Multi Optimization Problem Research Articles

A new solution approach for non-convex combined heat and power economic dispatch problem considering power loss

The combined heat and power economic dispatch (CHPED) problem is a non-convex multivariate global optimization problem. The objective of the problem is to reduce total production costs while imposing a variety of constraints and meeting the demand for power and heat. Three recently presented metaheuristic approaches, Slime Mould Algorithm (SMA), COOT algorithm and Marine Predators Algorithm (MPA), are applied for solving CHPED problem. Studies dealing with the CHPED problem in the literature often do not consider valve points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, all at once. Furthermore, power losses are neglected especially in large-scale problems. In this study, the CHPED problem is solved by considering all operational constraints including active power transmission losses. Three separate case studies with dimensions of 11 units, 48 units, and 96 units were used in the tests under various limitations. The experimental results revealed that MPA outperformed not only SMA, and COOT but also the algorithms proposed previously in the literature.

Multi-Stage optimization under uncertainty in reverse logistics operations: An industrial scenario

The major concern of reverse logistics operations involves reducing logistics costs, improving after sales service, waste disposal and providing good quality service in today's green environment. Process optimization involving uncertainty under reverse logistics set-up is a major challenge. There is a need to consider the dynamics of the real situation because of the variation of product/process characteristics to make the system more robust. A comparative analysis and the need for multi-stage optimization are illustrated here based on a single stage optimization model after performing its sensitivity analysis. Accordingly, a multi-stage optimization problem is formulated here to solve the cost optimization problem of charge mix under a reverse logistics set-up of a foundry business and to deal with the uncertainties involved in a practical business scenario. The proposed framework can be effectively implemented in a similar reverse logistics environment considering uncertainties of the process parameters/product characteristics.

Joint Particle Swarm Optimization of Power and Phase Shift for IRS-Aided D2D Underlaying Cellular Systems.

Device-to-device (D2D) communication is a promising wireless communication technology which can effectively reduce the traffic load of the base station and improve the spectral efficiency. The application of intelligent reflective surfaces (IRS) in D2D communication systems can further improve the throughput, but the problem of interference suppression becomes more complex and challenging due to the introduction of new links. Therefore, how to perform effective and low-complexity optimal radio resource allocation is still a problem to be solved in IRS-assisted D2D communication systems. To this end, a low-complexity power and phase shift joint optimization algorithm based on particle swarm optimization is proposed in this paper. First, a multivariable joint optimization problem for the uplink cellular network with IRS-assisted D2D communication is established, where multiple DUEs are allowed to share a CUE's sub-channel. However, the proposed problem considering the joint optimization of power and phase shift, with the objective of maximizing the system sum rate and the constraints of the minimum user signal-to-interference-plus-noise ratio (SINR), is a non-convex non-linear model and is hard to solve. Different from the existing work, instead of decomposing this optimization problem into two sub-problems and optimizing the two variables separately, we jointly optimize them based on Particle Swarm Optimization (PSO). Then, a fitness function with a penalty term is established, and a penalty value priority update scheme is designed for discrete phase shift optimization variables and continuous power optimization variables. Finally, the performance analysis and simulation results show that the proposed algorithm is close to the iterative algorithm in terms of sum rate, but lower in power consumption. In particular, when the number of D2D users is four, the power consumption is reduced by 20%. In addition, compared with PSO and distributed PSO, the sum rate of the proposed algorithm increases by about 10.2% and 38.3%, respectively, when the number of D2D users is four.

Prediction of Seismic Bearing Capacity Considering Nonlinearity and Dilatancy by Sequential Quadratic Programming

Most of the published literature regarding bearing capacity are often focused on linear and associative soils. Concerning the intrinsic strength nonlinearity in dilatancy soils, this study investigates the problem of the seismic bearing capacity in the framework of the kinematic theorem of limit analysis. The conventional linear Mohr–Coulomb criterion is substituted with a nonlinear power law criterion to depict the nonlinearity of the soil strength. The non-associative feature of soil materials is considered by defining a nonlinear dilatancy coefficient. A generalized tangential technique is accordingly introduced to linearize the strength envelope for making the nonlinear criterion tractable in the analysis. A non-symmetrical translational failure mechanism that is comprised of several rigid wedges is used to characterize the failure of the foundation at the limit state. Moreover, the seismic action is considered by the classic pseudo-static method. Based upon the energy equilibrium theory of the upper-bound limit analysis, new analytical solutions are derived from the work-balanced equation with nonlinearity and dilatancy. This rigorous upper-bound solution is formulated as a multivariate optimization problem and is readily addressed by sequential quadratic programming (SQP). To verify the reliability of the new expressions, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. The comparative results show a good agreement with previous works, and the correctness and rationality of the new analytical solutions are validated. The detailed parametric study reveals that, in the non-associative flow soils, the ultimate bearing capacity is significantly decreased with a reduction in the dilatancy coefficient. Particularly in the linear condition, namely m = 1, the larger the internal friction angle is, the more obvious the influence of the non-associative feature on the bearing capacity is.

The further adventures of Lynn Eyar, Ty Minvariant, and Connie Volution

My favorite homework problems challenge students to grow beyond direct procedural mathematics, engaging their reasoning with higher level tasks from Bloom's Taxonomy: Analyze, Evaluate, & Create. This whirlwind tour presents four flavors of signal processing homework problems. First, graph-based conceptual problems require students to reason from figures, rather than deriving equations. These problems scaffold students as they transfer intuition from closed form analytic equations to the often messy time series and power spectra obtained with real world data. Second, Matlab problems require students to work with audio data on problems that are often deliberately underspecified. These problems introduce students to the cyclic trial and error nature of engineering design. Third, module problems require students to design systems to meet a specification, while also considering some form of cost. Real engineering is almost always a multivariate optimization problem balancing performance with constraints. Finally, story problems require students to identify common misconceptions in the mouths of fictional peers. Team dynamics reward engineers who can succinctly identify the shortcomings or misconceptions in poor approaches as well advocate on behalf of their own designs. This talk may include some audience participation.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

An Enhanced Multioperator Runge–Kutta Algorithm for Optimizing Complex Water Engineering Problems

Water engineering problems are typically nonlinear, multivariable, and multimodal optimization problems. Accurate water engineering problem optimization helps predict these systems’ performance. This paper proposes a novel optimization algorithm named enhanced multioperator Runge–Kutta optimization (EMRUN) to accurately solve different types of water engineering problems. The EMRUN’s novelty is focused mainly on enhancing the exploration stage, utilizing the Runge–Kutta search mechanism (RK-SM), the covariance matrix adaptation evolution strategy (CMA-ES) techniques, and improving the exploitation stage by using the enhanced solution quality (IESQ) and sequential quadratic programming (SQP) methods. In addition to that, adaptive parameters were included to improve the stability of these two stages. The superior performance of EMRUN is initially tested against a set of CEC-17 benchmark functions. Afterward, the proposed algorithm extracts parameters from an eight-parameter Muskingum model. Finally, the EMRUM is applied to a practical hydropower multireservoir system. The experimental findings show that EMRUN performs much better than advanced optimization approaches. Furthermore, the EMRUN has demonstrated the ability to converge up to 99.99% of the global solution. According to the findings, the suggested method is a competitive algorithm that should be considered in optimizing water engineering problems.

On the Value of Dynamism in Transit Networks

The rise of on-demand mobility technologies over the past decade has sparked interest in the integration of traditional transit and on-demand systems. One of the main reasons behind this is the potential to address a fundamental trade-off in transit: the ridership versus coverage dilemma. However, unlike purely fixed systems or purely on-demand systems, integrated systems are not well understood; their planning and operational problems are significantly more challenging, and their broader implications are the source of a heated debate. Motivated by this debate, we introduce the dynamicity gap, a general concept that quantifies the attainable benefit of allowing (but not requiring) dynamic components in the response strategy to a multistage optimization problem. Although computing the dynamicity gap exactly may be intractable, we develop an analytical framework with which to approximate it as a function of problem input parameters. The framework allows us to certify the value of dynamism (i.e., a dynamicity gap greater than one) for certain combinations of problem input parameters. We showcase our approach with two sets of computational experiments, from which we gain both qualitative and quantitative insights about the settings in which the integration of transit and on-demand systems may certifiably be a worthwhile investment.Funding: This work was partially supported by the National Science Foundation [Grants DMS-1839346 and CNS-1952011]. Part of this research was performed while the authors were visiting the Institute for Pure and Applied Mathematics, which is supported by the National Science Foundation [Grant DMS-1925919].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1193 .

Image denoising based on a new anisotropic mean curvature model

A number of variational models for image denoising have been proposed in the last few years in order to advance the denoising performance. To improve the denoising quality, it is very significant to describe the local structure of image in the proposed models. To this end, this paper proposes a novel denoising model which combines the gradient operator $ \nabla $ with the adaptive weighted matrix $ W $ in the mean curvature regularized term such that the proposed model can describe the local features in image efficiently. Since the proposed model is a high-order nonlinear and nonconvex optimization problem, we need to use the operator splitting method to tansform it into a multi-variable optimization problem and then the alternating direction method of multipliers (ADMM) can be applied to solve it. Numerical experiments demonstrate that the proposed model yields good performance compared with other well-known gradient-based models.

Analysis of Chaotic Maps for Global Optimization and a Hybrid Chaotic Pattern Search Algorithm for Optimizing the Reliability of a Bank

Optimization is an imperative feature in almost all fields of Engineering, Economics, and Sciences. Due to the advent of high-end computers and the gradual increase in the complexity of optimization problems, algorithms for numerical optimization have been developed. Numerous existing numerical optimization algorithms suffer from premature convergence, poor local/global search abilities, and high computational complexity. A chaotic optimization algorithm and a chaotic map could help overcome most of these setbacks. This paper offers a detailed study and analysis of five chaotic maps used for global Optimization, namely Chebyshev, Cubic, ICMIC, Neuron, and Sine maps. This work also proposes a pioneering global optimization method, Hybrid Chaotic Pattern Search Algorithm (HCPSA), for finding the global minimum for multivariable unconstrained optimization problems. Numerical results over 12 benchmark functions and comparative results (comparison of accuracy and computational time) with some popular algorithms evidence the effectiveness of the proposed algorithm for higher dimensional non-linear functions. The efficient usage of chaotic maps has helped reduce the computational time to evaluate the optimum for higher dimensional non-linear functions. To showcase the use of HCPSA in a real-world problem, we have taken the problem of analyzing financial ratios for predicting bankruptcy. Banks predict bankruptcy from the start of their businesses to determine their financial stability. In this work, we initially perform Logistic Regression (LR) on the data obtained from the banks to get the reliability function with financial ratios as decision variables. After this, the function is maximized using HCPSA and a Chebyshev map. This methodology is beneficial for decision-makers within a bank to maximize the reliability of the financial ratios and, most essential, to protect the bank from disasters. Comparative results of reliability prediction using HCPSA and PSO and a non-parametric statistical test proves that the proposed algorithm is better in terms of accuracy.

Optimizations of Multi Optima Problems Using the Genetic Algorithm, Punch-Out Method, and Least Exponent Method

The Genetic Algorithm (GA) is a very effective global search algorithm. When the dimension of the optimization problem becomes great, it is not a simple task for methods, such as gradient methods. For the accuracy of a given solution, the search frequency of the variables necessary for a variable axis is far greater with the dimension increase of the solution vector. When the smoothness of the problem is good, the small frequency of the variable will do, with the progress of the generations. However, when the problem has many sharp peaks, such as in data regression, several frequencies of the variable in each variable axis are needed to result in a tremendous total number of individuals. In order to resolve this kind of ineffectiveness for many variables with a moderate number of individuals, a punch-out method is proposed for effectively finding the optimum. The least square method is revisited here to suggest least exponent method to take care of the outlier problem in data regression.

Conceptual design and sizing optimization based on minimum energy consumption of lift-cruise type eVTOL aircraft powered by battery and fuel cell for urban air mobility

In conceptual studies and prototypes of aerial vehicles for Urban Air Mobility, batteries are generally adopted as only energy sources. However, batteries have a long charging time that is not suitable for consecutive flights, and a low energy density that limits the range and flight time of the aircraft. For this reason, the hybrid propulsion solution consisting of a battery and a fuel cell has attracted attention in aviation in recent years. This study proposes the conceptual design of a VTOL (Vertical Take-Off and Landing) aircraft for passenger transportation in metropolitan areas by the synergic optimization of the aircraft configuration and the sizing of the propulsion system aimed at minimizing the power request in cruise. In the proposed conceptual design method, VTOL type aircraft is powered by either the battery or the fuel cell according to the flight phase. A multivariate nonlinear optimization problem using as goal the minimization of the fuel cell size is solved. The optimal values of battery size, wing loading, aspect ratio, endurance speed, aircraft weight, maximum lift coefficient, disk loading, rotor solidity, and zero-lift drag coefficient are determined from the solution of the optimization problem.

Electrically large aperture horn array antenna with low side lobe level for Ku‐band frequency

AbstractUsing electrically large antennas for array applications may cause grating lobes and this can change the array pattern. To achieve a low side lobe level for boresight pattern for linear or planar array antennas, in the literature it is seen that the common method is the use of feeding each antenna with some amplitude distribution and keeping the distance between the antennas less than a wavelength. However, in this study the distance between the antennas is chosen to be greater than a wavelength. Therefore, the common methods cannot be used. To achieve a low side lob level in the radiation pattern for an array of antennas composed of antennas with a distance greater than one wavelength. The aperture length of each antenna is chosen to be variable and an analytical solution method is used to calculate the amplitude of each aperture field of the horn antennas. Thus, the determination of unit horns' optimal aperture lengths Li can be considered a multivariable optimization problem. This challenging problem was achieved using a novel meta‐heuristic optimization algorithm called the differential evolutionary algorithm (DEA), where the aperture lengths of each array element are taken as inputs to find the optimal side lobe level (SLL). Based on the obtained solutions, a 4 × 1 horn array antenna design alongside its feed network was designed for Ku‐band applications. The design of the array is simulated in CST simulation software, and the obtained simulated results had been compared with experimental results and counterpart designs in the literature.

Electrolyte Channel Design By Physical Model and Machine Learning

Thick electrode is highly effective to increase the specific energy of a battery cell, but the associated increase in transport distance causes a major barrier for fast charging. We introduce a bio-inspired electrolyte channel design into thick electrodes to improve the cell performance, especially under fast charging conditions. The effects of channel length, width, tapering degree and active material width on the electrochemical performance and mechanical integrity are investigated. Machine learning by deep neural network (DNN) is developed to relate the geometrical parameters of channels to the overall cell performance. Integrating machine learning with the Markov chain Monte Carlo gradient descent optimization, we demonstrate that the complicated multivariable channel geometry optimization problem can be efficiently solved. The results show that within a certain range of geometrical parameters, the specific energy, specific capacity and specific power can be greatly improved. At the same time, the maximum first principal stress which is in the cathode region next to the separator can be significantly reduced, giving better mechanical integrity. Comparing to conventional designed cells without electrolyte channels, we show a 79% increase in specific energy using channel design optimization. This study provides a design strategy and optimization method to achieve significantly improved battery performance

Ameliorated artificial hummingbird algorithm for coordinated wind-solar-thermal generation scheduling problem in multiobjective framework

This paper proposed an optimization technique, namely ameliorated artificial hummingbird algorithm (AAHA), that blends artificial hummingbird algorithm (AHA) with simplex search strategy (SSS) to solve the coordinated wind-solar-thermal generation scheduling problem. The AAHA simulates the foraging behaviour of hummingbirds for food, including guided, territorial, and migration foraging. Guided foraging helps in the higher exploration in the initial stages, and territorial foraging performs the exploitation in its neighbourhood. Migration foraging explores the search space. The SSS enhances the weak territorial and migration foraging of AHA by improving the exploitation mechanism. The proposed method is simple and has less dependency on parameters to adjust. The solar and wind units are committed to ascertaining their share for uninterrupted supply. The price penalty method is applied to unify the emission of gaseous pollutants due to thermal generation with operating costs. To reduce the use of coal, renewable energy sources have been considered in this problem which results in reducing the pollutants’ emissions and saving in fuel costs. To solve the dynamic multivariable constrained optimization problem, the forward approach has been implemented. The performance of the proposed algorithm is tested on different electric test systems, and a statistical test justifies the results.

RIS-Assisted Receive Quadrature Space-Shift Keying: A New Paradigm and Performance Analysis

Reconfigurable intelligent surfaces (RISs) represent a promising candidate for sixth-generation (6G) wireless networks, as the RIS technology provides a new solution to control the propagation channel in order to improve the efficiency of a wireless link through enhancing the received signal power. In this paper, we propose RIS-assisted receive quadrature space shift keying (RIS-RQSSK), which enhances the spectral efficiency of an RIS-based index modulation (IM) system by using the real and imaginary dimensions independently for the purpose of IM. Therefore, the error rate performance of the system is improved as all RIS elements reflect the incident transmit signal toward both selected receive antennas. At the receiver, a low-complexity but effective greedy detector (GD) can be employed which determines the maximum energy per dimension at the receive antennas. A max-min optimization problem is defined to maximize the received signal-to-noise ratio (SNR) components at both selected receive antennas; an analytical solution is provided based on Lagrange duality. In particular, the multi-variable optimization problem is shown to reduce to the solution of a single-variable equation, which results in a very simple design procedure. In addition, we investigate the average bit error probability (ABEP) of the proposed RIS-RQSSK system and derive a closed-form approximate upper bound on the ABEP. We also provide extensive numerical simulations to validate our derivations. Numerical results show that the proposed RIS-RQSSK scheme substantially outperforms recent prominent benchmark schemes. This enhancement considerably increases with an increasing number of receive antennas.

Multistage optimization of a petroleum production system with material balance model

In this paper, we propose a mathematical formulation for the optimal management over time of an oil production network as a multistage optimization problem. The proposed model differs from common practice where the reservoir of the oil production network is approximated by decline curves or by black-box simulators. We model the reservoir as a controlled (non-linear) dynamical system by using material balance equations, under the standard assumptions that the fluids follow a black-oil model and that the reservoir has a tank-like behavior. The state of the dynamical system has five dimensions: the total volume of respectively oil, gas, and water in the reservoir; the total pore volume; and the reservoir pressure. We use a dynamic programming algorithm to numerically solve the multistage optimization problem on two specific instances of the general optimization problem where the state dimension can be reduced from dimension five to dimension one or two. More precisely, the first numerical application consists in optimizing the production of a dry gas reservoir which is subdivided in two tanks and which leads to a two-dimensional state (one dimension per tank), whereas the second numerical application tackles an oil reservoir with water injection which leads to a two-dimensional state. The two applications illustrate that our approach handles interconnected tanks (in the dry gas case) and that our approach allows optimization beyond first recovery of oil (in the oil with water injection case). We also provide numerical and theoretical comparisons with decline curves in the dry gas application.

A Master-Slave Salp Swarm Algorithm Optimizer for Hybrid Energy Storage System Control Strategy in Electric Vehicles

Pure electric vehicles provide an enticing ecofriendly alternative to traditional fossil fuel combustion engine locomotives. Batteries have primarily been used to store energy in electric vehicles; however, peak load demand and transient power leading to decreased battery lifespan have bred interest in hybrid energy storage systems in electric vehicles. Management of energy drawn from a hybrid energy storage system (HESS) in electric vehicles is a real-time multistage optimization problem aimed at minimizing energy consumption while aptly distributing energy drawn from the battery and capacitor to enhance the battery life cycle. This paper explores the feasibility of a master-slave salp swarm optimization algorithm (MSSSA) (metaheuristic algorithm) in a HESS control strategy for electric vehicles. Introducing a master-slave learning approach to the salp swarm algorithm (SSA) improves its performance by increasing its convergence rate while maintaining a balance between exploration and exploitation phases of the algorithm. A comparison of the MSSSA results with the SSA (salp swarm algorithm), DA (dynamic algorithm), WOA (whale optimization algorithm), MFO (moth flame optimization algorithm), GA (genetic algorithm), and PSO (particle swarm optimization algorithm) on benchmark test functions and dynamic program simulation of an electric vehicle’s HESS control strategy and shows preeminence of the MSSSA control strategy for HESS.

Workload management and server speed setting for cost‐performance ratio optimization

AbstractThe cost‐performance tradeoff is a fundamental issue in a data center for cloud computing, which is closely related to two key metrics that both cloud consumers and service providers care the most, that is, quality of service and cost of service. While there are different definitions of quality of service, the average response time is a common choice of performance metric. While there are various considerations in cost of service, the average power consumption is a common choice of cost metric. Hence, the cost‐performance tradeoff becomes the power‐performance tradeoff. In this article, we deal with the power‐performance tradeoff at the data center level. We study cost‐performance ratio optimization by using the techniques of workload management and server speed setting. In particular, we make the following tangible contributions. We solve three optimization problems, that is, (1) the workload management problem—to find a workload distribution, such that the cost‐performance ratio is minimized; (2) the server speed setting problem—to find a server speed setting, such that the cost‐performance ratio is minimized; (3) the workload management and server speed setting problem—to find a workload distribution and a server speed setting, such that the cost‐performance ratio is minimized. All the three optimization problems are analytically defined as multivariable optimization problems based on M/M/m queueing systems for multiple heterogeneous multiserver systems, together with two power consumption models, that is, the idle‐speed model and the constant‐speed model. Our approach makes it possible to quantitatively evaluate and optimize the cost‐performance ratio of a data center within a rigorously developed framework. Each multivariable optimization problem is transformed to a nonlinear system of equations. Due to the sophistication of these equations, they are solved algorithmically by a numerical procedure. Furthermore, we provide approximate, accurate, and analytical solutions to the first two problems. Performance data are demonstrated for each problem, and the accuracy of our approximate solutions are also discussed. To the best of the author's knowledge, this is the first paper which analytically and algorithmically minimizes the cost‐performance ratio of a data center with multiple heterogeneous multiserver systems using the techniques of workload management and server speed setting.

Thermal-Economic Optimization of Plate–Fin Heat Exchanger Using Improved Gaussian Quantum-Behaved Particle Swarm Algorithm

Heat exchangers are usually designed using a sophisticated process of trial-and-error to find proper values of unknown parameters which satisfy given requirements. Recently, the design of heat exchangers using evolutionary optimization algorithms has received attention. The major aim of the present study is to propose an improved Gaussian quantum-behaved particle swarm optimization (GQPSO) algorithm for enhanced optimization performance and its verification through application to a multivariable thermal-economic optimization problem of a crossflow plate–fin heat exchanger (PFHE). Three single objective functions: the number of entropy generation units (NEGUs), total annual cost (TAC), and heat exchanger surface area (A), were minimized separately by evaluating optimal values of seven unknown variables using four different PSO-based methods. By comparing the obtained best fitness values, the improved GQPSO approach could search quickly for better global optimal solutions by preventing particles from falling to the local minimum due to its modified local attractor scheme based on the Gaussian distributed random numbers. For example, the proposed GQPSO could predict further improved best fitness values of 40% for NEGUs, 17% for TAC, and 4.5% for A, respectively. Consequently, the present study suggests that the improved GQPSO approach with the modified local attractor scheme can be efficient in rapidly finding more suitable solutions for optimizing the thermal-economic problem of the crossflow PFHE.