Formulation Of Optimization Problem Research Articles

A new optimal strategy for energy minimization in wireless sensor networks

In recent years, evolutionary and metaheuristic algorithms have emerged as crucial tools for optimization in the field of artificial intelligence. These algorithms have the potential to revolutionize various aspects of our lives by leveraging the multidisciplinary nature of wireless sensor networks (WSNs). This study aims to introduce genetic and simulated annealing algorithms as effective solutions for enhancing WSN performance. Our contribution entails two main phases. Firstly, we establish mathematical models and formulate objectives as a nonlinear constrained optimization problem. Secondly, we develop two algorithmic solutions to address the formulated optimization problem. The obtained results from multiple simulations demonstrate the positive impact of the proposed strategies on improving network performance in terms of energy consumption.

Maximum power optimization of a direct-drive wind turbine connected to PMSG using multi-objective genetic algorithm

This work aimed to develop and evaluate a maximum power point tracking (MPPT) control system for a wind energy conversion system (WECS) based on a permanent magnet synchronous generator (PMSG). PMSG is commonly used to generate direct-drive and variable-speed wind energy. Initially, the generator and converter on the DC load side are controlled to follow the wind speed reference set by the MPPT algorithm. The paper presents the optimization problem formulation, including the optimization space, constraints, and objectives. The genetic algorithm (GA) is used to extract the maximum power from the WECS in this design improvement. In this study, to control and stabilize the maximum power point (MPP) of the wind turbine, a proportional integral (PI) controller and a GA heuristic approach were utilized. The GA approach was employed to determine the best settings (Kp, Ki) using MATLAB/Simulink with a 12.3 kW PMSG to model and simulate the proposed system. Based on four performance indicators-integrated squared error (ISE), integrated absolute error (IAE), integrated time absolute error (ITAE), and integrated time squared error (ITSE), the GA approach was used to optimize the controller settings. The results of the simulation show that the wind turbine (WT) can effectively track the necessary MPP. The simulation's output also includes generated power, DC bus voltage, electromagnetic torque, and currents.

Robust topology and discrete fiber orientation optimization under principal material uncertainty

This paper introduces a formulation of the robust topology optimization problem that is tailored for designing fiber-reinforced composite structures with spatially varying principal mechanical properties. Specifically, a methodology is developed that incorporates the spatial variability in the engineering constants of the composite lamina into the concurrent topology (i.e., material distribution) and morphology (i.e., fiber orientation distribution) optimization problem for the minimization of the robust compliance function. The spatial variability in the mechanical properties of the lamina is modeled as a homogeneous random field within the design domain by means of the Karhunen-Loe´ve series expansion, and is thereafter intrusively propagated into the stochastic finite element analysis of the composite structure. To carry out the stochastic finite element analysis per iteration of the optimization cycle, the first-order perturbation method is utilized for approximating the current state variables of the physical system. The resulting robust topology and fiber orientation optimization problem is formulated step-by-step for the minimization of the robust compliance function. With the view of solving the optimization problem at hand by means of gradient-based solution algorithms, the first-order derivatives of the involved design functions w.r.t. the associated design variables are analytically derived. The present work concludes with a series of numerical examples, focusing on the benchmark academic case studies of the 2D cantilever and the half part of the Messerschmitt-Bölkow-Blohm beam, aiming to demonstrate the developed methodology as well as to explore the effect that different parameterization instances of the random field bear on the predicted topology and morphology of the beams.

Towards autonomous learning and optimisation in textile production: data-driven simulation approach for optimiser validation

AbstractThe textile industry is a traditional industry branch that remains highly relevant in Europe. The industry is under pressure to remain profitable in this high-wage region. As one promising approach, data-driven methods can be used for process optimisation in order to reduce waste, increase profitability and relieve mental burden on staff members. However, approaches from research rarely get adopted into practice. We identify the high dimensionality of textile production processes leading to high model uncertainty as well as an incomplete problem formulation as the two main problems. We argue that some form of an autonomous learning agent can address this challenge, when it safely explores advantageous, unknown new settings by interacting with the process. Our main goal is to facilitate the adoption of promising research into practical applications. The main contributions of this paper include the derivation and formulation of a probabilistic optimisation problem for high-dimensional, stationary production processes. We also create a highly adaptable simulation of the textile carded nonwovens production process in Python that implements the optimisation problem. Economic and technical behavior of the process is approximated using both Gaussian Process Regression (GPR) models trained with industrial data as well as physics-motivated explicit models. This ’simulation first’-approach makes the development of autonomous learning agents for practical applications feasible because it allows for cheap testing and validation before physical trials. Future work will include the comparison of the performance of different agent approaches.

Variational quantum circuit learning-enabled robust optimization for AI data center energy control and decarbonization

As the demand for artificial intelligence (AI) models and applications continues to grow, data centers that handle AI workloads are experiencing a rise in energy consumption and associated carbon footprint. This work proposes a variational quantum computing-based robust optimization (VQC-RO) framework for control and energy management in large-scale data centers to address the computational challenges and overcome limitations of conventional model-based and model-free strategies. The VQC-RO framework integrates variational quantum circuits (VQCs) with classical optimization to enable efficient and uncertainty-aware control of energy systems in AI data centers. Quantum algorithms executed on noisy intermediate-scale quantum (NISQ) devices are used for value function estimation trained with Q-learning, leading to the formulation of a robust optimization problem with uncertain coefficients. The quantum computing-based robust control strategy is designed to address uncertainties associated with weather conditions and renewable energy generation while optimizing energy consumption in AI data centers. This work also outlines the computational experiments conducted at various AI data center locations in the United States to analyze the reduction in power consumption and carbon emission levels associated with the proposed quantum computing-based robust control framework. This work contributes a novel approach to energy-efficient and sustainable data center operation, promising to reduce carbon emissions and energy consumption in large-scale data centers handling AI workloads by 9.8 % and 12.5 %, respectively.

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

Multiple-arc optimization of low-thrust Earth–Moon orbit transfers leveraging implicit costate transformation

This work focuses on minimum-time low-thrust orbit transfers from a prescribed low Earth orbit to a specified low lunar orbit. The well-established indirect formulation of minimum-time orbit transfers is extended to a multibody dynamical framework, with initial and final orbits around two distinct primaries. To do this, different representations, useful for describing orbit dynamics, are introduced, i.e., modified equinoctial elements (MEE) and Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or Moon, allows simple writing of the boundary conditions about the two celestial bodies, but requires the formulation of a multiple-arc trajectory optimization problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In the numerical solution process, the transition between the two MEE representations uses CC, which play the role of convenient intermediate, matching variables. The multiple-arc formulation at hand leads to identifying a set of intermediate necessary conditions for optimality, at the transition between the two legs. This research proves that a closed-form solution to these intermediate conditions exists, leveraging implicit costate transformation. As a result, the parameter set for an indirect algorithm retains the reduced size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution in this study) is proposed as the numerical solution method, together with the definition of a layered fitness function, aimed at facilitating convergence. The minimum-time trajectory of interest is sought in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer path. The numerical results unequivocally prove that the approach developed in this research is effective for determining minimum-time low-thrust Earth–Moon orbit transfers.

Joint optimization for computation offloading and 3C resource allocations over wireless-powered and NOMA-enabled multi-access MEC

Multi-access mobile edge computing (MEC) enables mobile users (MUs) to offload tasks to proximal multiple MEC servers for fast task processing. Since MUs generally have stringent delay requirements and limited energy and MEC servers have finite communication, computation, and caching (3C) resources, the joint co-design and optimization over computation offloading and 3C resource allocation for wireless-powered multi-access MEC systems have been highly demanded, while having not been well studied yet. We consider a wireless-powered multi-access MEC, where multiple energy harvesting (EH) based MUs and multiple base stations (BSs) each equipped with an MEC server coexist. Each MU first harvests energy from nearby MEC servers, and then offloads its sub-tasks to multiple MEC servers concurrently based on non-orthogonal multiple access (NOMA), so as to reduce data offloading delay. We first formulate a delay minimization problem, by jointly optimizing MUs’ computation offloading, MEC servers’ computation and caching resources allocation, and system communication resources allocation. Then we propose an alternating direction multiplier method (ADMM) based distributed scheme to decompose the formulated optimization problem into several sub-problems, and use the block coordinate descending (BCD) method and the successive convex approximation (SCA) method to transform all sub-problems each corresponding to one MEC server to convex subproblems. Finally, we validate and evaluate our proposed scheme through numerical analyses, which show that our proposed distributed scheme can greatly reduce the min–max delay of all MUs by allowing each MU’s concurrent data offloading to multiple MEC servers using NOMA and by jointly optimizing computation offloading and 3C resource allocations. Also, the delay imposed by our proposed scheme is much smaller than that imposed by the Interior Point method, which shows the effectiveness of our proposed scheme.

Multi-UAV and IRS placement for secure data transmission in NOMA-enabled wireless networks

In this paper, we investigate multi-unmanned aerial vehicle (UAV)-enabled intelligent reflecting surface (IRS)-assisted non-orthogonal multiple access (NOMA) downlink networks for secure data transmission in the presence of an intruder. Since Line of Sight (LoS) communication is obstructed, UAVs are utilized as aerial base stations to transmit confidential data to ground users with the assistance of IRS. The objective is to optimize the placement of UAVs and IRS, phase shift of the IRS, and transmit beamforming of the UAVs in order to maximize the network secrecy rate. The formulated optimization problem is non-convex in nature, posing a challenge in finding the optimal solution using conventional techniques. To tackle this problem, we propose a novel algorithm called balanced grey wolf optimizer and differential evolution (B-GWODE). This algorithm not only leverages the advantages of both the GWO and DE algorithms but also incorporates parameter modifications to mitigate the issue of premature convergence and to strike a suitable balance between exploration and exploitation. This hybrid approach efficiently search the solution space and obtain the optimal configuration that maximizes the network secrecy rate. Simulation results demonstrate the superiority of our proposed B-GWODE algorithm over the benchmark methods.

Case Article—Prescriptive Analytics for Entrepreneurial Growth: Data-Driven Strategic Decision Making at iParty Bangkok Co., Ltd.

This case centers around the dilemma faced by the female owner of a balloon decoration business: whether to outsource transportation of balloon arrangements to third-party providers or handle the transportation of some orders in house. The case illustrates a path to answering the strategic business question through solving a sequence of vehicle routing problems (VRPs) of increasing complexity. The focus of the case is not only on solving VRPs, but also on teaching a practical framework for (1) framing a business problem as a prescriptive analytics problem; (2) researching appropriate concepts, prior publications, and tools; (3) setting up an optimization problem formulation, estimating the necessary inputs, and obtaining a solution; (4) deciding on the appropriate level of formulation complexity needed; and (5) mapping the results from the models to a response to the original business question. Realistic data and Excel models and are provided. The case is appropriate for use in courses in optimization, operations research, and business analytics at either the advanced undergraduate or master’s/MBA level. Supplemental Material: The Teaching Note and supplemental data are available at https://www.informs.org/Publications/Subscribe/Access-Restricted-Materials .

Determining Fast Battery Charging Profiles Using an Equivalent Circuit Model and a Direct Optimal Control Approach

This work used an electrical equivalent circuit model combined with a temperature model and computational optimal control methods to determine minimum time charging profiles for a lithium–ion battery. To effectively address the problem, an optimal control problem formulation and direct solution approach were adopted. The results showed that, in most cases studied, the solution to the battery’s fast-charging problem resembled the constant current–constant voltage (CC-CV) charging protocol, with the advantage being that our proposed approach optimally determined the switching time between the CC and CV phases, as well as the final time of the charging process. Considering path constraints related to the terminal voltage and temperature gradient between the cell core and case, the results also showed that additional rules could be incorporated into the protocol to protect the battery against under/over voltage-related damage and high-temperature differences between the core and its case. This work addressed several challenges and knowledge gaps, including emulating the CC-CV protocol using a multi-phase optimal control approach and direct collocation methods, and improving it by including efficiency and degradation terms in the objective function and safety constraints. To the authors’ knowledge, this is the first time the CC-CV protocol has been represented as the solution to a multi-phase optimal control problem.

Distributed Real-Time Feedback Optimization for Renewable Energy Sources and Vehicle-to-Grid Power Compensation of Electric Vehicle Chargers in Distribution Systems

A novel distributed feedback optimization-based controller for electric vehicle (EV) chargers and renewable energy sources (RESs) in distribution systems is proposed. The proposed controller utilizes the flexibility in EV chargers’ active and reactive power consumption to offer the desirable vehicle-to-grid services. Instead of using the conventional cascaded PI controllers, a new optimization-based approach is proposed to control RESs to track their power injection setpoints. The proposed controller formulates the control targets as a single constrained optimization problem, i.e., to minimize the critical bus voltage magnitude deviations while driving RESs to follow their power setpoints, thereby fulfilling the EV charging requirements and regulating their power outputs and bus voltage magnitudes to stay within their limits. A distributed feedback optimization-based control algorithm is designed for EV chargers and RESs to steer the system trajectories of the distribution systems towards the optimal solution of the formulated optimization problem. Simulation results show that the proposed controller can always steer the test system to the optimal solution of the optimization problem. The advantages of the real-time vehicle-to-grid power compensation of EV chargers are also demonstrated.

Optimizing Engineered Products for Their Social Impacts on Multiple Stakeholders

Abstract Engineered products are often optimized based on engineering requirements, user requirements, cost, and performance. This strategy is well suited for most applications, but products designed specifically to improve the lives of users and communities would benefit from an approach that helps engineers optimize a product based also on its social impacts. This paper introduces several optimization problem formulations adapted from multi-stakeholder strategies in the economics and business management literature. Each optimization problem formulation optimizes a product’s social impact according to the ideology and principles inherent to the adapted multi-stakeholder strategy. A case study is presented for a cassava peeling machine that is being developed for farmers in the Brazilian Amazon. Finally, the resulting peeler design configurations and social impacts are discussed to illustrate the advantages and disadvantages of each strategy.

Optimal economical sizing of a PV-battery grid-connected system for fast charging station of electric vehicles using modified snake optimization algorithm

This paper presents a methodology for the optimal sizing of a proposed photovoltaic (PV)-battery grid-connected system for fast charging station of electric vehicles (FCSEVs) in Cairo, Egypt. The key objectives of the formulated optimization problem are to minimize the total system cost and to guarantee the validity of the energy balance principle within the considered system. The paper also develops a novel energy management strategy, which is designed based on two widely adopted pricing strategies, for optimally managing the power flow within the considered system with the purpose of reaching the optimum sizes of the considered system components. In addition, the paper suggests a modification to the Snake optimization (SO) algorithm, which is used to solve the formulated optimization problem using MATLAB software. Moreover, a comparison is conducted among the proposed modified Snake optimization (MSO) algorithm and four other common meta-heuristic optimization algorithms to validate the viability of the suggested MSO algorithm in achieving the desired eventual aims of the sizing process. Furthermore, a techno-economic study is carried out to assess the economic viability of the proposed system for each of the two adopted pricing strategies over the project lifetime. The yielded results indicated that the developed energy management strategy is capable of managing the energy flow within the considered system effectively. Also, they demonstrated that the suggested MSO algorithm can yield the best optimal solutions for the formulated optimization problem for each of the two adopted pricing strategies compared to the other considered optimization algorithms.

Multi-feature SEIR model for epidemic analysis and vaccine prioritization.

The SEIR (susceptible-exposed-infected-recovered) model has become a valuable tool for studying infectious disease dynamics and predicting the spread of diseases, particularly concerning the COVID pandemic. However, existing models often oversimplify population characteristics and fail to account for differences in disease sensitivity and social contact rates that can vary significantly among individuals. To address these limitations, we have developed a new multi-feature SEIR model that considers the heterogeneity of health conditions (disease sensitivity) and social activity levels (contact rates) among populations affected by infectious diseases. Our model has been validated using the data of the confirmed COVID cases in Allegheny County (Pennsylvania, USA) and Hamilton County (Ohio, USA). The results demonstrate that our model outperforms traditional SEIR models regarding predictive accuracy. In addition, we have used our multi-feature SEIR model to propose and evaluate different vaccine prioritization strategies tailored to the characteristics of heterogeneous populations. We have formulated optimization problems to determine effective vaccine distribution strategies. We have designed extensive numerical simulations to compare vaccine distribution strategies in different scenarios. Overall, our multi-feature SEIR model enhances the existing models and provides a more accurate picture of disease dynamics. It can help to inform public health interventions during pandemics/epidemics.

Optimizing energy efficiency in heterogeneous networks: An integrated stochastic geometry approach with novel sleep mode strategies and QoS framework.

The quest for energy efficiency (EE) in multi-tier Heterogeneous Networks (HetNets) is observed within the context of surging high-speed data demands and the rapid proliferation of wireless devices. The analysis of existing literature underscores the need for more comprehensive strategies to realize genuinely energy-efficient HetNets. This research work contributes significantly by employing a systematic methodology, utilizing This model facilitates the assessment of network performance by considering the spatial distribution of network elements. The stochastic nature of the PPP allows for a realistic representation of the random spatial deployment of base stations and users in multi-tier HetNets. Additionally, an analytical framework for Quality of Service (QoS) provision based on D-DOSS simplifies the understanding of user-base station relationships and offers essential performance metrics. Moreover, an optimization problem formulation, considering coverage, energy maximization, and delay minimization constraints, aims to strike a balance between key network attributes. This research not only addresses crucial challenges in creating EE HetNets but also lays a foundation for future advancements in wireless network design, operation, and management, ultimately benefiting network operators and end-users alike amidst the growing demand for high-speed data and the increasing prevalence of wireless devices. The proposed D-DOSS approach not only offers insights for the systematic design and analysis of EE HetNets but also systematically outperforms other state-of-the-art techniques presented. The improvement in energy efficiency systematically ranges from 67% (min side) to 98% (max side), systematically demonstrating the effectiveness of the proposed strategy in achieving higher energy efficiency compared to existing strategies. This systematic research work establishes a strong foundation for the systematic evolution of energy-efficient HetNets. The systematic methodology employed ensures a comprehensive understanding of the complex interplay of network dynamics and user requirements in a multi-tiered environment.

Interval reservoir computing: theory and case studies

The time series data in many applications, for example, wind power and vehicle trajectory, show significant uncertainty. Using a single prediction value of wind power as feedback information for wind turbine control or unit commitment is not enough since the uncertainty of the prediction is not described. This paper addresses the uncertainty issue in time series data forecasting by proposing the novel interval reservoir computing method. The proposed interval reservoir computing can capture the underlying evolution of the stochastic dynamical system for time series data using the recurrent neural network (RNN). On the other hand, by formulating a chance-constrained optimization problem, interval reservoir computing outputs a set of parameters in the RNN, which maps to an interval of prediction values. The capacity of the interval is the smallest one satisfying the condition that the probability of having a prediction inside the interval is lower than the required level. The scenario approach solves the formulated chance-constrained optimization problem. We implemented an experimental data-based validation to evaluate the proposed method. The validation results show that the proposed interval reservoir computing can give a tight interval of time series data forecasting values for wind power and traffic trajectory. In addition, the confidence probability over the feasibility goes to 1 very quickly as the sample number increases.

Enhanced Optimization of Composite Laminates: Multi-Objective Genetic Algorithms with Improved Ply-Stacking Sequences.

This study introduces multi-objective genetic algorithms for optimizing the stacking sequence of lightweight composite structures. Notably, significant emphasis is placed on adhering to engineering design guidelines specific to stacking sequence design. These guidelines are effectively integrated into the optimization problem formulation as either constraints or additional objectives. To enhance the initialization process, a novel strategy is proposed based on mechanical considerations. The method is then applied to optimize a composite laminate in terms of weight, inverse reserve factor, and buckling load factor. Three laminates were considered, and the influence of the design and the material composition on their mechanical properties were studied. This research demonstrated that a new stacking sequence [906/454/06] resulted in improved optimum designs compared to the traditional stacking sequence comprising plies at 0°, 45°, and 90° angles. These outcomes can be deemed the optimum stacking sequence, making them valuable for future applications in unmanned aerial vehicle (UAV) structures.

A Formulation of Structural Design Optimization Problems for Quantum Annealing

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems.

Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review

Economic Dispatch Problems (EDP) refer to the process of determining the power output of generation units such that the electricity demand of the system is satisfied at a minimum cost while technical and operational constraints of the system are satisfied. This procedure is vital in the efficient energy management of electricity networks since it can ensure the reliable and efficient operation of power systems. As power systems transition from conventional to modern ones, new components and constraints are introduced to power systems, making the EDP increasingly complex. This highlights the importance of developing advanced optimization techniques that can efficiently handle these new complexities to ensure optimal operation and cost-effectiveness of power systems. This review paper provides a comprehensive exploration of the EDP, encompassing its mathematical formulation and the examination of commonly used problem formulation techniques, including single and multi-objective optimization methods. It also explores the progression of paradigms in economic dispatch, tracing the journey from traditional methods to contemporary strategies in power system management. The paper categorizes the commonly utilized techniques for solving EDP into four groups: conventional mathematical approaches, uncertainty modelling methods, artificial intelligence-driven techniques, and hybrid algorithms. It identifies critical research gaps, a predominant focus on single-case studies that limit the generalizability of findings, and the challenge of comparing research due to arbitrary system choices and formulation variations. The present paper calls for the implementation of standardized evaluation criteria and the inclusion of a diverse range of case studies to enhance the practicality of optimization techniques in the field.