Non-convex Combinatorial Problem Research Articles

Optimization of Hybrid Composite Laminates with Distinct Ply Thicknesses Using Integer Programming

Optimization of constant-stiffness composite laminates with discrete values of fiber orientations and ply thicknesses is a nonconvex combinatorial problem. Recent studies show that this problem can be efficiently solved using the mixed integer program (MIP) by reformulating lamination parameters as functions of decision variables that represent fiber orientation and thickness choices. These formulations are limited to analyzing laminates having plies of the same thickness and material. This paper extends the previously employed lamination parameter reformulation to enable laminate designs with plies of different thicknesses and materials, thereby leading to MIP with cubic constraints. The linearization techniques are employed to convert cubic constraints of buckling load factors in terms of binary variables into sets of linear constraints that are efficiently solved with optimization algorithms for MIPs. It is shown that the use of distinct ply thicknesses in the optimization further reduces the mass of single-material laminates made with carbon-fiber-reinforced polymer when compared with previous studies using the same material. Additionally, the combination of plies made of glass-fiber-reinforced polymer and carbon-fiber-reinforced polymer with distinct thicknesses is shown to reduce the weight penalty when optimized for cost minimization in comparison to plies with uniform thickness.

Energy-Efficient Service-Aware Multi-Connectivity Scheduler for Uplink Multi-Layer Non-Terrestrial Networks

This paper introduces the concept of energy efficiency (EE) in the uplink with the capability of multi-connectivity (MC) in a multi-orbit non-terrestrial network (NTN), where user terminals (UTs) can be simultaneously served by more than one satellite to achieve higher peak throughput at reduced energy consumption. This concept also considers the service classification of the users, so that network dimensioning is performed in order to satisfy the quality of service (QoS) requirement of users. MC can increase throughput, but this entails increased power consumption at user terminal for uplink transmissions. To this end, an energy-efficient service-aware multi-connectivity (EE-SAMC) scheduling algorithm is developed in this paper to improve the EE of uplink communications. EE-SAMC uses available radio resources and propagation information to intelligently define a dynamic resource allocation pattern, that optimally routes traffic so as to reduce the energy consumption at the UT while ensuring QoS is maximized. EE-SAMC is designed based on the formulation of a non-convex combinatorial problem, it is solved in two ways involving firstly an optimization solution and secondly a heuristic approach. The effectiveness of EE-SAMC is compared with random allocation, round robin and heuristic schedulers in terms of EE, throughput and delay; EE-SAMC outperforms all schedulers.

Deep-Learning-Based Resource Allocation for Time-Sensitive Device-to-Device Networks.

Ultra-reliable and low-latency communication (URLLC) is considered as one of the major use cases in 5G networks to support the emerging mission-critical applications. One of the possible tools to achieve URLLC is the device-to-device (D2D) network. Due to the physical proximity of communicating devices, D2D networks can significantly improve the latency and reliability performance of wireless communication. However, the resource management of D2D networks is usually a non-convex combinatorial problem that is difficult to solve. Traditional methods usually optimize the resource allocation in an iterative way, which leads to high computational complexity. In this paper, we investigate the resource allocation problem in the time-sensitive D2D network where the latency and reliability performance is modeled by the achievable rate in the short blocklength regime. We first design a game theory-based algorithm as the baseline. Then, we propose a deep learning (DL)-based resource management framework using deep neural network (DNN). The simulation results show that the proposed DL-based method achieves almost the same performance as the baseline algorithm, while it is more time-efficient due to the end-to-end structure.

Graph Embedding-Based Wireless Link Scheduling With Few Training Samples

Link scheduling in device-to-device (D2D) networks is usually formulated as a non-convex combinatorial problem, which is generally NP-hard and difficult to get the optimal solution. Traditional methods to solve this problem are mainly based on mathematical optimization techniques, where accurate channel state information (CSI), usually obtained through channel estimation and feedback, is needed. To overcome the high computational complexity of the traditional methods and eliminate the costly channel estimation stage, machine leaning (ML) has been introduced recently to address the wireless link scheduling problems. In this article, we propose a novel graph embedding based method for link scheduling in D2D networks. We first construct a fully-connected directed graph for the D2D network, where each D2D pair is a node while interference links among D2D pairs are the edges. Then we compute a low-dimensional feature vector for each node in the graph. The graph embedding process is based on the distances of both communication and interference links, therefore without requiring the accurate CSI. By utilizing a multi-layer classifier, a scheduling strategy can be learned in a supervised manner based on the graph embedding results for each node. We also propose an unsupervised manner to train the graph embedding based method to further reinforce the scalability and develop a K-nearest neighbor graph representation method to reduce the computational complexity. Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods but is with only hundreds of training network layouts. It is also competitive in terms of scalability and generalizability to more complicated scenarios.

Algorithms for joint sensor and control nodes selection in dynamic networks

The problem of placing or selecting sensors and control nodes plays a pivotal role in the operation of dynamic networks. This paper proposes optimal algorithms and heuristics to solve the Simultaneous Sensor and Actuator Selection Problem (SSASP) in linear dynamic networks. In particular, a sufficiency condition of static output feedback stabilizability is used to obtain the minimal set of sensors and control nodes needed to stabilize an unstable network. We then show that SSASP can be written as a mixed-integer nonconvex problem. To solve this nonconvex combinatorial problem, three methods based on (i) mixed-integer nonlinear programming, (ii) binary search algorithms, and (iii) simple heuristics are proposed. The first method yields optimal solutions to SSASP—given that some constants are appropriately selected. The second method requires a database of binary sensor/actuator combinations, returns optimal solutions, and necessitates no tuning parameters. The third approach is a heuristic that yields suboptimal solutions but is computationally attractive. The theoretical properties of these methods are discussed and numerical tests on dynamic networks showcase the trade-off between optimality and computational time.

Resource allocation in small cell networks with time‐averaged rate constraints

This work is motivated by the following observation: modern wireless applications such as content prefetching, allow different extent of delay tolerance, thus in practice users may have different time-averaged data rates during a certain period of time. In this study, the authors consider resource allocation in small cell networks under time-varying channels while each user has an individual time-averaged rate requirement. Stochastic optimisation model is employed to minimise the time-averaged power consumption of small base stations subject to individual user's time-averaged rate constraint. They develop an online power optimal resource allocation (PORA) algorithm to achieve the optimal power allocation and subcarrier assignment decisions without prior knowledge of channel statistics. Furthermore, considering that the power allocation and subcarrier assignment problem is a nonconvex combinatorial problem, they further develop an iterative heuristic algorithm with polynomial complexity. Simulation results show the effectiveness of PORA and verify the theoretical analysis on the network performance.

Modified particle swarm optimisation with a novel initialisation for finding optimal solution to the transmission expansion planning problem

The transmission expansion planning (TEP) problem consists of determining when and where new circuits are needed and should be installed to serve the growing demand for electric power. TEP is a hard, large-scale, non-linear, mixed-integer and non-convex combinatorial problem. Finding the solution for the TEP problem is very difficult as the number of options to be analysed and compared increases exponentially with the size of the network. This study presents an application of the modified particle swarm optimisation technique, with a novel initialisation (population monitored for complementary magnitudes initialisation), for improved performance (in terms of success rate and convergence) to the highly complex TEP problem. Here, the DC model of the transmission network is considered. The success of the proposed methodology has been tested on the Garver 6-bus system, IEEE 24-bus system and Southern Brazilian 46-bus system and validated.

Coordinated Scheduling and Power Allocation in Downlink Multicell OFDMA Networks

We consider a multicell orthogonal frequency-division multiple-access (OFDMA) wireless network with universal frequency reuse and treat the problem of cochannel interference mitigation via base station coordination in the downlink. Assuming that coordinated access points only share channel quality measurements but not user data symbols, we propose to select the set of cochannel users and the power allocation across tones to maximize the weighted system sum rate subject to per-base-station power constraints. Since this is a nonconvex combinatorial problem, efficient suboptimal algorithms are presented and discussed, each requiring a different level of coordination among base stations and a different feedback signaling overhead. Simulation results are provided to assess the performances of the proposed strategies.

Conjunctive Use of Surface and Groundwater for Coastal and Deltaic Systems

A regional conjunctive use model is developed for a near-real deltaic aquifer system, irrigated from a diversion system, with some reference to hydrogeoclimatic conditions prevalent in the east coastal deltas of India. Water resources are sufficiently available in these regions under average monsoon rainfall conditions, but their distribution in space and time has been ever challenging to water managers. Surface-water availability shows temporal fluctuations in terms of floods and droughts, and groundwater availability shows mainly spatial variability in terms of quality and quantity due to the hydrogeologic setting, boundary conditions, and aquifer properties. The combined simulation-optimization model proposed in this study is solved as a nonlinear, nonconvex combinatorial problem using a simulated annealing algorithm and an existing sharp interface model. The computational burden is managed within practical time frames by replacing the flow simulator with artificial neural networks and using efficient algorithmic guidance.