Weighted Tchebycheff Approach Research Articles

Multi-Objective Robust Beamforming for Integrated Satellite and Aerial Networks Supporting Heterogeneous Services

An integrated satellite and aerial network (ISAN) is considered a promising candidate to provide seamless connectivity for future wireless communication systems. In this paper, we propose a multi-objective based robust beamforming (BF) scheme for an ISAN to support heterogeneous services with high flexibility, where the satellite network serves various heterogeneous satellite terminals through multicast non-orthogonal multiple access (MC-NOMA), while the aerial network offers services to many internet of things devices using layered division multiplexing (LDM). Specifically, we first formulate a multi-objective optimization problem (MOOP) to achieve a good trade-off between sum rate maximization and total transmit power minimization. To tackle this mathematically intractable problem, we exploit the weighted Tchebycheff approach to transform the MOOP into a single-objective problem. Since only the angular information based channel state information is available, we exploit the angular discretization method and sequential convex approximation to design a robust BF algorithm to obtain the Pareto optimal solutions. Finally, simulation results demonstrated that our proposed scheme can achieve a optimal trade-off between multiple performance metrics with high spectrum and energy efficiency, so as to support heterogeneous services in the ISAN and fill the gap of only single type of serivce in the existing ISAN works.

Performance Tradeoff of MVNOs in OFDMA-Based Virtualized Wireless Networks

In this paper, we analyze the tradeoff between the profits gained by mobile virtual network operators (MVNOs) in an orthogonal frequency division multiple access (OFDMA)-based virtualized wireless networks (VWNs). In this respect, MVNOs rent the network resources from a mobile network operator (MNO) to create virtual resources based on allocated rates and the cost due to allocated transmit powers in two different strategies: resource-based isolation strategy and rate-based isolation strategy. In resource-based isolation strategy, it is assumed that the whole bandwidth in each base station is divided equally between MVNOs whereas in rate-based isolation strategy, the whole bandwidth in each base station is allocated dynamically between MVNOs. We then formulate a multi-objective optimization problem (MOOP) to show the tradeoff between the maximum profit of each MVNO. To solve the formulated MOOP, we adopt the weighted Tchebycheff approach, which can provide the complete Pareto optimal region for nonconvex problems. Thus, by developing such formulation, we will be able to find the best profit gained by MVNOs. We also employ monotonic optimization to obtain the global optimal solutions of the non-convex problems by applying polyblock outer approximation algorithm. Our numerical results show the importance of the aforementioned tradeoffs and confirm that the proposed geometric programming (GP) based algorithm achieves excellent performance as compared to the monotonic method.

Multi-objective robust secure beamforming for cognitive satellite and UAV networks

A multi-objective optimization based robust beam-forming (BF) scheme is proposed to realize secure transmission in a cognitive satellite and unmanned aerial vehicle (UAV) network. Since the satellite network coexists with the UAV network, we first consider both achievable secrecy rate maximization and total transmit power minimization, and formulate a multi-objective optimization problem (MOOP) using the weighted Tchebycheff approach. Then, by supposing that only imperfect channel state information based on the angular information is available, we propose a method combining angular discretization with Taylor approximation to transform the non-convex objective function and constraints to the convex ones. Next, we adopt semi-definite programming together with randomization technology to solve the original MOOP and obtain the BF weight vector. Finally, simulation results illustrate that the Pareto optimal trade-off can be achieved, and the superiority of our proposed scheme is confirmed by comparing with the existing BF schemes.

A bi-objective robust optimization approach for the management of infectious wastes with demand uncertainty during a pandemic

The current global COVID-19 pandemic attracts public attention to the management of waste generated by health-care activities. Due to the hazardous nature, infectious waste requires the design of a multi-tiered system to provide cost-efficient and eco-friendly services of waste collection, transportation, treatment, and final disposal. However, the impact of uncertainties has not been well studied in the existing literature. Considering the presence of random waste generation during a pandemic, we aim to answer the following questions: 1) where to locate temporary transfer stations and temporary treatment centers; 2) how to plan collection tours among the small generation nodes and temporary transfer stations; 3) how to plan the direct transportation from large generation nodes to treatment centers; 4) how to transport waste from temporary transfer stations to treatment centers, and 5) how to transport wastes from treatment centers to disposal facilities. The relevant cost and associated risk are respectively formulated and assessed using a scenario-based bi-objective robust approach. The complexity of the resulting mathematical model motivated the adaption and comparison of three multi-objective optimization approaches, including the goal programming method, a lexicographic weighted Tchebycheff approach, and an augmented ϵ-constraint solution technique. A case study based on the real situation in Wuhan, China, during the COVID-19 outbreak is conducted to demonstrate the workability of the proposed model and provide managerial insights for infectious waste management. The computational results show that our proposed model can more than double the demand fulfillment rate at an approximately 40% lower cost when facing a distinctively high increment in the amount of infectious waste.

Power Efficient Secure Full-Duplex SWIPT Using NOMA and D2D with Imperfect CSI.

The secure full-duplex (FD) simultaneous wireless information and power transfer (SWIPT) system and non-orthogonal multiple access (NOMA) have been deemed two promising technologies for the next generation of wireless communication. In this paper, the network is combined with device-to-device (D2D) and a practical bounded channel state information (CSI) estimation scheme. A system total transmit power minimization problem is studied and formulated as a multi-objective optimization (MOO) problem via the weighted Tchebycheff approach. A set of linear matrix inequalities (LMI) is used to transform the non-convex form of constraints into the convex form. Considering the imperfect CSI of the potential eavesdropper for robust power allocation, a bounded transmission beamforming vector design along with artificial noise (AN) is used, while satisfying the requirements from the secrecy rates as well as the energy harvesting (EH) task. Numerical simulation results validate the convergence performance and the trade-off between the uplink (UL) and downlink (DL) data transmit power. It is also shown that by FD and NOMA, the performance of the proposed algorithm is higher than that of half-duplex (HD) and orthogonal multiple access (OMA).

Delay-Aware Resource Management for Multi-Service Coexisting LTE-D2D Networks With Wireless Network Virtualization

To satisfy the rapid growth of data service demands on the limited spectrum resources, wireless network virtualization (WNV) has been proposed as a promising technology in the future wireless networks. Meanwhile, Device-to-Device (D2D) communication, as an underlay to cellular networks, is also a proposed solution to promote the spectrum efficiency. However, it is a challenge to design an appropriate virtual resource slicing strategy among different wireless service providers in the two-tier LTE-D2D networks. In this paper, considering dynamic traffic arrivals and time-varying channel conditions, the virtualized resource management in the multi-service coexisting LTE-D2D networks is formulated into a multi-objective stochastic optimization problem. Leveraging on weighted Tchebycheff approach and Lyapunov optimization technique, the multi-objective stochastic optimization problem can be transformed into a delay-aware optimization problem, which is a mixed-integer nonlinear programming (MINLP) problem and can be transformed into a convex one by a series of reformulation. A distributed algorithm based on the alternating direction method of multipliers (ADMM) is proposed to obtain a close-to-optimal solution with a lower computational complexity. Finally, the simulation results show that the proposed scheme can achieve a performance-delay tradeoff related to the control factor V with at most 0.2% performance loss compared with the optimal solution.

Multi-Objective Optimization for Full-Duplex SWIPT Systems

This paper studies a multi-objective optimization (MOO) problem in full-duplex (FD) networks with simultaneous wireless information and power transfer (SWIPT). In the considered networks, an FD base station (BS) communicates with multiple half-duplex (HD) uplink (UL) and downlink (DL) users simultaneously. The energy receivers (ERs) harvest energy from the ambient radio frequency (RF) signals and may act as potential eavesdroppers. Specifically, there exists two conflicting yet important system design objectives, i.e., secrecy energy efficiency (SEE) maximization and energy harvesting efficiency (EHE) maximization. An MOO design based on the weighted Tchebycheff approach is proposed to investigate the tradeoff between these two design objectives. The proposed design takes into account the quality-of-service (QoS) guarantees of secrecy rate and energy harvesting (EH) under the imperfect channel state information (CSI) of ERs. The formulated MOO problem is solved with a two-layer optimization algorithm, where the modified Dinkelbach method is applied to deal with the generalized fractional programming (FP) in the outer layer problem and semidefinite relaxation (SDR), successive convex approximation (SCA) as well as S-procedure methods are applied to transfer the inner layer problem into a convex iterative program. Moreover, we propose a suboptimal solution to the formulated problem and analyze the computational complexities. Finally, numerical results are provided to demonstrate the effectiveness of the proposed algorithms and reveal a tradeoff region between SEE and EHE.

Multi-objective optimization design for multi-source multicasting MIMO AF relay systems

In this paper, we consider a multi-source multicasting two-hop multi-input multi-output amplify-forward (AF) relay system, where multiple source nodes multicast their own messages to a group of receivers with the cooperation of an AF relay node. In particular, we aim at minimizing the transmission power consumption and the mean-squared error (MSE) of the receiver estimated signal simultaneously. However, the two objectives are coupled and even conflicting. In view of this, a multi-objective optimization (MOO) framework is adopted to achieve the trade-off between the two objectives. The formulated MOO problem (MOOP) takes into account the constraints of the MSE upper bound and the maximum transmission power budget. Since the MOOP is non-convex and hard to tackle, we propose a resource allocation algorithm by exploiting the weighted Tchebycheff approach and the optimal structure of the relay precoding matrix. Simulation results not only demonstrate the effectiveness of the proposed algorithm, but also unveil an important trade-off between the total power consumption and the MSE at receivers.

Robust Multi-Objective Beamforming Design for Power Efficient and Secure Communication in MU-MISO Networks

In this paper, we consider transmission optimization in a multiple-input-single-output downlink network, in which each user is wiretapped by a specific eavesdropper. Particularly, we aim to minimize the total transmit power and maximize the sum secrecy rate (SSR) of the system simultaneously, under the assumption that the channel state information (CSI) of the eavesdroppers is not perfectly known at the transmitter. Considering the conflict between two objectives, a multi-objective optimization (MOO) framework based on the weighted Tchebycheff approach is proposed. The formulated MOO problem is non-convex and intractable. To tackle it, several auxiliary variables are introduced and the corresponding Taylor series expansion is employed to linearize the term related to each auxiliary variable. Then, the non-convexity resulting from the CSI errors is recast as a convex one with the aid of ${S}$ -procedure and Cauchy–Schwarz inequality. Based on above treatments, a robust iterative algorithm is proposed to solve the original problem. Simulation results not only demonstrate the effectiveness of the proposed design, but also unveil the tradeoff between the total transmit power and the SSR.

A lexicographic weighted Tchebycheff approach for multi-constrained multi-objective optimization of the surface grinding process

ABSTRACTIn this article a multi-objective mathematical model is developed to minimize total time and cost while maximizing the production rate and surface finish quality in the grinding process. The model aims to determine optimal values of the decision variables considering process constraints. A lexicographic weighted Tchebycheff approach is developed to obtain efficient Pareto-optimal solutions of the problem in both rough and finished conditions. Utilizing a polyhedral branch-and-cut algorithm, the lexicographic weighted Tchebycheff model of the proposed multi-objective model is solved using GAMS software. The Pareto-optimal solutions provide a proper trade-off between conflicting objective functions which helps the decision maker to select the best values for the decision variables. Sensitivity analyses are performed to determine the effect of change in the grain size, grinding ratio, feed rate, labour cost per hour, length of workpiece, wheel diameter and downfeed of grinding parameters on each value of the objective function.

Multiobjective Resource Allocation for Secure Communication in Cognitive Radio Networks With Wireless Information and Power Transfer

In this paper, we study resource allocation for multiuser multiple-input–single-output secondary communication systems with multiple system design objectives. We consider cognitive radio (CR) networks where the secondary receivers are able to harvest energy from the radio frequency when they are idle. The secondary system provides simultaneous wireless power and secure information transfer to the secondary receivers. We propose a multiobjective optimization framework for the design of a Pareto-optimal resource allocation algorithm based on the weighted Tchebycheff approach. In particular, the algorithm design incorporates three important system design objectives: total transmit power minimization, energy harvesting efficiency maximization, and interference-power-leakage-to-transmit-power ratio minimization. The proposed framework takes into account a quality-of-service (QoS) requirement regarding communication secrecy in the secondary system and the imperfection of the channel state information (CSI) of potential eavesdroppers (idle secondary receivers and primary receivers) at the secondary transmitter. The proposed framework includes total harvested power maximization and interference power leakage minimization as special cases. The adopted multiobjective optimization problem is nonconvex and is recast as a convex optimization problem via semidefinite programming (SDP) relaxation. It is shown that the global optimal solution of the original problem can be constructed by exploiting both the primal and the dual optimal solutions of the SDP-relaxed problem. Moreover, two suboptimal resource allocation schemes for the case when the solution of the dual problem is unavailable for constructing the optimal solution are proposed. Numerical results not only demonstrate the close-to-optimal performance of the proposed suboptimal schemes but unveil an interesting tradeoff among the considered conflicting system design objectives as well.

An integration design optimization framework of robust design, axiomatic design, and reliability-based design

Robust design, axiomatic design, and reliability-based design provide effective approaches to deal with quality problems, and their integration will achieve better quality improvement. An integration design optimization framework of robust design, axiomatic design, and reliability-based design is proposed in this paper. First, the fitted response model of each quality characteristic is obtained by response surface methodology and the mean square error (MSE) estimation is given by a second-order Taylor series approximation expansion. Then the multiple quality characteristics robust design model is developed by the MSE criteria. Finally, the independence axiom constraints for decoupling and reliability constraints are integrated into the multiple quality characteristics robust design model, and the integration design optimization framework is formulated, where the weighted Tchebycheff approach is adopted to solve the multiple objective programming. An illustrative example is presented at the end, and the results show that the proposed approach can obtain better trade-offs among conflicting quality characteristics, variability, coupling degree and reliability requirements. Copyright © 2011 John Wiley & Sons, Ltd.

Studies on a biobjective robust design optimization problem

The vast majority of the multiobjective robust design research reported in the literature has been performed under the assumption of multiple quality characteristics. This paper differs in that the process mean and variance are considered to be a biobjective problem since the primary goal of robust design is to determine the optimal robust design factor settings by minimizing performance variability and deviation from a target value of a product. A more comprehensive set of solutions is developed using a lexicographic weighted Tchebycheff approach to the biobjective robust design model rather than the approaches traditionally used in the dual-response approach to obtain efficient solutions. Numerical examples show that the proposed model is far more effective than the traditional weighted sum approach. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix with mathematical proof, figures, and tables.]

An Interactive Multistage ε-Inequality Constraint Method For Multiple Objectives Decision Making

Multiple objectives decision making (MODM) in engineering design refers to obtaining a preferred optimal solution in the context of conflicting design objectives. Problems with multiple objectives do not have a unique optimal solution but a set of Pareto optimal solutions. This paper presents a new interactive multistage MODM method which captures a decision maker’s preference structure in order to obtain a preferred Pareto solution even for non-convex problems. Representative subsets of an entire Pareto optimal set are generated and expanded based on the decision maker’s preference. The ε-constraint method is used to constrain the multiple objectives problem based on the decision maker’s feedback. In addition, ideas from an interactive weighted Tchebycheff approach are applied to reduce the feasible region at each stage, ensuring that the process eventually converges to a preferred solution. The method is demonstrated with two examples: (i) a simple two-bar truss design, and (ii) a more complicated problem in power electronic module design.