location problem

Electric vehicles are a promising selection to deal with climate change and energy crises. However, the development of electric vehicles is impeded by various barriers including shortened driving range, lack of charging facilities, and long recharging periods. Setting additional charging facilities is essential to construct an efficient charging network. Previous studies neglected accessibility-oriented indicators to locate charging stations. This study locates charging stations by maximizing the space-time-electricity accessibility of electric vehicle travelers. For the accessibility-oriented charging station location problem, we formulate a multi-commodity network flow model in the space-time-electricity network. Then, we reformulate this model into a two-stage integer program and develop a Benders decomposition method with stabilizing techniques. At each iteration, a relaxed Benders master problem (RMP) and a set of dual routing subproblems (DSPs) are solved. The RMP provides an ascending lower bound and a feasible charging station location scheme. These DSPs generate a set of Benders optimality cuts for RMP and a feasible solution to update the upper bound. All instances in three transportation networks are solved optimally, showing that the stabilizing techniques can significantly improve the performance of the standard Benders decomposition method.

Solving resource-constrained project scheduling problems under different activity assumptions

Much research has focused on Resource-Constrained Project Scheduling Problems (RCPSP(A)), where the focus has been on limited or even inadequate resources as a type of risk to implement project activities and decrease completion time. Activity interruption assumptions are considered in this paper. The RCPSP(B) is the RCPSP(A) when the non-preemption assumption is relaxed but the RCPSP(D) is the RCPSP(A) when both the non-preemption and the fixed resources are relaxed. A fundamental assertion of this paper is that the A, B, and D scheduling interruption categories can be interchanged with sufficient managerial effort. Effectively, this becomes a constraint relaxation problem. Because the capacity to manage scheduling interruptions is limited, the issue is which category A activities should be relaxed to type B and D, and which category B activities should be relaxed to type D. This paper introduces the interruptible and flexible planning project activity concept and presents a heuristic method to accomplish the reassessment of category types from A to B and D. First, the heuristic changes the interruptible activities (IAs) under categories A, B, and D. Secondly, critical interruptible activities (CIAs) that have significant impacts in reducing the project makespan are identified. This increases the manager's decision choices with respect to scheduling activities as category type A, B, or D. The methodology facilitates an understanding of how A, B, and D interpretability assumptions affect the project makespan and helps project manager to selectively choose how specific activities in a project should be managed.

Small Signal Anti-Jamming Scheme Based on a DMA Linear Array under Strong Jamming

Considering the difficulty of receiving small signals under strong electromagnetic jamming, this paper proposes a small-signal anti-jamming scheme based on a single dynamic metamaterial antenna (DMA). Our scheme uses the dynamic-adjustable characteristics of the DMA to perform spatial filtering at the antenna radio frequency (RF) front-end, to suppress strong jamming signals in advance and to improve the receiver’s ability to receive and demodulate small signals. Specifically, we take the maximization of signal-to-interference-plus-noise ratio (SINR) as the optimization goal, transform the fractional non-convex objective function model into a quasi-convex semi-definite relaxation (SDR) problem, and use the Charnes-Cooper (CC) transform algorithm to find the optimal DMA array-element codeword-state matrix. Simulation results show that DMA has better spatial-beamforming capability than traditional antenna arrays, and the proposed scheme can better resist strong jamming. DMA realizes the effect of digital beamforming at the back end of the traditional communication system, has the advantages of traditional digital-spatial filtering, and further improves the receiver’s ability to receive and demodulate small signals.

A co-evolutionary algorithm with elite archive strategy for generating diverse high-quality satellite range schedules

AbstractSatellite range scheduling, a multi-constrained combinatorial optimization problem, is crucial to guaranteeing the normal operation and application of onboard satellites. Traditional methods are dedicated to finding one optimal schedule, having ignored the problem may process multiple high-quality schedules. To provide a set of alternative schedules while maintaining the solution quality, we propose a co-evolutionary algorithm with elite archive strategy (COEAS) in this article. In COEAS, two populations are evolved to solve the original and relaxed problem in terms of schedule quality and diversity, respectively. During the evolution, the populations maintain a weak cooperation and only share the information in offspring combination phase. Further, an elite archive strategy is derived to identify and preserve potential stagnated and optimal individuals. In this strategy, the promising individuals would further participate in parent mating and offspring replacement for the dual purpose of maintaining potential optima recovery and fine-tuning the population. The experimental results show that the proposed algorithm is better than comparison algorithms in terms of efficacy (obtaining higher quality schedule), diversity (locating more optimal schedules) and flexibility (providing better alternatives).

Fractional Model of Multiple Trapping with Charge Leakage: Transient Photoconductivity and Transit–Time Dispersion

The model of multiple trapping into energy-distributed states is a successful tool to describe the transport of nonequilibrium charge carriers in amorphous semiconductors. Under certain conditions, the model leads to anomalous diffusion equations that contain time fractional derivatives. From this perspective, the multiple-trapping model can be used to interpret fractional transport equations, formulate initial and boundary conditions for them, and to construct numerical methods for solving fractional kinetic equations. Here, we shortly review the application of fractional multiple-trapping equations to problems of transient photoconductivity relaxation and transit–time dispersion in the time-of-flight experiment and discuss the connection of the multiple-trapping model with generalized fractional kinetic equations. Different types of charge leakage are discussed. The tempered fractional relaxation is obtained for recombination via localized states and distributed order equations arise for the non-exponential density of states presented as a weighted mixture of exponential functions. Analytical solutions for photocurrent decay in transient photoconductivity and time-of-flight experiments are provided for several simplified situations.

Problem characterization of unique shortest path routing

To demonstrate the necessity and importance of solving the unique shortest path routing problem based on and tailored to a complete formulation, the problem characteristics with respect to objective functions, constraints, and solution qualities are studied in this paper, including the impacts of objective functions and lower & upper bounds of the problem. To illustrate the advantage of developing an exact solution approach to the problem, the resulting routing performance from the unique shortest path routing problem is compared with those from using two default methods as well as those from two relaxed problems. It is shown that by solving the problem based on a complete formulation and an exact algorithm, the resulting routing performance is notably improved, relative to that from using the two default methods, and is competitively close to the lower bounds.

Consideration of Supervision of Mesotherapy Needles for Cosmetic Injection

With the development of medical aesthetics industry in China, sodium hyaluronic is injected into the facial dermis with multi needles to relieve wrinkles, thick pores, skin relaxation and other aging problems, is more and more popular nowadays. The wide application of mesotherapy for cosmetic injection and the subsequent adverse events are widely reported. This study attempts to explore the adverse events and countermeasures for the application of mesotherapy from the perspective of medical device supervision.

Distributed Markov Chain Redesign for Multiagent Decision-Making Problems

In this article, we consider the problem of modifying in a distributed way the transition probabilities of a Markov chain over an undirected graph in order to achieve a desired limiting distribution, while minimizing the variation from the current weights. This problem setting could be used to model a (graph-based) distributed decision-making process where static agents, e.g., elements of Internet of Things (IoT) networks, are required to achieve a common objective while adapting to different operational conditions, e.g., monitoring of time-varying and spatial-varying phenomena. This could be effectively used to describe several applications settings, ranging from sensor-network-based border patrolling to IoT-based environmental precision farming. In this context, our contribution is threefold: 1) we show that, under the assumption that a global optimal solution exists, then such a solution can be computed by solving a relaxed problem, where the irreducibility and aperiodicity constraints are lifted; 2) we derive an algebraic optimality condition for the relaxed problem; and 3) we design a distributed algorithm that provably converges towards this optimality condition.

Motion Parameter Estimation for Mobile Sources Using Semidefinite Programming

In this paper, we address the motion parameter estimation problem using time difference of arrival (TDOA) measurements, where a mobile source starts from an initial position with constant velocity. The problem is formulated as three non-convex constrained weighted least squares (CWLS) problems. Owing to their non-convex nature, local convergence may occur when solving them by an iterative algorithm, implying good estimates are not guaranteed. We propose to solve these CWLS problems by applying semidefinite relaxation (SDR) to generate three different semidefinite programming (SDP) problems, namely, the motion unconstrained semidefinite programming (MU-SDP), motion constrained semidefinite programming (MC-SDP), and motion parameter direct semidefinite programming (MPD-SDP). The MU-SDP, MC-SDP, and MPD-SDP methods are then extended to the scenario of unknown propagation speed (PS), which is common in underwater and underground localizations. Specifically, for this scenario, the two-step MU-SDP, two-step MC-SDP, and two-step MPD-SDP methods are designed to keep the relaxed SDP problems tight by introducing the penalty function. Simulation results show that MU-SDP performs worse than MC-SDP and MPD-SDP owing to the ignorance of the motion equation, and MC-SDP and MPD-SDP are able to reach the Cramér-Rao lower bound (CRLB) accuracy.

Latency Optimization for Luby Transform Coded Computation in Wireless Networks

Luby transform (LT) code has attracted a significant attention due to its rateless property and low decoding complexity in distributed computing networks. However, for wireless networks, the frequent interaction in LT coded computation can give rise to the latency bottleneck considering the communication overhead of interaction. In this letter, we study a novel LT coded computation scheme for heterogeneous wireless networks. Considering nodes with the disparate computation and transmission capabilities, we propose a block-design based wireless LT coded computation (BD-WLTCC) scheme to balance both computation and transmission latency. First, we pre-allocate the maximum transmission rounds due to the limited bandwidth of wireless channel. Then, we design the sub-block size for each node by formulating a nonconvex optimization problem to avoid the frequent interaction. Finally, the sub-optimal sub-block size is obtained by solving the relaxed problem iteratively. And the optimized results provably reveal the generalization of existing works. Simulation results show the superiority of our scheme.

MAXIMUM PRINCIPLE FOR SINGULAR CONTROL PROBLEMS OF SYSTEMS DRIVEN BY MARTINGALE MEASURES

We provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.

CALCULATION OF REINFORCED CONCRETE STRUCTURES: CONSIDERATIONS ON DEVELOPING NEW THEORY

Introduction. Current regulatory documents in the field of concrete and reinforced concrete are based mainly on research results obtained in the past century.Aim. This article addresses the approaches to improve the theory of calculation of concrete and reinforced concrete structures, in the light of the accumulated knowledge.Materials and methods. Since concrete structures belong to non-conservative systems, it is inaccurate to determine the forces arising in them using standard methods of structural mechanics. To achieve this goal, the deformation and relaxation problems for an axially compressed concrete fiber were solved following the A.A. Gvozdev and K.Z. Galustov’s two-component theory of creep, where deformations are categorized on the basis of reversibility.Results. Historical background was provided. Proposed by the authors of this article is a solution to the deformation and relaxation problems for the elementary part of a concrete structure for the case of axial compression, since such an event is impossible. In this regard, it was suggested that estimating the loss of stability by Euler is also incorrect. It was observed that the achieved maximum load-bearing capacity of the construction is equivalent to zero resistibility, with a progressive collapse occurring. For further research, it was proposed to use the hypothesis of a straight normal, assuming that this law is valid in the absence of tangential stresses in the studied sections of the structure.Conclusions. To improve the theory of calculation of concrete and reinforced concrete structures, it is necessary to revise drastically the existing approach to scientific research.

On the origin of polarization fatigue and Curie–von Schweidler relaxation current in Pb(Zrx,Ti1−x)O3 ferroelectric thin films: A unique mechanism based on charge trapping by interface defects

This article discusses the widespread problem of polarization fatigue in ferroelectric materials. After a review of the bibliographical data on this topic but also on the older and equally widespread problem of dielectric relaxation in solids, a possible correlation between these two phenomena is established by observing that the decrease with time of polarization obeys the Curie–von Schweidler (CVS) law like the relaxation current. An electrical model involving a charge trapping mechanism by electronic defects in bandgap at the contact/ferroelectric interface is then developed, which simultaneously explains polarization fatigue and relaxation current. The CVS law is found considering interface traps with a continuum of time constants. This study sheds new light on the origin of these phenomena, which remain unexplained to date.

Distributed Detection Over Blockchain-Aided Internet of Things in the Presence of Attacks

Distributed detection over a blockchain-aided Internet of Things (BIoT) network in the presence of attacks is considered, where the integrated blockchain is employed to secure data exchanges over the BIoT as well as data storage at the agents of the BIoT. We consider a general adversary model where attackers jointly exploit the vulnerability of IoT devices and that of the blockchain employed in the BIoT. The optimal attacking strategy which minimizes the Kullback-Leibler divergence is pursued. It can be shown that this optimization problem is nonconvex, and hence it is generally intractable to find the globally optimal solution to such a problem. To overcome this issue, we first propose a relaxation method that can convert the original nonconvex optimization problem into a convex optimization problem, and then the analytic expression for the optimal solution to the relaxed convex optimization problem is derived. The optimal value of the relaxed convex optimization problem provides a detection performance guarantee for the BIoT in the presence of attacks. In addition, we develop a coordinate descent algorithm which is based on a capped water-filling method to solve the relaxed convex optimization problem, and moreover, we show that the convergence of the proposed coordinate descent algorithm can be guaranteed.

Computing Stabilizing Feedback Gains via a Model-Free Policy Gradient Method

In spite of the lack of convexity, convergence and sample complexity properties were recently established for the random search method applied to the linear quadratic regulator (LQR) problem. Since policy gradient approaches require an initial stabilizing controller, we propose a model-free algorithm that searches over the set of state-feedback gains and returns a stabilizing controller in a finite number of iterations. Our algorithm involves a sequence of relaxed LQR problems for which the associated domains converge to the set of stabilizing controllers for the original continuous-time linear time-invariant system. Starting from a stabilizing controller for the relaxed problem, the proposed approach alternates between updating the controller via policy gradient iterations and decreasing relaxation parameter in the LQR cost while preserving stability at all iterations. By properly tuning the relaxation parameter updates we ensure that the cost values do not exceed a uniform threshold and establish computable bounds on the total number of iterations.