Nonlinear Programming Problem Research Articles

A Multi-Agent RL Algorithm for Dynamic Task Offloading in D2D-MEC Network with Energy Harvesting.

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms.

SOLVING FUZZY NONLINEAR PROGRAMMING PROBLEMS WITH EXTERIOR PENALTY FUZZY VALUED FUNCTIONS

In this article, we explore the exterior penalty fuzzy valued function method for Fuzzy Nonlinear Programming Problems (FNLPP). We present methods of penalty fuzzy valued function for solving constrained optimization problems by converting to unconstrained optimization problems. Triangular fuzzy numbers are used to represent the problem’s decision variables and coefficients. Using a new fuzzy arithmetic and fuzzy ranking method on the parametric form of triangular fuzzy numbers, the optimal solution of the FNLPP is found by applying the exterior penalty fuzzy valued function method without changing to its equivalent crisp form. We present a numerical example of the suggested method and compare the results to those produced by existing methods

Dynamic modeling and contraction metric-based tube model predictive control for mineral hydraulic collection

Efficient mineral hydraulic collection is a key issue in the mining of deep-sea minerals, where the collection efficiency is related to the lifted fluid velocity and the mineral particle velocity. In this paper, a robust control contraction metric (RCCM)-based tube model predictive control (Tube-MPC) for efficient mineral hydraulic collection is proposed. Firstly, a simplified control model is designed with empirical formula of hydrodynamic forces to avoid the computational burden in solution of the fluid equations. Secondly, a nonlinear programing problem (NLP) for efficiency optimization is formulated to calculate the nominal control law and the optimal state. To address external disturbance and model mismatch from the simplified model, a robust control contraction metric is utilized to calculate the feedback control law to track the optimal state. Finally, numerical simulations and experiments are conducted to verify the mineral hydraulic collection performance of the control strategy.

SMITS: Social and Mobility aware Intelligent Task Scheduling in Vehicular Fog Computing — A Federated DRL Approach

Vehicular fog computing (VFC) has become an enticing research hot spot to provide resources for the Internet of Vehicles (IoV) application requests. Moreover, with the massive expansion of services in vehicular fog networks such as augmented reality, 3-D gaming, and autonomous driving, the allocation of fog computing resources to IoV applications constraining the deadline and energy consumption of the vehicles is becoming challenging. In this paper, we investigate a task scheduling problem in vehicular fog networks to jointly optimize the success rate of vehicular tasks and energy consumption of vehicles by considering the moving paths of the vehicles and the social relationships among the vehicles. In this problem, we model the social relationship among the vehicles based on their communication patterns and social characteristics to improve the success rate of the tasks. We also incorporate the mobility of vehicles using the Markov renewal process (MRP) technique. Initially, we formulate a mixed integer nonlinear programming (MINLP) problem for the proposed problem and further prove it to be an NP-hard problem. To solve the proposed problem, we design a federated deep reinforcement learning (FDRL) mechanism by converting the problem into a Markov decision process (MDP) problem. We compare our proposed algorithm with existing scheduling approaches, and simulation results show that the proposed algorithm performs efficiently for task scheduling problems. The proposed algorithm achieved a substantial improvement of 12% in the maximization of the success rate and 36% in the minimization of the energy consumption compared to the existing algorithms.

A cloud-edge collaborative computing framework using potential games for space-air-ground integrated IoT

As a critical component of space-air-ground integrated IoT, the aerial network provides highly reliable, low-latency and ubiquitous information services to ground users by virtue of their high mobility, easy deployment and low cost. However, the current computation and resource management model of air-ground integrated networks are insufficient to meet the latency demanding of emerging intelligent services such as autonomous systems, extended reality and haptic feedback. To tackle these challenges, we propose a computation offloading and optimization method based on potential game. First, we construct an cloud-edge collaborative computing model. Secondly, we construct Offloading Decision Objective Functions (ODOF) with the objective of minimum task processing latency and energy consumption. ODOF is proved to be a Mixed Inferior Nonlinear Programming (MINLP) problem, which is hard to solve. ODOF is converted to be a full potential game, and the Nash equilibrium solution exists. Then, a computational resource allocation algorithm based on Karush–Kuhn–Tucker (KKT) conditions is proposed to solve resource allocation problem. On this basis, a distributed game-based computational offloading algorithm is proposed to minimize the offloading cost. Extensive simulation results demonstrate that the convergence performance of the proposed algorithm is reduced by 50%, the convergence time is reduced by 13.3% and the average task processing delay is reduced by 10%.

Simultaneous Minimization of Water Age and Pressure in Water Distribution Systems by Pressure Reducing Valves

Pressure reducing valves (PRVs) are essentially used to reduce operational pressures in water distribution systems (WDSs) to minimize water leakage. However, water age in a WDS is an important variable describing the water quality and should be kept as low as possible. Therefore, the aim of this study is to investigate the possibility and potential of simultaneously minimizing both pressure and water age by using PRVs. To determine the optimal location and setting of PRVs, a mixed-integer nonlinear programming (MINLP) problem is formulated with minimization of the sum of the weighted total water age and pressure as the objective function, where the weighting factor can be defined by the user’s preference. The equality constraints consist of the hydraulic equations and water age functions to describe pressure and water age in the distribution network, while the inequality constraints ensure them in the defined operating ranges, respectively. Applying the proposed approach to two case studies, the results show that both water age and pressure can indeed be significantly reduced by the optimized position and setting of the PRVs.

Transmission Expansion Planning Considering Storage, Flexible AC Transmission System, Losses, and Contingencies to Integrate Wind Power

To meet future load projection with the integration of renewable sources, the transmission system must be planned optimally. Thus, this paper introduces a comparative analysis and comprehensive methodology for transmission expansion planning (TEP), incorporating the combined effects of wind power, losses, N-1 contingency, a FACTS, and storage in a flexible environment. Specifically, the optimal placement of the FACTS, known as series capacitive compensation (SCC) devices, is used. The intraday constraints associated with wind power and energy storage are represented by the methodology of typical days jointly with the load scenarios light, heavy, and medium. The TEP problem is formulated as a mixed-integer nonlinear programming (MINLP) problem through a DC model and is solved using a specialized genetic algorithm. This algorithm is also used to determine the optimal placement of SCC devices and storage systems in expansion planning. The proposed methodology is then used to perform a comparison of the effect of the different technologies on the robustness and cost of the final solution of the TEP problem. Three test systems were used to perform the comparative analyses, namely the Garver system, the IEEE-24 system, and a real-world Colombian power system of 93 buses. The results indicate that energy storage and SCC devices lead to a decrease in transmission requirements and overall investment, enabling the effective integration of wind farms.

A business process network efficiency model for handling conflicting information

In today's big data era, where a significant volume of business data is generated daily, managing conflicting information within business process networks is crucial for maintaining operational efficiency. This paper addresses this challenge by proposing an efficiency model for business process networks tailored to handle conflict information, drawing on queuing theory and evidence theory. Firstly, we introduce a novel approach for measuring conflict information based on evidence theory and Pignistic probability transformation theory. Next, we tailor efficiency models for the four fundamental structures found in business process networks: sequential, selective, parallel, and loop structures, using queuing theory to manage conflict information effectively in each scenario. We further extend this approach by conceptualizing virtual business activities, allowing us to view the entire business process network as a sequential structure of virtual business activities, facilitating efficiency measurement across the network. Utilizing these measurements, we formulate the queuing service of the business process network as a nonlinear programming problem aimed at minimizing time, thus determining the optimal service rate for business process activities. Finally, we demonstrate the applicability and effectiveness of our proposed model through an experimental analysis focused on the railway intermodal transportation business process. The experimental results indicate that our model significantly reduces the impact of conflicting information, leading to a measurable improvement in the efficiency of the business process network. Specifically, the model achieves a notable enhancement in the coordination and execution of intermodal transportation activities, thereby streamlining operations and reducing decision-making uncertainties. This structured approach not only addresses the challenge of managing conflicting information within business process networks but also provides a clear framework for understanding and optimizing network efficiency.

Tradeoff Between Age of Information and Operation Time for UAV Sensing Over Multi-Cell Cellular Networks

Unmanned aerial vehicles (UAVs) have a significant potential for sensing applications in further cellular networks due to their extensive coverage and flexible deployment. In this paper, we consider a multi-cell cellular network with a cellular-connected UAV, which senses data with onboard sensors and uploads sensory data to the ground base stations (BSs). To evaluate the freshness of sensory data, we employ the concept of age of information (AoI), which is defined as the time elapsed since the latest successful transmission of sensory data. A lower AoI implies fresher sensory data, which may lead to the increase of UAV operation time. To balance such tradeoff, we aim to minimize the weighted sum of operation time and total AoI for the UAV by jointly optimizing transmission scheduling, BS association, as well as UAV trajectory. The problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve due to the time-varying propagation channels. To this end, we first characterize the average communication performance with statistic channel information, and then develop a search algorithm to obtain the optimal solution via employing the optimal structure as well as convex optimization techniques, while a low-complexity Double Graph based Algorithm (DGA) is developed to obtain a suboptimal solution. Then, by taking into account the site-specific performance and making fast decisions online, we propose a Deep reinforcement Learning Algorithm (DLA). Compared to DGA, DLA can adapt to the specific local environment and obtain a solution more rapidly once the training process is completed. Simulation results show that the proposed algorithms outperform the benchmarks about 30%, and achieve flexible tradeoff between operation time and AoI of UAV sensing, which is not available by considering just one objective.

Joint Service Caching, Resource Allocation and Task Offloading for MEC-Based Networks: A Multi-Layer Optimization Approach

To provide reliable and elastic Multi-access edge computing services, one feasible solution is to federate geographically proximate edge servers to form a logically centralized resource pool. Optimization of such systems, however, becomes challenging. In this paper, we study the problem of maximizing users' QoE in a MEC-based network, through jointly optimizing service caching, resource allocation and task offloading decisions. We formulate a mixed-integer nonlinear programming (MINLP) problem for the task and establish its NP-hardness. To tackle it efficiently, we propose a novel two-stage algorithmic solution based on approximation and decomposition theory. The proposed algorithm achieves high system performance while at the same time, ensures all constraints from different layers are satisfied. Meanwhile, the structure of the algorithm also fits the multi-layer optimizing feature, making it suitable to be implemented at different layers. In addition, we propose a distributed and online version of our mechanism with very limited information exchange between MEC servers, and further demonstrate how the cost of service switches from real MEC systems can be incorporated into our framework. We evaluate our mechanisms through simulations with both synthetic and real-world traces, and results indicate they are effective as compared to representative baseline algorithms.

An optimization model for monthly time-step drilling schedule under planned field production

The field production profile over the yearly horizon is planned for a balance between economy, security, and sustainability of energy. An optimal drilling schedule is required to achieve the planned production profile with minimized drilling frequency and summation. In this study, we treat each possible production process of each well as a dependent time series and the basic unit. Then we ensemble all of them into a tensor. Based on formulated tensor calculation and Lasso regularization, a linear mathematical optimization model for well drilling schedule was developed. The model is aimed at minimizing production profile error while optimizing drilling frequency and summation. Although the model proposed in this work requires more memory consumption to be solved using a computer, it is assured as a linear model and could be numerically globally solved in a stable and efficient way using gradient descent, avoiding complex nonlinear programming problems. Main input data and parameters involved in the model are analyzed in detail to understand the effects of different production parameters on the drilling schedule and production profile. The proposed model in this work can evaluate the manual drilling schedule and automatically generate an optimized drilling schedule for the gas field, significantly reducing development plan formulation time.

A Topology Control Algorithm Taking into Account Energy and Quality of Transmission for Software-Defined Wireless Sensor Network

The efficient use of energy in wireless sensor networks is critical for extending node lifetime. The network topology is one of the factors that have a significant impact on the energy usage at the nodes and the quality of transmission (QoT) in the network. We propose a topology control algorithm for softwaredefined wireless sensor networks (SDWSNs) in this paper. Our method is to formulate topology control algorithm as a nonlinear programming (NP) problem with the objective to optimizing two metrics, maximum communication range, and desired degree. This NP problem is solved at the SDWSN controller by employing the genetic algorithm (GA) to determine the best topology. The simulation results show that the proposed algorithm outperforms the Max Power algorithm in terms of average node degree and energy expansion ratio.

Multi-User Computation Offloading and Resource Allocation Algorithm in a Vehicular Edge Network.

In Vehicular Edge Computing Network (VECN) scenarios, the mobility of vehicles causes the uncertainty of channel state information, which makes it difficult to guarantee the Quality of Service (QoS) in the process of computation offloading and the resource allocation of a Vehicular Edge Computing Server (VECS). A multi-user computation offloading and resource allocation optimization model and a computation offloading and resource allocation algorithm based on the Deep Deterministic Policy Gradient (DDPG) are proposed to address this problem. Firstly, the problem is modeled as a Mixed Integer Nonlinear Programming (MINLP) problem according to the optimization objective of minimizing the total system delay. Then, in response to the large state space and the coexistence of discrete and continuous variables in the action space, a reinforcement learning algorithm based on DDPG is proposed. Finally, the proposed method is used to solve the problem and compared with the other three benchmark schemes. Compared with the baseline algorithms, the proposed scheme can effectively select the task offloading mode and reasonably allocate VECS computing resources, ensure the QoS of task execution, and have a certain stability and scalability. Simulation results show that the total completion time of the proposed scheme can be reduced by 24-29% compared with the existing state-of-the-art techniques.

Packing Soft Polygons in a Minimum Height Rectangular Target Domain

The paper studies packing polygons of variable shapes, regarding the stretching coefficient, in a rectangular target domain of minimum height. Packing objects of a variable shape have a wide spectrum of applications, e.g, in biology, materials science, mechanics, land allocation, and logistics. Interest in these problems is also due to the modeling of the structures of porous media under pressure, e.g., for creating test models of artificial digital cores. Elements of porous media can be deformed under the influence of an external force, but the mass of each particle remains unchanged. This corresponds to conservation of area for the two-dimensional case. Polygonal objects must be completely contained within the target domain (containment constraint) and do not overlap (non-overlapping constraint), provided they have free translations, continuous rotations, stretch transformations, and conserve their area. The phi-function technique is used for an analytical description of the placement constraints for variable shape polygons. Quasi-phi-functions for describing non-overlapping constraints and phi-functions for describing containment constraints are defined. The packing problem is presented in the form of a nonlinear programming model. A solution strategy is proposed, which consists of the following stages: generation of feasible starting points; search for local minima of the problem of packing soft polygons for each starting point using the decomposition algorithm; choosing the best local minimum found at the previous stage. To search for smart starting arrangements, an optimization algorithm for packing original polygons using their homothetic transformations is applied. Decomposition of the problem of packing polygons of variable shapes is based on an iterative procedure that allows reducing a large-scale problem to a sequence of smaller nonlinear programming problems (linear to the number of objects). Numerical examples are provided for oriented rectangles and non-oriented regular polygons. Keywords: packing, polygons, stretch transformation, rectangular container, quasi-phi-functions, optimization, decomposition algorithm.

Biogas upgrading—Computer-aided ionic liquid absorbent design and process evaluation

Biogas is a renewable energy source and needs to be upgraded to biomethane for injection into the natural gas grid or use as fuel. To design ionic liquid (IL) solvents for biogas upgrading, a computer-aided ionic liquid design (CAILD) method and the corresponding process simulation are presented. The UNIFAC-IL model is employed to calculate the solubility of gases in ILs, while group contribution (GC) based models are used to predict the physicochemical properties of ILs. By using the performance index (PI) as the objective function and the structural feasibility and physicochemical properties as constraints, a mixed-integer nonlinear programming (MINLP) problem is formulated and solved by the generate-and-test method. Two IL solvents, [MMPY][Tf2N] (1,3-dimethylpyridinium bis(trifluoromethylsulfonyl)imide) and [MMPY][eFAP] (1,3-dimethylpyridinium tris(pentafluoroethyl) trifluorophosphate), are found to be the optimal IL solvents from 880 IL candidates. To perform the process simulation by using the designed ILs, the parameters for the equations of calculation of required properties are regressed. A sensitivity analysis is performed to find the optimal conditions for the process. Finally, the developed process is compared with the water-scrubbing process for biogas upgrading.

Establishing a hierarchical local market structure using multi-cut Benders decomposition

Local electricity markets (LEMs) such as peer-to-peer (P2P) and community-based markets allow prosumers and consumers to exchange electricity products and services locally. In order to coordinate electricity trading and flexibility services, this paper proposes a hierarchical prosumer-centric market framework with a hybrid LEM and a local flexibility market (LFM). Multi-cut Benders decomposition (MCBD) is employed to decompose the integrated hybrid LEM into a centralized P2P market and multiple community-based markets. The aggregators coordinate energy sources and demands of households in low voltage (LV) distribution networks (DN) as virtual power plants (VPPs) and engage in trading through a P2P market over the medium voltage (MV) DN. In addition, a modified MCBD (M-MCBD) approach is proposed to accelerate the convergence process. The LFM is operated by the distribution system operator (DSO) and is formulated as a mixed-integer nonlinear programming (MINLP) problem which is further relaxed to a mixed-integer second-order cone programming (MI-SOCP) problem. The case study demonstrates that aggregators were able to collaborate on trading within the hybrid LEM to minimize the costs incurred by prosumers within the network. Furthermore, the proposed M-MCBD method improves the scalability of the MCBD by enhancing its convergence speed and accuracy, as demonstrated by testing on problems of varying scales.

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. The code and data are available at https://github.com/cassiebuhler/conservation-dfo.

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

Demand for imaging of large area targets by space-based assets such as constellations of Earth Observation Satellites (EOS) is on the rise for different applications. The area targets coverage cannot be achieved by a single satellite in a single observation opportunity, as the region for imaging spreads wider than the coverage swaths of imaging sensors. Hence, the imaging satellites are scheduled in a cooperative way to achieve maximum coverage of the area in a given planning time horizon. The scheduling algorithms also aim to maximize or minimize some specific objectives of interest while simultaneously complying with all resource constraints for an efficient use of precious space resources. As the current generation satellites are highly agile, there are many ways of choosing an imaging location in the target area for each single observation opportunity of a satellite. Even though the possible imaging region in continuous space is discretized into a finite number of strips for each observation, the huge combinatorial search space formed with all satellites’ imaging opportunities makes the problem intractable. Thus, the area target imaging scheduling is a complex combinatorial NP-hard optimization problem. Many exact and heuristic methods were evolved to provide a solution to this scheduling problem. Even though the exact methods solve the problem to optimality, they are limited to smaller problem instances because of the high computational complexities involved in those methods. More focus is seen in the literature on heuristic approaches as they guarantee scheduling performance with feasible solutions within an acceptable computational complexity. This paper presents our efficient heuristic approach proposed for the scheduling problem for imaging a large area target using a constellation of multiple satellites. Our approach is an extension of a widely used greedy approach in combination with insights from dynamic programming. In this paper, first we addressed the scheduling problem by describing it in detail and formulating it into a non-linear integer programming problem, considering the multi-objectives of achieving maximum coverage and minimum imaging resolution. The solution to the problem comprises two phases, namely the area decomposition phase and the scheduling phase. In the area decomposition phase, the area target is divided into strips dynamically for each observation opportunity of a satellite. Then exact observation period of each strip is computed using a simplified semi-analytical computational method. In the scheduling phase, we applied our heuristic search strategy, namely Forward and Backward Heuristic Search (FBHS) to obtain a near optimal solution within an acceptable computational time. Through the extensive simulations conducted under various scenarios, the effectiveness of the proposed method is verified in comparison with the baseline greedy approach.

Dynamic microgrid formation for resilient distribution systems considering large-scale deployment of mobile energy resources

Microgrids (MGs) are promising solutions to improve power distribution system (PDS) resilience against natural disasters. However, the existing MG formation approaches based on the linearized Distflow (LinDistflow) model always demand MG roots and their corresponding topologies. This can result in an increased number of variables and constraints in the optimization problem, and deteriorate their computational performance. To this end, an adaptive LinDistflow model is proposed based on the single commodity flow model in graph theory in this paper. Specifically, we show that active and reactive powers can be represented as commodities, which are sent from one node to each of its adjacent nodes in the graph. Then, the power flow and nodal voltage calculation based on the commodity flow only requires adjacent node information of the original topology rather than various MG topologies caused by the dynamic deployment of mobile energy resources (MERs). Furthermore, by incorporating the adaptive LinDistflow model as constraints, a dynamic MG formation approach is proposed for resilient load restoration considering large-scale MER deployment. The problem is formulated as a mixed-integer nonlinear programming problem (MINLP). A linearization technique is proposed based on the propositional logic constraints. It employs the propositional logic that partitions the solution space into two separated regions. Accordingly, the region that the solution lies in can be selected linearly. The effectiveness of the proposed approach is demonstrated based on the IEEE 37-Node, 123-Node and 8500-Node Test Feeders.

Handling noise and overfitting in surrogate models based on non-uniform rational basis spline entities

This paper proposes a general and systematic approach to generate a surrogate model based on non-uniform rational basis spline (NURBS) hyper-surfaces as a solution of a constrained non-linear programming problem, which is solved through a gradient-based algorithm by considering two formulations. The first formulation, which is the general one, is prone to the curse of dimensionality. The second one separates dimensions in the NURBS domain and allows saving computational time and resources. The optimisation process consists of three steps, which are solved sequentially. Each step is characterised by different design variables and solving strategies. The gradient of the cost function, for both formulations and for each optimisation step, is derived analytically by exploiting the properties of NURBS entities, hence enhancing computational efficiency and accuracy. One of the main features of the presented methodology lies the incorporation of a smoothing term in the problem formulation. This term plays a crucial role in controlling overfitting phenomenon and attenuating local oscillations within the dataset. These oscillations may be due to various sources, such as inherent noise, model instabilities, measurement uncertainties, or numerical precision limitations. The effectiveness of the proposed approach is tested on both analytical benchmark problems and real-world engineering problems taken from the literature.