Mixed Integer Nonlinear Programming Problem Research Articles

Optimal Task Allocation for Battery-Assisted and Price-Aware Mobile Edge Computing

In this paper, we propose a battery-assisted approach to improve energy efficiency for mobile edge computing (MEC) networks by utilizing the space-time-varying characteristics of electricity price. We formulate a price-aware task allocation problem (PATA) that jointly considers the cost for task computation, the cost of task offloading, and the cost of battery degradation. PATA is seemingly a mixed integer non-linear programming problem. By a graph-based reformulation, solving PATA is mapped to finding minimum cost flows or convex cost flows in the graph. This discovery reveals that the global optimum of PATA is obtained in polynomial time. Performance evaluation manifests that the proposed approach significantly outperforms other approaches.

Joint Power Control and Resource Allocation for Optimizing the D2D User Performance of Full-Duplex D2D Underlying Cellular Networks

D2D communication is a promising technology for enhancing spectral efficiency (SE) in cellular networks, and full-duplex (FD) has the potential to double SE. Due to D2D’s short-distance communication and low transmittance power, it is natural to integrate FD into D2D, creating FD-D2D to underlay a cellular network to further improve SE. However, the residual self-interference (RSI) resulting from FD-D2D and interference arising from spectrum sharing between D2D users (DUs) and cellular users (CUs) can restrict D2D link performance. Therefore, we propose an FD-D2D underlying cellular system in which DUs jointly share uplink and downlink spectral resources with CUs. Moreover, we present two algorithms to enhance the performance experience of DUs while improving the system’s SE. For the first algorithm, we tackle an optimization problem aimed at maximizing the sum rate of FD-DUs in the system while adhering to transmittance power constraints. This problem is formulated as a mixed-integer nonlinear programming problem (MINLP), known for its mathematical complexity and NP-hard nature. In order to address this MINLP, our first algorithm decomposes it into two subproblems: power control and spectral resource allocation. The power control aspect is treated as a nonlinear problem, which we solve through one-dimensional searching. Meanwhile, spectral resource allocation is achieved using the Kuhn–Munkres algorithm, determining the pairing of CUs and DUs sharing the same spectrum. As for the second algorithm, our objective is to enhance the individual performance of FD-DUs by maximizing the minimum rate among them, ensuring more uniform rate performance across all FD-DUs. In order to solve this optimization problem, we propose a novel spectral resource allocation algorithm based on bisection searching and the Kuhn–Munkres algorithm, whereas the power control aspect remains the same as in the first algorithm. The numerical results demonstrate that our proposed algorithm effectively enhances the performance of DUs in an FD-D2D underlying cellular network when compared to the sum rate maximization design.

A PDDQNLP Algorithm for Energy Efficient Computation Offloading in UAV-Assisted MEC

Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) is a promising technology to provide computational services to ground terminal devices (TDs) in remote areas or for emergency incidents with its flexibility and mobility. This paper aims to maximize the UAV’s energy efficiency while considering the fairness of offloading. We formulate this optimization problem by jointly considering the UAV flight time, the UAV 3D trajectory, the TD binary offloading decisions, and the time allocated to TDs, which is a mixed-integer nonlinear programming problem. The problem is transformed into two sub-problems and we propose a PDDQNLP (parametrized dueling deep Q-network and linear programming) algorithm based on the combination of deep reinforcement learning (DRL) and linear programming (LP) to address them. For the first sub-problem, a DRL-based algorithm is used to optimize the TD offloading decisions, the UAV trajectory, and the UAV flight time. The action space is hybrid that contains discrete actions (e.g., binary offloading) and continuous actions (e.g., UAV flight time). Therefore, we parameterize the action space and propose the PDDQN algorithm, which combines the DDPG algorithm for handling the continuous action space and the Dueling DQN algorithm for handling the discrete action space. According to the solution obtained from the first sub-problem, the LP is used to adjust the time allocated to TDs in the second sub-problem. The numerical results show that the PDDQNLP algorithm outperforms its counterparts.

Coalitional Game Based Resource Allocation in D2D-Enabled V2V Communication

The joint resource block (RB) allocation and power optimization problem is studied to maximize the sum-rate of the vehicle-to-vehicle (V2V) links in the device-to-device (D2D)-enabled V2V communication system, where one feasible cellular user (FCU) can share its RB with multiple V2V pairs. The problem is first formulated as a nonconvex mixed-integer nonlinear programming (MINLP) problem with constraint of the maximum interference power in the FCU links. Using the game theory, two coalition formation algorithms are proposed to accomplish V2V link partitioning and FCU selection, where the transferable utility functions are introduced to minimize the interference among the V2V links and the FCU links for the optimal RB allocation. The successive convex approximation (SCA) is used to transform the original problem into a convex one and the Lagrangian dual method is further applied to obtain the optimal transmit power of the V2V links. Finally, numerical results demonstrate the efficiency of the proposed resource allocation algorithm in terms of the system sum-rate.

On the Use of Mobile Power Sources in Distribution Networks Under Endogenous Uncertainty

Mobile power sources (MPSs) have promising potential for spatiotemporal flexibility exchange in power distribution systems (DS). They can be strategically employed to enhance the network resilience when facing the aftermath of high-impact low-probability (HILP) events. This paper proposes a novel service restoration formulation that models and accounts for the endogenous uncertainty in the MPSs routing and scheduling decision making. The proposed restoration model is formulated as a mixed-integer nonlinear programming (MINLP) problem with nonconvex continuous relaxation. We derive computationally tractable linearization procedures to reformulate the MINLP model as an equivalent mixed-integer linear programming (MILP) problem. Case studies on the IEEE 33-node and 123-node test systems demonstrate the role of incorporating endogenous uncertainties in the decision-making process and the effectiveness of the proposed restoration scheme in boosting the DS resilience.

Resilience-oriented comparative study of SOP-based service restoration in distribution systems

Soft open points (SOPs) can perform load shifting and voltage improvement, and are critical to improving distribution service restoration (DSR) during power outages. Although multiple DSR strategies utilizing local resources have been reported, their effectiveness has not been sufficiently studied. To solve this problem and utilize the flexibility of SOP, a comparative study of different strategies for SOP-based DSR is presented in this paper. First, various SOP-based DSR models, including single-source, single-island model (SSM), islanding partition model (IPM) and multi-source collaborative model (MCM), are proposed and formulated as mixed-integer nonlinear programming (MINLP) problems, incorporating static voltage characteristics of loads. Second, to enhance the solution efficiency, mixed-integer second order cone programming is introduced to convert the MINLP problems into easily solvable convex optimization problems. A restorative index is defined to evaluate the effectiveness of various SOP-based DSR strategies. Finally, a comparative simulation analysis of the proposed models on the IEEE 33-bus system illustrates that SOP-based MCM achieves an 94 % power output for distributed energy resources, while exhibiting the lowest RI for the total loads, standing at just 9.5 %. Furthermore, the RI for critical loads consistently remains at 0, demonstrating the superiority of SOP-based MCM in comparison to other strategies.

Specialized scatter search algorithm for optimal transmission switching with voltage control

This article presents a specialized scatter search (SS) algorithm to solve the optimal transmission switching (OTS) problem considering voltage control, with the objective of reducing operational costs. The nonlinear ac operation of the network is considered, and discrete variables are used to represent the states of the lines, positions of the taps of the transformers, and the states of shunt reactive compensators. The resulting formulation is a mixed-integer nonlinear programming problem, which is nonconvex and hard to solve. The proposed SS algorithm manages the discrete variables of the problem, which becomes a nonlinear programming (NLP) problem when the discrete variables are fixed. The NLP problem is then solved by an optimization solver, which returns all other continuous variables of the problem to the SS algorithm. Tests were conducted using eleven benchmark systems. The results indicated that the SS algorithm is efficient for solving the problem.

A differential evolution algorithm for solving mixed-integer nonlinear programming problems

Many engineering optimization problems fall into the category of Mixed-Integer Nonlinear Programming (MINLP) problems, which combine nonlinear relations, constraint conditions, and different types of variables, including continuous, integer, and/or discrete variables. Solving MINLP problems can be a challenging exploration process since their landscape can be composed of many discontinuous feasible parts with different sizes. In this scheme, Evolutionary Algorithms (EAs) often fail to generate enough diversity to explore the discontinuous feasible parts. Consequently, EAs are vulnerable to being attracted to larger discontinuous feasible parts, even if they are not promising regions. In this paper, a new proposal based on two fundamental strategies is presented to improve the performance of the differential evolution algorithm when solving MINLP problems. The first strategy considers a set of “good fitness-infeasible solutions” that contribute to exploring promising regions from infeasible contours. It reduces the vulnerability of the solutions to be attracted to larger discontinuous feasible parts with unpromising objective function values. The second is a composite trial vector generation to improve the combinatorial exploration while ensuring a robust convergence capacity toward the final solution. Sixteen well-known MINLP problems are used in several experiments to evaluate the performance of the proposed algorithm, comparing it to state-of-the-art EAs. The results provided by the proposal show a better performance in terms of quality, robustness, and computational cost.

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.

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.

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.

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.

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.

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.

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.

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.

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.