Nonlinear Programming Problem Research Articles

Distributed Multi-Agent Approach for Achieving Energy Efficiency and Computational Offloading in MECNs Using Asynchronous Advantage Actor-Critic

Mobile edge computing networks (MECNs) based on hierarchical cloud computing have the ability to provide abundant resources to support the next-generation internet of things (IoT) network, which relies on artificial intelligence (AI). To address the instantaneous service and computation demands of IoT entities, AI-based solutions, particularly the deep reinforcement learning (DRL) strategy, have been intensively studied in both the academic and industrial fields. However, there are still many open challenges, namely, the lengthening convergence phenomena of the agent, network dynamics, resource diversity, and mode selection, which need to be tackled. A mixed integer non-linear fractional programming (MINLFP) problem is formulated to maximize computing and radio resources while maintaining quality of service (QoS) for every user’s equipment. We adopt the advanced asynchronous advantage actor-critic (A3C) approach to take full advantage of distributed multi-agent-based solutions for achieving energy efficiency in MECNs. The proposed approach, which employs A3C for computing offloading and resource allocation, is shown through numerical results to significantly reduce energy consumption and improve energy efficiency. This method’s effectiveness is further shown by comparing it to other benchmarks.

Trajectory optimization and tracking control of free-flying space robots for capturing non-cooperative tumbling objects

This paper investigates the problem of capturing non-cooperative tumbling objects by free-flying space robots. To solve the two challenges of task constraints and base-manipulator coupling, a pseudospectral method based trajectory optimization and a reinforcement learning based tracking control are proposed for the free-flying space robots. Multiple constrains, including dynamics, field of view and obstacle avoidance, are considered in trajectory optimization. The adaptive segmented Radau pseudospectral method is used to discretize the energy-optimal trajectory problem into a nonlinear programming problem. By adaptively dividing the global time interval into multiple subintervals, higher-order interpolation polynomials are avoided. A reinforcement learning based parameter tuning method is proposed for the base controller to suppress the reaction torque caused by the manipulator. Numerical simulations and experiments on air-bearing testbed verify the effectiveness of our methods in terms of planning efficiency and tracking precision.

Deep reinforcement learning based trajectory design and resource allocation for task-aware multi-UAV enabled MEC networks

Computing tasks in the air is an important form of mobile edge computing (MEC) to improve the quality of service and enhance network coverage. In this paper, we investigate a multi-UAV cooperative computing model and massive devices access scenario in a service area without infrastructure. There are various types of ground devices with different tasks. Moreover, we consider that the UAV executing tasks of devices need to cache the content that task required. Therefore, we propose a multi-UAV enabled MEC network based on task awareness where each UAV caches some programs to execute tasks offloaded from devices. To minimize completion time, a joint UAV trajectory design, access decision and resource allocation problem is formulated. To address this intractable mixed integer non-linear programming problem, a multi-agent trajectory design and resource allocation (MATR) algorithm is proposed, where the multi-agent deep deterministic policy gradient (MADDPG) is applied. Considering the complexity of high-dimensional continuous action space, we introduce the particle swarm optimization (PSO) algorithm to jointly optimize access decisions, and computation resource allocation to reduce action space. In addition, we discuss the impact of the size of UAV cache space and the location of ground devices on the completion time. Simulation results show that the MATR algorithm can significantly reduce the completion time compared to the baselines.

Trajectory optimization for collaborative recovery of parafoil systems using unmanned vessel

Traditional trajectory optimization methods for the parafoil system set fixed-point landing as the objective. However, in recent payload fairing recovery missions, the recovery system comprising two parafoils is collaboratively recovered by a mobile vehicle, posing new challenges to the current trajectory optimization technique. In order to recover two parafoil systems autonomously with an unmanned surface vessel, this paper presents a trajectory optimization framework composed of three following component processes consecutively. Firstly, a feasibility judgment algorithm based on reachable boundary estimation is designed to determine the possibility of recovering two parafoil systems. Secondly, the decoupled-then-simultaneous strategy is proposed to enhance the convergence of solving the collaborative recovery problem. Thirdly, the finite-element collocation approach is utilized to convert the formulated trajectory optimization problems into nonlinear programming (NLP) problems, which are solved by a highly efficient NLP solver. Simulation results show that the proposed trajectory optimization framework can efficiently generate the optimal trajectory for recovering two parafoil systems with a vessel.

An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

Comparing perspective reformulations for piecewise-convex optimization

We aim at generalizing formulations for non-convex piecewise-linear problems to mathematical programs whose non-convexities are only expressed in terms of piecewise-convex univariate functions. This is motivated by solving Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique. We theoretically and computationally compare different formulations, showing that, unlike in the linear case, they are not equivalent when perspective reformulation is applied to strengthen the formulation of each single segment.

Multi-IRS-Aided Millimeter-Wave Multi-User MISO Systems for Power Minimization Using Generalized Benders Decomposition

Difficulties in controlling IRSs to form the optimized passive beamforming have rarely been considered in intelligent reflecting surface (IRS)-aided systems, which are summarized as follows: 1) sending the optimized passive precoding vectors to the IRS controller incurs significant control overheads; 2) implementing the optimized passive precoding needs to set massive modes in the IRS control circuit. To address these issues, we investigate codebook-based passive beamforming for multi-IRS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems, where the control overheads are reduced to several scalars and the number of modes set in the IRS control circuit is reduced to that of codewords. Moreover, we formulate a joint passive and active precoding problem in the multi-IRS-aided mmWave MU-MISO system as a mixed-integer nonlinear programming (MINLP) problem, and then develop a generalized Benders decomposition (GBD)-based joint passive and active precoding algorithm. The proposed algorithm offers near-optimal performance (≥ 99.9%) with significantly-reduced computational complexity. Simulation results show that the proposed algorithm achieves energy savings of up to 50% and 95%, compared to the benchmark by the maximum ratio transmission and that without IRSs, respectively. In addition, the energy savings increase with the number of reflecting elements packed on each IRS as well as that of codewords.

Height-Fixed UAV Enabled Energy-Efficient Data Collection in RIS-Aided Wireless Sensor Networks

Wireless sensor nodes (SNs) are usually energy-limited, a low energy efficiency of SN may be caused by the occlusion of transmission link in the unmanned aerial vehicle (UAV)-enabled data collection. Reconfigurable intelligent surfaces (RISs) provide potential communication opportunities by reflecting and enhancing the signal, thus increasing SNs’ energy efficiency. This paper investigates energy-efficient data collection aided by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> RIS elements, where a height-fixed and flight time-constrained UAV is considered as the collector, a tractable air-to-ground channel model is established considering the cascaded RIS channel and time-varying trajectory of UAV, and energy consumption of SNs is minimized. Specifically, coupling two intractable fourth-order moment variables, the air-to-ground channel model is processed into an easily computable expression through the Gamma function. Furthermore, based on the proposed two RIS deployment schemes, maximum energy consumption of SNs minimization problem is formulated as a non-convex mixed-integer nonlinear programming (NMNP) problem with optimization of UAV trajectory and SNs wake-up schedules. Additionally, through the slack technique and Taylor expansion, the NMNP problem is decoupled as linear programming and quadratically constrained quadratic programming, and an effective algorithm is designed to obtain the sub-optimal solution. Simulations prove the validity of our algorithm and RIS deployment insights are given for SNs energy saving.

Joint Task Offloading and Resource Allocation for Fog-Based Intelligent Transportation Systems: A UAV-Enabled Multi-Hop Collaboration Paradigm

Unmanned aerial vehicles (UAVs) have been widely used in Intelligent Transportation Systems (ITS) due to their rapid deployment and high mobility, which are considered as a promising solution to expand the scope of communication, especially in inaccessible areas. However, there is a lack of a universal and extensible multi-hop collaboration model in the existing research on UAV-involved ITS. In this paper, we innovatively introduce a novel UAV-enabled multi-hop collaborative fog computing (FC) system model, in which several moving UAVs with unpredictable locations provide effective and efficient communication and computation services for ground user equipments (UEs). With this model, we mathematically formulate a joint user association, UAV association, task offloading, transmission power, computation resource allocation, and UAV location optimization problem, which is a mixed integer nonlinear programming (MINLP) problem and challenging to deal with. To solve the non-convex problem, we propose a novel multi-hop collaborative algorithm to derive the optimal task offloading and resource allocation decisions for each UAV. Simulation results demonstrate the superiority of the UAV-enabled multi-hop collaborative FC system and validate the effectiveness of the proposed scheme.

IDESS: a toolbox for identification and automated design of stochastic gene circuits.

One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Coordinated Optimization of Emergency Response Resources in Transportation-Power Distribution Networks Under Extreme Events

The proliferation of electric vehicles (EVs) and the increasing interdependence across power distribution networks (DNs) and transportation networks (TNs) have increased the complexity and vulnerability of the two systems in extreme circumstances. As the interdependence of two infrastructures tightens over time, it is viewed as a dire necessity to strengthen the resilience of the coordinated transportation-power distribution networks (TDNs) against natural disasters. This paper constructs a coordinated optimization method of TN traffic link reversing, DN line switching, and fast charging pile management, to improve the TDN performance in the emergency response stage after disasters. A dynamic TN model and a multi-period DN model are integrated in TDN modeling to capture flow propagations and state variations among time intervals. The coordinated optimization for TDN emergency response is designed as a mixed-integer nonlinear programming (MINLP) problem with high-order objective functions and nonlinear constraints to minimize TN travel costs and DN active and reactive power shortages. An accuracy-aware adaptive piecewise linearization approach combined with Gray code-based encoding is utilized to improve the computational efficiency for solving the TDN optimization problem. Numerical simulations show that the TDN performance is enhanced by coordinating various DN and TN resources, as compared with those of separate and conventional topology controls. The proposed TDN solution method has significantly reduced the computation time for managing extreme conditions while guaranteeing the accuracy of the results as compared with those of the nonlinear model and the linearized model by uniform piecewise linearization.

Maximizing the Connectivity of Network Slicing Enabled Internet of Vehicle With Differentiated Services

The advent of 5G opens up hitherto unimagined opportunities for delivering the much-anticipated Internet of Vehicles (IoV). There are two typical types of services in IoV, i.e., safety service and non-safety service. However, the existing IoV framework cannot efficiently support the differentiated IoV services. In addition, maximizing the number of accessed vehicles/users is another critical issue in IoV, especially in the dense urban area. To address these problems, in this paper, we utilize the emerging network slicing technology to support different services and employ Non-Orthogonal Multiple Access technology (NOMA) to help increase the connectivity. In particular, for the safety service, we take advantage of the finite blocklength capacity to correctly record the delay. Our goal is to maximize the connectivity of users by jointly considering the user association and their beamforming vectors, under the restrictions of limited physical resource. The problem is formulated as a Mixed-Integer Nonlinear Programming problem (MINLP). To tackle the intractable MINLP, we propose a two-stage scheme. Firstly, we exploit efficient approaches to solve the beamforming problem, i.e., successive convex approximation, semidefinite relaxation and second-order cone programming. Secondly, we propose a low-complexity Greedy User Association (GUA) algorithm to solve the user association problem. Finally, comprehensive simulations verify that our proposed GUA algorithm is close to global optimal solution and outperforms the benchmark schemes.

A Tractable Linearization-Based Approximated Solution Methodology to Stochastic Multi-Period AC Security-Constrained Optimal Power Flow

The growing presence of renewable energy sources (RES), energy storage systems (ESSs) and flexible loads (FLs) in power systems necessitates a new approach to N-1 security in day-ahead operation planning considering stochasticity and time coupling. To this end, a comprehensive approach based on stochastic multi-period AC security-constrained optimal power flow (S-MP-AC-SCOPF) was proposed recently in a form of a large-scale non-linear programming problem, which is not scalable. This paper proposes the first-time new tractable solution methodology for the most complete AC-SCOPF problem to date: S-MP-AC-SCOPF. As other main novelty, the proposed methodology achieves tractability by solving sequentially a limited number of different linear approximations of the full S-MP-AC-SCOPF problem. These linear approximations differ in terms of: state dependency regarding losses approximation, carefully reduced sets of constraints or tightening of critical constraints. The performance of the methodology is demonstrated in power system models of Sweden and Portugal. Extensive numerical experiments have shown that the methodology is able to reduce progressively until complete removal the number of violated thermal or voltage constraints. It leads to reasonably accurate solution with small optimality gap within few iterations and is at least 85% faster than the competitor IPOPT solver.

Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Optimizing multistage processes, such as distillation or absorption, is a complex mixed-integer nonlinear programming (MINLP) problem. Relaxing integer into continuous variables and solving the easier nonlinear programming (NLP) problem is an optimization idea for the multistage process. In this paper, we propose a relaxation method based on the efficiency parameter. When the efficiency parameter is 1 or 0, the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage. And non-integer efficiency represents partial existence. A multi-component absorption case shows a natural penalty for non-integer efficiency, which can assist the efficiency parameter converging to 0 or 1. However, its penalty is weaker than the existing relaxation models, such as the bypass efficiency model. In a simple distillation case, we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.

Transfers to Frozen Orbits Around Planetary Moons Using Manifolds of Averaged Dynamics

A novel methodology is proposed to design the transfers from halo orbits to low-eccentricity, high-inclination frozen orbits around planetary moons, with applications to the Jupiter-Europa system. The manifolds of averaged dynamics are used to reduce the transfer ΔV cost. A one-degree-of-freedom dynamical model around Europa, incorporating effects of Jupiter’s third-body perturbation and Europa’s nonspherical gravity, is established via double-averaging. Europa frozen orbits are calculated and classified into five groups according to their stability and locations in the phase space. The phase portraits indicate that low-eccentricity, high-inclination frozen orbits are always unstable, and manifolds are found to be associated with them. The transfers from halo orbits to these frozen orbits are designed by inserting into the manifolds first and then following the natural evolution until the arrival at the target frozen orbit. A nonlinear programming problem is established to optimize the transfers. Through the analytical derivations, the optimization model is simplified and finally solved by the particle swarm optimization algorithm. The efficiency of the proposed methodology is demonstrated by numerical experiments, which indicate that the transfer ΔV cost can be reduced by approximately 10 to 40% at the expense of longer transfer time.

An optimization model for the layout of a branching water distribution system

This paper presents an optimization model for the layout of a branching water distribution system. The goal is to minimize construction costs while meeting the system's demands. The study utilizes the general algebraic modeling system (GAMS) to optimize a non-looping water distribution system. The methodology involves determining the existence and diameter of connections between demand nodes. The optimization problem is formulated as a mixed-integer non-linear programming (MINLP) problem. A simplified layout is used to illustrate the constraints and validate the model. The explicit model implemented in GAMS yields optimal solutions and demonstrates the effectiveness of the approach. The results highlight the decisions on connection existence, flow, and pipe diameter, contributing to cost minimization. The findings from this study provide insights for optimizing the design of branching water distribution systems and reducing construction costs.

Optimal service provisioning in IoT fog-based environment for QoS-aware delay-sensitive application

This paper addresses the escalating challenges posed by the ever-increasing data volume, velocity, and the demand for low-latency applications, driven by the proliferation of smart devices and Internet of Things (IoT) applications. To mitigate service delay and enhance Quality of Service (QoS), we introduce a hybrid optimization of Particle Swarm (PSO) and Chemical Reaction (CRO) to improve service delay in FogPlan, an offline framework that prioritizes QoS and enables dynamic fog service deployment. The method optimizes fog service allocation based on incoming traffic to each fog node, formulating it as an Integer Non-Linear Programming (INLP) problem, considering various service attributes and costs. Our proposed algorithm aims to minimize service delay and QoS degradation. The evaluation using real MAWI Working Group traffic data demonstrates a substantial 29.34% reduction in service delay, a 66.02% decrease in service costs, and a noteworthy 50.15% reduction in delay violations compared to the FogPlan framework.

Joint mixed-timescale optimization of content caching and delivery policy in NOMA-based vehicular networks

Recently, the development of Internet of Vehicles (IoV) and the increasing popularity of video applications have led to the fast-growing in-car video demand causing numerous challenges in wireless networks. Pre-caching and non-orthogonal multiple access (NOMA) have been regarded as two effective techniques to alleviate the mentioned challenge. In this paper, we propose a cache-aided cooperative transmission to maximize the quality of service (QoS) in the NOMA-based vehicular network. A QoS-oriented joint optimization problem is formulated, which incorporates power allocation, content caching, and delivery strategy. Considering, on the one hand, the slow update rate of cache content and, on the other hand, frequent handovers of vehicles between different transmitters, a mixed-timescale optimization is proposed where the serving cache is updated in a long-term phase, while content delivery and power allocation are optimized in a short-term phase. In the proposed approach, content caching is determined based on future user requests, vehicle tracking, and other delivery information. To make this possible, we leverage a substantial number of stochastic samples to approximate content caching in the long-term caching phase. Due to the NOMA-based transmission and integral variables, the setting leads to a Mixed Integer Non-Linear Programming (MINLP) problem, which is NP-hard. To solve this problem, an iterative method based on sample average approximation (SAA) and Successive Convex Approximation (SCA) is applied. Simulations demonstrate that the proposed algorithm can achieve better QoS than other recently proposed transmission schemes.

Neutrosophic hyperbolic programming strategy for uncertain multi-objective transportation problem

This paper suggests a neutrosophic hyperbolic programming approach based on the hyperbolic membership function to get an efficient solution for an uncertain multi-objective transportation problem where the uncertain normal distribution presents uncertainty. This technique provides flexibility to the decision-maker to select various confidence levels according to his/her own choice and analyze the satisfaction percentage of the obtained optimal compromise solution along with its truth, indeterminacy, and falsity values. In this approach, the parameters are changed from uncertain to crisp by using the inverse measure theorem, and the neutrosophic non-linear hyperbolic membership functions are used to convert the whole model into a non-linear programming problem in a neutrosophic environment. The advantages of our recommended method in real-world applications are effectively illustrated by a numerical illustration. This illustration also makes it easier to compare the results attained using our suggested strategy to those obtained using the methodologies put forward by Uddin et al. (2021) and Miah et al. (2022). Also, MATLAB software (version R2019a,64bit(win64)) is used to develop the code for the solution of this non-linear uncertain multi-objective transportation problem.

Distributed safe trajectory optimization for large-scale spacecraft formation reconfiguration

This paper presents a distributed trajectory optimization algorithm for the reconfiguration of large-scale spacecraft formation, which uses a low thrust propulsion system to safely guide the spacecraft formation to a desired formation. Formation reconfiguration is formulated as a trajectory optimization problem with complex constraints, and the relative motion is accurately described by a nonlinear relative dynamics considering J2 perturbation. The collision avoidance constraint is convexified into a tangent plane to ensure the accuracy of the solution. The resulting nonlinear trajectory optimization problem is solved by applying the hp-adaptive pseudospectral method to convert it into a nonlinear programming problem. In order to overcome the disadvantage of huge computation of centralized algorithm considering collision avoidance, “predicted trajectory” is introduced to transmit information between spacecraft, and the parallel computing is implemented. Finally, a numerical simulation is given to verify the computational efficiency and collision avoidance effectiveness of the proposed distributed algorithm.