Defined Optimization Problem Research Articles

Resource allocation in paired users: Optimization‐assisted user grouping for fairness improvement of NOMA

SummaryThe solution of resource allocation is based on NOMA and OMA structures that are suboptimal to satisfy the demanding QoS and higher data rate requirements compared to EE requirements in 5G cellular networks. In this work, the resource allocation problem in the hybrid MC‐NOMA system is solved. The system achieves the trade‐off between spectral and energy efficiency (EE) with the lowest rate of user requirements. The system's resource allocation, including power allocation, is considered the crucial factor and is identified as a single‐objective problem. The suggested work focuses on user pairing and allocation on paired users following processing. The user grouping is designed to connect near‐ and far‐users with high C3 to increase the fairness of NOMA. As a result, this work considers multiple goals, such as C3 maximization, spectrum efficiency, and energy efficiency. This paper aims to present a novel hybrid optimization model with the combination of coati and bald eagle optimization algorithms, to solve the defined optimization problem. The experimental results show that the suggested system outperforms the conventional algorithms by evaluating different performance measures such as channel correlation, spectrum efficiency, energy efficiency, and power allocation.

Advanced tree‐seed optimization based fractional‐order PID controller design for simplified decoupled industrial tank systems

AbstractControlling coupled tank systems is challenging due to interactions between tanks, nonlinear dynamics, time delays, uncertainties, and cross‐coupling effects. The design of effective control strategies to address these complexities while ensuring stability and robust performance is difficult. Hence, this study focuses on presenting an innovative approach to enhance level control in coupled tank systems by employing a fractional‐order proportional‐integral‐derivative (FOPID) controller. The FOPID controller is designed by imposing constraints on the performance metric and closed‐loop gain. Besides, the defined optimization problem is solved by employing a tree seed algorithm. Further, the stability is analyzed graphically using the singular value analysis. The inherent complexities of coupled tank systems are effectively addressed by designing decouplers. The unique characteristics of the tree seed algorithm to navigate complex solution spaces and its effective handling of constraints offer a robust optimization framework. The validity and efficiency of the proposed method are analyzed in a range of simulation experiments conducted on distinct interconnected tank systems. Besides, the stability is verified graphically. The analysis highlights the effectiveness of the control law in handling uncertainties and disturbances. Besides, the proposed method reduces the settling time to around . Through a systematic integration of optimization and comprehensive stability analysis, the study provides a holistic solution for optimizing level control in coupled tank systems.

Online Deterministic Annealing for Classification and Clustering.

Inherent in virtually every iterative machine learning algorithm is the problem of hyperparameter tuning, which includes three major design parameters: 1) the complexity of the model, e.g., the number of neurons in a neural network; 2) the initial conditions, which heavily affect the behavior of the algorithm; and 3) the dissimilarity measure used to quantify its performance. We introduce an online prototype-based learning algorithm that can be viewed as a progressively growing competitive-learning neural network architecture for classification and clustering. The learning rule of the proposed approach is formulated as an online gradient-free stochastic approximation algorithm that solves a sequence of appropriately defined optimization problems, simulating an annealing process. The annealing nature of the algorithm contributes to avoiding poor local minima, offers robustness with respect to the initial conditions, and provides a means to progressively increase the complexity of the learning model, through an intuitive bifurcation phenomenon. The proposed approach is interpretable, requires minimal hyperparameter tuning, and allows online control over the performance-complexity tradeoff. Finally, we show that Bregman divergences appear naturally as a family of dissimilarity measures that play a central role in both the performance and the computational complexity of the learning algorithm.

Extensions to traffic control modeling store-and-forward

The store-and-forward traffic model is widely used because of its simplicity and reasonable comprehension. Its results determine the duration of the green light according to a preset cycle. This paper builds further on the currently existing model: it expands the definitional domain of the optimization problem by adding additional probabilistic requirements regarding the number of vehicles in a street segment between intersections controlled by traffic lights. The defined optimization problem minimizes the probability of increasing the number of vehicles in the considered transport network. A further extension of the store-and-forward model allows the control domain to contain both green lights and cycle durations. Such optimal control allows the achievement of additional objective functions such as minimizing the number of vehicles in the network and minimizing the total time spent through the network. The definition of this control problem is done through a bi-level hierarchical formalization involving the store-and-forward model. The derived extended models are numerically tested and compared with real cases, giving preference to the derived extensions of the classical store-and-forward model.

Novel Ordering-Based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature recover a graph through learning a causal order (c-order). We advocate for a novel order called removable order (r-order) as they are advantageous over c-orders for structure learning. This is because r-orders are the minimizers of an appropriately defined optimization problem that could be either solved exactly (using a reinforcement learning approach) or approximately (using a hill-climbing search). Moreover, the r-orders (unlike c-orders) are invariant among all the graphs in a MEC and include c-orders as a subset. Given that set of r-orders is often significantly larger than the set of c-orders, it is easier for the optimization problem to find an r-order instead of a c-order. We evaluate the performance and the scalability of our proposed approaches on both real-world and randomly generated networks.

Management of renewable-based multi-energy microgrids with energy storage and integrated electric vehicles considering uncertainties

One of the best solutions to overcome environmental, technical as well as economic problems in the power system is the use of Plug-in hybrid electric vehicles (PHEVs). The penetration of a large number of PHEVs in the power system and the possibility of their proper control and management provide benefits of a large energy storage system for the distribution system operator. However, the correct management of PHEVs along with renewable energy sources (RESs) is a very important challenge that requires more research in this field. The main goal of the article is the scheduling of a microgrid with several PHEVs and RESs in order to achieve economic, technical and environmental benefits. To obtain more accurate results in microgrid operation, the intermittent behavior of renewable resources, PHEVs and loads has been modeled using the Mont Carlo simulation (MCS). Uncertainty parameters considered in this article include the charging demand of PHEVs, loads, electricity price and output power of RESs. The objective function is to reach minimum total costs considering the technical constraints. In order to resolve the defined optimization problem, including the objective function and the constraints of the problem, the modified sparrow search (MSS) algorithm is applied. The recommended technique is simulated on the test network with the MATLAB software and the outcomes are compared with conventional algorithms. As the results of the simulations show the suggested scheme performs superior performance than other optimization algorithms.

3D Global Path Planning Optimization for Cellular-Connected UAVs under Link Reliability Constraint.

This paper proposes an effective global path planning technique for cellular-connected UAVs to enhance the reliability of unmanned aerial vehicles' (UAVs) flights operating beyond the visual line of sight (BVLOS). Cellular networks are considered one of the leading enabler technologies to provide a ubiquitous and reliable communication link for UAVs. First, this paper investigates a reliable aerial zone based on an extensive aerial drive test in a 4G network within a suburban environment. Then, the path planning problem for the cellular-connected UAVs is formulated under communication link reliability and power consumption constraints. To provide a realistic optimization solution, all constraints of the optimization problem are defined based on real-world scenarios; in addition, the presence of static obstacles and no-fly zones is considered in the path planning problem. Two powerful intelligent optimization algorithms, the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm, are used to solve the defined optimization problem. Moreover, a combination of both algorithms, referred to as PSO-GA, is used to overcome the inherent shortcomings of the algorithms. The performances of the algorithms are compared under different scenarios in simulation environments. According to the statistical analysis of the aerial drive test, existing 4G base stations are able to provide reliable aerial coverage up to a radius of 500 m and a height of 85 m. The statistical analysis of the optimization results shows that PSO-GA is a more stable and effective algorithm to rapidly converge to a feasible solution for UAV path planning problems, with a far faster execution time compared with PSO and GA, about two times. To validate the performance of the proposed solution, the simulation results are compared with the real-world aerial drive test results. The results comparison proves the effectiveness of the proposed path planning method in suburban environments with 4G coverage. The proposed method can be extended by identifying the aerial link reliability of 5G networks to solve the UAV global path planning problem in the current 5G deployment.

Infill well placement optimization for secondary development of waterflooding oilfields with SPSA algorithm

A significant amount of bypassed oil resources often remain in a mature waterflooding reservoir because of non-uniform sweep caused by natural complexities of a subsurface reservoir and improper management of the reservoir. Infill drilling is one of the most attractive options for increasing oil recovery in consequence of its operational simplicity, low risk and promising results. Determining optimal infill well placements in heterogeneous mature reservoirs is a critical and challenging task that has a significant impact on the recovery performance and economic revenue of subsurface remaining oil resources. An integrated framework is constructed to attain best-obtained optimal location and completion of infill wells in multi-layer mature oil reservoirs. The placement of an infill vertical well is parameterized in terms of two sets of variables that define the location and completion respectively. A variant of SPSA algorithm is used to solve the defined optimization problem. The performance of the proposed algorithm is first tested for the joint optimization of well location and completion of an injection well using a synthetic model. The results show that the algorithm with average SPSA gradients outperforms the single SPSA gradient method both in solution and convergence rate. Besides, there are two plateaus on the performance curve of all algorithms: on the first plateau, each algorithm is approaching to its optimal well location with relatively little change on the completion parameters, while on the second plateau, each algorithm obtains the corresponding optimal completions. A complex heterogeneous reservoir model is then constructed by using the data of a mature oil reservoir in Shengli Oilfield in China to design an optimal 10 years’ infill drilling program. Four vertical production wells are placed in the oil-rich regions and both simultaneous and sequential algorithms are tried to obtain their optimal locations and completions. The performances of simultaneous joint optimization and sequential joint optimization are compared and as a result it is recommended to use sequential joint optimization as the optimization algorithm in the integrated framework.

Macrocell–femtocell resource allocation via hybrid optimization algorithm

PurposeFemtocells are low-power, inexpensive base stations (BS) used in business enterprises or homes. They could offer higher SNR in a smaller coverage area to enhance the data rates and QoS. Deployment of femtocell is expected to the witness constant development in upcoming years. Despite of all these benefits, there are certain challenges to be resolved that includes management of overlaying MC, interference among femtocells and the resource allocation between 2 tiers.Design/methodology/approachThis work analyses the issues on cross-tier interfering and resource allocation alleviation in “full-duplex (FD) Orthogonal Frequency Division Multiple Access (OFDMA) oriented Heterogeneous Networks (HetNets) that includes macrocell as well as underlying femtocells”. This work concerns on three foremost contributions: portraying a single objective issue including subcarrier allocation, price allocation and power allocation of macrocell–femtocell networks. Moreover, this work introduces a novel Cat Swarm Mated-Lion algorithm (CSM-LA) for solving the defined optimization problem in macrocell–femtocell networks. At last, the supremacy of adopted scheme is proved over traditional models regarding statistical and convergence analysis.FindingsBy concerning the cost function, the developed CSM-LA attained 87.5, 60, 93.75 and 93.75% better than LM, WOA, LA and CSO respectively. For utility analysis, it accomplished 70.58% better than LM, 88.23% superior to GWO, 85.88% superior to WOA and 88.23% better than CSO. For statistical analysis, the median performance of developed CSM-LA attained better results, which was 80.52% superior to LA, 80.74% better than GWO, 72% superior to WOA and 48.7% better than LA. Hence, the developed CSM-LA proved its performance in terms of improved results and revealed its betterment over the conventional models.Originality/valueThis paper adopts a latest optimization algorithm called CSM-LA for analyzing the issues on cross-tier interfering and resource allocation alleviation in full-duplex (FD) orthogonal frequency division multiple access (OFDMA) oriented heterogeneous networks (HetNets). This is the first work that utilizes CSM-LA framework that proposes a new CSM-LA model for power control and resource allocation by considering the multi-objectives like price, subcarrier and power as well.

Improved Coverage and Connectivity via Weighted Node Deployment in Solar Insecticidal Lamp Internet of Things

As an important physical control technology, solar insecticidal lamp (SIL) can effectively prevent and control the occurrence of pests. The combination of SILs and wireless sensor networks (WSNs) initiates a novel agricultural Internet of Things (IoT), i.e., SIL-IoTs, to simultaneously kill pests and transmit pest information. In this article, we study the weighted SIL deployment problem (wSILDP) in SIL-IoTs, where weighted locations on ridges are prespecified and some of them are selected to deploy SILs. Different from the existing studies whose optimization objective is to minimize the deployment cost, we consider the deployment cost and the total weight of selected locations jointly. We formulate the wSILDP as the weighted set cover (WSC) problem and propose a layered deployment method based on greedy algorithm (LDMGA) to solve the defined optimization problem. The LDMGA is composed of two phases. First, SILs are deployed layer by layer from the boundary to the center until the entire farmland is completely covered. Second, on the basis of three design operations, i.e., substitution, deletion and fusion, the suboptimal locations obtained in the first phase are fine-tuned to achieve the minimum deployment cost together with the maximum total weight for meeting the coverage and connectivity requirements. Simulation results clearly demonstrate that the proposed method outperforms three peer algorithms in terms of deployment cost and total weight.

The Use of a Simulation Model for High-Runner Strategy Implementation in Warehouse Logistics

This paper examines the use of computer simulation methods to streamline the process of picking materials within warehouse logistics. The article describes the use of a genetic algorithm to optimize the storage of materials in shelving positions, in accordance with the method of High-Runner Strategy. The goal is to minimize the time needed for picking. The presented procedure enables the creation of a software tool in the form of an optimization model that can be used for the needs of the optimization of warehouse logistics processes within various types of production processes. There is a defined optimization problem in the form of a resistance function, which is of general validity. The optimization is represented using the example of 400 types of material items in 34 categories, stored in six rack rows. Using a simulation model, a comparison of a normal and an optimized state is realized, while a time saving of 48 min 36 s is achieved. The mentioned saving was achieved within one working day. However, the application of an approach based on the use of optimization using a genetic algorithm is not limited by the number of material items or the number of categories and shelves. The acquired knowledge demonstrates the application possibilities of the genetic algorithm method, even for the lowest levels of enterprise logistics, where the application of this approach is not yet a matter of course but, rather, a rarity.

Multiobjective blast-resistance optimization of gradient foam sandwiched cylindrical container

The design and multiobjective optimization of graded foam-cored sandwich cylinders (GFSCs) composed of tubular face sheets and layered gradient foam core under internal air-blast loading were examined. The response surface method and nondominated sorting genetic algorithm were used in the defined optimization problem to determine the optimal face-sheet thickness and core gradient as well as achieve the minimum specific deflection of outer face sheet (SDF) and maximum specific energy absorption (SEA). Multiobjective optimization was subsequently conducted to obtain the Pareto front and improve the blast-resistant performance of the optimum GFSC configuration. Results obtained via these optimizations further indicated that the optimal GFSCs demonstrated better energy absorption characteristics than ordinary sandwich cylinders. Under the same SDF, SEA increased by 75.4% and 45.0% compared with that of the initial baseline design when the core gradient and face-sheet thickness were individually optimized, respectively. The joint optimization of face-sheet thicknesses and core gradient could significantly improve the blast-resistant performance by 171.1%. The optimization of GFSCs should primarily optimize the design variables with high-price performance ratio while reasonably arranging the design variable quantity, ensuring the controllable cost of calculation, and significantly improving the blast-resistant performance. The results also showed that the strength of CFSCs and the interaction between the face sheets and the core improved the blast-resistant capacity. The design optimization results could provide appropriate guidance in the crashworthiness design of GFSCs.

Experimental and numerical investigation of thermoplastic honeycomb sandwich structures under bending loading

Sandwich structures have attracted increasing attention in engineering applications due to their lightweight effect and energy absorbing capacity. In the current work, fully-thermoplastic honeycomb sandwich structures with 100% recyclability were developed, which consisted of continuous glass fiber-reinforced polypropylene (PP/GF) face sheets, polypropylene (PP) core and assembled using thermoplastic adhesive films. The experimental tests and numerical analysis were conducted to investigate the bending behavior and energy absorption of PP-based sandwich structures. Firstly, a series of three-point bending experiments were tested and the influences of structural factors on bending behaviors were investigated. The typical deformation modes were explored and the damaged microstructure of face-sheets were observed. Finite element models of the sandwich structures were developed to capture the deformation process, and the simulation results were validated with the experimental data. Afterwards, a multi-objective optimization was performed to seek for the maximum specific energy absorption together with the minimum initial peak force simultaneously. Response surface method was adopted to construct objective response functions and used for the defined optimization problem.

On learning with shift-invariant structures

In this paper, we describe new results and algorithms, based on circulant matrices, for the task of learning shift-invariant components from training data. We deal with the shift-invariant dictionary learning problem which we formulate using circulant and convolutional matrices (including unions of such matrices), define optimization problems that describe our goals and propose efficient ways to solve them. Based on these findings, we also show how to learn a wavelet-like dictionary from training data. We connect our work with various previous results from the literature and we show the effectiveness of our proposed algorithms using synthetic as well as real ECG signals and images.

Structural topological optimization with dynamic fatigue constraints subject to dynamic random loads

More attention has been attracted to engineering structural design on fatigue failure, while few works are devoted to topology optimizations considering dynamic fatigue failure under random vibrations. In this paper, a new layout optimization method is proposed to consider high-cycle dynamic fatigue constraints which are caused by periodic random dynamic loads. Being incorporated with the rational approximation for material properties (RAMP), the optimization model is built, where the objective function is the structural weight, and the dynamic fatigue failure constraints are applied in the structure. According to the Crossland’s criterion, the dynamic fatigue constraints can be formulated by the peak value of the period fluctuating dynamic stress that never exceed the threshold. Then, the Kreisselmeier–Steinhauser (KS) aggregation function is introduced to reduce the number of dynamic fatigue failure constraints. To overcome stress concentration phenomenon, the P-norm aggregation function is introduced to the objective function as a penalty term. Moreover, a new penalty approach is introduced to solve stress singularity, and a constraint-limit-variant method is adopted to obtain stable convergent topologies. The sensitivity of the dynamic fatigue constraints with respect to the design variables is derived so as to form the approximate functions for the dynamic fatigue constraint functions and the objective function. Finally, based on the sensitivity and dual theory, the defined optimization problem is solved by the aforementioned algorithm. The results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.

Risk-averse classification

We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for associating distinct risk functional to each classes. The risk may be measured by different (non-linear in probability) measures, We analyze the structure of the new classifier design problem and establish its theoretical relation to known risk-neutral design problems. In particular, we show that the risk-sharing classification problem is equivalent to an implicitly defined optimization problem with unequal, implicitly defined but unknown, weights for each data point. We implement our methodology in a binary classification scenario on several different data sets and carry out numerical comparison with classifiers which are obtained using the Huber loss function and other loss functions known in the literature. We formulate specific risk-averse support vector machines in order to demonstrate the viability of our method.

Groebner bases algorithm for optimal PMU placement

In this paper a new method for solving optimal phasor measurement units (PMU) placement problem for full observability in power systems is proposed. A new algorithm is based on forming and solving Groebner bases set of equations for a defined optimization problem. The technique of Groebner bases is applicable wherever the problem may be presented by the set of polynomials and as such, it can be found in a variety of applied mathematics problems. Groebner bases of the set of polynomials represents the canonical form equivalent to the original set, similar to the way the row echelon form for linear systems represents the triangular form of the linear equations set. The canonical form of the Groebner bases polynomials, along with the utilization of recursive algorithms, allows the solution to be effortlessly obtained. Optimal phasor measurement units placement (OPP) problem can be presented in a linear or nonlinear polynomial form, both of which are used in this paper. The settings of OPP problem have been proposed in this paper with the inclusion of zero injection buses (ZIBs), in normal system states and considering contingency related to PMU outage. The problem formulation is defined according to the application of Groebner bases technique. The proposed model is capable of obtaining the full set of optimal solutions instead of only one or partial solutions. The efficiency of the proposed method is tested on IEEE 14-bus, IEEE 24-bus, IEEE 30-bus, IEEE 118-bus and Polish 2383-bus test system and the results are compared with those of some recently reported methods.

Numerical optimization methods comparison based on the CFD conduction-convection heat transfer case

PurposeIn some types of industries, the best possible design, in terms of thermal and flow performance, determines the success or failure of the company. This applies, among others, to the sectional elements that form doors, windows or prefabricated building walls. The purpose of this paper is to show the possibilities and limitations of the different response surface methods for optimization in the case where natural convection phenomenon appears inside the sectional structures.Design/methodology/approachA three-layered wall with air gap is used as a cross-section heat flow model. Response surface algorithms for optimization, which can be found in commercial software, e.g. ANSYS/WORKBENCH, can help to optimize geometrical structure of components to achieve bigger or smaller heat flux value. In this paper, the optimization methodology of the design of experiments (DOE) and different response surface (RS) methods are used.FindingsOptimal results obtained with the use of genetic aggregation, standard RS, Kriging, non-parametric regression and neural network methods are compared with direct CFD and analytical calculations. Different limitations and advantages of the RS methods make individual methods more appropriate for different issues. For a properly defined optimization problem, the heat flux value approximated for the optimal geometry agrees with the direct CFD simulations.Practical implicationsThe presented investigations show how to use response surface optimization methods for thermal optimization of the sectional elements and their applications to obtain reliable results.Originality/valueThis paper presents the value of the use of RS methods in CFD-based geometry optimization. The study also shows that the RS optimization methods can approximate thermal properties under natural convection development conditions.

Particle Swarm Optimization of PID Controller under Constraints on Performance and Robustness

This paper presents a design procedure of the PID controller where optimal parameters of controller * * * *p i d f (k ,k ,k ,T ) areobtained by solving the constrained optimization problem. The objective function is given in the form of the Integral of Absolute Error(IAE) under specifications to achieve predictable performance and robustness. The constraints within the optimization problem setupare desired maximum sensitivity, desired maximum complementary sensitivity and maximum sensitivity to measurement noise underhigh frequencies. The optimization problem is transformed to an unconstrained problem using penalty function approach. Solution tothe optimization problem is obtained using Particle Swarm algorithm (PSO) which leads to an efficient suppression of disturbance aswell as an adequate reference tracking performance of the closed-loop system with negligible overshoot. The suggested method isapplicable to the large class of stable, integral and unstable processes, processes with oscillatory dynamics with and without dead-time.Effectiveness of the proposed design procedure is verified via numerical simulations on test batch consisting of processes typicallyencountered in industry. Paper also provides two another solutions of the defined optimization problem using genetic algorithm (GA)and fminunc trust region based approach (TR). Performance of the PSO, GA, and TR based control system is compared with thoseusing recently proposed maximization of proportional gain denoted with max(kp) method. Although the present paper is focused to tunethe PID controller, the same procedure may be used to design PI controller, lead and lag compensators, high-order controllers as well asfractional-order controllers.

Demand response with heuristic control strategies for modulating heat pumps

The flexibility of electrical heating devices can contribute to overcoming the challenges caused by increasing shares of volatile renewable energy sources in the energy system. Especially modulating heat pumps are suitable for using intelligent control strategies that vary the pumps’ power output based on demand response signals. In this paper, we define optimization problems for minimizing the heating costs and the surplus energy of a residential area, and we introduce novel heuristic control strategies for modulating heat pumps to solve these problems. The heuristic control strategies make use of a privacy preserving control and communication architecture that combines central and decentralized control approaches. All buildings use an underfloor heating system and a domestic hot water tank as thermal storages. Compared to a conventional control strategy, the results show average cost reductions of between 4.1% and 13.3% for the cost minimization heuristics, and average improvements of between 38.3% and 52.6% for the surplus energy minimization heuristic. Contrary to approaches for finding the globally optimal solution, the introduced heuristic control strategies have significantly lower computational times and do not require perfect foresight regarding future demands and electricity generation.