Integer Optimization Problem Research Articles

A market mechanism for multiple air traffic resources

We introduce a model that extends the concept of air traffic flow management slot to the concept of time window, allowing to effectively deal with a network of interacting regulations. The model aims at minimising the total cost of delay of a time window allocation to flights and is based on an integer programming problem. It consists in a market-based mechanism between flights and a central authority to trade time windows, which fulfils the properties of individual rationality (every participating airline has a non-negative profit from the mechanism) and weak budget-balance (the mechanism requires no external subsidisation). Equity is assumed to be respected because the First Planned First Served allocation is an endowment guaranteed to all flights and allocated for free. The proposed market mechanism can be implemented in a distributed manner preventing the disclosure of confidential information by airlines, and is based on the Lagrangian relaxation of the integer optimisation problem, solved through the subgradient algorithm. We present some computational experiments conducted to test the model on some real instances of air traffic data.

Collaborative cloud-edge-end task offloading with task dependency based on deep reinforcement learning

With the explosive growth of the Internet of Things (IoT), IoT devices generate massive amounts of data and demand, which poses a huge challenge to IoT devices with limited CPU computing capability and battery capacity. Due to the dependency relationship in complex applications and network environments, effective offloading in such scenarios is complicated. In this paper, we address the problem of computation offloading with task dependency in the cloud–edge-end collaboration scenario including multi-user, multi-core edge servers, and a cloud server. We model multiple task dependencies using the directed acyclic graph (DAG) and formalize the offloading problem as a multi-objective mixed integer optimization problem. To solve this problem, a Task Priority and Deep Reinforcement learning-based Task Offloading algorithm (TPDRTO) is proposed. The task offloading decision is represented as a Markov Decision Process (MDP). Meanwhile, based on the task priority, an optimized Deep Reinforcement Learning (DRL) method with action-mask is proposed to leverage the computing resources of the cloud and edge servers and obtain the optimal policies of computation offloading. Experimental results show that the TPDRTO algorithm can effectively tradeoff and reduce the average energy consumption and time delay of IoT devices.

Quantum approximate optimization algorithm for qudit systems

A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a max-$k$-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

A Genetic Algorithm for Solving Nonlinear Optimization Problem with Max-Archimedean Bipolar Fuzzy Relation Equations

This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm.

UAV Trajectory Design and Power Optimization for Terahertz Band-Integrated Sensing and Communications

Sixth generation (6G) wireless networks require very low latency and an ultra-high data rate, which have become the main challenges for future wireless communications. To effectively balance the requirements of 6G and the extreme shortage of capacity within the existing wireless networks, sensing-assisted communications in the terahertz (THz) band with unmanned aerial vehicles (UAVs) is proposed. In this scenario, the THz-UAV acts as an aerial base station to provide information on users and sensing signals and detect the THz channel to assist UAV communication. However, communication and sensing signals that use the same resources can cause interference with each other. Therefore, we research a cooperative method of co-existence between sensing and communication signals in the same frequency and time allocation to reduce the interference. We then formulate an optimization problem to minimize the total delay by jointly optimizing the UAV trajectory, frequency association, and transmission power of each user. The resulting problem is a non-convex and mixed integer optimization problem, which is challenging to solve. By resorting to the Lagrange multiplier and proximal policy optimization (PPO) method, we propose an overall alternating optimization algorithm to solve this problem in an iterative way. Specifically, given the UAV location and frequency, the sub-problem of the sensing and communication transmission powers is transformed into a convex problem, which is solved by the Lagrange multiplier method. Second, in each iteration, for given sensing and communication transmission powers, we relax the discrete variable to a continuous variable and use the PPO algorithm to tackle the sub-problem of joint optimization of the UAV location and frequency. The results show that the proposed algorithm reduces the delay and improves the transmission rate when compared with the conventional greedy algorithm.

Learning-based Trajectory Optimization for a Twin Robotic CT System

Non-circular twin robot computed tomography (CT) systems provide a high degree of flexibility in positioning the X-ray source and detector. This makes the design of optimal CT trajectories particularly important, as it can potentially allow for a reduction in the number of projections required for image acquisition. Therefore, the optimization of CT trajectories is a key area of research in this field. This paper presents a method for optimising the trajectory of a non-circular twin robot computed tomography system, using a so-called detectability index to guide the optimization process. The proposed method involves simulating possible X-ray projections that are reachable by the robotic CT system and using a regressive ResNet-34 to predict the detectability index of each projection. An integer optimization problem is then used to generate an optimised CT trajectory based on this prediction, with the haversine distance between projections serving as an additional constraint. The performance of the ResNet-34 is evaluated on unseen projections. It effectively predicted the detectability index for a spherical sampling space, allowing for the optimization of arbitrary CT trajectories. In addition, the method was able to identify valuable projections according to the detectability index, enabling the reconstruction of a test object with only 30 out of 800 of the previously acquired projections without significant loss of information in the reconstruction domain.

Joint Offloading Scheduling and Resource Allocation in Vehicular Edge Computing: A Two Layer Solution

Vehicular Edge Computing (VEC) is a promising paradigm for autonomous driving. It can reduce delay and energy consumption of tasks. The problem of joint task offloading scheduling and resource allocation in VEC is a challenge issue. In this paper, we investigate the problem of joint task offloading, task scheduling, and resource allocation in VEC, and the fast changing channel between a vehicle and an edge server. A target problem of joint considering task offloading scheduling, resource allocation and time-varying channel in VEC is formulated. The goal is to minimize the delay and energy consumption of tasks to guarantee the Quality of Service (QoS) of VEC. Constraints on the completion time, the energy consumption, and the computing capability are considered for each task. The resulting mixed integer optimization problem is decomposed into a two-layer optimization problem. In the upper layer, we use a Deep Q-Network (DQN) to solve the task offloading scheduling problem. In the lower level, the CPU frequency allocation is determined using the Gradient Descent (GD) method. Numerical results illustrate that the proposed algorithm can minimize the delay and energy consumption of VEC for different network parameter settings.

Cross-Layer Optimization: Joint User Scheduling and Beamforming Design With QoS Support in Joint Transmission Networks

User scheduling and beamforming design are two crucial yet coupled topics for multiuser wireless communication systems. They are usually addressed separately with conventional optimization methods. In this paper, cross-layer optimization problem is considered, namely, the user scheduling and beamforming are jointly discussed, subjecting to the requirement of per-user quality of service and the maximum allowable transmit power for multicell multiuser joint transmission networks. To achieve the goal, a mixed discrete-continuous variables combinational optimization problem is investigated with aiming at maximizing the sum rate of the communication system. To circumvent the original non-convex problem with dynamic solution space, we first transform it into a 0-1 integer and continuous variables optimization problem, and then obtain a tractable form with continuous variables by exploiting the characteristics of the 0-1 integer constraints. Finally, the scheduled users and the optimized beamforming vectors are simultaneously calculated by an alternating optimization algorithm. We also theoretically prove that the base stations allocate zero power to the unscheduled users. Furthermore, two heuristic optimization algorithms are proposed respectively based on brute-force search and greedy search. Numerical results validate the effectiveness of our proposed methods, and the optimization approach gets relatively balanced results compared with the other two approaches.

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.

Multi-Delay Identification of Rare Earth Extraction Process Based on Improved Time-Correlation Analysis.

The rare earth extraction process has significant time delay characteristics, making it challenging to identify the time delay and establish an accurate mathematical model. This paper proposes a multi-delay identification method based on improved time-correlation analysis. Firstly, the data are preprocessed by grey relational analysis, and the time delay sequence and time-correlation data matrix are constructed. The time-correlation analysis matrix is defined, and the H∞ norm quantifies the correlation degree of the data sequence. Thus the multi-delay identification problem is transformed into an integer optimization problem. Secondly, an improved discrete state transition algorithm is used for optimization to obtain multi-delay. Finally, based on an Neodymium (Nd) component content model constructed by a wavelet neural network, the performance of the proposed method is compared with the unimproved time delay identification method and the model without an identification method. The results show that the proposed algorithm improves optimization accuracy, convergence speed, and stability. The performance of the component content model after time delay identification is significantly improved using the proposed method, which verifies its effectiveness in the time delay identification of the rare earth extraction process.

Autonomous Task Planning Method for Multi-Satellite System Based on a Hybrid Genetic Algorithm

The increasing number of satellites for specific space tasks makes it difficult for traditional satellite task planning that relies on ground station planning and on-board execution to fully exploit the overall effectiveness of satellites. Meanwhile, the complex and changeable environment in space also poses challenges to the management of multi-satellite systems (MSS). To address the above issues, this paper formulates a mixed integer optimization problem to solve the autonomous task planning for MSS. First, we constructed a multi-agent-based on-board autonomous management and multi-satellite collaboration architecture. Based on this architecture, we propose a hybrid genetic algorithm with simulated annealing (H-GASA) to solve the multi-satellite cooperative autonomous task planning (MSCATP). With the H-GASA, a heuristic task scheduling scheme was developed to deal with possible task conflicts in MSCATP. Finally, a simulation scenario was established to validate our proposed H-GASA, which exhibits a superior performance in terms of computational power and success rate compared to existing algorithms.

Population-based discrete state transition algorithm with decomposition and knowledge guidance applied to electrolytic cell maintenance decision

With continuous scale expansion and higher safety requirements in modern aluminum electrolysis, it is more and more necessary to realize an intelligent decision-making for shutting-down and running of aluminum reduction cells (SRARC). However, this realization needs to solve a special single-objective constrained integer optimization problem (SCIOP), where the key challenge is a high requirement for the constraint-handling ability. In this paper, based on a high-scalability intelligent optimization algorithm called discrete state transition algorithm (DSTA), a population-based DSTA with decomposition and knowledge guidance (PDSTA/D-S) is proposed. This PDSTA/D-S improves the constraint-handling ability of DSTA from three aspects. Firstly, a hybrid framework combining DSTA with genetic algorithm is proposed. Secondly, a decomposition-based multi-objective optimization for constrained problems with uniformly-angled weighted sum vector is proposed. Thirdly, the manual decision-making is transferred to a knowledge-based transformation operator of DSTA. Therefore, a high-level performance of decision-making for SRARC can be obtained. The related experiments on a SRARC which is built from the practical production have demonstrated that the proposed PDSTA/D-S not only makes an effective improvement of DSTA from three aspects, but also has a more advanced performance compared with other existing high-performance intelligent optimization algorithms.

Topological analysis of water distribution networks for optimal leak localization

This paper introduces two methodologies to provide an optimum sensor deployment layout, one based on a model-based approach and the other entirely data-driven. The first method is formulated as an integer optimization problem, an optimization criterion consisting of minimizing the average topological distance. The second method is a new methodology to provide an optimum sensor placement regarding how many sensors to install without using hydraulic information but just exploiting the knowledge of the topology of the Water Distribution Networks. The method uses the Girvan-Newman clustering algorithm to ensure complete coverage of the network and the study of the installation of pressure sensors in the central nodes of each group, selected according to different metrics of topological centrality. The approach is illustrated in the Modena network.

Application and assessment of divide-and-conquer-based heuristic algorithms for some integer optimization problems

In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman Problem (TSP). For each case, the algorithm is introduced, together with the design of numerical experiments, in order to empirically establish its performance from both points of view: its computational time and its numerical accuracy.

Sensitivity analysis for the optimization of switched dynamical processes with state-dependent switching conditions and its application

This paper considers an optimization problem of switched dynamical processes, which is essentially a mixed integer optimization problem. Unlike the existing optimization problem, the state-dependent switching strategy is adopted to design the switching rules. Our main contributions are as follows. Firstly, by introducing a discrete-valued function, a control vector parameterization technique, and a novel relaxation technique, the switched dynamical process optimization problem is approximated by using a more tractable nonlinear constrained parameter optimization problem. Unlike the existing works, the number of locally optimal solution does not increase due to the relaxation transformation. Next, in order to obtain a numerical solution of this parameter optimization problem, a novel penalty function approach is developed. Unlike existing penalty functions, this novel penalty function is neither quadratic nor linear, and has exponential convergence rates. Furthermore, a sensitivity analysis method is developed for investigating the effect of small perturbations in constraints and switching conditions on the objective function. Finally, a dynamic optimization problem in cancer chemotherapy process is presented to illustrate the effectiveness of the approach provided by this paper. Numerical simulation results show that the approach provided by this paper is low time-consuming, has faster convergence speed, can obtain a better objective function value than the existing methods, and is robust for the small perturbations in constraints and switching conditions.

Cost-Minimizing Hexahedral Mesh Refinement by Sheet Inflation

Abstract In this paper, a novel hexahedral refinement method is introduced which finds the optimal tradeoff between the number of inserted elements and inserted singularities according to user-prescribed weighting. The input of our algorithm is the hexahedral mesh with quads tagged for refinement. The quad sets to be inserted by sheet inflation are determined by solving a integer optimization problem to minimize the number of inserted elements and inserted singularities while maintaining mesh consistency. Finally, we design the optimized sheet structures by selecting the optimal local shrink set at the cross section of intersecting quad sets to ensure the quality of mesh refinement. The refinement scheme can be applied iteratively until the mesh density meets the requirements. Experimental results for some mechanical parts verified the effectiveness of the proposed method.

Genetic Algorithm for Optimizing Energy Efficiency in Downlink mmWave NOMA System with Imperfect CSI

Nonorthogonal multiple access (NOMA) is considered a promising technique for improving energy efficiency (EE) in beyond-5G wireless systems. In this paper, we investigate the maximization of EE of downlink wireless systems by combining mmWave with NOMA technologies, considering the asymmetric required data rate of user applications. We propose a genetic algorithm (GA) to solve the non-convex energy efficiency problem for an imperfect CSI downlink mmWave NOMA system. The studied mixed-integer optimization problem was converted to an integer optimization problem and solved using a GA, which determines the best clustering members in mmWave NOMA. The required population size of the proposed GA was determined to evaluate its effectiveness for a massive number of users. In addition, the GA’s convergence to the optimal solution for light traffic and relatively heavy traffic was also analyzed. Our results illustrate that the solution obtained solution via GA is almost equal to the optimal value and outperforms the conventional orthogonal multiple access, where the EE is improved by more than 75%. Finally, the impact of the estimation error of CSI on the system performance was evaluated at different required SINR scenarios. The results show that EE is degraded in the case of imperfect CSI case but is still close to the optimal solution.

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.

Optimal power quality monitor placement to ensure reliable monitoring of sensitive loads in the presence of voltage sags and harmonic resonances conditions

Nowadays, sensitive nonlinear loads such as load commutated inverter drives are increasingly being used by industrial consumers. In one hand, sensitive nonlinear loads can induce parallel resonance condition to the network and in the other hand their continuous operation may be interrupted due to voltage sags. Therefore, power quality parameters associated with the secure performance of sensitive nonlinear loads must be monitored to avoid the adverse effects of parallel resonances and financial losses due to voltage sags. In this paper, a new approach based on the area of vulnerability to voltage sags and harmonic resonance mode analysis is proposed to determine the optimal number and the best location of power quality monitors (PQMs). The proposed method is formulated as a linear integer optimization problem which is simply solved. In addition, in case where a budget limitation does not allow to purchase the required number of monitors and the optimization problem does not converge an alternative approach is proposed for allocating very limited number of monitors in a hierarchical manner to ensure monitoring of the most severe conditions. The proposed approach is applied on the IEEE 30-bus system and an Iranian real industrial network. © 2017 Elsevier Inc. All rights reserved.