Set Of Constraints Research Articles

Planning Speed Mode of All-Wheel Drive Autonomous Vehicles Considering Complete Constraint Set

The study aims to improve the technique of motion planning for all-wheel drive (AWD) autonomous vehicles (AVs) by including torque vectoring (TV) models and extended physical constraints. Four schemes for realizing the TV drive were considered: with braking internal wheels, using a rear-axle sport differential (SD), with braking front internal wheel and rear-axle SD, and with SDs on both axles. The mathematical model combines 2.5D vehicle dynamics model and a simplified drivetrain model with the self-locking central differential. The inverse approach implies optimizing the distribution of kinematic parameters by imposing a set of constraints. The optimization procedure uses the sequential quadratic programming (SQP) technique for the nonlinear constrained minimization. The Gaussian N-point quadrature scheme provides numerical integration. The distribution of control parameters (torque, braking moments, SDs’ friction moment) is performed by evaluating linear and nonlinear algebraic equations inside of optimization. The technique proposed demonstrates an essential difference between forecasts built with a pure kinematic model and those considering the vehicle’s drive/control features. Therefore, this approach contributes to the predictive accuracy and widening model properties by increasing the number of references, including for actuators and mechanisms.

Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities

Recently a class of second-order cone representable convex inequalities called lifted bilinear cover inequalities were introduced, which are valid for a set described by a separable bilinear constraint together with bounds on variables. In this paper, we study the computational potential of these inequalities for separable bilinear optimization problems. We first prove that the semidefinite programming relaxation provides no benefit over the McCormick relaxation for such problems. We then design a simple randomized separation heuristic for lifted bilinear cover inequalities. In our computational experiments, we separate many rounds of these inequalities starting from McCormick’s relaxation of instances where each constraint is a separable bilinear constraint set. We demonstrate that there is a significant improvement in the performance of a state-of-the-art global solver in terms of gap closed, when these inequalities are added at the root node compared with when they are not. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: S. S. Dey gratefully acknowledges the support by the Office of Naval Research [Grant N000141912323].

On exceptional QP-manifolds

The connection between two recent descriptions of tensor hierarchies — namely, infinity-enhanced Leibniz algebroids, given by Bonezzi & Hohm and Lavau & Palmkvist, and the p-brane QP-manifolds constructed by Arvanitakis — is made precise. This is done by presenting a duality-covariant version of latter.The construction is based on the QP-manifold T⋆[n]T[1]M × ℋ[n], where M corresponds to the internal manifold of a supergravity compactification and ℋ[n] to a degree-shifted version of the infinity-enhanced Leibniz algebroid. Imposing that the canonical Q-structure on T⋆[n]T[1]M is the derivative operator on ℋ leads to a set of constraints. Solutions to these constraints correspond to 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS p-branes, suggesting that this is a new incarnation of a brane scan. Reduction w.r.t. to these constraints reproduces the known p-brane QP-manifolds. This is shown explicitly for the SL(3)×SL(2)- and SL(5)-theories.Furthermore, this setting is used to speculate about exceptional ‘extended spaces’ and QP-manifolds associated to Leibniz algebras. A proposal is made to realise differential graded manifolds associated to Leibniz algebras as non-Poisson subspaces (i.e. not Poisson reductions) of QP-manifolds similar to the above. Two examples for this proposal are discussed: generalised fluxes (including the dilaton flux) of O(d, d) and the 3-bracket flux for the SL(5)-theory.

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in O(|Sigma |^{3.726}(n+k) + |Sigma |^{1.726}nk) time, where n is the number of leaves, k is the number of characters, and Sigma is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.

Distributed switched model-based predictive control for distributed large-scale systems with switched topology

Distributed switched large-scale systems are composed by dynamically coupled subsystems, in which interactions among subsystems vary over time according a switching signal. This paper presents a distributed robust switched model-based predictive control (DSwMPC) to control such systems. The proposed method guarantees stabilising the origin of the whole closed-loop system and ensures the constraints satisfaction in the presence of an unknown switching signal. In the distributed model-based predictive control (DMPC) used in this work, by considering the interactions among subsystems as an additive disturbance, the effect of the switch is reflected on the dynamic equation, local, and consistency constraint sets of the nominal subsystems. To compensate the effect of switching signal which creates a time-varying network topology, a robust tube-based switched model-based predictive control (RSwMPC) with switch–robust control invariant set as the target set robust to unknown mode switching is used as local controller. The scheme performance is assessed using three typical examples. The simulation results show that the input and state constraints are satisfied by the proposed DSwMPC at all times. They also validate that the closed-loop system converges to the origin. Also, a comparison of the DSwMPC with a centralised SwMPC (CSwMPC) and a decentralised SwMPC (DeSwMPC) are performed.

A resilient inter-organizational workflow assignment plan selection approach: Application to a digital health use case

Workflow Management Systems are rapidly evolving and increasingly used in a variety of industries, allowing organizations to automate and enhance their business processes. Hence, they are open to collaboration throw inter-organizational workflows to achieve common objectives. Thus, organizations could thereby adapt to highly dynamic environments and abrupt sudden changes like during epidemics. One of the particular interests for security researchers is to ensure workflow resiliency, which means ensuring the completion of the workflow execution given a defined set of security constraints without violating the security policy. However, the rigid application of security constraints restricts some task-organization assignments, which leads to the workflow satisfiability problem. Moreover, a wise selection of collaborating organizations is very important for secure resilient inter-organizational workflow execution. Therefore, we aim in this paper to propose a resilient inter-organizational workflow assignment plan selection approach to select a valid task-organization plan that allows a resilient inter-organizational workflow complete execution. Our proposed approach, uses the task priority concept, Bayesian inference, and a hybrid multi-criteria decision-making approach based on the methods Analytical Hierarchical Process and Grey Technique for Order of Preference by Similarity to Ideal Solution. As a result, the proposed approach selects the best assignment plan for a resilient execution of the Inter-Organizational Workflow, in addition to delegates for each task-organization assignment if available.

Optimisation of livestock routing on farms

A grass-based livestock farm will typically be partitioned into a set of fields which may not be contiguous. The livestock in question will be distributed among these fields plus a set of buildings. This distribution will change over time as a result of livestock being routed between different locations. This change in distribution is not a random process. It is instead planned by the farmer to satisfy a set of constraints while minimising workload. The set of constraints in question are designed to maximise the performance of the farm and, in many cases, will be large.In this work, we refer to the above planning problem as the Livestock Routing Problem (LRP). We propose modelling the LRP as an integer program, which is a specific type of mathematical optimisation problem. Our model is general in nature whereby many farming activities can be incorporated. These activities include rotational grazing, silage production and livestock breeding.In our analysis we consider many different instances of the LRP and attempt to solve these instances using an off-the-shelf integer program solver. In most cases, an optimal or close to optimal solution is found in reasonable time. These results demonstrate that the proposed methods could be used within a decision support system for livestock farmers and, in turn, reduce the workload associated with the routing of livestock.

Distributed strategies for mixed equilibrium problems: Continuous-time theoretical approaches

In this paper, the mixed equilibrium problem is studied by employing a continuous-time multi-agent system, where the objective of agents is to cooperatively find a point from the feasible set such that the sum of bifunctions with a free-variable is nonnegative. Different from existing works on mixed equilibrium problems with only convex set constraints, we consider a more general case where the feasible set is constrained by a set of convex inequalities. Moreover, each agent only has access to the information of its own bifunction and inequality constraint function, as well as the information of a local convex set. To handle this problem, the Karush–Kuhn–Tucker condition that is suitable for continuous-time theoretical approaches is provided, and a continuous-time distributed primal–dual algorithm is proposed. Under mild assumptions on the graph and bifunctions, we prove that the states of all agents asymptotically converge to the common solution of the mixed equilibrium problem. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.

Reach-Avoid Verification Based on Convex Optimization

In this paper we propose novel sufficient conditions for verifying reach-avoid properties of continuous-time systems modelled by ordinary differential equations (ODEs). Given a system, an initial set, a safe set and a target set of states, we say that the reach-avoid property holds, if for all initial conditions in the initial set, any trajectory of the system starting at them will eventually, i.e. in unbounded yet finite time, enter the target set while remaining inside the safe set until that first target hit (that is, if the system starting from the initial set can reach the target set safely). Based on a discount value function, two sets of quantified constraints are derived for verifying the reach-avoid property via the computation of exponential/asymptotic guidance-barrier functions (they form a barrier escorting the system to the target set safely at an exponential or asymptotic rate). It is interesting to find that one set of constraints whose solution is termed exponential guidance-barrier functions is just a simplified version of the existing one derived from the moment based method, while the other one whose solution is termed asymptotic guidance-barrier functions is completely new. Furthermore, built upon this new set of constraints, we derive a set of more expressive constraints, which includes the aforementioned two sets of constraints as special instances, providing more chances for verifying the reach-avoid property successfully. Finally, several examples demonstrate the theoretical developments and performance of proposed sufficient conditions using semi-definite programming methods.

A fair multi-commodity two-echelon distribution problem

In the context of a short and local supply chain of fresh produce in the public sector, we introduce a fair multi-commodity two-echelon distribution problem. A decision maker has to decide on the planning of the first-echelon collection trips of commodities from suppliers to distribution centers equitably and on the second-echelon delivery routes of commodities from the centers to customers. In addition to the classic objective of minimizing the total transportation cost in vehicle routing problems, the goal is to make sure that all suppliers receive an equitable service with regard to their profits. This is done by introducing fairness measures into the problem as a set of constraints. We use two widely used inequality metrics from the literature and present a novel problem-specific equity measure as well. We model the problem as a mixed-integer program using an arc-route-based formulation and suggest a matheuristic to solve the problem. Through numerical experiments, we analyze the performance of our matheuristic on a series of generated instances and on the instances of a French fresh produce supply chain from the literature. We evaluate the efficacy of the three used fairness schemes with regard to a series of key performance metrics and investigate the strengths and weaknesses of the different fairness measures. Moreover, we study the trade-off between enforcing fairness and optimizing transportation costs to come up with insights for the managers of the supply chain.

Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems

This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach.

Consensus Seeking in Large-Scale Multiagent Systems With Hierarchical Switching-Backbone Topology.

Recent developments in multiagent consensus problems have heightened the role of network topology when the agent number increases largely. The existing works assume that the convergence evolution typically proceeds over a peer-to-peer architecture where agents are treated equally and communicate directly with perceived one-hop neighbors, thus resulting in slower convergence speed. In this article, we first extract the backbone network topology to provide a hierarchical organization over the original multiagent system (MAS). Second, we introduce a geometric convergence method based on the constraint set (CS) under periodically extracted switching-backbone topologies. Finally, we derive a fully decentralized framework named hierarchical switching-backbone MAS (HSBMAS) that is designed to conduct agents converge to a common stable equilibrium. Provable connectivity and convergence guarantees of the framework are provided when the initial topology is connected. Extensive simulation results on different-type and varying-density topologies have shown the superiority of the proposed framework.

Distributed GNE Seeking Strategy for Second-Integrator Multiplayer Systems Over Directed Topologies.

This article studies the generalized Nash equilibrium (GNE) seeking problem of second-integrator multiplayer systems. In particular, each player is endowed with an individual payoff function with respect to collective decision variables, and simultaneously, a coupling inequality constraint and a set constraint are imposed to each player. The players communicate with their local neighbors over a directed topology. To begin with, a distributed-observer-based seeking strategy is synthesized by leveraging a proper composite variable. It is first demonstrated using nonsmooth analysis that the established distributed observer enables each player to accurately estimate the decision variables of others in terms of a strongly connected topology condition. Upon this basis, all the decision variables are then shown to converge to the expected GNE asymptotically borrowing from convex theory. In addition, three extension results are also given under the built GNE seeking framework. First, under the postulation that the velocity information is unavailable, a velocity-free distributed GNE seeking strategy is synthesized for second-integrator systems by implementing a proper auxiliary dynamics. Second, we consider nonlinear Euler-Lagrange systems with unknown inertia parameters and synthesize an improved distributed GNE seeking strategy resorting to an adaptation technique. Third, we focus on integrator chain systems and synthesize a modified distributed GNE seeking strategy using a new composite variable based on a proper coordinate transformation. For three extension cases, we all show in detail the achievement of the GNE seeking objective. Finally, a practical example is simulated to confirm the built GNE seeking results.

Modeling of Frequency Security Constraints and Quantification of Frequency Control Reserve Capacities for Unit Commitment

The high penetration of converter-based renewable energy sources has brought challenges to the power system frequency control. It is essential to consider the frequency security constraints and frequency control reserve requirements in unit commitment (UC). First, a novel extreme learning machine-based method is proposed to approximate the highly nonlinear frequency nadir constraint (FNC) by a set of linear constraints. Second, considering the variation of the frequency insecurity risk under the changing operational condition, we propose to optimize the primary frequency control (PFC) droop gains and reserve capacities in the UC model to provide diverse control efforts in different risk levels adaptively. Third, a secondary frequency control (SFC) reserve capacity quantification method is proposed by combining the Copula theory and distributionally robust optimization technique. The UC simulation is conducted on the IEEE 118-bus system to test the proposed optimal PFC droop gain strategy and SFC reserve capacity quantification method. Simulation results show that the proposed optimal PFC droop gain strategy is better than the traditional fixed PFC droop gain setting on economic efficiency and operational flexibility. Besides, the SFC reserve capacity calculated by the proposed method is more appropriate than the actual SFC reserve capacity in the historical operation.

A Transparent Data-Driven Method for Stability-Constrained Load Restoration Considering Multi-Phase Load Dynamics

Load dynamics significantly complex the system stability behavior during the load restoration process after an outage event. It is highly challenging to model the load dynamics and solve the stability-constrained load restoration problem. In this paper, the load dynamic model considering the inrush phase and enduring phase of the cold load pickup effects are firstly modeled. Then, the load restoration optimization model is formulated with stability constraints, ramping constraints, and system operation models. A transparent data-driven method based on optimal decision trees is developed to address all the short-term stability criteria (including frequency, voltage, and transient stability) considering the inrush phase of load dynamics. A set of accurate, linear, and tractable stability constraints are extracted offline and implemented for fast online decision-making. Numerical studies based on the New-England testing system are conducted to validate the proposed method.

Advanced Equivalent Consumption Minimization Strategy for Fuel Cell Hybrid Electric Vehicles

This paper aims to develop an Advanced Equivalent Consumption Minimization Strategy (AECMS) for efficient fuel cell hybrid electric vehicles (FCHEV). The Equivalent Consumption Minimization Strategy (ECMS) is one of the most feasible solutions for hybrid electric vehicles as it has less complexity and low computational cost in making the optimal control decision. However, typical ECMS designs with fixed gain use could not enhance an optimal energy control when dealing with multi decisive factors for highly non-linear and uncertain systems like FCHEVs. To address this control challenge, the AECMS is developed as the combination of the ECMS and an adaptive equivalence factor to optimally split the energy flow between the fuel cell and battery in the FCHEV. First, a cost function is formulated based on two key objectives which are power consumptions of the fuel cell and battery, the equivalence factor and a set of soft and hard constraints, considering the number of fuel cell start/stop, fuel cell optimal operating range, state of charge (SoC) range, temperature ranges and power limits. Second, the adaptive equivalence factor is newly designed as the combination of states and dynamics of the fuel cell and battery and corresponding weighting factors. Third, fuzzy inferences are derived to adjust online the weighting factors in an adaptive manner according to the working conditions of the energy sources, subsequently improving the overall vehicle energy efficiency and maintaining the battery SoC while prolonging their lifetime. Numerical simulations using a FCHEV model have been carried out under UDDS and HWFET drive cycles to illustrate the superior performance of the AECMS against the traditional ECMS.

Optimal Pose Design for Close-Proximity On-Orbit Inspection

Close-proximity on-orbit inspection is a critical ability to initiate on-orbit servicing operations, required technology for space exploration missions. It is challenging to solve an optimal inspection trajectory planning problem that provides a complete target observation due to major difficulties. First, the inspection requirements must be defined and imposed on the problem as a set of path constraints that result in a nondeterministic-polynomial-time-hard problem. Second, the optimization problem, including highly nonconvex constraints, is very difficult to solve directly using an optimal control solver. Additionally, it requires proper initialization of states and control variables, which is critical in such problems. To overcome these difficulties, this paper proposes a novel formulation and method of solution for a full six-degrees-of-freedom optimal inspection motion planning problem. Optimal inspection trajectories are designed for a rigid-body spacecraft, which performs close, continuous, and complete observation of rigid, nonrotating, and nonaccelerating known targets. The inspection and collision avoidance constraints are defined in explicit forms that rectify the nondifferentiability of the problem and satisfy the inspection requirements. A pseudospectral optimal control solver is implemented to numerically solve the trajectory optimization problem. The proposed methodology is applicable to any robotic inspection mission. Simulations are presented as a validation of the proposed methodology and the achieved optimality.

An AC-Feasible Linear Model in Distribution Networks With Energy Storage

With the increasing deployment of distributed energy resources (DERs), dispatching DERs subject to operational constraints in distribution networks draws much attention. One challenge is the non-convexities in 1) system-wide AC power flow constraints and 2) the individual complementarity constraint of energy storage. To resolve this challenge, this paper studies an AC-feasible linear model in distribution networks with energy storage, including its formulation, analysis, and applications. First, an AC-feasible linear model is formulated as a set of linear constraints on controllable DERs and uncontrollable power demand by 1) converting the non-convex system-wide constraints into linear constraints based on the Brouwer's fixed-point theorem and the second-order Taylor expansion, and 2) replacing the non-convex individual complementarity constraint of energy storage with one properly designed linear constraint. Furthermore, to analyze the power demand level at which the proposed linear model can provide a solution, this paper proposes an examination-based projection method under the Monte Carlo framework to handle projections of thousands of dimensions from linear constraints over time periods. Finally, the potential applications of our AC-feasible linear model are discussed. Numerical experiments are conducted in the IEEE 33-bus and 136-bus test systems to demonstrate the effectiveness of the proposed methods.

Notice of Violation of IEEE Publication Principles: An Efficient Nonlinear Quantized Constant Envelope Precoding for Massive MU-MIMO Systems

Notice of Violation of IEEE Publication Principles <BR><BR>"An Efficient Nonlinear Quantized Constant Envelope Precoding for Massive MU-MIMO Systems," <BR>by R. Liang, H. Li, W. Zhang, C. Liu and Y. Guo, <BR>in IEEE Systems Journal, Early Access <BR><BR>After a careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <BR><BR>This paper contains content from the papers cited below. Credit notices were used, but due to the absence of quotation marks or offset text, the copied content is not clearly referenced or specifically identified. <BR><BR>"VLSI Design of a 3-bit Constant-Modulus Precoder for Massive MU-MIMO," <BR>by O. Castañeda, S. Jacobsson, G. Durisi, T. Goldstein and C. Studer, <BR>in the Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), May 2018 <BR><BR>"Quantized Precoding for Massive MU-MIMO," <BR>by S. Jacobsson, G. Durisi, M. Coldrey, T. Goldstein and C. Studer, <BR>in IEEE Transactions on Communications, vol. 65, no. 11, pp. 4670-4684, November 2017 <BR><BR> <br/> Massive multiuser multiple-input&#x2013;multiple-output (MU-MIMO) systems are foreseen as the key technology in next-generation wireless communication systems. However, many radio-frequency (RF) chains will require high power consumption and lots of hardware cost. One of the practical solutions is using low-resolution discrete phase shifters (PSs) for each antenna and RF chain. This article designs a nonlinear quantized constant envelope precoding algorithm for MU-MIMO systems with low-resolution discrete PS at the base station. In this algorithm, the quantized constant envelope precoding problem is presented as a nonconvex optimization problem. The multiuser interference is minimized by solving the optimal precoded vector and the associated precoding factors. First, we consider relaxing the nonconvex constraint on the 1-bit quantized constant envelope precoding to a continuous set of convex constraints on the unit circle. Afterwards, the semidefinite relaxation method is used to tackle the equivalent 1-bit quantized precoding problem. We further extend the algorithm to provide multi-bit quantized constant envelop precoding. Finally, the simulations are carried out under various conditions and compared with the most advanced precoding methods. The results demonstrate that this algorithm achieves a comparable performance to the existing precoding methods. At the same time, the corresponding performance-complexity tradeoff is more conducive to the expansion of the proposed algorithm to the multibit case.

A Single-Loop Algorithm for Weighted Sum Rate Maximization in Multiuser MIMO Systems With Per-Antenna Power Constraints

This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.