Signomial Programming Research Articles

A deep reinforcement learning framework and its implementation for UAV-aided covert communication

In this work, we consider an Unmanned Aerial Vehicle (UAV)-aided covert transmission network, which adopts the uplink transmission of Communication Nodes (CNs) as a cover to facilitate covert transmission to a Primary Communication Node (PCN). Specifically, all nodes transmit to the UAV exploiting uplink non-Orthogonal Multiple Access (NOMA), while the UAV performs covert transmission to the PCN at the same frequency. To minimize the average age of covert information, we formulate a joint optimization problem of UAV trajectory and power allocation designing subject to multi-dimensional constraints including covertness demand, communication quality requirement, maximum flying speed, and the maximum available resources. To address this problem, we embed Signomial Programming (SP) into Deep Reinforcement Learning (DRL) and propose a DRL framework capable of handling the constrained Markov decision processes, named SP embedded Soft Actor-Critic (SSAC). By adopting SSAC, we achieve the joint optimization of UAV trajectory and power allocation. Our simulations show the optimized UAV trajectory and verify the superiority of SSAC compared with various existing baseline schemes. The results of this study suggest that by maintaining appropriate distances from both the PCN and CNs, one can effectively enhance the performance of covert communication by reducing the detection probability of the CNs.

Solid-State Electroaerodynamic Aircraft Design Using Signomial Programming

Electroaerodynamics (EAD) is a form of airbreathing electric propulsion that uses high voltages to produce and accelerate ions, generating thrust without any moving parts. This method of solid-state propulsion is nearly silent and produces no direct combustion emissions. This paper describes a program for designing and optimizing fixed-wing solid-state aircraft propelled solely using EAD. Signomial programming (SP), an emerging method of efficient multidisciplinary design optimization, is employed. The program incorporates performance models for state-of-the-art EAD thrusters, and for custom high-voltage power electronics. It can be used to generate vehicle specifications, or to assess the effect of technological improvements on vehicle performance. The program was used to design and build a flight demonstrator aircraft, based on a goal of achieving steady level flight. In 2017–2018, the demonstrator successfully achieved steady level flight, a first for a fixed-wing electric aircraft with solid-state propulsion. The unproven nature of the EAD propulsion system necessitated a design philosophy centered around minimal technical risk, affecting configuration selection and choice of objective function. A similar design philosophy may prove useful for other design projects with unproven propulsion systems. Finally, endurance values greater than 30 min are achievable with recent improvements in EAD thruster and battery technology.

A signomial programming-based approach for multi-echelon supply chain disruption risk assessment with robust dynamic Bayesian network

Disruption risk assessment is a primary and crucial step before taking measures to mitigate the negative impact of disruptions propagating along supply chains (SCs). Recently, robust dynamic Bayesian network (DBN) provides a valid tool for disruption risk estimation under the ripple effect in a data-scarce environment. However, existing literature has not considered such disruption risk assessment for multi-echelon SCs that are usually structurally complicated and thus vulnerable to disruptions with ripple effects. Motivated by this fact, we study the disruption risk assessment problem under the ripple effect for a multi-echelon SC with several suppliers and one manufacturer, in which only probability intervals of the suppliers’ states and those of the related disruption propagations are known. The aim is to acquire a robust risk estimation, measured by the worst-case total weighted probabilities for the manufacturer in the disrupted state over a time horizon. For the problem, a nonconvex nonlinear programming model is established to obtain the worst-case risk estimation. To efficiently solve the problem, a novel signomial programming (SP)-based approach is developed for finding near-optimal solutions. Numerical experiments on instances in the literature and our randomly generated instances are conducted to evaluate the efficiency of the proposed method. Besides, managerial insights are drawn.

Fan and Motor Co-Optimization for a Distributed Electric Aircraft Propulsion System

An integrated modeling approach is presented for the conceptual design of electric aircraft propulsors, with application to NASA’s hydrogen fuel-cell powered transport aircraft concept, being developed under the CHEETA (Center for High-Efficiency Electrical Technologies for Aircraft) program. The distributed boundary layer ingesting (BLI) fan module and the fan-hub embedded MgB2 based fully superconducting (SC) electric motors are modeled together using Signomial Programming (SP). An all-at-once SP optimization eliminates external design iterations between modules and provides sensitivities to design parameters as part of the optimization solution. In addition, the approach developed here is modular and component models can be easily added to study various aircraft architectures. A trade space exploration of CHEETA propulsors indicates a highly-distributed 32 wing and fuselage mounted propulsors configuration, powered by 0.5 MW and 1.6 MW motors, respectively, as the optimal, yielding 16% reduction in the aircraft electric energy consumption relative to a conventional twin electric under-wing propulsors design. However, the design selected is a 9 propulsors configuration with 2.4 MW motors (power range more suitable for fully SC architecture), with about 14% power savings. The fan-embedded motor architecture leads to fan hub-to-tip ratios of up to 0.5, which are higher than typical.

Joint Hovering Height, Power, and Rate Optimization for Air-to-Ground UAV-RSMA Covert Communications

In this paper, we investigate covert communications for an unmanned aerial vehicle (UAV)-aided rate-splitting multiple access (RSMA) system in which the UAV transmits to the covert and public users separately while shielding covert transmissions from a warden. Under the RSMA principles, the messages of the covert and public users are converted to common and private streams for air-to-ground transmissions. Subject to the quality of service (QoS) requirements of the public user and covertness constraint of the UAV-aid RSMA (UAV-RSMA) system, the aim of covert communication design is to maximize the covert rate by jointly optimizing the transmit power allocation, common rate allocation, and UAV hovering height, which each contribute to the uncertainty of the warden’s binary decision and attempts to enhance communication performance. To address the non-convex covert rate maximization problem in addition to the highly coupled system parameters, we decouple the original problem into three subproblems of transmit power allocation, common rate allocation, and UAV hovering height. We derive the optimal solutions for each of the subproblems of the transmit power and rate allocations and formulate a signomial programming problem to tackle UAV hovering height optimization. The simulation results indicate the superior covert rate performance achieved by the proposed AO algorithm and demonstrate that the proposed UAV-RSMA scheme achieves a higher covert rate than the benchmark schemes.

Optimal Hovering Height and Power Allocation for UAV-Aided NOMA Covert Communication System

In this letter, we consider an unmanned aerial vehicle (UAV) aided covert communication system in which the UAV provides downlink transmission to the public user and covert user with non-orthogonal multiple access (NOMA). In the considered system, the covert performance can be effectively enhanced by the mobility of the UAV and the transmission from UAV to the public user. Aiming at improving the covert signal-to-noise ratio (SNR), we jointly optimize the hovering height and power allocation of UAV and formulate a signomial programming (SP) problem. To tackle the nonconvex optimization, we develop a successive geometric programming approximation (SGPA) algorithm. The optimal hovering height and power allocation are provided with numerical results and the outperformance of our design is verified.

Nonlinear fuzzy fractional signomial programming problem: A fuzzy geometric programming solution approach

Fuzzy fractional signomial programming problem is a relatively new optimization problem. In real world problems, some variables may vacillate because of various reasons. To tackle these vacillating variables, vagueness is considered in form of fuzzy sets. In this paper, a nonlinear fuzzy fractional signomial programming problem is considered with all its coefficients in objective functions as well as constraints are fuzzy numbers. Two solution approaches are developed based on signomial geometric programming comprising nearest interval approximation with parametric interval valued functions and fuzzy α-cut with min–max approach. To demonstrate the proposed methods, two illustrative numerical examples are solved and the results are comparatively discussed showing its feasibility and effectiveness.

Some power allocation algorithms for cognitive uplink satellite systems

Cognitive satellite communication (SatCom) is rapidly emerging as a promising technology to overcome the scarcity of the exclusive licensed band model in order to fulfill the increasing demand for high data rate services. The paper addresses power allocation methods for multi-operator multi-beam uplink satellite communication systems co-existing with a Ka-band terrestrial network, using cognitive radio paradigm. Such a scenario is especially challenging because of (i) the coexisting multiple SatCom operators over the cognitive band need to coordinate the use of their resources under limited inter-operator information exchange, and (ii) nonlinear onboard high power amplifier (HPA) which leads to nonlinear interference between users and beams. In order to tackle the first challenge, we propose distributed power allocation algorithms including the standard Alternate Direction Multiplier Method (ADMM); Regarding the HPA nonlinear impairment, we propose nonlinear-aware power allocation based on Signomial Programming. The proposed solutions outperform state-of-the-art in both cases.

User Scheduling and Power Allocation for Precoded Multi-Beam High Throughput Satellite Systems With Individual Quality of Service Constraints

For extensive coverage areas, multi-beam high throughput satellite (HTS) communication is a promising technology that plays a crucial role in delivering broadband services to many users with diverse Quality of Service (QoS) requirements. This article focuses on multi-beam HTS systems where all beams reuse the same spectrum. In particular, we propose a novel user scheduling and power allocation design capable of providing guarantees in terms of the individual QoS requirements while maximizing the system throughput under a limited power budget. Precoding is employed in the forward link to mitigate mutual interference among the users in multiple-access scenarios over different coherence time intervals. The combinatorial optimization structure from user scheduling requires an extremely high cost to obtain the global optimum even when a reduced number of users fit into a time slot. Therefore, we propose a heuristic algorithm yielding a good trade-off between performance and computational complexity, applicable to a static operation framework of geostationary (GEO) satellite networks. Although the power allocation optimization is signomial programming, non-convex on a standard form, the solution can be lower bounded by the global optimum of a geometric program with a hidden convex structure. A local solution to the joint user scheduling and power allocation problem is consequently obtained by a successive optimization approach. Numerical results demonstrate the effectiveness of our algorithms on GEO satellite networks by providing better QoS satisfaction combined with outstanding overall system throughput.

Design of Avionics Network Architecture Under a Reliability Constraint

Reliability is an important aspect of operating safety-critical applications of networked systems, such as in avionics. In order to ensure sufficient reliability, one approach is to apply redundancy. However, redundancy may be costly if the degree of redundancy is too high. This article proposes an optimization-based framework for guaranteeing the desired reliability of any graph-based networked system. It focuses on integrated modular avionics architecture, based on the use of minimally redundant components. This framework consists of two steps. The first is to compute the minimum number of components within the architecture, using a geometric program. The second is to determine the topology with the minimal number of connections between these components, using a signomial program. Finally, the method is illustrated on a small example network and a larger network of the A350 avionics architecture.

Data fitting with signomial programming compatible difference of convex functions

Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general methods for optimization. While techniques exist for fitting GP compatible models to data, no models have been proposed that take advantage of the increased modeling flexibility available in SP. Here, a new Difference of Softmax Affine function is constructed by utilizing existing methods of GP compatible fitting in Difference of Convex (DC) functions. This new function class is fit to data in log–log space and becomes either a signomial or a set of signomials upon inverse transformation. Examples presented here include simple test cases in 1D and 2D, and a fit to the performance data of the NACA 24xx family of airfoils. In each case, RMS error is driven to less than 1%.

Optimal Aircraft Design Decisions Under Uncertainty Using Robust Signomial Programming

Aircraft design benefits from optimization under uncertainty since design feasibility and performance can have large sensitivities to uncertain parameters. Legacy methods of uncertainty protection do not adequately explain the tradeoffs between feasibility and optimality, and they require prior engineering knowledge that may not be available for new system concepts. Furthermore, stochastic optimization over parameter distributions is computationally intractable for solving high-dimensional nonlinear design optimization problems. This paper proposes an efficient solution method for engineering design optimization problems under uncertainty using robust signomial programs (RSPs). Signomial programs (SPs) have demonstrated potential in solving multidisciplinary optimization problems, and the formulation of RSPs enables conceptual design that captures parametric uncertainty with probabilistic guarantees of constraint satisfaction. The proposed method transforms stochastic optimization problems to deterministic problems by considering the worst-case robust counterpart of each design constraint over a parameter uncertainty set, provided that each constraint is SP representable. The RSP formulation extends an existing robust geometric program (RGP) formulation by allowing difference-of-log-convex constraints that appear in many design problems. The RSP is solved efficiently and deterministically using a sequence of local RGP approximations. RSPs are then applied to unmanned aircraft design, and they are used to rigorously explore the tradeoff between robustness and optimality in design decisions.

Energy-Aware Stochastic UAV-Assisted Surveillance

With the ease of deployment, capabilities of evading the jammers and obscuring their existence, unmanned aerial vehicles (UAVs) are one of the most suitable candidates to perform surveillance. There exists a body of literature in which the inspectors follow a deterministic trajectory to conduct surveillance, which results in a predictable environment for malicious entities. Thus, introducing randomness to the surveillance is of particular interest. In this work, we propose a novel framework for stochastic UAV-assisted surveillance that i) inherently considers the battery constraints of the UAVs, ii) proposes random moving patterns modeled via random walks, and iii) adds another degree of randomness to the system via considering probabilistic inspections. We formulate the problem of interest, i.e., obtaining the energy-efficient random walk and inspection policies of the UAVs subject to probabilistic constraints on inspection criteria of the sites and battery consumption of the UAVs, which turns out to be signomial programming that is highly non-convex. To solve it, we propose a centralized and a distributed algorithm along with their performance guarantee. This work contributes to both UAV-assisted surveillance and classic random walk literature by designing random walks with random inspection policies on weighted graphs with energy limited random walkers.

Sparse FIR Filter Design Based on Signomial Programming

The goal of sparse FIR filter design is to minimize the number of nonzero filter coefficients, while keeping its frequency response within specified boundaries. Such a design can be formally expressed via minimization of l0-norm of filter’s impulse response. Unfortunately, the corresponding minimization problem has combinatorial complexity. Therefore, many design methods are developed, which solve the problem approximately, or which solve the approximate problem exactly. In this paper, we propose an approach, which is based on the approximation of the l0-norm by an lp-norm with 0 < p < 1. We minimize the lp-norm using recently developed method for signomial programming (SGP). Our design starts with forming a SGP problem that describes filter specifications. The optimum solution of the problem is then found by using iterative procedure, which solves a geometric program in each iteration. The filters whose magnitude responses are constrained in minimax sense are considered. The design examples are provided illustrating that the proposed method, in most cases, results in filters with higher sparsity than those of the filters obtained by recently published methods.

Distributed Optimization Framework for In-Network Data Processing

In-Network Processing (INP) is an effective way to aggregate and process data from different sources and forward the aggregated data to other nodes for further processing until it reaches the end user. There is a trade-off between energy consumption for processing data and communication energy spent on transferring the data. An essential requirement in the INP process is to ensure that the user expectation of quality of information (QoI) is delivered during the process. Using wireless sensor networks for illustration and with the aim of minimizing the total energy consumption of the system, we study and formulate the trade-off problem as a nonlinear optimization problem where the goal is to determine the optimal data reduction rate, while satisfying the QoI required by the user. The formulated problem is a Signomial Programming (SP) problem, which is a non-convex optimization problem. We propose two solution frameworks. First, we introduce an equivalent problem which is still SP and non-convex as the original one, but we prove that the strong duality property holds, and propose an efficient distributed algorithm to obtain the optimal data reduction rates, while delivering the required QoI. The second framework applies to the system with identical nodes and parameter settings. In such cases, we prove that the complexity of the problem can be reduced logarithmically. We evaluate our proposed frameworks under different parameter settings and illustrate the validity and performance of the proposed techniques through extensive simulation.

Optimal placement for repair-efficient erasure codes in geo-diverse storage centres

Erasure codes are increasingly being used by storage providers to reduce the cost of reliably storing large volumes of data. As compared to the default mechanism of triple replication, erasure codes result in optimal storage efficiency, but require significant network and disk usage during repair of failed data. The repair process is particularly complicated for storage clusters with data centres spread across a wide geographical area. For such geo-diverse clusters, the recovery performance of the code used depends more on the network throughput and latency than on the computations required for decoding. Hence, the recovery performance of most erasure codes can be improved if the surviving blocks for effecting a node repair are placed optimally.This article affirms the idea by proposing an optimization framework for placement of blocks in geo-distributed storage clusters, addressing the open problem posed by Dimakis et al. in their celebrated paper on network coding. To this end, a signomial program is formulated that yields the optimal placement minimizing the average single-block repair cost over large number of files. Though non-convex, the structure of the problem allows us to use a monomial approximation to solve the problem efficiently. MATLAB simulation results and equivalent translation to implementation with popular codes used in Hadoop storage setting are presented, that validate our framework. The idea could be applied to any coded geo-diverse storage system to achieve significant benefits in repair performance during node failures.

Finding all global optima of engineering design problems with discrete signomial terms

ABSTRACTMany engineering design problems are frequently modelled as nonlinear programming problems with discrete signomial terms. In general, signomial programs are very difficult to solve for obtaining the globally optimal solution. This study reformulates the engineering design problem with discrete signomial terms as a mixed-integer linear program and finds all alternative global optima. Compared with existing exact methods, the proposed method uses fewer variables and constraints in the reformulated model and therefore efficiently solves the engineering problem to derive all global optima. Illustrative examples from the literature are solved to demonstrate the usefulness and efficiency of the proposed method.

Joint Time and Power Allocation in Multi-Cell Wireless Powered Communication Networks

This paper investigates the joint time and power allocation in a multi-cell wireless powered communication network (WPCN) with successive interference cancellation. In the WPCN, the hybrid access points broadcast wireless energy to all users and then the users utilize the harvested energy to transmit information simultaneously in a spectrum-sharing fashion. The max-min fairness throughput optimization and max-sum throughput optimization problems are formulated to analyze the system performance. However, both of the two optimization problems are nonconvex due to the complicated co-channel interference and the coupled time and power variables. To deal with this challenge, efficient two-stage approaches are proposed to transform them into more tractable ones. Specifically, for the max-min fairness throughput optimization problem, we first convert the power allocation problem into geometric programming (GP) problem for given time allocation and then optimize the time allocation. For the max-sum throughput optimization problem, we first transform the power allocation problem into a signomial programming problem with fixed time allocation, which is further approximated as a GP one. Then, time allocation is optimized. The simulation results validate the effectiveness of the two proposed approaches. In addition, it is shown that the “doubly near-far” issue can be well addressed by the max-min fairness throughput optimization.

Efficient Aircraft Multidisciplinary Design Optimization and Sensitivity Analysis via Signomial Programming

This paper proposes a new methodology for physics-based aircraft multidisciplinary design optimization (MDO) and sensitivity analysis. The proposed architecture uses signomial programming (SP), a type of difference-of-convex optimization that is solved iteratively as a series of log-convex problems. A requirement of SP is that all constraints and objective functions must have explicit signomial formulas. The SP MDO architecture facilitates the low-cost computation of optimal sensitivities through Lagrange duality. The specific example of commercial aircraft MDO is considered. Using SP, a small-, medium-, and large-scale benchmark problem is solved 16, 39, and 26 times faster, respectively, than Transport Aircraft System Optimization (TASOPT), a comparable and widely used aircraft MDO tool. The SP solution times include computation of all optimal parameter and constraint sensitivities, a feature unique to the presented architecture. The reliability of SP is demonstrated by converging a commercial aircraft MDO problem for a number of different objective functions and evaluating both traditional and nontraditional aircraft configurations. While the presented example is commercial aircraft MDO, the SP MDO architecture is applicable to a range of engineering optimization problems.

Power-Fractionizing Mechanism: Achieving Joint User Scheduling and Power Allocation via Geometric Programming

In the 4G and forthcoming 5G, the throughput is largely improved. Let edge users be the users beyond a certain distance to the associated BS in their covering cell, where the receiving intended signal is relative small. Throughput of edge users is the key metric measuring system performance. Originally designed for improving the performance of edge users under different scenarios, many technologies of user scheduling and power allocation, such as coordinated multipoint and Nash noncooperative power game are proposed. However, the existing algorithms are generally heuristic leading to a large performance gap in different scenarios. In this paper, we formulate a joint optimization to integrate user scheduling and power allocation into a unified optimization framework. By proposing a novel power-fractionizing mechanism, binary optimization can be avoided and the scheduling can be incorporated into the power allocation process. Thereafter, the joint optimization problem is then transformed into a signomial programming (SP) problem, which is further approximated by iteratively solving a series of tractable geometric programming problems that can converge to at least a local optimum of the SP problem. Unlike the existing heuristic algorithms dedicated to specific scenarios, our algorithm is more robust and environment adaptive. Simulation results show that the proposed joint optimization outperforms the existing heuristic approaches by significantly improving the total edge user throughput with stable performance.