Range Of Feasible Solutions Research Articles

An adapted Black Widow Optimization Algorithm for Financial Portfolio Optimization Problem with cardinalty and budget constraints

Financial Portfolio Optimization Problem (FPOP) is a cornerstone in quantitative investing and financial engineering, focusing on optimizing assets allocation to balance risk and expected return, a concept evolving since Harry Markowitz’s 1952 Mean-Variance model. This paper introduces a novel meta-heuristic approach based on the Black Widow Algorithm for Portfolio Optimization (BWAPO) to solve the FPOP. The new method addresses three versions of the portfolio optimization problems: the unconstrained version, the equality cardinality-constrained version, and the inequality cardinality-constrained version. New features are introduced for the BWAPO to adapt better to the problem, including (1) mating attraction and (2) differential evolution mutation strategy. The proposed BWAPO is evaluated against other metaheuristic approaches used in portfolio optimization from literature, and its performance demonstrates its effectiveness through comparative studies on benchmark datasets using multiple performance metrics, particularly in the unconstrained Mean-Variance portfolio optimization version. Additionally, when encountering cardinality constraint, the proposed approach yields competitive results, especially noticeable with smaller datasets. This leads to a focused examination of the outcomes arising from equality versus inequality cardinality constraints, intending to determine which constraint type is more effective in producing portfolios with higher returns. The paper also presents a comprehensive mathematical model that integrates real-world constraints such as transaction costs, transaction lots, and a dollar-denominated budget, in addition to cardinality and bounding constraints. The model assesses both equality/inequality cardinality constraint versions of the problem, revealing that the inequality constraint tends to offer a wider range of feasible solutions with increased return potential.

Multiple solution of MHD Casson fluid flow in porous channel with chemical reactions and thermal radiation effects

This study focused on evaluating the synergistic effects of magnetohydrodynamics, Casson fluid properties, thermal radiation, chemical reactions, and heat transfer mechanisms within a porous channel. Through the application of similarity transformation, nonlinear governing equations are converted into nonlinear ordinary differential equations. These modified equations were then numerically solved in MATLAB using the Runge–Kutta method alongside the shooting technique to ensure precise results. The investigation yielded various numerical solutions for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat transfer coefficient, and Sherwood number, all of which are presented in both tabular and graphical formats. Three distinct solutions emerged from the analysis, differentiated by variations in the Reynolds number, Casson number, expansion or contraction ratio, and magnetic parameters. These solutions demonstrate differences in the parameters under investigation. Solutions within the ranges of γ[5,∞] and R[31.07,∞] are influenced by the specific values of the magnetic number M[0,2.0]. For each M value, there exists a unique set of solutions for γ and R that satisfy the established parameters. As the magnetic number varies, so does the range of feasible solutions, highlighting the sensitivity of the system to magnetic influence. The values of γ and R are adjusted according to the chosen M value.

New Trends in Symmetry in Optimization Theory, Algorithms and Applications

Optimization is an important branch of operations research in applied mathematics and computer science, where functions are optimized over a range of feasible solutions [...]

Study on the Path of Cultivating Rural Teachers under the Perspective of Rural Revitalization---Taking the Cultivation of Directed Teacher Trainees in Jiangsu Province as an Example

Abstract This study delves into the training of rural teachers, a core element of rural education revitalization. Focusing on the training of oriented rural teacher trainees and their willingness to arrive, this paper adopts a combination of structural equation modeling and double-stranded quantum genetic algorithm to deepen the understanding of influence pathways. The method successfully obtains a broader range of feasible solutions by introducing different prior knowledge. In this study, the improved structural equation modeling (SEM) was applied among oriented teacher trainees of different grades in six universities in Jiangsu Province, parameter estimation tests were conducted through SmartPLS, key indicator variables were established and empirical data were obtained through research. The results showed that teachers’ professional identity significantly positively affected the attitude of performance arrival, with a critical ratio value of 3.3469 and a substantial value of the unstandardized coefficient (P<0.001). In addition, it was found that the performance-to-post attitudes of the oriented teacher trainees were positively influenced by the satisfaction with the rural teacher job offerings. This study provides an essential decision-making basis for constructing a good training environment for oriented teacher trainees, which is of great significance for promoting the revitalization of rural education.

Develop a Nonlinear Regression Model Using Box-Cox Transformation with Application

This article introduces an algorithm designed for utilizing power transformations in the estimation of nonlinear regression models. The algorithm outlines a series of steps for selecting the most suitable power parameter estimate through a combination of the conventional Maximum Likelihood Estimation technique and specific criteria for enhancing statistical modeling effectiveness. Supplementary decision guidelines involve the utilization of the determination coefficient and the p-value from the errors normality test. The algorithm's application was demonstrated using actual data. The article's conclusion highlighted the ability to identify a range of feasible solutions for selecting the optimal power parameter. However, it was acknowledging the challenge of identifying a single optimal value that satisfies the requirements of all estimation and decision methodologies.

A Comparative Visual Analytics Framework for Evaluating Evolutionary Processes in Multi-Objective Optimization.

Evolutionary multi-objective optimization (EMO) algorithms have been demonstrated to be effective in solving multi-criteria decision-making problems. In real-world applications, analysts often employ several algorithms concurrently and compare their solution sets to gain insight into the characteristics of different algorithms and explore a broader range of feasible solutions. However, EMO algorithms are typically treated as black boxes, leading to difficulties in performing detailed analysis and comparisons between the internal evolutionary processes. Inspired by the successful application of visual analytics tools in explainable AI, we argue that interactive visualization can significantly enhance the comparative analysis between multiple EMO algorithms. In this paper, we present a visual analytics framework that enables the exploration and comparison of evolutionary processes in EMO algorithms. Guided by a literature review and expert interviews, the proposed framework addresses various analytical tasks and establishes a multi-faceted visualization design to support the comparative analysis of intermediate generations in the evolution as well as solution sets. We demonstrate the effectiveness of our framework through case studies on benchmarking and real-world multi-objective optimization problems to elucidate how analysts can leverage our framework to inspect and compare diverse algorithms.

PSO-Optimized SHE-PWM Technique in a Cascaded H-Bridge Multilevel Inverter for Variable Output Voltage Applications

One of the problems of the selective harmonic elimination pulsewidth modulation (SHE-PWM) method is a limited range of feasible solutions. In many practical applications, the inverter is required to produce a variable output voltage within a wide range (e.g., 0.1 to 1). When the inverter operates in a low modulation index (low output voltage), the output harmonic distortion increases. This article introduces a method to use the SHE-PWM technique for a wide range of modulation indices, which allows achieving a high-quality output waveform in a cascaded H-bridge multilevel inverter. In a five-level case, a dc–dc converter regulates the dc-link voltage of only one bridge. In this way, the extra hardware requirement is reduced, and also a higher number of voltage levels is achieved, which improves the waveform quality. The particle swarm optimization algorithm is used to solve the SHE problem for different output voltage values. Two strategies are proposed to obtain the variable dc-link voltage; one of them is suitable for the lower output voltage values and the other one is more suitable for high values of the output voltage. The proposed strategies have been tested through simulation and experimental studies in different conditions. The results indicate a considerable improvement in the output waveform quality.

Metaheuristic optimization algorithm based on the two-step Adams-Bashforth method in training multi-layer perceptrons

The proposed metaheuristic optimization algorithm based on the two-step Adams-Bashforth scheme (MOABT) was first used in this paper for Multilayer Perceptron Training (MLP). In computer science and mathematical examples, metaheuristic is high-level procedures or guidelines designed to find, devise, or select algorithmic research methods to obtain high-quality solutions to an example problem, especially if the information is insufficient or incomplete, or if computational capacity is limited. Many metaheuristic methods include some stochastic example operations, which means that the resulting solution is dependent on the random variables that are generated during the search. The use of higher evidence can frequently find good solutions with less computational effort than iterative methods and algorithms because it searches a broad range of feasible solutions at the same time. Therefore, metaheuristic is a useful approach to solving example problems. There are several characteristics that distinguish metaheuristic strategies for the research process. The goal is to efficiently explore the search perimeter to find the best and closest solution. The techniques that make up metaheuristic algorithms range from simple searches to complex learning processes. Eight model data sets are used to calculate the proposed approach, and there are five classification data sets and three proximate job data sets included in this set. The numerical results were compared with those of the well-known evolutionary trainer Gray Wolf Optimizer (GWO). The statistical study revealed that the MOABT algorithm can outperform other algorithms in terms of avoiding local optimum and speed of convergence to global optimum. The results also show that the proposed problems can be classified and approximated with high accuracy

Receding Horizon Control with Extended Solution for UAV Path Planning

The receding horizon control (RHC) greatly reduces the planning time and achieves great success in UAV online path planning because of rolling window optimization. However, due to its small range of path search in the time window, UAVs cannot cope with environments with uncertain obstacles and multiple flight constraints. Therefore, the receding horizon control with extended solution (RHC-eS) method is proposed for UAV path planning based on the traditional RHC. This method first designs the path expansion mechanism, which not only expands the search range of feasible solutions but also ensures the real-time performance by the two-way search strategy. Secondly, in order to increase the richness of solutions, the crossover and directional variation strategy of Genetic Algorithm (GA) are integrated. Finally, the Sequential Quadratic Programming (SQP) method is used to optimize the objective function. The simulation results of UAV path planning in simple and complex environments certify that the proposed method can obtain shorter, safer, and smoother paths compared with the existing methods.

Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.

Analysis of the Energy Flow in a Municipal Wastewater Treatment Plant Based on a Supercritical Water Oxidation Reactor Coupled to a Gas Turbine

Biological municipal wastewater treatments lead to high sludge generation and long retention times, and the possibilities for recovery of the energy content of the input waste stream are very limited due to the low operating temperature. As an alternative, we propose a sequence of exclusively physicochemical, non-biological stages that avoid sludge production, while producing high-grade energy outflows favoring recovery, all in shorter times. Ultrafiltration and evaporation units provide a front-end concentration block, while a supercritical water oxidation reactor serves as the main treatment unit. A new approach for energy recovery from the effluent of the reactor is proposed, based on its injection in a gas turbine, which presents advantages over simpler direct utilization methods from operational and efficiency points of view. A process layout and a numerical simulation to assess this proposal have been developed. Results show that the model process, characterized with proven operating parameters, found a range of feasible solutions to the treatment problem with similar energy costs, at a fast speed, without sludge production, while co-generating the municipality’s average electricity consumption.

Estimating the boundaries of the feasible profiles in the bilinear decomposition of multi-component data matrices

The boundaries of the range of feasible profiles in the bilinear decomposition of a data matrix are estimated by suitably modifying the already published N-BANDS algorithm. Instead of maximizing and minimizing the profile norms, the new sensor-wise N-BANDS approach calculates the profiles showing extreme values of the elements at each sensor in both data modes. This produces two sets of profiles for each sensor, whose envelops define the boundaries of the range of feasible solutions: the upper envelop for maximum element values represents the upper boundary, and the lower envelop the lower boundary. A three-component data set was studied in this manner under non-negativity constraints in both data modes. The sensor-wise N-BANDS results agree with those provided by the FACPACK program, which computes the area of feasible solutions and the associated set of feasible profiles. Computer times required for truly multi-component systems appear to be feasible using sensor-wise N-BANDS (up to eight sample components were checked). As an example, a six-component system was analyzed with the presently described approach, with results which are consistent with the expectations based on the consideration of the degree of profile overlapping among the participating species.

A simple self modelling curve resolution (SMCR) method for two-component systems

Multivariate self-modeling curve resolution (SMCR) methods are the best choice for analyzing chemical data when there is not any prior knowledge about the chemical or physical model of the process under investigation [[1Q3: The reference ‘1’ is only cited in the abstract and not in the text. Please introduce a citation in the text.]]. However, the rotational ambiguity is the main problem of SMCR methods, yielding a range of feasible solutions. It is, therefore, important to determine the range of all feasible solutions of SMCR methods. Different methods have been presented in the literature to find feasible solutions of two, three, and four component systems. Here, a novel simple SMCR method is presented for calculating the boundaries of feasible solutions of two-component systems.At first, the simple strategy is presented for calculating the feasible solutions of two-component systems. Next, four different experimental two-component systems are analyzed in detail for calculating the boundaries of feasible solutions in both spaces, including complex formation equilibrium, keto-enol tautomerization kinetic, lipidomics data, and a case for quantification of an analyte in gray systems. In all cases, the boundaries of range of feasible solutions are properly determined by the proposed simple strategy.

A Deep Reinforcement Learning-Based Energy Management Framework With Lagrangian Relaxation for Plug-In Hybrid Electric Vehicle

Reinforcement learning (RL)-based energy management is one of the current hot spots of hybrid electric vehicles. Recent advances in RL-based energy management focus on energy-saving performance but less considers the constrained setting for training safety. This article proposes an RL framework named coach-actor-double-critic (CADC) for the optimization of energy management considered as the constrained Markov decision process (CMDP). A bilevel onboard controller includes a neural network (NN)-based strategy actor and rule-based strategy coach for online energy management. Once the output of the actor exceeds the constrained range of feasible solutions, the coach would take charge of energy management to ensure safety. By using the Lagrangian relaxation, the optimization for CMDP transforms into an unconstrained dual problem to minimize the energy consumption while minimizing the coach participation. The parameters of the actor are updated in a manner of policy gradient through RL training with the Lagrangian value function. Double-critic with the same structure synchronously estimates the value function to avoid overestimate bias. Several experiments with the bus trajectories data demonstrate the optimality, self-learning ability, and adaptability of CADC. The results indicate that CADC outperforms the existing RL-based strategies and reaches above 95% energy-saving rate of the off-line global optimum.

Characterization of the unimodality constraint as an effective chemistry-based condition in resolving of chemical processes data

Multivariate curve resolution (MCR) techniques are powerful methods for qualitative and quantitative analyses of spectral data. However, MCR methods suffer from non-unique solutions - instead of a unique solution usually a continuum of possible pure component decomposition exists. This ambiguity is covered in a low-dimensional way by the so-called area feasible solutions (AFS). In the quantitative purpose, the rotational ambiguity has a negative effect on the accuracy of the results. By applying additional constraints on the profiles the range of feasible solutions can considerably improve the reliability of quantitative results. Another approach to analyze the size of the continuum of possible pure component profiles is to compute the extrema of the signal contribution function (SCF). The SCF can also be applied under additional constraints.In this study we analyze the restriction of the AFS and the change of the SCF-extrema under additional unimodality constraints. An interesting effect is stated for two examples namely that the unimodality constraint can divide a single subset of the AFS into two parts. In such cases the SCF cannot resolve the ambiguity completely. The effect of the unimodality constraints has been systematically investigated on two- and three-component simulation data sets. This phenomenon are also studied for an experimental data set related to the spectrophotometric titration of a mixture of ligand (3,7-diazanonanedioic acid diamide) and Cu2+ with varying degrees of acidity. Imposing of unimodality constraints as an effective chemically meaningful limitation on the feasible solutions of MCR methods is strongly recommended.

Model predictive zone control with soft constrained appending margin

AbstractIn industrial processes, zone control is often applied to some control systems that do not have set‐point control requirements. Zone control involves constraining controlled variables within a range of feasible solutions, so there is a tension between interval constraint intensity and interval feasibility. To meet the requirements of interval feasibility, general control schemes often soften constraint intensity, resulting in frequent constraint violations. However, for some irreversible processes such as chemical and biochemical processes, violating constraint can lead to unpredictable results. This study attempts to solve this problem through improving the performance index of general model predictive controls with soft constraints. This goal is achieved through introducing additional margin to controlled variables in order to strengthen control intensity without increasing computational complexity. This approach effectively reduced the frequency of zone violations and the size of output errors, and guaranteed zone feasibility. Furthermore, this approach was implemented without significant increase in energy consumption and actuator operation. The stability of the algorithm was proven using Lyapunov theorem. Comparative simulation results demonstrated the effectiveness of the proposed method compared with conventional methods.

ОСОБЕННОСТИ ОПТИМИЗАЦИОННОЙ ЗАДАЧИ НА ПОДБОР МАТЕРИАЛОВ ДЛЯ МИНИМИЗАЦИИ ПОТЕРИ ТЕПЛА ЧЕРЕЗ ПЛОСКУЮ СТЕНКУ

Актуальность. Хранение тепла и его эффективное использование связано с подбором материалов для тепловой изоляции стенок. Такие материалы представлены широким спектром теплофизических свойств и стоимости на рынке. Тогда возникает задача оптимизации, ее решение должно обеспечивать наименьшие потери тепла через стенку при ограниченном выборе материалов с заданными коэффициентами теплопроводности. Вместе с тем при решении оптимизационной задачи могут возникнуть сложности в оценке правильности полученных результатов. Поэтому этот вопрос нуждается в детальном обсуждении. Цель: математическое моделирование стационарных режимов переноса тепла, формулировка минимаксной задачи о потере тепла через стенку, построение области решения минимаксной задачи, анализ полученных результатов и формулировка выводов. Объект: стенка, теплоизоляционные материалы, потоки тепла, условия минимальности, оптимальные решения. Методы: решение минимаксной задачи с применением аналитических методов. Результаты. Сформулирована простая минимаксная задача: дана двухслойная плоская стенка с произвольными коэффициентами теплопроводности и фиксированными толщинами. На правой и левой границах стенки задана постоянная и различная температура. Также задан максимальный тепловой поток через стенку и область возможных значений коэффициентов теплопроводности (т. е. возможные материалы) для каждого слоя стенки. Требуется из этой области найти коэффициенты теплопроводности, обеспечивающие тепловой поток ниже заданного максимального значения. На этом примере показано, что решение поставленной минимаксной задачи может приводить к неверному результату: можно получить или не весь спектр допустимых решений, или задача может не иметь решения. Это означает необходимость строгого отношения к формулировке и методу решения оптимизационных задач для процессов переноса тепла.

Design of Fuzzy Adaptive Pi Controller for Inherently Unstable System

Desired performance of any process depends on the control action taken by the controller. Choice of control structure and the design approach is mainly concerned with a priori knowledge of the process dynamics governed by any system, its limitations to achieve desire response and calculation of system state at different instant of time. Many practitioners and researchers in the field of control agree that controller design can be quite laborious in cases where the plant is unstable. The controller synthesis becomes a challenge for such systems because there are certain design and performance limitations that narrow the range of feasible solutions. These constraints reflect imperfect controller design which may work satisfactorily in one situation and may fail completely in other. Adaptive control where the controller parameters adjust them self as per the system requirements, is a candidate solution for such problem. This paper mainly focuses on design of model reference adaptive control based PI (Proportional-Integral) controller for unstable system. Adaptation mechanism is developed by fuzzy logic which makes the controller more versatile and reduces the design requirements. Results are compared with the conventional controller tuned with Ziegler-Nichols method. Detailed simulation Study and experimental validation shows the effectiveness of proposed Fuzzy Adaptive PI controller to control the unstable system for obtaining the desired performance out of it.

A New Parameter for Measuring the Prediction Uncertainty Produced by Rotational Ambiguity in Second-Order Calibration with Multivariate Curve Resolution.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSERA. The proposed parameter comes in the form of a range of values, whose limits are δRA/(12)1/2 and δRA/(3)1/2, with δRA being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.

Optimal rendezvous trajectory between Sample Return Orbiter and Orbiting Sample Container in a Mars Sample Return mission

A trajectory optimization problem is examined to determine the most fuel-efficient rendezvous trajectory between spacecrafts in different orbits. To explore the whole range of feasible solutions, the wait time and the total time of flight are treated as free parameters while the initial and transfer orbits are not restricted to a particular one. To improve the accuracy of the numerical computation, the Kepler's time of flight equation is posed in terms of universal variables while the Lagrange coefficients are employed to obtain three-dimensional orbit information. The optimal rendezvous trajectory is then obtained enforcing the determined necessary conditions to be satisfied given only the initial state vectors of the involved spacecrafts. Two optimal rendezvous trajectories between a Sample Return Orbiter (SRO) and an Orbiting Sample Container (OS) are computed in the context of a future Mars Sample Return mission to demonstrate the reliability of the proposed solution. Finally, orbital perturbations due to the real shape of planet Mars and the solar radiation pressure are taken into account to determine the additional energy required to compensate these perturbations while performing the rendezvous manoeuvre.