Power-Efficient Wireless Coverage Using Minimum Number of UAVs

Unmanned aerial vehicles (UAVs) can be deployed as backup aerial base stations due to cellular outage either during or post natural disaster. In this paper, an approach involving multi-UAV three-dimensional (3D) deployment with power-efficient planning was proposed with the objective of minimizing the number of UAVs used to provide wireless coverage to all outdoor and indoor users that minimizes the required UAV transmit power and satisfies users’ required data rate. More specifically, the proposed algorithm iteratively invoked a clustering algorithm and an efficient UAV 3D placement algorithm, which aimed for maximum wireless coverage using the minimum number of UAVs while minimizing the required UAV transmit power. Two scenarios where users are uniformly and non-uniformly distributed were considered. The proposed algorithm that employed a Particle Swarm Optimization (PSO)-based clustering algorithm resulted in a lower number of UAVs needed to serve all users compared with that when a K-means clustering algorithm was employed. Furthermore, the proposed algorithm that iteratively invoked a PSO-based clustering algorithm and PSO-based efficient UAV 3D placement algorithms reduced the execution time by a factor of ≈1/17 and ≈1/79, respectively, compared to that when the Genetic Algorithm (GA)-based and Artificial Bees Colony (ABC)-based efficient UAV 3D placement algorithms were employed. For the uniform distribution scenario, it was observed that the proposed algorithm required six UAVs to ensure 100% user coverage, whilst the benchmarker algorithm that utilized Circle Packing Theory (CPT) required five UAVs but at the expense of 67% of coverage density.

Improved interval methods for solving circle packing problems in the unit square

In this work computer-assisted optimality proofs are given for the problems of finding the densest packings of 31, 32, and 33 non-overlapping equal circles in a square. In a study of 2005, a fully interval arithmetic based global optimization method was introduced for the problem class, solving the cases 28, 29, 30. Until now, these were the largest problem instances solved on a computer. Using the techniques of that paper, the estimated solution time for the next three cases would have been 3–6 CPU months. In the present paper this former method is improved in both its local and global search phases. We discuss a new interval-based polygon representation of the core local method for eliminating suboptimal regions, which has a simpler implementation, easier proof of correctness, and faster behaviour than the former one. Furthermore, a modified strategy is presented for the global phase of the search, including improved symmetry filtering and tile pattern matching. With the new method the cases $$n=31,32,33$$ n = 31 , 32 , 33 have been solved in 26, 61, and 13 CPU hours, giving high precision enclosures for all global optimizers and the optimum value. After eliminating the hardware and compiler improvements since the former study, the new proof technique became roughly about 40–100 times faster than the previous one. In addition, the new implementation is suitable for solving the next few circle packing instances with similar computational effort.

Cost- and Energy-Efficient Aerial Communication Networks with Interleaved Hovering and Flying

This work proposes a methodology for the energy-and cost-efficient 3-D deployment of an unmanned aerial vehicle (UAV)-based aerial access point (AAP), that exchanges a given amount of independent data with a set of ground user equipment (UE). Considering a fly-hover-communicate transmission scheme, the most energy-efficient 3-D hovering points (HPs) of the AAP are determined by decoupling the problem in the horizontal and vertical dimensions. First, we derive analytically the optimal hovering altitude that jointly maximizes the downlink and uplink global energy efficiency (GEE) of the system. Next, we propose the multilevel circle packing (MCP) algorithm to determine the minimal number of HPs and their associated horizontal coordinates, such that the AAP covers all the UEs in the given geographical area. A cost analysis is carried out to observe the variation of both fixed and variable costs; these are then minimized by suitably selecting the AAP's battery parameters, like the depth of discharge (DOD), defined as the portion of battery capacity that is consumed during a discharge cycle, and the velocity of the UAV. Simulation results show that: the UAV energy consumption has a significant impact on the 3-D HPs of the AAP; the time spent during the substitution swap of an out of power AAP has a major influence on the operational cost; the cost of the system can be optimized by suitably selecting the onboard battery and the UAV flight parameters.

Cost- and Energy-Efficient Aerial Communication Networks with Interleaved Hovering and Flying

This work proposes a methodology for the energy-and cost-efficient 3-D deployment of an unmanned aerial vehicle (UAV)-based aerial access point (AAP), that exchanges a given amount of independent data with a set of ground user equipment (UE). Considering a fly-hover-communicate transmission scheme, the most energy-efficient 3-D hovering points (HPs) of the AAP are determined by decoupling the problem in the horizontal and vertical dimensions. First, we derive analytically the optimal hovering altitude that jointly maximizes the downlink and uplink global energy efficiency (GEE) of the system. Next, we propose the multilevel circle packing (MCP) algorithm to determine the minimal number of HPs and their associated horizontal coordinates, such that the AAP covers all the UEs in the given geographical area. A cost analysis is carried out to observe the variation of both fixed and variable costs; these are then minimized by suitably selecting the AAP's battery parameters, like the depth of discharge (DOD), defined as the portion of battery capacity that is consumed during a discharge cycle, and the velocity of the UAV. Simulation results show that: the UAV energy consumption has a significant impact on the 3-D HPs of the AAP; the time spent during the substitution swap of an out of power AAP has a major influence on the operational cost; the cost of the system can be optimized by suitably selecting the onboard battery and the UAV flight parameters.

Self-organized optimal packing of kinesin-5 driven microtubule asters scale with cell size

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors such as in syncytia form intracellular patterns, but the mechanical principles are not clear. Here, we report oocytes of the marine ascidian Phallusia mammillata treated with a drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, i.e. divide it into polygonal structures, dominated by hexagons in a kinesin-5 dependent manner, while inter-aster MTs form ‘mini-spindles’. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to MTs per aster, MT lengths and kinesin-5 density. Simulations predict the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the ‘circle packing problem’, suggesting an intrinsic mechanical pattern forming module potentially relevant to understand the role of collective mechanics of cytoskeletal elements in embryogenesis.

Multi-objective Optimization Approach to Malfatti's Problem

In this work, we consider the multi-objective optimization problem based on the circle packing problem, particularly, extended Malfatti's problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined for the first time from a view point of global optimization theory and algorithm in (Enkhbat, 2016). Also, a game theory approach has been applied to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply the the multi-objective optimization approach to the problem. Using the weighted sum method, we reduce this problem to optimization problem with nonconvex constraints. For solving numerically the weighted sum optimization problem, we apply KKT conditions and find Pareto stationary points. Also, we estimate upper bounds of the global value of the objective function by Lagrange duality. Numerical results are provided.