Objective Optimization Problem Research Articles

Power allocation scheme for sum rate and fairness trade-off in downlink NOMA networks

Non-orthogonal multiple access (NOMA) is an essential enabler technology that is expected to help satisfy the key requirements of increased system throughput in future wireless networks. However, another equally important aspect that should go hand-in-hand with system throughput is user fairness for any network. But, to the best of our knowledge, even though there have been works that look at system throughput or user fairness maximization for NOMA-based networks, they looked at these as a single objective optimization problem, where one is the objective and the other is one of the constraints. However, quite often, joint optimization of both system throughput and user fairness is required to make optimized decisions in the face of trade-offs between these two equally important but conflicting objectives. In this regard, this paper formulates a multi-objective optimization problem to jointly maximize the sum rate and user fairness in a downlink transmission NOMA system, through optimize power allocation (PA), under system-imposed constraints. A weighted sum approach is used to turn the multi-objective optimization problem into a single-objective optimization problem to make it analytically tractable. The optimized PA is then obtained using Lagrange dual decomposition method and Karush–Kuhn–Tucker (KKT) conditions. Using our derived expressions, we propose an iterative PA algorithm that converges fast enough to be employed in practical NOMA networks. We also present simulation results to highlight the effectiveness of the proposed solution. Further, the performance of the proposed method is compared with that of the benchmark methods.

The Multiobjective Control Based on Tolerance Optimization in a Multienergy System

To address the issue of multiobjective control in multienergy systems with diverse operational objectives, a two-stage optimization framework based on expected point tolerance has been proposed in this paper. In the first stage, a single objective function is used for optimization control to obtain the expected point of the multiobjective optimization problem. Then, in the second stage, by defining the allowable deviation between each optimization objective and the expected point, the original multiobjective optimization problem is transformed into a single objective optimization problem solution with tolerance measurement. Finally, in the simulation scene of a multienergy system, it is demonstrated that compared with the optimal results under each single objective method, the proposed method increases power line loss, maximum voltage deviation, new energy consumption, and economy by 2.22, 2.30, 1.02, and 2.45 times, respectively. Compared with the suboptimal results, the proposed method reduces power line loss by 22.26, 1.74, 1.09, and 0.97 times, respectively. Combining the shape of the Pareto frontier, it is demonstrated that the proposed method can comprehensively consider the needs of multiple power optimization objectives for forming a more reasonable and effective system optimization scheduling and also provide a new approach for solving multiobjective optimization problems.

Attaining robust performance targets in data envelopment analysis with application to efficiency evaluation of airports

We consider a ratio-based efficiency analysis in view of achieving performance targets by Decision Making Units. The targets refer to the efficiency scores or ranks and the truth of pairwise preference relations. These outcomes can be instantiated for at least one or all feasible weights associated with inputs and outputs. We discuss Multiple Objective Optimization problems that minimize the required reductions of consumed resources or increases of produced results needed to reach the pre-defined aims. The proposed models offer great flexibility to the Decision Maker, who can indicate which factors should be modified and to which extent. The evolutionary optimization algorithm computes a set of solutions that exhibit the trade-offs between expected modifications of various factors. They can serve as the basis for interactively selecting the most preferred solution to be implemented in practice. The use of the proposed framework is illustrated in the problem of analyzing the efficiency of Polish airports.

Finite mixture models for multiscale dynamics in Chinese financial markets

A novel statistical machine learning technique for decomposing, analyzing, and modeling complex time series is presented in this paper. This methodology is based on unsupervised classification methods using finite mixtures, which have been widely used in factor analysis to extract essential information from multivariate static data in a parsimonious manner. Here, they are applied in a purely dynamic framework to create a new family of autoregressive models. The selection of the number of components and appropriate geometric template in these models is based on a set of information criteria that require solving a multiple objective optimization problem. To ensure the most adequate models are selected, the problem is augmented with a simulation instruction, providing a robust criterion for assignment. Experiments on real financial data sampled over the COVID-19 pandemic demonstrate the potential of this approach as a promising alternative to the well-known Box-Jenkins methodology. The proposed method offers flexibility, accuracy, and stability, making it suitable for a variety of applications in financial modeling and other fields where complex time series data analysis is required.

A review on multi objective optimization problems and advancement on its solutions

A plenty of literatures are available for finding solution of optimization problem of single objective. Very few literatures are available for finding solution of optimization problem with multi objective optimization. Many researchers analysing multi objective problems by treating as single objective, keeping rest of variables as constant. With the tremendous rise of innovations in evolutionary computation, that has added feathers to Multi Objective Optimization techniques.

OPTIMAL SIZING OF SOLAR-WIND HYBRID MICROGRID USING IMPROVED GREY WOLF OPTIMIZATION ALGORITHM A CASE STUDY OF KADUNA - NIGERIA

This paper presents an improved grey wolf optimization algorithm (IGWOA) for optimal sizing of an isolated photovoltaic (PV), wind turbine (WT), and battery energy storage (BES) hybrid microgrid. To demonstrate the effectiveness of the proposed approach, atmospheric data sets comprising of wind, solar, and temperature of Kaduna International Airport were collected from Nigerian Meteorological Agency while the load demand data was collected from Kaduna International Airport Electricity Distribution Center. The microgrid optimal sizing was formulated as a constrained single objective optimization problem. Constraints including, loss of power supply probability (LPSP), power balance, generation limits and battery state of charge (SOC) were imposed. Three simulation scenarios were considered. Firstly, the target allowable maximum LPSP was fixed at 25% and the algorithm was able to determine the optimal sizing of the hybrid microgrid components and minimize the initial cost from 169,880.00 USD to 112,356.40 USD per annum resulting in 34% savings in cost. Secondly, the effect of the target allowable maximum LPSP variation was investigated, and it was found that the total installed capacity of the system decreases with increase in LPSP thereby decreasing the total cost. Additionally, a novel electricity price index (EPI) was introduced in order to quantify the degree of optimality of the solution. The EPI was found to increase exponentially with increase in LPSP, resulting in an EPI of < 0.05USD/kWh at 20% LPSP. Lastly, to validate the proposed approach, a comparative analysis between the IGWOA and other algorithms was carried out, and the proposed IGWOA proved applicable.

Efficient Multi-Objective Simulation Metamodeling for Researchers

Solving multiple objective optimization problems can be computationally intensive even when experiments can be performed with the help of a simulation model. There are many methodologies that can achieve good tradeoffs between solution quality and resource use. One possibility is using an intermediate “model of a model” (metamodel) built on experimental responses from the underlying simulation model and an optimization heuristic that leverages the metamodel to explore the input space more efficiently. However, determining the best metamodel and optimizer pairing for a specific problem is not directly obvious from the problem itself, and not all domains have experimental answers to this conundrum. This paper introduces a discrete multiple objective simulation metamodeling and optimization methodology that allows algorithmic testing and evaluation of four Metamodel-Optimizer (MO) pairs for different problems. For running our experiments, we have implemented a test environment in R and tested four different MO pairs on four different problem scenarios in the Operations Research domain. The results of our experiments suggest that patterns of relative performance between the four MO pairs tested differ in terms of computational time costs for the four problems studied. With additional integration of problems, metamodels and optimizers, the opportunity to identify ex ante the best MO pair to employ for a general problem can lead to a more profitable use of metamodel optimization.

MOEA/D with customized replacement neighborhood and dynamic resource allocation for solving 3L-SDHVRP

Split delivery heterogeneous vehicle routing problem with three-dimensional loading (3L-SDHVRP) is a critical issue in manufacturing logistics. Current mainstream research formulates this problem as a single objective optimization problem, which fails to reveal the relationship among multiple conflicting objectives and cannot provide various trade-off solutions for decision-makers in real-world logistics scenarios. This paper concentrates on a multi-objective 3L-SDHVRP and proposes a multi-objective evolutionary algorithm based on decomposition with customized replacement neighborhood and dynamic resource allocation (called MOEA/D-RD) to deal with it. The numerical experiments on the dataset from the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021) show the superior performance of the proposed method over some state-of-the-art ones. The source code of MOEA/D-RD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEAD-RD.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

Accurate identification and confidence evaluation of automatic generation control command execution effect based on deep learning fusion model

With the increasing complexity of the power grid, the precision of the thermal power units' execution of automatic generation control (AGC) commands is gradually increasing the impact on the online regulation of the power grid. The deviation between the actual output of thermal power units and the AGC command of the grid will not only affect the consumption of new energy output, but also endanger the safe operation of the grid. This paper introduces “deep learning” technology to solve the problem. Firstly, an AGC command execution effect identification and confidence evaluation algorithm (ACEEI-CEA) is proposed. The algorithm builds a neural network model to accurately predict the unit output and the confidence evaluation of the prediction results. Next, a high-dimensional input preprocessing strategy based on variational autoencoder (VAE) is proposed to reduce the dimensionality of the model input attributes, improving the convergence and accuracy of the model. Finally, an AGC optimal command fast inversion solution method (AOCFISM) is designed. This method transforms the unit output deviation problem into an objective optimisation problem. And improve the efficiency of solving the optimal AGC command value by constraining the unit command value. The calculation results show that the error of the prediction results of the model proposed in this paper is 5% lower than that of the traditional neural network. The difference between the output value of the optimal AGC command and the expected output value obtained is less than 0.5 MV, which can support AGC online decision-making.© 2017 Elsevier Inc. All rights reserved.

Enhanced Solutions to Intuitionistic Fuzzy Multiobjective Linear Fractional Optimization Problems via Lexicographic Method

Optimization involving fuzzy numbers generally, and intuitionistic fuzzy numbers particularly is more and more an essential part of any computational intelligence method; and might be of interest in modeling fuzzy control systems, or carrying out a fuzzy sensitivity analysis. The recent literature includes many research papers related to both theoretical modelling, and practical implementation of fuzzy decision support systems. Fuzzy optimization is one of the main part in such decisionmaking tools. A realistic solution to a fuzzy optimization problem is always desired, and similarly, a Pareto optimal solution to a multiple objective optimization problem is always a need. In this paper we analyze the shortcomings; and eliminate the weaknesses of a solution approach from the literature proposed by Moges et al. in 2023. Firstly, Moges et al. used an accuracy function to de-fuzzify the original intuitionistic fuzzy optimization problem; then linearized the obtained crisp problem; and finally involved fuzzy goals to solve the derived multiple objective linear problem. We present two faulty key points of their approach, namely the de-fuzzification and linearization steps; prove the inappropriateness of their results; and propose some improvements. The final aim in addressing the first key point is to clarify the border between defuzzifications made in accordance to true theoretical statements, and those made for modeling reasons. The methodological improvement we propose is related to the second key point and it assures that Pareto optimal solutions - highly required in multiple objective optimization - are obtained. To illustrate our point of view, we use a numerical example from the literature, and report better numerical results derived by the improved methodology.

Multi-Objective Optimization in the Presence of OGIPFC Using NSMMP Algorithm

Background: Customers expect quality, uninterrupted power with cost-effective electricity in the latest trend. However, outages, severe storms, old infrastructure, and cost pressures can lead to ambiguity in power generation and transmission. To improve line power transmission capability, the right flexible AC transmission systems (FACTS) device may save millions of dollars. Methods: In this study, a FACTS controller named Optimal Generalized Interline Power Flow Controller (OGIPFC) was developed. Furthermore, for optimization, the Modified Marine Predator Algorithm (MMPA), which is a modification of the recently developed Marine Predator Algorithm (MPA). The optimum technique was used to evaluate a set of prioritized considered objective minimizations. A variety of factors must be maximized, such as generation cost, emissions, and power loss. Results: The performance of the proposed algorithm was analysed on benchmark test functions, and then single objective optimization problems of standard IEEE-30 bus system were solved and compared with the existing algorithms. The proposed algorithm was restricted to solving the single objective problem only, so it was further implemented with non-dominating sorting to solve the multiobjective optimization problem. The proposed multi-objective version is named as Non-dominating Sorting Modified Marine Predator Algorithm (NSMMPA), and it was validated on benchmark test functions and the IEEE-30 bus system. Conclusion: Finally, the OPF problem was solved with the incorporation of OGIPFC using the proposed methods, which resulted in better solutions and made the system more effective in operation.

Exploring New Directions in Higher Education Aided by Artificial Intelligence Technology

Abstract This paper’s objective optimization problem belongs to the encoding problem of real numbers, and the classical particle swarm optimization algorithm is chosen. The establishment of intelligent learning model was finally completed through the assumption of model components, initial model establishment, model cycle evaluation and validation. First, after the implementation of the E-GPPE-C education model, the test was conducted on the educated people, and the AI literacy questionnaire was also distributed to the students before and after the implementation of the model education. Second, a statistical analysis explores which technologies will most likely be applied to higher education. Finally, the variability of higher education subject relations under the influence of AI and related ethical issues were explored. The results show that the highest score on the students’ final test was 96. 20 students scored more than 80 points, indicating that half of the students had a solid grasp of the knowledge and applications related to the E-GPPE-C model, and that there was a vast difference between the degree of AI knowledge and skill mastery before and after the implementation of education. Natural language understanding, computer vision, and biometrics are the three technologies most suitable for application in higher education.

Using VIKOR and RSM-DA in the optimization of dry turning of 9XC steel

Dry turning is an effective method for reducing the production costs and environmental impact of machining processes. In this study, the effect of cutting speed (Vc), feed rate (fz), and depth of cut (ap) on the surface roughness (Ra) and material removal rate (MRR) of 9XC steel during dry turning was investigated. A Box-Behnken experimental design was employed to analyze the main effects and interaction effects of these cutting parameters. In this research, the combining Response Surface Methodology - Desirability Approach (RSM-DA) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method were both employed for solving multiple objective optimization problems, and their performance was compared. The results from both methods can be assessed based on their ability to identify the optimal set of parameters that simultaneously optimize surface quality and production rate, as well as their computational efficiency and ease of implementation. Both RSM-DA and VIKOR have been found effective for solving multi-objective optimization problems, such as optimizing cutting parameters in dry turning. While RSM-DA is a statistical tool that combines multiple objectives into a single function, VIKOR is a decision-making method that ranks alternatives based on multiple criteria. The choice of which method to use depends on the specific requirements of the problem and the availability of resources for implementation. The research results show that both VIKOR and RSM-DA are suitable for solving the multi-objective optimization problem of the turning process. According to the VIKOR method, the optimum cutting conditions were found to be a cutting speed Vc of 120 m/min, a depth of cut ap of 0.1 mm a feed rate fz of 0.06 mm/rev, and, which resulted in a surface roughness of 0.209 um and a material removal rate of 0.72 cm3/min. Meanwhile, RSM-DA predicts the optimal Ra and MRR values of 0.254 um and 3.36 cm3/min, respectively; corresponding to the Vc of 180m/min, fz of 0.06mm/rev and ap of 0.3mm; That means, the increasing the value of surface roughness by 21.5% will increase the MRR by 366.7%. The findings of this study can provide guidance for selecting the appropriate cutting parameters for dry turning of 9XC steel to achieve desired surface roughness Ra and material removal rate MRR in the specific case.

Multi-Objective Optimization for IRS-Aidded Multi-user MIMO SWIPT Systems

In this paper, we investigate an intelligent reflecting surface (IRS) assisted simultaneous wireless information and power transfer (SWIPT) system in which users equipped with multiple antennas exploit power-splitting (PS) strategies for simultaneously information decoding (ID) and energy harvesting (EH). Different from the majority of previous studies which focused on single objective optimization problems (SOOPs) and assumed the linearity of EH models, in this paper, we aim at studying the multi-objective optimization problem (MOOP) of the sum rate (SR) and the totalharvested energy (HE) subject to the maximum transmit power (TP) constraint, the user quality of service (QoS), and HE requirements at each user with taking a practical non-linear EH (NLEH) model into consideration. To investigate insightful tradeoffs between the achievable SR and total HE, we adopt the modified weighted Tchebycheff method to transform the MOOP into a SOOP. However, solving the SOOPs and modified SOOP is mathematically difficult due to the non-convexity of the object functions and the constraints of the coupled variables of the base station (BS) transmit precoding matrices (TPMs), the user PS ratios (PSRs), and the IRS phase shift matrix (PSM). To address these challenges, an alternating optimization (AO) framework is used to decompose the formulated design problem into sub-problems. In addition, we apply the majorization-minimization (MM) approach to transform the sub-problems into convex optimization ones. Finally, numerical simulation results are conducted to verify the tradeoffs between the SR and the total amount of HE. The numerical results also indicate that the considered system using the IRS with optimal phase shifts provides considerable performance improvement in terms of the achievable SR and HE as compared to the counterparts without using the IRS or with the IRS of fixed phase shifts.

Speedy Hierarchical Eco-Planning for Connected Multi-Stack Fuel Cell Vehicles via Health-Conscious Decentralized Convex Optimization

<div>Connected fuel cell vehicles (C-FCVs) have gained increasing attention for solving traffic congestion and environmental pollution issues. To reduce operational costs, increase driving range, and improve driver comfort, simultaneously optimizing C-FCV speed trajectories and powertrain operation is a promising approach. Nevertheless, this remains difficult due to heavy computational demands and the complexity of real-time traffic scenarios. To resolve these issues, this article proposes a two-level eco-driving strategy consisting of speed planning and energy management layers. In the top layer, the speed planning predictor first predicts dynamic traffic constraints using the long short-term memory (LSTM) model. Second, a model predictive control (MPC) framework optimizes speed trajectories under dynamic traffic constraints, considering hydrogen consumption, ride comfort, and traffic flow efficiency. A multivariable polynomial hydrogen consumption model is also introduced to reduce computational time. In the bottom layer, the decentralized MPC framework uses the calculated speed trajectory to figure out how to allocate the power optimally between the fuel cell modules and the battery pack. The objective of the optimization problem is to reduce hydrogen consumption and mitigate component degradation by focusing on targets such as the operating range of state of charge (SoC), as well as battery and fuel cell degradation. Simulation results show that the proposed decentralized eco-planning strategy can optimize the speed trajectory to make the ride much more comfortable with a small amount of jerkiness (−0.18 to 0.18 m/s<sup>3</sup>) and reduce the amount of hydrogen used per unit distance by 7.28% and the amount of degradation by 5.33%.</div>

Sizing and energy management of standalone hybrid renewable energy systems based on economic predictive control

This paper aims to design and run a standalone hybrid renewable energy System (HRES) feeding residential building load. The suggested HRES encompasses photovoltaic panels and wind turbines as energy sources, combined with a hydrogen subsystem and a bank of batteries for energy storage. The meteorological input data includes irradiance, temperature, and wind speed for four seasonal weeks. These data sets are collected for a rural site situated in the town of Ras Munif, northern Jordan. The load profiles characterize a selected benchmark residential building. Consequently, a bi-level mixed integer nonlinear programming (BMINLP) problem is formulated to incorporate the designing problem with the energy management process. The upper level represents the sizing problem, while the lower level problem denotes the energy management strategy (EMS). Each problem has its independent objective function, constraints, and optimization variables. The EMS is an economic-based single objective optimization problem expressed as a mixed integer linear programming (MILP) problem. On the contrary, a mixed integer nonlinear programming (MINLP) approach frames the sizing problem to optimize a techno-economic-based multi-objective function. The interaction between the two problems is that the lower problem is an embedded constraint of the upper problem. Moreover, the candidate solutions from the upper problem are treated as fixed parameters in the lower problem. A multi-objective genetic algorithm is used to execute the overall problem by the MATLAB toolbox. The technical and economic performance parameters, including the investment cost, maintenance, operating costs, and others, are assessed based on the best findings. The key finding demonstrates that the summer week has the lowest total cost and energy loss factor, with around 132,000 $ and 0, respectively. Furthermore, the findings reveal that the entire system's energy loss factor for each sample period is less than 0.0009. This value is substantially less than the permitted limit of 0.01.

Multi-objective adaptive trajectory optimization for industrial robot based on acceleration continuity constraint

In noncontact machining, such as welding and spraying, running efficiency and smoothness have been a bottleneck problem in trajectory optimisation of industrial robots. When the dynamic and mechanical properties of robots are fully utilised, significant impact are often produced. Thus, reducing the process impact of the robot and achieving a balance between the efficiency and smoothness of the operation process are complex problems that need to be solved. The trajectory optimisation problem is modelled based on the excellent properties of the convex-optimization (CO) problem. CO parameters were introduced to solve the inconsistency between the constrained and planned spaces. To obtain the weight factor of the multi-objective optimisation problem, a multi-objective adaptive optimisation method was proposed to select the optimal parameters. Aiming at the large process impact of the optimisation problem, which considers running time as the main optimisation objective, an acceleration continuity constraint method was proposed based on the smoothing path. Finally, the objective optimisation problem was transformed into a standardised second-order cone programming problem to complete the solution. The experimental results show that the proposed method can improve the robot operation efficiency and reduce the process impact by approximately 26% and 22%, respectively, from three aspects: optimum time, balance between efficiency and impact, and acceleration continuity.

Distributed Generation Allocation in Distribution Network for Energy Losses Reduction

Abstract This paper presents a method for distributed generation (DG) allocation in medium voltage (MV) distribution system based on energy loss minimization. The main objective of the research is to design, implement and test a DG allocation (siting and sizing) method and to investigate how optimal DG allocation influence the operational parameters of the system from the Distribution System Operator (DSO) perspective. The problem is formulated as a single objective optimization problem solved by using both genetic algorithm and particle swarm optimization techniques. Model of a realistic Electric Power Distribution System (EPDS) and IEEE 37-bus EPDS are used as test systems. The results confirm that proposed algorithms can be used for practical DG allocation. The research presented contributes to the field as it provides a DG allocation method for energy loss reduction performed on a EPDS which can be applied in realistic planning and regulatory situations using open-source software.

A Novel Evolutionary Algorithm: One-Dimensional Subspaces Optimization Algorithm (1D-SOA)

This paper introduces an evolutionary algorithm for n-dimensional single objective optimization problems: One-Dimensional Subspaces Optimization Algorithm (1D-SOA). The algorithm starts with an initial population in randomly selected positions. For each individual, a percentage of the total number of dimensions is selected, each dimension corresponding to a one-dimensional subspace. Later, it performs a symmetric search for the nearest local optima in all the selected one-dimensional subspaces (1D-S), for each individual at a time. The search stops if the new position does not improve the value of the objective function over all the selected 1D-S. The performance of the algorithm was compared against 11 algorithms and tested with 30 benchmark functions in 2 dimensions (D) and 30D. The proposed algorithm showed a better performance than all other studied algorithms for large dimensions.