Two-level Optimization Approach Research Articles

Stochastic Resource Optimization for Wireless Powered Hybrid Coded Edge Computing Networks

With the ubiquitous sensing enabled by the Internet-of-Things (IoT), massive amount of data is generated every second, transforming the way we interact with the world. To manage big data and enable analytics at the edge of the network, large amount of computation power is required to perform the computation intensive tasks. However, the energy-constrained IoT devices are not able to perform the computation tasks without compromising the quality-of-service of the applications. In this paper, we propose a hybrid network in which users can fully offload their computation tasks to edge servers through coded edge offloading or perform local computation with the wireless power transfer derived from coalitions of unmanned aerial vehicles (UAVs) serving as mobile charging stations. To minimize the cost of the network, we consider a two-level optimization approach. At the lower level, an optimal UAV coalition that minimizes the network cost is formed. At the upper level, the computation approach for each user is decided while taking into account the stochastic nature of wireless charging efficiency. Given the interrelation between the two levels, we adopt the backward induction optimization strategy to jointly derive the optimal coalition structure and computation approach for each user. In the performance evaluation, we provide extensive sensitivity analyses to study the performance of the cost minimization approaches amid varying network parameters. Moreover, we show that our approach outperforms deterministic optimization approaches in network cost minimization.

Centimeter-level-precision seafloor geodetic positioning model with self-structured empirical sound speed profile

In-field Sound Speed Profile (SSP) measurement is still indispensable for achieving centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning in current state of the art. However, in-field SSP measurement on the one hand causes a huge cost and on the other hand prevents GNSS-A from global seafloor geodesy especially for real-time applications. We propose an Empirical Sound Speed Profile (ESSP) model with three unknown temperature parameters jointly estimated with the seafloor geodetic station coordinates, which is called the 1st-level optimization. Furthermore, regarding the sound speed variations of ESSP we propose a so-called 2nd-level optimization to achieve the centimeter-level-precision positioning for monitoring the seafloor tectonic movement. Long-term seafloor geodetic data analysis shows that, the proposed two-level optimization approach can achieve almost the same positioning result with that based on the in-field SSP. The influence of substituting the in-field SSP with ESSP on the horizontal coordinates is less than 3 mm, while that on the vertical coordinate is only 2–3 cm in the standard deviation sense.

Comprehensive optimization of urban building cluster morphology based on microclimate: A two-level optimization approach

Building cluster morphology plays a crucial role in shaping urban microclimate. Due to the global warming and urban expansion, urban microclimate environment has encountered several problems, like extreme heat or cold stress events. The practical design of building clusters often involves multi-scale, multi-faceted problems and contradiction points which is always challenging to solve. This paper proposes a “two-level” optimization framework for the layout and form design of building clusters in the aspect of engineering applications. A case design project is used to demonstrate the effectiveness of the proposed framework through detailed seasonal simulation. Results show that, comparing with the base case, the candidate design plan (i.e., Plan C) is attractive given the mean UTCI of the selected locations is lower by 0.73 °C in the cooling season noon and higher by 1.91 °C in the heating season at night. Results also indicate that the layout of a building cluster has greater impacts on the outdoor thermal environment during the heating season than the cooling season. Considering Plan C still has a heat/cold stress, further refinements have been performed on the local micro climate to adjust the wind corridor and solar radiation at the lower-level of architectural form. Finally, comprehensive design strategies have been synthesized for the building cluster design.

Neural-network-assisted optimization of a close-range multi-spacecraft rendezvous mission based on a multi-impulse maneuvering strategy

Rendezvous mission planning between service spacecraft and multiple close-range target spacecraft in the on-orbit service application is studied, using multiple impulses based on the Clohessy-Wiltshire equation as a maneuvering strategy. An impulsive correction method is proposed to avoid rendezvous errors. The optimization objectives of this work include the minimum total velocity increase and the minimum mission time. A two-level optimization approach is developed to find the Pareto-optimal set of the above multi-objective optimization problem. In the low-level optimization, the propellant-optimal impulsive trajectory for the rendezvous between the SSc and each target spacecraft at a fixed maneuver duration is solved by a proposed iterative optimization algorithm with a double loop. On the other hand, the rendezvous sequence and maneuver duration are optimized by a proposed neural-network-assisted evolutionary algorithm in up-level optimization, which combines the feedforward neural network with the elitist multi-objective genetic algorithm (NSGA-II). Finally, representative simulation examples are presented to verify the proposed optimization algorithm and demonstrate its superiority over the traditional algorithm.

Two-level Approach for Heterogeneous Multi-Robot Optimal Navigation

This paper proposes a two-level optimization approach for a multi-robot navigation problem. Our aim is to achieve tasks with optimal strategies, optimal trajectory planning and to give better and feasible solutions. Optimal alternatives are selected by combining game theory strategic decision with an optimal trajectory planning method. This is solved at the top level by applying Sequential Quadratic Programming (SQP). At the bottom, Pure Nash equilibrium is solved using the Simulated Annealing (SA) algorithm. The trajectory planning for the multi-robot system is performed by decomposition where the b-spline technique is initially used to describe the robots path in an environment with obstacles. The cubic spline technique is then introduced to set up the motion along the desired path. The kinematic and dynamic constraints inherent to the robot behavior are taken into account and collision constraints are handled by penalization. The proposed approach is applied to heterogeneous Unicycle Wheeled Mobile Robots and simulated in endowed obstacles environment. Optimal collision-free trajectories of the robot team are obtained with smooth line paths and good-quality solutions. Simulation results are given to show the effectiveness and robustness of proposed algorithm.

A zonal optimization solution to reliability security constraint unit commitment with wind uncertainty

In restructured power systems, Independent System Operator manages and handles the Reliability-Security Constraint Unit Commitment problems including reliability and security issues. In this paper, a novel two-level optimization approach is proposed to achieve reliable, secure, and optimal generation units’ schedule while wind generation units are presents, in which the power system is divided to a number of zones. Uncertainties and time-dependent sources such as wind generation units are the most significant reasons for reliability challenges. In the proposed approach, load forecast and wind generation units’ uncertainty have been considered. An intelligent search technique is implemented for reliability study. The proposed method is evaluated by simulation of the 6-bus, 118-bus, and 4672-bus test systems. The two-level optimization is compared to robust optimization and centralized methods. The results show the effectiveness and significance of this method.

Two-level optimization approach with accelerated proximal gradient for objective measures in sparse speech reconstruction

<p style='text-indent:20px;'>Compressive speech enhancement makes use of the sparseness of speech and the non-sparseness of noise in time-frequency representation to perform speech enhancement. However, reconstructing the sparsest output may not necessarily translate to a good enhanced speech signal as speech distortion may be at risk. This paper proposes a two level optimization approach to incorporate objective quality measures in compressive speech enhancement. The proposed method combines the accelerated proximal gradient approach and a global one dimensional optimization method to solve the sparse reconstruction. By incorporating objective quality measures in the optimization process, the reconstructed output is not only sparse but also maintains the highest objective quality score possible. In other words, the sparse speech reconstruction process is now quality sparse speech reconstruction. Experimental results in a compressive speech enhancement consistently show score improvement in objectives measures in different noisy environments compared to the non-optimized method. Additionally, the proposed optimization yields a higher convergence rate with a lower computational complexity compared to the existing methods.</p>

A Two-Level Optimization Approach For Engineer-To-Order Project Scheduling*

This paper presents a new formulation of the flexible job-shop scheduling problem with outsourcing options adapted for Engineer-To-Order (ETO) products. Our formulation enables modeling complex product structures with flexible precedence relations between elements and operations. Having a significant role in the ETO context, the specificity of non-physical operations (design and engineering) is taken into account. Indeed, non-physical operations are subject to a validation stage, can be iterated in case of non-validation, and are executed once for several identical elements. The proposed approach is governed by a new ETO strategy to overcome the impact of the design uncertainty and element cancellations (time and financial wastes). First, the production and purchase of the most uncertain elements are delayed at the latest while their design is validated early. Besides, in the presence of similar elements, an element can be saved when cancelled by being used as a sub-part of another one. The proposed approach sequentially solves two mathematical models. The first model aims to minimise the makespan and outsourcing costs. The second model maximizes the solution robustness and the ability of saving elements while being governed by the completion time and project cost, output of the first model. The obtained results and a comparative study show the efficiency and robustness of the proposal.

Two-level optimization approach to tree-level forest planning

Laser scanning and individual-tree detection are used increasingly in forest inventories. As a consequence, methods that optimize forest management at the level of individual trees will be gradually developed and adopted. The current study proposed a hierarchical two-level optimization method for tree-level planning where the cutting years are optimized at the higher level. The lower-level optimization allocates the trees to the cutting events in an optimal way. The higher-level optimization employed differential evolution whereas the lower-level problem was solved with the simulated annealing metaheuristic. The method was demonstrated with a 30 ​m ​× ​30 ​m sample plot of planted Larix olgensis . The baseline case maximized the net present value as the only management objective. The solution suggested heavy thinning from above and a rotation length of 62 years. The baseline problem was enhanced to mixed stands where species diversity was used as another management objective. The method was also demonstrated in a problem that considered the complexity of stand structure, in addition to net present value. The objective variables that were used to measure complexity were the Shannon index (species diversity), Gini index (tree size diversity), and the index of Clark and Evans, which was used to describe the spatial distribution of trees. The article also presents a method to include natural advance regeneration in the optimization problem and optimize the parameters of simulated annealing simultaneously with the cutting years. The study showed that optimization approaches developed for forest-level planning can be adapted to problems where treatment prescriptions are required for individual trees.

A novel two-stage optimization method for the reliability based security constraints unit commitment in presence of wind units

In the restructured power system environment, independent system operator solves the Reliability-security constraint unit commitment (R–SCUC) problem that included reliability, economic issue and security. Therefore, in the modern bulk of power systems, the existing centralized methods cannot solve the complex issues such as large power system complexity. In this paper, a novel two-level optimization approach for a reliable, secure, and optimal generation scheduling is proposed. The power system is divided into several zones, in which each one solves its own R–SCUC problem. In the face of different uncertainties and time-dependent sources such as wind units there is new challenges in power systems reliability. In the proposed approach, load forecasting and wind units simulated based on the Gaussian probability distribution function and weibull probability distribution function (PDF), respectively. Energy bid modeling is formulated to fit the R–SCUC problem. In order to take into account reliability model, intelligent search techniques, i.e., TEENS, LOLP, are implemented in the whole power system. The proposed methods are performed in a 6-bus network, IEEE 118-bus and IEEE 4672-bus test systems. The presented approach has been programed by GAMS, and the results show the effectiveness of the proposed methodology to enhance security and reliability of the power system.

Optimization for overall planning of space-station on-orbit activities and logistics

This paper develops a problem formulation corresponding to the long-term overall operation planning for large-scale space-station missions that need to be executed in 3–5 years. The space station overall operation planning consists of the on-orbit activity allocation and its supporting logistics design. A two-level optimization approach is proposed to solve this complicated problem hierarchically by using a multi-objective evolutionary algorithm. The first-level problem is to optimize the overall allocation scheme of on-orbit activities to achieve the activity distribution equilibrium on logistics demand, resource requirement, and activity characteristics. The second-level problem is to optimize the launch time and loading scheme of visiting vehicles under multiple constraints to meet the on-board supply demand, and a pretreatment strategy is proposed based on the space-station logistics domain knowledge to resolve constraints a priori. Numerical results indicate that the proposed formulation for space-station overall operation planning is effective, and the proposed pretreatment approach can reduce the difficulty of satisfying multiple constraints in optimization.

Secure Cooperative Transmission for Mixed RF/FSO Spectrum Sharing Networks

This paper is concerned with the secrecy rate based optimization problems in a mixed radio frequency (RF) / free space optical (FSO) spectrum sharing network, wherein multiple single-antenna secondary users (SUs) are connected to a decode and forward (DF) single-antenna relay through RF links and the relay is connected with the secondary destination through an FSO link. The RF and FSO channels are assumed to follow Rayleigh and Gamma-Gamma distributions with the effect of pointing errors, respectively. The three schemes, i.e., direct transmission, single-user cooperative jamming and multi-user cooperative beamforming jamming, are proposed to improve the physical-layer information security in the presence of a single-antenna eavesdropper. The mutual interference between the primary and secondary networks is considered. The problems are to jointly optimize the SU transmit power and jamming power for the best secrecy performance under both the RF and FSO dominant cases. Such problems are nonconvex. The Dinkelbach approach is adopted to solve the optimization in the direct transmission and single-user cooperative jamming schemes and a two-level optimization approach with semi-definite relaxation (SDR) is applied to obtain the solution for the multi-user cooperative beamforming scheme. Moreover, the SDR optimality is proved by Karush-Kuhn-Tucker conditions analysis. Simulation results are provided, and the results show that the proposed multi-user cooperative beamforming jamming can attain the higher achievable secrecy rate than the zero-forcing beamforming scheme and other two suboptimal designs.

A two-level approach for three-dimensional micro-siting optimization of large-scale wind farms

For three-dimensional micro-siting of large-scale wind farms, it is difficult for the traditional once-and-for-all approach to search for optimal solutions when tuning all the turbine locations and heights simultaneously. In this paper, a two-level optimization approach is presented for three-dimensional micro-siting optimization of large-scale wind farms. The proposed approach uses a hierarchical structure, where the wind farm is considered as a compound that consists of several blocks with identical sizes. A multi-objective algorithm is used to optimize one block, producing a set of block candidates. Then the compound-level algorithm optimizes the whole wind farm layout by searching among all possible combinations of the block candidates. The proposed approach is tested on 24 cases with different choices and combinations of objective, wind scenario and number of turbines. The results show that the proposed method can significantly reduce the difficulty of searching for the optimal solution, and demonstrates noticeable improvements than the traditional one-level approach.

Sound Radiation Analysis of Constrained Layer Damping Structures Based on Two-Level Optimization.

Constrained layer damping (CLD) is an effective method for suppressing the vibration and sound radiation of lightweight structures. In this article, a two-level optimization approach is presented as a systematic methodology to design position layouts and thickness configurations of CLD materials for suppressing the sound power of vibrating structures. A two-level optimization model for the CLD structure is developed, considering sound radiation power as the objective function and different additional mass fractions as constraints. The proposed approach applies a modified bi-directional evolutionary structural optimization (BESO) method to obtain several optimal position layouts of CLD materials pasted on the base structure, and sound power sensitivity analysis is formulated based on sound radiation modes for the position optimization of CLD materials. Two strategies based on the distributions of average normalized elemental kinetic energy and strain energy of the base plate are proposed to divide optimal position layouts of CLD materials into several subareas, and a genetic algorithm (GA) is employed to optimally reconfigure the thicknesses of CLD materials in the subareas. Numerical examples are provided to illustrate the validity and efficiency of this approach. The sound radiation power radiated from the vibrating plate, which is treated with multiple position layouts and thickness reconfigurations of CLD materials, is emphatically discussed.

Elastic Constants Determination of Composite Plates Using Measured Strains

A strain-based elastic constant identification method is proposed to determine the elastic constants of fiber-reinforced composite rectangular laminates using three measured strains of the plates subjected to uniaxial load testing. In the proposed method, the measured normal strains in 0°, and 45°, and 90° directions, respectively, of the plate made of one composite material subjected to uniaxial tensile testing are used to identify four elastic constants of the constituent composite material via a two-level optimization approach. The objective function used for constructing the two-level optimization problem consists of the sum of the differences between the experimental and theoretical predictions of the three strain components and a strain restraining function, which is used to help even up the effects of the measured strains on the identified elastic constants. The accuracy of the proposed method has been verified via an experimental approach.

Maslow Portfolio Selection for Individuals with Low Financial Sustainability

In this paper, we extend Maslow’s need hierarchy theory and the two-level optimization approach by developing the framework of the Maslow portfolio selection model (MPSM) by solving the two optimization problems to meet the need of individuals with low financial sustainability who prefer to satisfy their lower-level (safety) need first, and, thereafter, look for higher-level (self-actualization) need to maximize the optimal return. We illustrate our proposed model with real American stock data from the S&P index and conduct the out-of-sample analysis to compare the performance of our proposed Variance-CVaR (conditional value-at-risk) MPSM with both traditional mean-variance and mean-CVaR models. Our empirical analysis shows that our proposed Variance-CVaR MPSM is not only sustainable, but also obtains the best out-of-sample performance in the sense that the optimal portfolios obtained by using our proposed Variance-CVaR MPSM obtain the highest cumulative returns in the out-of-sample period among the models used in our paper. We note that our proposed model is not only suitable to individuals with low financial sustainability, but also suitable to institutions or investors with high financial sustainability.

A Two-Level Cross-Sectional Optimization Approach for Automotive Body Concept Design

Concept design is vital important in development of auto-body and it has great effects on later design work. In this paper, a two-level cross-sectional optimization approach is presented to shorten concept design cycles. First, an exact structural analysis approach for spatial semi-rigid framed structures, i.e., the transfer stiffness matrix method proposed in our previous study, is adopted for both static and dynamic analyses of body-in-white (BIW) structure. A two-level cross-sectional optimization approach is then proposed for an automotive BIW lightweight design, and genetic algorithm is used to solve the optimization models. Afterward, an object-oriented MATLAB toolbox, using distributed parallel computing techniques, is developed to promote the concept design of the BIW structure. Finally, relevant numerical examples demonstrate the validity and accuracy of the proposed method.

A novel two-level optimization approach for clustered vehicle routing problem

Abstract In this paper, we are addressing the clustered vehicle routing problem (CluVRP) which is a variant of the classical capacitated vehicle routing problem (CVRP). The following are the main characteristics of this problem: the vertices of the graph are partitioned into a given number of clusters and we are looking for a minimum-cost collection of routes starting and ending at the depot, visiting all the vertices exactly once, except the depot, and with the additional constraint that once a vehicle enters a cluster it visits all the vertices within the cluster before leaving it. We describe a novel two-level optimization approach for CluVRP obtained by decomposing the problem into two logical and natural smaller subproblems: an upper-level (global) subproblem and a lower-level (local) subproblem, and solving them separately. The goal of the first subproblem is to determine the (global) routes visiting the clusters using a genetic algorithm, while the goal of the second subproblem is, to determine for the above mentioned routes, the visiting order within the clusters. The second subproblem is solved by transforming each global route into a traveling salesman problem (TSP) which then is optimally computed using the Concorde TSP solver. Extensive computational results are reported and discussed for an often used set of benchmark instances. The obtained results show an improvement of the quality of the achieved solutions and prove the efficiency of our approach as compared to the existing methods from the literature.

Two-Level Design Optimization for Compression Stiffened Panel

In this paper, a two-level design optimization approach is presented for compression stiffened panel sizing. First, the stiffened panel design procedure is described by means of a structural index concept. This method is based on the analytical formulations for structures and is used for the preliminary design level. In this procedure, the final results have a general form without being restricted by the geometrical parameters. The final results can be used for sizing different types of compression stiffened panels. Using the results obtained in the first level, the surrogate-based optimization is employed for design optimization in the second level. The analysis tool in the second level is the finite element method. Using Sequential Quadratic Programming algorithm, a novel technique is developed to find the global optimum of the surrogate model. The proposed two-level design approach is employed for design optimization of a flanged stiffened panel. In this panel design problem, which has six design variables, an initial training set with 57 points is created. Using 173 infill points, the optimum solution is obtained. In comparison with the conventional optimization methods, the surrogate modeling reduces the required nonlinear buckling analyses significantly. An estimate of the required number of analyses in the conventional methods is 57,201. The results of both levels are compared with each other. The final results of the optimization process are the optimum design non-dimensional ratios for plate elements of the flanged stiffened panel.

Joint cooperative beamforming and artificial noise design for secure AF relay networks with energy-harvesting eavesdroppers

In this paper, we investigate physical layer security for simultaneous wireless information and power transfer in amplify-and-forward relay networks. We propose a joint robust cooperative beamforming and artificial noise scheme for secure communication and efficient wireless energy transfer. Specifically, by treating the energy receiver as a potential eavesdropper and assuming that only imperfect channel state information can be obtained, we formulate an optimization problem to maximize the worst-case secrecy rate between the source and the legitimate information receiver under both the power constraint at the relays and the wireless power harvest constraint at the energy receiver. Since such a problem is non-convex and hard to tackle, we propose a two-level optimization approach which involves a one-dimensional search and semidefinite relaxation. Simulation results show that the proposed robust scheme achieves better worst-case secrecy rate performance than other schemes.