Integer Nonlinear Optimization Problem Research Articles

A distributed randomized method for the identification of switched ARX systems

SummaryThe identification of switched systems amounts to a mixed integer nonlinear optimization problem, where the continuous variables are associated to the model parameterizations of the different modes, and the discrete ones are related to the switching signal (each data sample is assigned to a mode, and switching occurs when the mode assignment changes over time). In the batch form of the identification problem, the combinatorial complexity increases exponentially with the size of the training set, which makes the precise identification of the switching signal the most challenging task in the identification problem. To tackle this complexity we propose a distributed optimization approach, based on the solution of multiple instances of a much simpler problem, where switching can occur only at specific time instants (different for each subproblem), and an information sharing mechanism that preserves likely switching times to improve the local solutions. We employ an adapted version of a previously developed randomized algorithm to solve the individual subproblems. Another important feature of the proposed method is an a posteriori heuristic correction method, that is applied to further refine the switching locations based on the estimated local models before the information sharing phase. The performance of the proposed algorithm is analyzed and compared with other methods on synthetic datasets.

Lua APIs for mathematical optimization

In this paper we present our Lua programming language libraries that enable modeling and solving mixed integer linear and nonlinear mathematical optimization problems. On one side, these libraries provide a framework for developing algorithms written in Lua that use certain well known solvers within more complex procedures. On the other side, they facilitate the transformation of both input and output data of a mathematical programming problem, in order to compute the standardized coefficients that have to be transmitted to the solvers or prepare solution of solved problems for further data processing. Both of these use cases, together with Lua programming language simplicity, versatility and performance, make Lua a suitable programming language for use in scientific and engineering researches.

Multiagent Reinforcement Learning-Based Orbital Edge Offloading in SAGIN Supporting Internet of Remote Things

We investigate a computing task scheduling problem in space-air-ground integrated network (SAGIN) for Internet of remote Things (IoRT). In the considered scenario, the unmanned aerial vehicles (UAVs) collect computing tasks from IoRT devices and make offloading decisions, in which the tasks can be computed at the UAVs or offloaded to the low earth orbital (LEO) satellite. The optimization objective is to design offloading strategies for each UAV that maximum the number of tasks satisfies delay constraint and reduces the energy consumption of UAVs. We formulate this problem as a nonlinear integer optimization problem, and remodel it as a stochastic game to solve it. To copy with the dynamic and complexity environment, we propose a learning-based orbital edge offloading (LOEF) approach which can coordinate all UAVs to learn the optimal offloading strategies. This method is based on the Actor-Critic framework of multi-agent reinforcement learning, the Actor observes the environment and output the current offloading decision, the Critic evaluates the action of the Actor and coordinate the actions of all UAV to increase the reward of system. The simulation results show that the proposed offloading strategy converges fast, increases the number of satisfying the delay constraints tasks and the energy utilization of UAVs compared with the baseline strategies.

Coalitional game based sub-channel allocation for full-duplex-enabled mmWave IAB network in B5G

The combination of full-duplex communication (FDC) and millimeter wave integrated access and backhaul (mmWave IAB) is a highly implementable technique in beyond 5G era. However, the technical challenges such as sub-channel allocation and interference coordination must be effectively handled before the attractive benefits of the commercial implementation are enjoyed. In particular, the multiple user interference (MUI) is caused when the same sub-channel is shared by the concurrent links sourced from different transmitters, and the residual self-interference (RSI) is resulted from self-interference cancellation (SIC) in FDC. To this end, a coalitional game based sub-channel allocation mechanism is proposed for the full-duplex-enabled mmWave IAB network to maximize the total actual achievable rate. Firstly, the maximization problem of the sum actual achievable rate is formulated as an integer non-convex and non-linear optimization problem under the constriction of MUI and RSI, which is a non-polynomial hard (NP-Hard) problem, and it is intractable to obtain the optimal solution. Secondly, the formulated problem is transformed as a cooperative game, and a coalitional game based sub-channel allocation (CGSA) algorithm with lower computational complexity is proposed to obtain the sub-optimal solution. Thirdly, the properties of the proposed CGSA algorithm are discussed and analyzed from the aspects of stability and convergence, and it is proved that the final coalition partition formed by the proposed CGSA algorithm is Nash-stable. Fourthly, the proposed CGSA algorithm is compared with the reference algorithms under different scenarios, extensive simulations show that superiorities of the proposed CGSA algorithm are obvious including sum of achievable rate, number-ratio of user equipments with satisfied quality-of-service (QoS)requirement and iterations of algorithm convergence.

Solving the 1-median problem on a network with continuous demand and demand surplus

In this paper we address the problem of locating a delivery business with a production capacity. It is a variant of the 1-median location problem on a network, in which demand is assumed to be distributed along the edges and nodes of the network. However, instead of assuming that all the demand must be served, the location for a facility is sought minimizing the expected distance to a fraction of the demand.The problem is expressed as a Mixed Integer Nonlinear Optimization problem, solved by means of a geometric Branch and Bound algorithm.

Resource Allocation for NOMA-Enabled Cognitive Satellite–UAV–Terrestrial Networks With Imperfect CSI

Recently, non-orthogonal multiple access (NOMA)-enabled cognitive satellite-unmanned aerial vehicle (UAV)-terrestrial networks have attracted extensive attention for the advantages of enhancing spectrum efficiency and coping with the exponential growth of access users. In this paper, we propose a joint subchannel assignment and power allocation algorithm for NOMA-enabled cognitive satellite-UAV-terrestrial networks to further enhance the transmission performance, where imperfect channel state information is taken into consideration. Specifically, we formulate a mixed integer non-linear programming resource allocation problem to optimize the sum rate of the secondary network, in which the demands of the interference temperature constraint for primary users, the minimum transmission rate of each secondary user, the maximal transmitter power of the UAV, and the maximal number of secondary users that each subchannel can serve are satisfied. To tackle this tough non-convex problem, we first decouple it into two subproblems, namely, subchannel assignment and power allocation. Next, a heuristic subchannel assignment algorithm and a Taylor series and successive convex approximation-based power allocation algorithm are designed to solve the above subproblems, respectively. By alternately optimizing the sum rate of the secondary network, we finally solve the mixed integer non-linear programming optimization problem. Numerical results reveal the impacts of key parameters on system performance and indicate that our proposed scheme outperforms benchmarks in large-scale networks.

Data-driven multi-period modeling and optimization for the industrial steam system of large-scale refineries

Steam system modeling and optimization contributes toward low energy consumption for large-scale industrial refineries. However, formidable challenges have been generated by steam demand variation, the optimization of CO2 emissions and outsourced steam, the uncertainty of sudden equipment failures, and the introduction of new equipment. To address this issue, this work presents a novel steam system model with periodic process steam demand. The multiple cost factors of CO2 emission treatment and outsourced steam are considered and formulated as a mixed integer nonlinear programming optimization problem. A strategy to discretize the uncertainty of equipment failure into three main scenarios is proposed. The proposed model, strategy, and introduction of new equipment are demonstrated on three cases of industrial refinery steam systems. In case 1, the optimized operating costs have reduced by 1.5%. In case 2, the optimized average operating cost is 1,135,402 CNY/h. In case 3, with the introduction of the aromatics turbocharged turbine (ATT) and the letdown valve, the optimized operating costs are 1,292,182 CNY/h and 1,316,227 CNY/h respectively, confirming the feasibility of introducing ATTs.

Energy Management Capability in the Reconfigurable Distribution Networks with Distributed Generation for Minimization of Energy Loss

One of the approaches to improve operation indices, such as power loss and reliability, is to smoothen voltage profiles. Energy management of generation units and network reconfiguration are two methods to achieve this. Hence, the latter is presented in this paper in a distribution with distributed generation units. To this end, an objective function is formulated aiming to minimize power loss and enhance the operating situation of the network. This problem is subject to various constraints and limits such as AC power flow equations, operation limits, planning model, and operation model of distributed generations. It is an integer nonlinear optimization problem and is solved using the crow search algorithm and the optimal solution is obtained. Two major innovations of the study include modeling generation units’ operation and network configuration mathematical expression of operation indicators. The method is applied to a test system and results demonstrate the high performance of this approach in improving the operation of the network. Finding the solution in less time with a satisfying standard deviation are two advantages of the proposed algorithm. Adopting this method, the network operator can reduce power loss through proper management of distributed generation power and optimal scheduling of switches. Moreover, the obtained voltage profile is more desirable in comparison to that of power flow studies.

Fairness in maximal covering location problems

This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) α-fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

Service Routing in Multi-Tier Edge Computing: A Matching Game Approach

Although microservice envisioned as a promising approach for edge applications which can improves the development efficiency and the deployment productivity, it also leads to the operational complexity during service runtime. This leads to the emergence of service mesh, a decided infrastructure layer over microservices for reliable service-to-service communication. However, when migrating the service mesh to the multi-tier edge computing, the corresponding extensions on the top of service mesh is needed to overcome the challenges brought by the multi-tier edge servers, shared microservices and diverse QoS requirements. Therefore, in this paper, we investigate the problem of service routing to achieve the efficient microservice-based service provision in multi-tier edge computing. The objective is to route user requests to the optimal microservice instances with low service delay and resource cost. To this end, we first formulate the service routing problem as an integer non-linear optimization problem, which is NP-hard. Then we map it to a many-to-one matching problem by employing the matching game theory and propose a dependency-aware deferred acceptance algorithm with dynamic quota. The experimental results based on a real-world dataset demonstrate that our proposed algorithm can significantly outperform existing representative algorithms in terms of service delay and resource cost.

Joint patient selection and scheduling under no‐shows: Theory and application in proton therapy

We study how to admit and schedule heterogeneous patients by using simple, interpretable, yet effective policies when capacity is scarce, no‐show behavior is patient‐ and time‐dependent, service duration and reward are deterministic but patient‐dependent, and overtime is costly. Our work is motivated by the aforementioned operational challenges that typically face adopters of new technologies in the healthcare sector. We anchor our study on a partnership with the proton therapy center of Massachusetts General Hospital (MGH), which offers a new radiation technology for cancer patients. We formulate the problem as a nonlinear integer optimization problem. However, as the solution to this formulation lacks both tractability and interpretability, to be relevant to practice, we limit our study to simple and interpretable policies. In particular, we propose a simple index‐based rule and derive analytical performance guarantees for it. We also calibrate our model using empirical data from our partner hospital, and conduct a series of experiments to evaluate the performance of our proposed policy under practical circumstances. The analytical performance guarantees and our numerical experiments demonstrate (a) the strong performance of the proposed policies, and (b) their robustness to various practical considerations (e.g., to potential misspecification of no‐show probabilities). Our results show that our proposed policy, despite being a simple and interpretable index‐based rule, is capable of improving performance by about 20% at an organization such as MGH, and of delivering results that are not far from being optimal across a wide range of parameters that might vary between organizations. This suggests that the proposed policy can be viewed as an effective “one‐fits‐all” capacity allocation rule that can be used in a variety of environments in which operational challenges such as no‐shows and overtime costs need to be navigated using simple and interpretable rules.

Dual Pricing Optimization for Live Video Streaming in Mobile Edge Computing With Joint User Association and Resource Management

Mobile live video streaming is expected to become mainstream in the fifth generation (5G) mobile networks. To boost the Quality of Experience (QoE) of streaming services, the integration of Scalable Video Coding (SVC) with Mobile Edge Computing (MEC) becomes a natural candidate due to its scalability and the reliable transmission supports for real-time interactions. However, it still takes efforts to integrate MEC into video streaming services to exploit its full potentials. We find that the efficiency of the MEC-enabled cellular system can be significantly improved when the requests of users can be redirected to proper MEC servers through optimal user associations. In light of this observation, we jointly address the caching placement, video quality decision, and user association problem in the live video streaming service. Since the proposed nonlinear integer optimization problem is NP-hard, we first develop a two-step approach from a Lagrangian optimization under the dual pricing specification. Further, to have a computation-efficient solution and less performance loss, we provide a one-step Lagrangian dual pricing algorithm by the convex transformation of non-convex constraints. The simulations show that the service quality of live video streaming can be remarkably enhanced by the proposed algorithms in the MEC-enabled cellular system.

Voltage regulation and power loss mitigation by optimal allocation of energy storage systems in distribution systems considering wind power uncertainty

Due to the ever increasing in the energy demand and the growth of the pollution problem, further interest in renewable energy becomes prominent, especially wind energy. However, the intermittent nature of the wind speed results in the system's insecurity problems. Integrating the energy storage system (ESS) optimally is the best so far solution. In this paper, a probabilistic discretizing method is derived and generalized to consider the uncertainties of the wind generators. Moreover, a mixed integer non-linear optimisation problem is constructed comprises three objective functions to be minimized simultaneously. The objectives comprising the total operation and planning cost of ESSs, the average voltage deviation and average power losses. The solving method is a hybrid algorithm incorporates the non-dominated sorting genetic algorithm (NSGAII), multi-objective particle swarm optimisation (MOPSO) and a decision-making algorithm. The aim is to determine the optimal location and sizing of ESSs considering their reactive power capability. 69 radial bus distribution system is adopted to demonstrate the efficacy of the proposed hybrid algorithm and performing some case studies. The simulation results verified the capability of ESSs to enhance the voltage profile and reduce the power losses, notably when reactive power capability is examined.

Intelligent Resource Allocation Schemes for UAV-Swarm-Based Cooperative Sensing

Driven by the development of the smart Internet of Things (IoT), unmanned aerial vehicle (UAV) swarms have been widely applied to implement diverse sensing tasks for many IoT applications. By integrating resources of UAVs, a UAV swarm can collaboratively collect and process massive image data for fast system response. However, it is difficult to reduce the computing delay caused by overlapping sensing operations and insufficient computing resources. In addition, transmission delays among UAVs may be intensified due to limited bandwidth resources. To address the mentioned challenges, we propose a UAV-swarm-based hierarchical network architecture to jointly schedule sensing, computing, and communication resources. Specifically, multiple computing groups that are formed by UAVs execute image processing in a pipeline manner to improve computing resource utilization. In order to reduce task execution time, we formulate a nonlinear integer optimization problem for the coordination of heterogeneous resources. A multiagent reinforcement learning (MARL)-based algorithm is designed to find the optimal joint resource allocation strategy under sensing accuracy constraints. Simulation results demonstrate that our algorithm reduces the task execution time while significantly improving the computing resource utilization.

Buffer-Aware User Selection and Resource Allocation for an Opportunistic Cognitive Radio Network: A Cross-Layer Approach

In this paper, we focus on a cross-layer resource allocation problem for an opportunistic cognitive radio network, where secondary users (SUs) share a primary network’s licensed spectrum only when the primary network is sensed to be idle. We consider cooperative spectrum sensing, where SUs participate in sensing only when a benefit from resource allocation is guaranteed. Number of SUs for cooperative spectrum sensing is an important parameter as it defines both sensing and resource allocation performance. The fusion centre captures interaction between physical layer spectrum sensing, channel condition, and higher layer data buffer while selecting SUs for cooperative sensing. We consider heterogeneous data types at SUs’ data buffers during SU selection to make our system model more general. We form a mixed integer non-linear optimization problem, from which we select SUs’ set for sensing and resource allocation, appropriate sensing thresholds, and corresponding resource allocation parameters. Due to it’s combinatorial nature, the optimization problem is non-trivial. We devise an optimal algorithm to solve the optimization problem. Moreover, we also propose a computationally efficient and near-optimal greedy algorithm with suitable performance bounds. We also show advantage of our proposed optimal algorithms compared to other traditional methods through extensive simulations.

Energy‐efficient computation offloading and resource allocation in delay‐constrained vehicular edge network

SummaryCellular vehicular‐to‐everything (C‐V2X), as a key technology of Internet of Vehicles (IoV), is promised to be enhanced and strengthened to improve road traffic safety and achieve intelligent transportation in 6G era. However, computation‐intensive and latency‐sensitive computation tasks of autonomous driving create a great challenge for the computation and storage limited vehicles. Fortunately, mobile edge computing (MEC) architecture offers a possible solution for the challenge. In this paper, a joint computation offloading and resource allocation algorithm is proposed to solve the computation tasks offloading problem in the scenario of vehicular edge computing network. First, the computation offloading and resource allocation are jointly modeled as a mixed integer nonlinear optimization problem. Aiming at minimizing the total system cost (weighted sum of delay and energy consumption), a particle encoding method and a particle refinement algorithm are proposed based on the compression factor particle swarm optimization, and multilevel penalty function is adopted to deal with the constraints of the objective. Finally, experimental performances validate the effectiveness and feasibility of the proposed algorithm.

Intelligent Reflecting Surface-Aided Device-to-Device Communication: A Deep Reinforcement Learning Approach

Recently, the growing demand of various emerging applications in the realms of sixth-generation (6G) wireless networks has made the term internet of Things (IoT) very popular. Device-to-device (D2D) communication has emerged as one of the significant enablers for the 6G-based IoT network. Recently, the intelligent reflecting surface (IRS) has been considered as a hardware-efficient innovative scheme for future wireless networks due to its ability to mitigate propagation-induced impairments and to realize a smart radio environment. Such an IRS-assisted D2D underlay cellular network is investigated in this paper. Our aim is to maximize the network’s spectrum efficiency (SE) by jointly optimizing the transmit power of both the cellular users (CUs) and the D2D pairs, the resource reuse indicators, and the IRS reflection coefficients. Instead of using traditional optimization solution schemes to solve this mixed integer nonlinear optimization problem, a reinforcement learning (RL) approach is used in this paper. The IRS-assisted D2D communication network is structured by the Markov Decision Process (MDP) in the RL framework. First, a Q-learning-based solution is studied. Then, to make a scalable solution with large dimension state and action spaces, a deep Q-learning-based solution scheme using experience replay is proposed. Lastly, an actor-critic framework based on the deep deterministic policy gradient (DDPG) scheme is proposed to learn the optimal policy of the constructed optimization problem considering continuous-valued state and action spaces. Simulation outcomes reveal that the proposed RL-based solution schemes can provide significant SE enhancements compared to the existing optimization schemes.

A Three-Stage Alternative Optimization Promoting Multi-UAV-Assisted Mobile Offloading

A solution using multiple-relay method is presented to provide an efficient solution using UAV-assisted mobile devices to complete computation offloading tasks, which considers the UAVs in the offloading system to help mobile devices to offload tasks in remote areas. Additionally, a mixed integer nonlinear optimization (MINO) problem is constructed to maximize minimum user computational speed, and a three-stage iterative optimization algorithm is proposed to find a solution of the MINO problem. Simulation experiments are setup to verify the effectiveness of the devised methods, which show that our proposed algorithm and solution is superior to the single UAV method.

Mathematical programming formulations for the optimal stratification problem

This paper proposes two integer linear programming formulations to solve the optimal stratification problem (OSP). In this problem, once given the number of strata and the total sample size, the cutoff points and sample allocation should be determined jointly to minimize an expression of variance and to solve the OSP corresponding to an integer nonlinear optimization problem. One proposed formulation determines the optimal cutoff points considering classical allocation methods from the literature, and a second formulation produces the global optimum regarding the determination of the cutoff points and the sample allocation to the strata. Both formulations were implemented using Gurobi solver and applied to a set of 20 datasets from the literature, with population sizes ranging from 91 to 16,057, considering six different scenarios concerning the number of strata and sample sizes. The results obtained indicate that the formulations are a good alternative for the resolution of the OSP.

UAV Placement and Resource Allocation for Intelligent Reflecting Surface Assisted UAV-Based Wireless Networks

We design an unmanned aerial vehicle (UAV) based wireless network with wireless access and backhaul links leveraging an intelligent reflecting surface (IRS). This design aims to maximize the sum rate achieved by ground users (GUs) through optimizing the UAV placement, IRS phase shifts, and sub-channel assignments considering the wireless backhaul capacity constraint. To tackle the underlying mixed integer non-linear optimization problem (MINLP), we first derive the closed-form IRS phase shift solution; we then optimize the sub-channel assignment and UAV placement by using the alternating optimization method. Specifically, we propose an iterative sub-channel assignment method to efficiently utilize the bandwidth and balance bandwidth allocation for wireless access and backhaul links while maintaining the backhaul capacity constraint. Moreover, we employ the successive convex approximation (SCA) method to solve the UAV placement optimization sub-problem. We show the effectiveness of our proposed design via extensive numerical studies.