Second-order Cone Problem Research Articles

A reliable ensemble forecasting modeling approach for complex time series with distributionally robust optimization

Accurate ensemble forecast results provide strong support for management decisions. While the existing ensemble forecasting model ignores the requirement of directional accuracy making its prediction direction is usually error-prone. To address this issue, we develop a convex directional prediction error measure and subsequently construct a reliable ensemble forecasting model that minimizes the horizontal prediction error with the bounded directional prediction error. Mathematically, we provided the proper range of the required directional error level. Furthermore, we find the classical ensemble forecasting model is a special case of our study when the directional error level is larger than the upper bound we gave in this study. To deal with the possible deterioration of the individual model over time, we also considered its worst possible prediction performance by introducing the distributionally robust optimization (DRO) technique into the proposed reliable ensemble forecasting model. Technically, we showed that the DRO-based reliable ensemble forecasting model is convex and can be reformulated into a second-order cone problem which can be readily solved by off-the-shelf solvers. Finally, the effectiveness of the proposed reliable ensemble forecasting model and the DRO-based reliable ensemble forecasting model were validated on three different datasets, e.g., the exchange rate, the oil price, and the country risk index. To sum up, we construct a reliable ensemble forecasting model to simultaneously control the horizontal prediction error and directional prediction error of ensemble forecasting, and thus enhance the reliability of ensemble forecasting.

Improving interdependent urban power and gas distribution systems resilience through optimal scheduling of mobile emergency supply and repair resources

Urban electric power and natural gas systems, serving as the most critical facilities that provide fundamental support to people's daily life, have been increasingly interdependent in their operation over the past decades. This growing interdependency presents great challenges and demands for enhancing the resilience of the interdependent systems, particularly driven by the recent cold weather events. In this paper, we propose a comprehensive strategy for scheduling various types of emergency resources, including mobile and stationary generators, repair crews, and fuel tankers, with the goal of enhancing the resilience of interdependent power and gas distribution systems in the aftermath of disasters. In particular, the strategy incorporates the routing of mobile resources to orchestrate their dynamic moving behaviors. Fuel supply issue for mobile and stationary distributed generators is also addressed through modeling the fuel exchange processes among generators, fuel tankers, and locations. Furthermore, we present a model of repair process to fully capture the real-world repair activities, allowing varying numbers of repair crews to work in a cooperative way. The proposed strategy is formulated into a tractable mixed-integer second-order cone problem. Finally, case studies are carried out to demonstrate the effectiveness of the strategy in enhancing the resilience of the interdependent power and gas distribution systems.

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

A Novel Weighted Block Sparse DOA Estimation Based on Signal Subspace under Unknown Mutual Coupling

Optimization of Mobile Robotic Relay Operation for Minimal Average Wait Time

This paper considers trajectory planning for a mobile robot which persistently relays data between pairs of far-away communication nodes. Data accumulates stochastically at each source, and the robot must move to appropriate positions to enable data offload to the corresponding destination. The robot needs to minimize the average time that data waits at a source before being serviced. We are interested in finding optimal robotic routing policies consisting of 1) locations where the robot stops to relay (relay positions) and 2) conditional transition probabilities that determine the sequence in which the pairs are serviced. We first pose this problem as a non-convex problem that optimizes over both relay positions and transition probabilities. To find approximate solutions, we propose a novel algorithm which alternately optimizes relay positions and transition probabilities. For the former, we find efficient convex partitions of the non-convex relay regions, then formulate a mixed-integer second-order cone problem. For the latter, we find optimal transition probabilities via sequential least squares programming. We extensively analyze the proposed approach and mathematically characterize important system properties related to the robot’s long-term energy consumption and service rate. Finally, through extensive simulation with real channel parameters, we verify the efficacy of our approach.

Analytical uncertainty propagation for multi-period stochastic optimal power flow

The increase in renewable energy sources (RESs), like wind or solar power, results in growinguncertainty also in transmission grids. This affects grid stability through fluctuating energy supplyand an increased probability of overloaded lines. One key strategy to cope with this uncertainty isthe use of distributed energy storage systems (ESSs). In order to securely operate power systemscontaining renewables and use storage, optimization models are needed that both handle uncertaintyand apply ESSs. This paper introduces a compact dynamic stochastic chance-constrained DC optimalpower flow (CC-OPF) model, that minimizes generation costs and includes distributed ESSs. AssumingGaussian uncertainty, we use affine policies to obtain a tractable, analytically exact reformulation asa second-order cone problem (SOCP). We test the new model on five different IEEE networks withvarying sizes of 5, 39, 57, 118 and 300 nodes and include complexity analysis. The results showthat the model is computationally efficient and robust with respect to constraint violation risk. Thedistributed energy storage system leads to more stable operation with flattened generation profiles.Storage absorbed RES uncertainty, and reduced generation cost.

Distributionally robust multi-period portfolio selection subject to bankruptcy constraints

<p style='text-indent:20px;'>An optimization problem with moments information which suffers from distributional uncertainty can be handled through distributionally robust optimization. In this paper, we will consider distributionally robust multi-period portfolio selection since only moment information of portfolios can be gathered in practice. We will consider two different scenarios. One is that moments information can be obtained exactly and the other one is that the moments information is also uncertain. For the two scenarios, we will show how to transform the corresponding distributionally robust optimization problem into a second order cone problem (SOCP) which can be easily solved by existing methods. Some numerical experiments are presented to demonstrate the effectiveness of our proposed method.</p>

Real-Time Optimal Control for Eco-Driving and Powertrain Energy Management

This paper presents a real-time receding-horizon control solution for the optimal control problem on combined eco-driving and powertrain energy management for a series-hybrid electric vehicle. By defining the optimal control problem in the spatial domain, discretizing the dynamics and applying several relaxations to the constraints, the problem is formulated as a second-order cone problem. The online real-time solution is achieved through the reformulation into a receding horizon control problem. To reduce computational complexity, several move-blocking strategies are applied. Combining powertrain control of the hybrid powertrain with eco-driving, leads to a reduction of 33.7%, compared to only applying energy management.

Beamforming Optimization for Information Enhancement Transmission in MISO SWIPT with NOMA System

This paper mainly considers a communication network with multiple-input single-output (MISO), in which nonorthogonal multiple access (NOMA) decoding technology is adopted, and wireless power-carrying technology is used to enhance the transmission quality of user information in the communication network. Through joint optimization of power splitting ratio and beamforming vector, we aim at minimizing transmission power (base station transmit power and secondary transmit power) while satisfying the quality-of-service requirement of all users and minimum power for secondary transmission. The problem is a nonconvex optimization program, and it is difficult to get the optimal value directly. First, in order to solve the problem for two-user case, the original problem is transformed into a semidefinite programming (SDP) problem, and then, the iterative updating algorithm is used to approximate the optimal value. When the number of users is greater than two, the original problem is transformed into a second-order cone problem, in which we deal with a sequence of second-order cone programming (SOCP). Results verify that the optimal value of the sequence of SOCPs is not increasing and converges to a local optimal value. Detailed simulation experiments indicate that the algorithm improves the performance of NOMA downlink beamforming under the condition of enhancing information and eliminating network interference.

Joint planning of distribution network and electric vehicle charging station considering extreme weather events

In order to deal with the increasing demand for electric vehicle charging and the increasingly frequent extreme weather events, this paper proposes a distribution network-electric vehicle charging station planning method considering extreme ice and snow weather conditions. Firstly, the influence mechanism of extreme ice and snow weather on distribution network line failure rate and traffic network section capacity is studied. Then the Distflow optimal power flow model is established and relaxed into a second-order cone model. Secondly, based on Wardrop user equilibrium, the distribution of mixed traffic flow between electric vehicles and non-electric vehicles is studied and the model is linearized. Finally, considering the multiple faults of the distribution network in extreme ice and snow weather, the distribution network electricity and the electric vehicle charging station are coordinated to support the key loads of the distribution network. In this paper, a planning model is established with the objective function of minimizing the annualized investment cost and the weighted operating cost under normal and extreme weather conditions, and the proposed model as a mixed-integer second-order cone problem is solved by the Yalmip toolbox. The results show that the proposed joint planning model can improve the utilization rate of equipment investment and the daily operation economy on the premise of ensuring key load supply in extreme events.

Optimal 3D Placement of UAV-BS for Maximum Coverage Subject to User Priorities and Distributions

The usage of unmanned aerial vehicle (UAV) as a base station is in the spotlight to overcome the severe attenuation characteristics of short-wavelength radio in high-speed wireless networks. In this paper, we propose an optimal UAV deployment algorithm, considering the priority of ground nodes (GNs) in different wireless communication environments. Specifically, the optimal position of a UAV is determined so that as many high-priority GNs can be served rather than covering as many GNs as possible. The proposed optimization problem deals with two groups of GNs with different priorities and finds the optimal position of the UAV by solving the mixed-integer second-order cone problem (MISOCP). To verify the effectiveness of the proposed optimal UAV deployment algorithm, we conduct various evaluating scenarios with different urban environments and GN spatial distributions. We also compare the performance of the proposed algorithm with the conventional one. Simulation results show that the proposed scheme achieves superior coverage efficiency, throughput, and delay performance compared to the conventional algorithm, even when the environment and the spatial distribution of GNs are changed.

A mixed constant-stress smoothed-strain element with a cubic bubble function for elastoplastic analysis using second-order cone programming

This paper proposes a novel optimization-based finite element method with a mixed constant-stress smoothed-strain element to solve elastoplastic problems. The proposed computational framework has three advantages: (1) in the proposed mixed constant-stress smoothed-strain element, the strain is smoothed on the edge-based smoothing domain, and the stress is assumed to be constant in each smoothing domain; (2) the cubic bubble shape function is introduced at the centroid of the element to enrich the displacement field. This makes the proposed approach accurate and free of volumetric locking for low-order elements; (3) the discrete elastoplastic boundary-value problem is formulated as a standard second-order cone problem based on the generalized Hellinger–Reissner variational principle, which is quickly and efficiently solved by the primal-dual interior-point algorithm. The proposed approach is validated on several classical problems of geotechnical engineering: the bearing capacity of footing and pipe under small deformation and slope stability. All the obtained results demonstrate that the proposed method adopting the novel mixed constant-stress smoothed-strain element offers competitively high computational accuracy and efficiency.

Chance-constrained optimization for integrated local energy systems operation considering correlated wind generation

Energy hubs, which integrate multiple energy vectors through converters, can enhance the value of Integrated Local Energy Systems (ILES) via increased flexibility and reduced costs. However, uncertain renewable energy and the non-convex, non-linear properties of energy flows complicate the modelling and operation of energy hub systems. This paper develops chance-constrained optimization methods for planning and operation of energy hub systems under uncertainty. The non-linear formulations of power and gas flows are relaxed by convexification methods, leading to a formulation of Second Order Cone Problem (SOCP), which can be efficiently solved to global optimality. The correlation between geographically close wind generators connected to the hub systems is modelled by establishing their relation using Gaussian copula. The proposed chance-constrained optimization is demonstrated on a six-hub system within a multi-vector energy distribution network with 7 electrical buses and 7 gas nodes. The value of different levels of system integration through the installation of energy hubs is investigated. The results show that by combining system integration via energy hubs with chance constrained operation, the proposed method can reduce operating costs and increase renewable energy yields, thereby benefitting hub system operators and customers with reduced energy infrastructure investment and energy costs.

Optimal operation for coupled transportation and power networks considering information propagation

The growing number of electric vehicles (EVs) and the rapid development of wireless charging technology couple the transportation network (TN) and power distribution network (PDN). When local traffic events happen, transportation parameters are changed and drivers will change their driving behaviors accordingly. However, information spread by vehicle-to-vehicle communication takes time. Information asymmetry among EVs will break the original traffic equilibrium. Therefore, a transient state is caused between two steady states in TN. Meanwhile, the variation of traffic flow caused by information propagation will also influence the power flow in PDN. This paper investigates the interactive mechanism of coupled transportation network and power network during the transient and steady state. Considering road parameters, electricity price and information flow among vehicles, a model that combines traffic assignment model and clustered epidemiological differential equations is proposed to formulate spatio-temporal distribution of EVs. Distflow equations are employed and relaxed to a second-order cone problem. Then the locational marginal price (LMP) is formulated. To avoid massive parameters transfer between two networks, we use a best-response decomposition algorithm to iteratively calculate the electricity price and real-time traffic flow. The results of two coupled networks justify the necessity to take information propagation among vehicles into account to coordinate the operation of coupled TN and PDN.

Semi–definite programming for the nearest circulant semi–definite matrix problem

"Positive semi–definite circulant matrices arise in many important applications. The problem arises in various applications where the data collected in a matrix do not maintain the specified structure as is expected in the original system. The task is to retrieve useful information while maintaining the underlying physical feasibility often necessitates search for a good structured approximation of the data matrix. This paper construct structured circulant positive semi–definite matrix that is nearest to a given data matrix. The problem is converted into a semi–definite programming problem as well as a problem comprising a semi–defined program and second-order cone problem. The duality and optimality conditions are obtained and the primal-dual algorithm is outlined. Some of the numerical issues involved will be addressed including unsymmetrical of the problem. Computational results are presented."

3D placement of unmanned aerial vehicles and partially overlapped channel assignment for throughput maximization

This paper investigates a wireless system with multi-Unmanned Aerial Vehicles (UAVs) for improving the overall throughput. In contrast to previous studies that optimize the locations of UAVs and channel assignment separately, this paper considers the two issues jointly by exploiting Partially Overlapped Channels (POCs). The optimization problem of maximizing network throughput is formulated as a non-convex and non-linear problem. In order to find a practical solution, the problem is decomposed into two subproblems, which are iteratively optimized. First, the optimal locations of UAVs are determined under a fixed channel assignment scheme by solving the mixed-integer second-order cone problem. Second, an efficient POC allocation scheme is determined via the proposed channel assignment algorithm. Simulation results show that the proposed approach not only significantly improves system throughput and service reliability compared with the cases in which only orthogonal channels and stationary UAVs are considered, but also achieves similar performance using the exhaustive search algorithm with lower time complexity.

Outer approximation with conic certificates for mixed-integer convex problems

A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with $\mathcal{K}^*$ cuts derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all subproblems are well-posed, the algorithm detects infeasibility or unboundedness or returns an optimal solution in finite time. Using properties of the conic certificates, we show that the $\mathcal{K}^*$ cuts imply certain practically-relevant guarantees about the quality of the polyhedral relaxations, and demonstrate how to maintain helpful guarantees when the LP solver uses a positive feasibility tolerance. We discuss how to disaggregate $\mathcal{K}^*$ cuts in order to tighten the polyhedral relaxations and thereby improve the speed of convergence, and propose fast heuristic methods of obtaining useful $\mathcal{K}^*$ cuts. Our new open source MI-conic solver Pajarito (http://github.com/JuliaOpt/Pajarito.jl) uses an external mixed-integer linear (MILP) solver to manage the search tree and an external continuous conic solver for subproblems. Benchmarking on a library of mixed-integer second-order cone (MISOCP) problems, we find that Pajarito greatly outperforms Bonmin (the leading open source alternative) and is competitive with CPLEX's specialized MISOCP algorithm. We demonstrate the robustness of Pajarito by solving diverse MI-conic problems involving mixtures of positive semidefinite, second-order, and exponential cones, and provide evidence for the practical value of our analyses and enhancements of $\mathcal{K}^*$ cuts.

Enhanced Coordinated Operations of Electric Power and Transportation Networks via EV Charging Services

Electric power and transportation networks become increasingly coupled through electric vehicles (EV) charging station (EVCS) as the penetration of EVs continues to grow. In this paper, we propose a holistic framework to enhance the operation of coordinated electric power distribution network (PDN) and urban transportation network (UTN) via EV charging services. Under this framework, a bi-level model is formulated to optimally determine EVCS charging service fees (CSF) for guiding EV charging behaviors and minimizing the total social cost. At the upper level, PDN with wind power generation is formulated as a second-order cone problem (SOCP) where CSF is determined. Given the settings calculated at the upper level, the lower level problem is described as a traffic assignment problem (TAP) which is subject to the user equilibrium (UE) principle and captures the individual rationality of single EV owners in UTN. The uncertainties in wind power output and origin-destination (O-D) traffic demands are considered in the proposed model and a deep reinforcement learning (DRL)-based solution framework is developed to decouple and approximately solve the stochastic bi-level problem. Both gradient-based and gradient-free training algorithms are implemented in this paper and the respective results are compared. The case studies on a 5-node system, 24-node Sioux-Falls system and real-world Xi'an city in China are conducted to verify the effectiveness of the proposed model, which demonstrates the enhanced operation of coordinated PDN and UTN networks by reducing the traffic congestion and improving the integration of renewable energy.

Transmit Beamforming for Layered Physical Layer Security

In this paper, we propose a novel layered physical layer security model, which is the extension of the traditional physical layer security to the domain of multiple-layer information security. It has a hierarchical information security structure that every transmitted message has a security level, while every user has a security clearance. Users can only decode the messages with security levels lower than or equal to their clearance, otherwise they will be deemed as eavesdroppers. Based on the framework of the layered information security and assuming perfect channel state information of all users, an artificial-noise-aided optimal beamforming scheme is proposed to minimize the total transmit power at the base station, while satisfying the minimum secrecy rate requirements of all secret messages. Due to the intrinsical complexity of the formulated nonconvex problem, a safe and convex reformulation based on the first-order Taylor series expansion method is proposed to generate a tractable approximation. A successive convex approximation-based algorithm is then proposed, which solves a series of second-order cone problems with convergence to the stationary point of the original problem. We also consider the imperfect channel state information case, and then propose a worst-case robust design to overcome the influence of channel uncertainties. Semi-definite relaxation method and S-procedure are utilized to get a computationally efficient lower bound of the intractable power minimization problem. Moreover, we investigate the application of the suboptimal zero-forcing-based beamforming scheme in the system to tradeoff the achievable performance and the computational complexity. Simulation results are provided to demonstrate the effectiveness of our proposed schemes.

Chance-Constrained Unit Commitment With N-1 Security and Wind Uncertainty

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch. In particular, the variability of wind generation increases the risk of unexpected overloads and cascading events. To address these questions, we present an N-1 security and chance-constrained unit commitment (SCCUC) that includes models of generation reserves that respond to wind fluctuations and component outages. We formulate the SCCUC as a mixed-integer, second-order cone problem that limits the probability of failure. We develop a modified Benders decomposition algorithm to solve the problem to optimality and present detailed case studies on the IEEE RTS-96 three area and the IEEE 300 NESTA test systems. The case studies assess the economic impacts of contingencies and various degrees of wind power penetration and demonstrate the effectiveness and scalability of the algorithm.

Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems

In this paper, we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules—the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to his relative priority, other allocatees’ preferences, and resource availability. We model such systems as multiclass, multiserver queuing systems that are potentially unstable or in transient regime. We propose a novel robust optimization solution methodology that builds on the assignment problem. For first-come, first-served systems, our approach yields a mixed-integer programming formulation. For the important case where there is a hierarchy in the resource types, we strengthen our formulation through a drastic variable reduction and also propose a highly scalable heuristic, involving only the solution of a convex optimization problem (usually a second-order cone problem). We back the heuristic with an approximation guarantee that becomes tighter for larger problem sizes. We illustrate the generalizability of our approach by studying systems that operate under different priority rules, such as class priority. Numerical studies demonstrate that our approach outperforms simulation. We showcase how our methodology can be applied to assist patients in the U.S. deceased-donor kidney waitlist. We calibrate our model using historical data to estimate patients’ wait times based on their kidney quality preferences, blood type, location, and rank in the waitlist. This paper was accepted by Yinyu Ye, optimization.