Conventional Optimization Methods Research Articles

Optimal Relay Node Selection for Robust Data Forwarding Over Time-Varying IoT Networks

Mobility-tolerant data forwarding over time-varying IoT networks is a challenging problem. Selection of a relay node at every instant in time is crucial and calls for robust and distributed methods to improve the quality of services in such networks. In this paper, an optimal relay node selection method is proposed for robust data forwarding in time-varying networks. The proposed method selects a relay node based on joint optimization of two network parameters, namely data latency and link reliability. The Pareto front of this multi-objective optimization problem is used to illustrate the tradeoff between low data latency and high link reliability. The proposed optimal relay node selection method first identifies all possible relay nodes at every time instant. The weights of the bi-objective problem are updated at every hop and an optimal relay node is selected among all the possible relay nodes, by solving the joint optimization problem. During performance evaluation, random spatial patterns of Internet of Things (IoT) devices are modeled using the homogeneous Poisson point processes. The connectivity duration information of all the IoT devices with their neighbors is updated continuously and a relay node found is in an online manner. Simulation results indicate that the proposed method significantly improves data latency and the packet loss risk for data forwarding over time-varying IoT networks, when compared to conventional single parameter optimization methods. The proposed data forwarding method indicates additional gains in terms of transmission range, mobility tolerance, packet replication cost, and connectivity parameters of the time-varying IoT network.

Deep Reinforcement Learning for Online Computation Offloading in Wireless Powered Mobile-Edge Computing Networks

Wireless powered mobile-edge computing (MEC) has recently emerged as a promising paradigm to enhance the data processing capability of low-power networks, such as wireless sensor networks and internet of things (IoT). In this paper, we consider a wireless powered MEC network that adopts a binary offloading policy, so that each computation task of wireless devices (WDs) is either executed locally or fully offloaded to an MEC server. Our goal is to acquire an online algorithm that optimally adapts task offloading decisions and wireless resource allocations to the time-varying wireless channel conditions. This requires quickly solving hard combinatorial optimization problems within the channel coherence time, which is hardly achievable with conventional numerical optimization methods. To tackle this problem, we propose a Deep Reinforcement learning-based Online Offloading (DROO) framework that implements a deep neural network as a scalable solution that learns the binary offloading decisions from the experience. It eliminates the need of solving combinatorial optimization problems, and thus greatly reduces the computational complexity especially in large-size networks. To further reduce the complexity, we propose an adaptive procedure that automatically adjusts the parameters of the DROO algorithm on the fly. Numerical results show that the proposed algorithm can achieve near-optimal performance while significantly decreasing the computation time by more than an order of magnitude compared with existing optimization methods. For example, the CPU execution latency of DROO is less than $0.1$ second in a $30$-user network, making real-time and optimal offloading truly viable even in a fast fading environment.

Design and experimental validation of self-supporting topologies for additive manufacturing

ABSTRACT Incorporating additive manufacturing (AM) constraints in topology optimisation can lead to performance optimality while ensuring manufacturability of designs. Numerical techniques have been previously proposed to obtain support-free designs in AM, however, few works have verified the manufacturability of their solutions. Physical verification of manufacturability becomes more critical recalling that the conventional density-based topology optimisation methods will inevitably require post-processing to smooth the boundaries before sending the results to a 3D printer. This paper presents the smooth design of self-supporting topologies using the combination of a new Solid Isotropic Microstructure with Penalisation method (SIMP) developed based on elemental volume fractions and an existing AM filter. Manufacturability of selected simulation results are verified with Fused Deposition Modeling (FDM) technology. It is illustrated that the proposed method is able to generate convergent self-supporting topologies which are printable using FDM.

Characterization of Gels Containing Pectin and Optimization of Gel Production by Taguchi Method in Food Industry

The objective of this research was to optimize the gel production by Taguchi Method as an optimization method and characterize gels by using attenuated total reflectance Fourier transform infrared (ATR – FTIR) and Raman spectroscopy. The statistical method results were obtained and analyzed comparatively in terms of improving both cost and quality for determination of optimum pro-cess parameters. This optimization method uses the S/N ratio as a measure of quality characteristics deviating from or nearing to the desired values. This method is expected to serve as an alternative to the conventional optimization method. Clear discrimina-tion and classification of all the studied gel products containing pectin were achieved by hierarchical clus-ter. As a result, the gels produced could be evaluated in food products such as ice cream, milk dessert or other gelatin containing products such as pharmaceuticals and cosmetics.

Towards real‐time through‐obstacle imaging based on compressed sensing for sparse objects

Although significant progress has been made in microwave imaging, real-time imaging, especially for objects behind walls or closed obstacles, remains a technical challenge. In this work, highly efficient imaging for complex-structured objects surrounded by a closed obstacle was experimentally demonstrated. The imaging equations are derived based on a combination of the inverse-scattering problem and the concept of compressed sensing. Making use of the spatial sparsity of objects and obstacles, the compressed imaging can be implemented using a time-division multi-antenna setup with reduced transmitting antennas. Owing to the spatial compressed sensing applied to the sparse imaging region and objects, the imaging time can be reduced by two orders of magnitude compared with the conventional twofold subspace-based optimisation method with a comparable imaging quality. Taking advantage of the sparsity of the entire imaging area, objects with larger relative permittivity can also be reconstructed. The proposed method can be potentially used in applications such as security examination through boxes. It also provides a new clue for solving the practicability difficulty faced by existing microwave imaging systems.

Transmission Network Expansion Planning – A Critical Review

Transmission Network Expansion Planning (TNEP) is determination of an optimal network configuration that satisfies the operational conditions for forecasted load growth under a particular generation expansion plan. TNEP may be broadly classified into static and dynamic network planning. Static TNEP (STNEP) deals with finding where and which type of new lines should be installed in an optimal way that minimizes the installation and operational cost. Dynamic TNEP (DTNEP) is more complex and aims at determining when to install the new lines (in addition to determination of where and which type of lines to be installed). Researchers have used mathematical optimization methods, heuristic methods and meta-heuristic methods to solve STNEP problem. DTNEP problem have been tackled using mathematical optimization methods and meta-heuristic methods by the researchers. This paper compiles the significant developments made in the area of TNEP using conventional (mathematical) optimization methods, and advanced (heuristic & meta-heuristic) optimization methods. After a thorough study of vast literature available on TNEP, critical comments and future scope have been presented to make the review study focused and useful for the researchers in this area.

Two-stage stochastic optimal operation model for hydropower station based on the approximate utility function of the carryover stage

Challenge remains to find the optimal carryover storage to balance the immediate and carryover utilities for long-term hydropower reservoir operation due to high uncertainties of long-term forecasts. Thus, this paper develops a two-stage stochastic optimal operation model to dynamically decide the optimal carryover storage. First, a successive iteration method based on periodic Markov characteristics of reservoir operation is proposed to obtain the approximate utility function of the carryover stage. Then, three two-stage stochastic optimal operation models based on different forecast accuracy (no forecasts, perfect forecasts, and uncertainty forecasts) are developed to guide the long-term hydropower reservoir operation. The applications shows that: 1) the back propagation neural network can approximate the utility function of the carryover stage with a high accuracy and avoid the need to predetermine the function type; 2) the approximate utility function of the carryover stage increases with the carryover storage and current inflow, and it changes gradually from a nearly linear surface to an approximate concave surface with the shift from the dry season to the flood season; 3) two-stage stochastic optimal operation models outperform the conventional operating rules and conventional optimization method in guiding the long-term hydropower operation.

Comparison of the Direct Method and the Maximum Principle in the Problem of the Aircraft Program Control Design

The article deals with the problem of program control design for a dynamic object defined by a nonlinear system of differential equations. Known methods of optimal control require the two-point boundary value problem solution, which in general is coupled with fundamental difficulties. Therefore, this paper proposes a technique that uses the direct method, in which the functional is minimized directly using a population-based algorithm. The use of direct methods is based on the assumption that control signals may be defined by a finite set of parameters. Then a scalar functional is formed, the numerical value of which measures the quality of the obtained solutions. In this case, the search for optimal control is reduced to the problem of single-criterion multi-parameter optimization. The practical importance of this approach is that it eliminates the need to solve a two-point boundary value problem. However, this results in another difficulty, since the approximation of control, in general, requires a large number of parameters. It is known that in this case, the effectiveness of conventional gradient numerical optimization methods decreases markedly. Therefore, it is proposed to take the next step and apply genetic or population-based optimization algorithms that have confirmed their performance in solving this class of problems. For this purpose the paper uses one of the modifications of the particle swarm algorithm. The technique is applied to a test problem describing the spatial movement of a maneuverable aircraft. The direct method is compared with two classical solutions based on the condition that the partial control derivatives of the Hamilton function are equal to zero and with the condition of Hamilton function maximum over controls (Pontryagin’s maximum principle). The presented results show the high degree of similarity between obtained controls for all considered methods of selecting the target functional. At the same time, the accuracy of classical algorithms turns out to be slightly worse, and they show a higher sensitivity to the quality of the initial approximation. Thus, the obtained results confirm the approximate equivalence of the direct method and the classical methods of program control design, at least for the class of problems under consideration. The practical significance of this research is that the use of the direct method is much simpler than solving a two-point boundary value problem necessary for classical algorithms.

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

AbstractInverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

A feasibility study of a risk-based stochastic optimization approach for radiation treatment planning under setup uncertainty

This article introduces a planner-driven flexible stochastic decision making model to develop radiation treatment plans for cancer patients under patient-setup uncertainty. The clinical goal is to deliver the prescribed amount of radiation dose to the target tissue(s) while sparing the organs nearby. However, it is difficult to achieve the goal because organs are often closely located in the body. Therefore, some tissues may receive a higher radiation dose than desired. To minimize such violations and allow to make a trade-off between tumor coverage and healthy tissue sparing, we present a chance constrained programming (CCP) optimization method. A planner can use the CCP approach to specify how much clinical violation can be allowed for a specific patient. Assuming that the uncertain dose distribution follows a known (or estimated) probability distribution function, the CCP model was tested using five clinical cases. The resulting treatment plans were compared with the plans generated by the conventional robust worst-case optimization method using dose-volume histograms. Our results support the CCP approach over the robust optimization method in terms of healthy tissues sparing and the clinical target dose requirements. Overall, the risk-based CCP model is not only flexible to accommodate the planner’s risk profile and to meet patient specific treatment goals, but has potential to compromise for overly-conservative treatment plans generated by robust optimization methods.

Optimal Operational Scheduling of Reconfigurable Microgrids in Presence of Renewable Energy Sources

Passive distribution networks are being converted into active ones by incorporating distributed means of energy generation, consumption, and storage, and the formation of so-called microgrids (MGs). As the next generation of MGs, reconfigurable microgrids (RMGs) are still in early phase studies, and require further research. RMGs facilitate the integration of distributed generators (DGs) into distribution systems and enable a reconfigurable network topology by the help of remote-controlled switches (RCSs). This paper proposes a day-ahead operational scheduling framework for RMGs by simultaneously making an optimal reconfiguration plan and dispatching controllable distributed generation units (DGUs) considering power loss minimization as an objective. A hybrid approach combining conventional particle swarm optimization (PSO) and selective PSO (SPSO) methods (PSO&SPSO) is suggested for solving this combinatorial, non-linear, and NP-hard complex optimization problem. PSO-based methods are primarily considered here for our optimization problem, since they are efficient for power system optimization problems, easy to code, have a faster convergence rate, and have a substructure that is suitable for parallel calculation rather than other optimization methods. In order to evaluate the suggested method’s performance, it is applied to an IEEE 33-bus radial distribution system that is considered as an RMG. One-hour resolution of the simultaneous network reconfiguration (NR) and the optimal dispatch (OD) of distributed DGs are carried out prior to this main study in order to validate the effectiveness and superiority of the proposed approach by comparing relevant recent studies in the literature.

Static and dynamic optimization of a pose adjusting mechanism considering parameter changes during construction

Abstract Having potentially high stiffness and good dynamic response, a parallel pose adjusting mechanism was proposed for being an attachment to a big serial robot of a macro-micro robotic system. This paper addresses its design optimization problem mainly concerning arrangements of design variables and objectives. Parameter changes during construction are added to the design variables in order to prevent the negative effects to the physical prototype. These parameter changes are interpreted as parameter uncertainty and modeled by probabilistic theory. For the objectives, both static and dynamic performances are simultaneously optimized by Pareto-based method. The involved performance indices are instantaneous energy based stiffness index, first natural frequency and execution mass. The optimization procedure is implemented as: (1) carrying out performance modeling and defining performance indices, (2) reformulating statistical objectives and probabilistic constraints considering parameter uncertainty, (3) conducting Pareto-based optimization with the aid of response surface method (RSM) and particle swarm optimization (PSO), (4) selecting optimal solution by searching for cooperative equilibrium point (CEP). By addressing parameter uncertainty and the best compromise among multiple objectives, the presented optimization procedure provides more reliable optimal parameters that would not be affected by minor parameter changes during construction, and less biased optimum between static and dynamic performances comparing with the conventional optimization methods. The proposed optimization method can also be applied to the other similar mechanisms.

Life-Cycle Optimization of a Chiller Plant with Quantified Analysis of Uncertainty and Reliability in Commercial Buildings

Conventional and most optimal design methods for chiller plants often address the annual cooling load distribution of buildings and their peak cooling loads based on typical meteorological year (TMY) data, while the peak cooling load only appears a few times during the life-cycle and the sized chiller plant usually operates within its low efficient region. In this paper, a robust optimal design method based on life-cycle total cost was employed to optimize the design of a chiller plant with quantified analysis of uncertainty and reliability. By using the proposed design method, the optimized chiller plant can operate at its highly efficient region under various cooling load conditions, and provide sufficient cooling capacity even alongside some equipment/systems with failures. The minimum life-cycle total cost, which consists of the capital cost, operation, and availability-risk cost, can be achieved through optimizing the total cooling capacity and the numbers/sizes of chillers. A case study was conducted to illustrate the detailed implementation process of the proposed method. The performance of this design method was evaluated by comparing with that of other design methods.

In Vivo Estimation of Head Tissue Conductivities Using Bound Constrained Optimization.

The conductivity of head tissues was noninvasively estimated using electrical impedance tomography technique. Instead of using conventional unconstrained optimization method to estimate the conductivities, a constrained method with the scaled-logistic function was employed to improve the very high sensitivity of the skull region resulting in accuracy and robustness improvement. Estimation of five conductivities i.e. scalp, skull, cerebrospinal fluid (CSF), grey matter (GM), and white matter (WM) conductivity was investigated by simulation on random and low-value initial guesses. Simulation results showed that the performance of the unconstrained method depended directly to the difference between the exact skull conductivity value and the initial guess value of the skull conductivity. However, the approached constrained method was independent of the guess selection. It can reduce the sensitivity of the skull region by 126 times and reduce the condition number of the sensitivity matrix by 13-17 times. The estimation resulted in only positive and in-range of reported conductivity values. The estimation error of the skull conductivity decreased by 15% and the robustness increased by 2 times. However, the estimation of the CSF, the WM, and the GM may be not reliable due to the very low sensitivity of these regions in both methods.

Data‐driven affinely adjustable distributionally robust framework for unit commitment based on Wasserstein metric

This study proposes a data-driven distributionally robust framework for unit commitment based on Wasserstein metric considering the wind power generation forecasting errors. The objective of the constructed model is to minimise the expected operating cost, including the generating cost, start-up and shut-down costs, and also the reserve cost, which overcomes the shortcomings of the conventional model without optimising the reserve capacity. What is more important, different from the conventional robust optimisation methods, wind power big data is fully utilised in this model to construct the ambiguity set without any presumption about its probability distribution. This is realised by Wasserstein ball with an empirical distribution as the centre. Thus, the proposed robust model is actually data-driven and can immunise the solutions against the worst-case distribution in the ambiguity set. In addition, the scale of the historical data is very critical for this method, the larger the scale is, the smaller the ambiguity set is and the less conservative the result is. Numerical results and Monte Carlo simulations on a real 75-bus system demonstrate the superiority of the proposed model.

An efficient space division–based width optimization method for RBF network using fuzzy clustering algorithms

The Radial Basis Function (RBF) network is one of the most widely used surrogate models in multidisciplinary design optimization. However, one of the challenges of applying the RBF network to engineering problems is how to efficiently optimize its width parameters. In this work, a novel space division–based width optimization (SDWO) method is proposed to decompose the complex multivariable width optimization into several small-scale single-variable width optimizations. The SDWO method consists of two main steps. First, a two-stage fuzzy clustering algorithm is carried out to group the samples and divide the input space into several overlapping local regions, and the overlapping degree is controlled by a dimensionless expansion factor. Second, in each local region, one small-scale local RBF network (LRBFN) is constructed by solving a single-variable optimization problem when the LRBFN is needed for prediction. All these LRBFNs are independent of each other and can be constructed in parallel. The proposed method is efficient and particularly suitable for large sample sets. Test results of four sample sets verify that the proposed SDWO method has better performance than the conventional width optimization method in terms of both training efficiency and approximation accuracy. An inter-stage structure optimization is carried out, which demonstrates the efficiency of the proposed method in practical engineering applications.

On-demand serum-free media formulations for human hematopoietic cell expansion using a high dimensional search algorithm

Substitution of serum and other clinically incompatible reagents is requisite for controlling product quality in a therapeutic cell manufacturing process. However, substitution with chemically defined compounds creates a complex, large-scale optimization problem due to the large number of possible factors and dose levels, making conventional process optimization methods ineffective. We present a framework for high-dimensional optimization of serum-free formulations for the expansion of human hematopoietic cells. Our model-free approach utilizes evolutionary computing principles to drive an experiment-based feedback control platform. We validate this method by optimizing serum-free formulations for first, TF-1 cells and second, primary T-cells. For each cell type, we successfully identify a set of serum-free formulations that support cell expansions similar to the serum-containing conditions commonly used to culture these cells, by experimentally testing less than 1 × 10−5 % of the total search space. We also demonstrate how this iterative search process can provide insights into factor interactions that contribute to supporting cell expansion.

Robust optimization for intensity-modulated proton therapy with soft spot sensitivity regularization.

Proton dose distribution is sensitive to uncertainties in range estimation and patient positioning. Currently, the proton robustness is managed by worst-case scenario optimization methods, which are computationally inefficient. To overcome these challenges, we develop a novel intensity-modulated proton therapy (IMPT) optimization method that integrates dose fidelity with a sensitivity term that describes dose perturbation as the result of range and positioning uncertainties. In the integrated optimization framework, the optimization cost function is formulated to include two terms: a dose fidelity term and a robustness term penalizing the inner product of the scanning spot sensitivity and intensity. The sensitivity of an IMPT scanning spot to perturbations is defined as the dose distribution variation induced by range and positioning errors. To evaluate the sensitivity, the spatial gradient of the dose distribution of a specific spot is first calculated. The spot sensitivity is then determined by the total absolute value of the directional gradients of all affected voxels. The fast iterative shrinkage-thresholding algorithm is used to solve the optimization problem. This method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The proposed sensitivity-regularized method (SenR) was implemented on both clinic target volume (CTV) and planning target volume (PTV). They were compared with conventional PTV-based optimization method (Conv) and CTV-based voxel-wise worst-case scenario optimization approach (WC). Under the nominal condition without uncertainties, the three methods achieved similar CTV dose coverage, while the CTV-based SenR approach better spared organs at risks (OARs) compared with the WC approach, with an average reduction of [Dmean, Dmax] of [4.72, 3.38] GyRBE for the SBT cases and [2.54, 3.33]GyRBE for the H&N cases. The OAR sparing of the PTV-based SenR method was comparable with the WC method. The WC method, and SenR approaches all improved the plan robustness from the conventional PTV-based method. On average, under range uncertainties, the lowest [D95%, V95%, V100%] of CTV were increased from [93.75%, 88.47%, 47.37%] in the Conv method, to [99.28%, 99.51%, 86.64%] in the WC method, [97.71%, 97.85%, 81.65%] in the SenR-CTV method and [98.77%, 99.30%, 85.12%] in the SenR-PTV method, respectively. Under setup uncertainties, the average lowest [D95%, V95%, V100%] of CTV were increased from [95.35%, 94.92%, 65.12%] in the Conv method, to [99.43%, 99.63%, 87.12%] in the WC method, [96.97%, 97.13%, 77.86%] in the SenR-CTV method, and [98.21%, 98.34%, 83.88%] in the SenR-PTV method, respectively. The runtime of the SenR optimization is eight times shorter than that of the voxel-wise worst-case method. We developed a novel computationally efficient robust optimization method for IMPT. The robustness is calculated as the spot sensitivity to both range and shift perturbations. The dose fidelity term is then regularized by the sensitivity term for the flexibility and trade-off between the dosimetry and the robustness. In the stress test, SenR is more resilient to unexpected uncertainties. These advantages in combination with its fast computation time make it a viable candidate for clinical IMPT planning.

Robust Design Optimization with Penalty Function for Electric Oil Pumps with BLDC Motors

In this paper, we propose and evaluate a robust design optimization (RDO) algorithm for the shape of a brushless DC (BLDC) motor used in an electric oil pump (EOP). The components of the EOP system and the control block diagram for driving the BLDC motor are described. Although the conventional deterministic design optimization (DDO) method derives an appropriate combination of design goals and target performance, DDO does not allow free searching of the entire design space because it is confined to preset experimental combinations of parameter levels. To solve this problem, we propose an efficient RDO method that improves the torque characteristics of BLDC motors by considering design variable uncertainties. The dimensions of the stator and the rotor were selected as the design variables for the optimal design and a penalty function was applied to address the disadvantages of the conventional Taguchi method. The optimal design results obtained through the proposed RDO algorithm were confirmed by finite element analysis, and the improvement in torque and output performance was confirmed through experimental dynamometer tests of a BLDC motor fabricated according to the optimization results.

Opposition-based learning for self-adaptive control parameters in differential evolution for optimal mechanism design

In recent decades, new optimization algorithms have attracted much attention from researchers in both gradient- and evolution-based optimal methods. Many strategy techniques are employed to enhance the effectiveness of optimal methods. One of the newest techniques is opposition-based learning (OBL), which shows more power in enhancing various optimization methods. This research presents a new edition of the Differential Evolution (DE) algorithm in which the OBL technique is applied to investigate the opposite point of each candidate of self-adaptive control parameters. In comparison with conventional optimal methods, the proposed method is used to solve benchmark-test optimal problems and applied to real optimizations. Simulation results show the effectiveness and improvement compared with some reference methodologies in terms of the convergence speed and stability of optimal results. © 2019 The Japan Society of Mechanical Engineers