MATLAB Optimization Toolbox Research Articles

Identification of Time-Wise Thermal Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient Problem

This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.

Retrieving the time-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer

PurposeIn order to include the non-negligible lag relaxation time feature that is characteristic of heat transfer in biological bodies, the classical Fourier's law of heat conduction has to be generalized as the Maxwell–Cattaneo law resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the unknown time-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from (non-intrusive) measurements of the temperature on an accessible sub-portion of the boundary that may be taken with an infrared scanner.Design/methodology/approachThe nonlinear and ill-posed problem is reformulated as a nonlinear minimization problem of a Tikhonov regularization functional subject to lower and upper simple bounds on the unknown coefficient. For the numerical discretization, an unconditionally stable direct solver based on the Crank–Nicolson finite-difference scheme is developed. The Tikhonov regularization functional is minimized iteratively by the built-in routine lsqnonlin from the MATLAB optimization toolbox. Numerical results for a benchmark test example are presented and thoroughly discussed, shedding light on the performance and effectiveness of the proposed methodology.FindingsThe inverse problem of obtaining the time-dependent blood perfusion coefficient and the temperature in the thermal-wave model of bio-heat transfer from extra boundary temperature measurement has been solved. In particular, the uniqueness of the solution to this inverse problem has been established. Furthermore, our proposed computational method demonstrated successful attainment of the perfusion coefficient and temperature, even when dealing with noisy data.Originality/valueThe originalities of the present paper are to account for such a more representative thermal-wave model of heat transfer in biological bodies and to investigate the possibility of determining its time-dependent blood perfusion coefficient from non-intrusive boundary temperature measurements.

Modeling the transmission dynamics of the co-infection of COVID-19 and Monkeypox diseases with optimal control strategies and cost–benefit analysis

This study explores a mathematical model in continuous time, elucidating the transmission dynamics of the co-infection of COVID-19 and Monkeypox. We implemented an optimal control strategy that includes adherence to wearing nose/face masks, practicing social distancing, employing rodenticides, and getting vaccinated against these lethal illnesses. The goal is to reduce their spread among people, consequently lessening their impact on the human population. Utilizing the discrete-time Pontryagin maximum principle, we determined optimal control strategies through an iterative approach to solve the optimal system. By utilizing the MATLAB optimization toolbox with the Runge–Kutta forward–backward sweep technique, we performed numerical simulations to demonstrate how these control parameters impact different sections of the human population, including both infected and uninfected compartments. We conducted a comprehensive cost–benefit analysis to identify the control measures that would produce the best outcome in minimizing both the expenses and the incidence of co-infection cases involving COVID-19 and Monkeypox diseases. Our analyses indicated that intensifying the utilization of nose/facemasks, rodenticides, personal protective equipments (PPEs) in Monkeypox treatment facilities, immunization, and implementing social distancing measures can notably diminish the prevalence of COVID-19, Monkeypox, and their concurrent infections among the human populace.

Mathematical Modeling of COVID‐19 Disease Dynamics With Contact Tracing: A Case Study in Ethiopia

In this paper, we developed a mathematical model for the dynamics of coronavirus disease (COVID‐19) transmission. The model embraces the notion of contact tracing and contaminated surfaces which are vital for disease control and contribute to disease transmission, respectively. We analyzed the model properties such as the positivity of the solution, invariant region, existence, and stability nature of equilibria. Besides, we computed the basic reproduction number R0. The local stability and the global stability of disease‐free equilibrium (DFE) points are proved by using the Routh–Hurwitz criteria and the Castillo‐Chavez and Song approach, respectively. LaSalle’s invariant principle is applied to prove the stability of an endemic equilibrium (EE) point. The possibility of bifurcation is discussed using the center manifold theory. We used real data on the spread and control of COVID‐19 disease in Ethiopia. Based on the data reported, we estimated the values of the parameters using the least squares method together with the fmin function in the MATLAB optimization toolbox. The sensitivity analysis of the model is explored numerically to illustrate the impact of the parameters on disease transmission. The study addressed that contact tracing is especially important because COVID‐19 often has asymptomatic carriers, and there are many asymptomatic individuals unaware in Ethiopia. The new infections would decrease in the communities by detecting and isolating COVID‐19 cases before they could spread the virus to others. Moreover, the study endorsed that the contaminated surface has contributed to disease transmission. The sensitivity analysis shows that if the rate of disinfected contaminated objects (ϕ) rises, then the transmission of the disease is reduced. Consequently, this study will aid in the fight against COVID‐19 policymakers and NGOs. It can also be used as a policy input for different countries under this crisis. Because of the mathematical modeling of this global pandemic, there is another point of view rather than public health research outputs. Additionally, with the concept of contact tracing and contaminated surfaces incorporated into the model, the result provides insight for disease prevention.

Simultaneous identification of the solely time‐dependent potential and source control terms from known moisture moments

Pseudo‐parabolic equations are commonly used as mathematical models in mechanics, biology, and physics to address various applied problems. One particular application involves describing moisture transfer dynamics in subsoil layers using pseudo‐parabolic equations. This manuscript examines the inverse problem (IP) of identifying the moisture transfer function, along with the time‐varying potential and source control terms, in a linear pseudo‐parabolic equation from known moisture moments. We prove the existence of a unique solution to the inverse problem for sufficiently small times by employing the contraction principle. The inverse problem is reformulated as a nonlinear least‐squares minimization problem, with the unknowns subjected to simple bounds. To guarantee stability, the Tikhonov regularization technique is utilized. For the numerical discretization, we develop the Crank–Nicolson finite‐difference method to solve the direct problem. To solve the nonlinear least‐squares minimization problem, we utilize the built‐in subroutine lsqnonlin from the MATLAB optimization toolbox. We present and thoroughly discuss numerical outcomes for a benchmark test example, providing insights into the performance and effectiveness of the proposed methodology.

Optimal energy management of grid-connected PV for HVAC cooling with ice thermal storage system

Studies have shown that reducing cooling energy costs and increasing operational efficiency may be achieved by utilizing ice thermal energy storage (ITES) technology while maintaining the thermal requirements in space cooling facilities. Optimal control of the ITES system and integration of renewable energy (RE) sources such as PV and geothermal, depending on the availability of resources and application, can further improve the operation of HVAC's cooling systems and mitigate the increased energy cost required for ice formation and overall cooling energy.This study presented optimal switching control of the ice-build chiller for ITES charging and PV power source. Inputs to the model, simulations, and validations were implemented using the available data, which include the historical exogenous meteorological data, temperatures at the inlet and exit of the plant components, manufacturer's information, and readings from the plant's SCADA chosen for the case study.The main aim of the study was to develop an optimal control model that minimizes the energy consumption and cost in the Ice built chiller and other devices, such as pump fans in the HVAC system, by optimal charge and discharge of the ITES and supplementary utilization of the greener energy source PV source under the time of use (ToU) tariff and desired cooling load demand. The case study for a healthcare building was considered in implementing the model.Simulations were implemented in the MATLAB optimization toolbox with the Solving Constrained Integer Programs (SCIP) solver, which was chosen to address mixed integer programming (MIP) problems. It incorporates algorithms like a branch and cut conflict analysis and pre-solving techniques to handle intricate optimization problems involving continuous and discrete decision variables.The optimal switching control model yields approximately 33 % of energy cost savings during the summer months that involve using the HVAC with ITES compared to the current system control (baseline). Additionally, the ITES temperature remained below 0 °C to maintain thermal requirements as an operation constraint. The inclusion of PV and battery options as a source of power to the pumps accounted for 10–15 % of the overall energy usage of the system. Optimal control of the system to utilize the stored energy during peak pricing and high demand periods eliminated the extreme dependence on grid energy in some instances. Despite the additional capital required for the controller, solar PV, and batteries installation, the study projects a return on investment within two years, with a 20-year lifetime energy cost savings estimate of 35 % if inflation and annual electricity price increases are estimated at 5 % and 10 %, respectively.

Stackelberg Security Game for Optimizing Cybersecurity Decisions in Cloud Computing

As it is difficult to cover all cybersecurity threats, an optimal defense strategy is one of the focal issues in cloud computing due to its dynamic abstraction and scalability. On this basis, Stackelberg security games (SSG) have received significant attention for their better deployment of limited security. To deal with uncertainty and incomplete information, we introduce a modified quantal response (Mod-QR) approach that incorporates bounded rationality and preference into the decision-making process. Formally, this can be done by using the quantal response equilibrium (QRE) framework to find a trade-off between the effectiveness and operating costs of cloud computing. In this case, the most effective countermeasures to defend the cloud can be viewed as a mixed strategy in which all the actions of the defender are played with a nonzero probability. This framework has been evaluated using an experimental study on MATLAB optimization toolbox to understand the behavioral aspects of cybersecurity actors and then to proactively protect cloud computing.

Design of the transmitter coil used in wireless power transfer system based on genetic algorithm

Performance of the wireless power transfer (WPT) system relies on the physical dimensions of the coupled coil, which should be optimally designed to meet required system performance and reduce the operating cost. This paper presents an optimal design based on genetic algorithm (GA) for the transmitter coil used in wireless power transfer system. Physical parameters of the circular flat spiral coil, including wire’s cross-sectional area, coil’s inner diameter, coil’s outer diameter, coil’s turn number, and space between each turn of the coil are considered. The design objective is to minimize the total wire length required by the coil subjected to both linear and nonlinear constraints. The design process is implemented on MATLAB optimization toolbox which is simple and accurate. The validity of proposed optimal coil design is verified by the experiment, which indicates that total wire length of the optimized coil can be reduced by 5.5 percent compared to the conventional coil without sacrificing the system performance. System efficiency obtained from the optimized coil can be improved up to 8.32 percent.

Optimal Dispatch of Concentrating Solar Thermal Power (CSP)-Wind Combined Power Generation System

The random nature of renewable energy leads to the instability of the balance state of the power grid, and the frequency and voltage of the grid also fluctuate. Considering that wind energy and solar thermal power generation can complement each other in terms of temporal output power, the heat storage system of the solar thermal power station is used to regulate the joint operation of the solar thermal power station and wind power generation, and an optimal scheduling method for promoting new energy consumption of solar thermal power station is proposed. Based on the solar thermal-wind combined power generation system, the method considers the operating characteristics and constraints of each unit and uses the MATLAB optimization toolbox to simulate and verify the IEEE-14 node system. The results show that the participation of wind power grid-connected time thermal power stations can alleviate the pressure of rapid output adjustment of traditional units and can ensure the economy of the system, and the operating cost is reduced by 51.5%. The curtailment air volume was reduced from the original 2.5015 MW to 0.83015 MW, maximizing new energy consumption.

Multi-objective optimization model of transmission error of nonlinear dynamic load of double helical gears

Abstract In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 107 mm3, and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 ∘ , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.

Research on Multi-Objective Optimization Model of Foundation Pit Dewatering Based on NSGA-II Algorithm

This study focuses on optimizing the foundation pit dewatering scheme using the foundation pit dewatering theory and the principles of multi-objective optimization. It explores the development of a multi-objective optimization model and efficient solution technology for foundation pit dewatering. This research focuses on the foundation pit dewatering project at the inverted siphon section of Xixiayuan canal head, specifically from pile number XZ0+326 to XZ0+500. It establishes an optimized mathematical model for foundation pit dewatering that incorporates three objectives. Additionally, a dewatering optimization program is developed by utilizing the MATLAB optimization toolbox and the multi-objective optimization algorithm program based on the NSGA-II algorithm (Gamultiobj). The multi-objective optimization mathematical model is solved, and a Pareto-optimal solution set with uniform distribution is obtained. The multi-objective optimization evaluation system based on AHP is constructed from the three aspects of dewatering cost, the impact of settlement on the environment, and the safety and stability of the foundation pit. The optimization scheme of the Pareto-optimal solution set is selected as the decision result to provide multiple feasible schemes for the dewatering construction of foundation pits. The optimization scheme is verified by using the GMS software. The simulation results demonstrate that the optimization scheme fulfills the requirements for water level and settlement control. Moreover, the developed optimization program efficiently solves the multi-objective optimization problem associated with foundation pit dewatering. Lastly, an evaluation system incorporating the NSGA-II algorithm and AHP is developed and utilized in the context of dewatering engineering in order to offer multiple viable optimal dewatering schemes.

Design optimization to minimize wake of wide-body transport aircraft

A cutting-edge sustainable airplane can improve performance and enhance profitability are the most significant future concerns for the aviation industry. This research aims to analyse and assess aircraft performance of mid-size transport aircraft through retrofit designs. An optimal design was employed using a non-linear optimization approach under two cases fuselage alone (case 1) and a combination of fuselage-wing-empennage (case 2). These two retrofit concepts were evaluated and compared with the baseline A310–200 aircraft. To compute the objective function for various cases, non-linear solver was used from MATLAB optimization tool box. Additionally, the parametric studies of aerodynamics, structural and operational performance analysis are carried out by using Advanced Aircraft Analysis (AAA) 5.0 software. Sensitivity analyses are performed to assess the overall effectiveness of the optimal design. The key findings of this paper obtained the following parameters as Maximum take-off Weight, empty weight, fuel weight, parasite drag coefficient, rate of climb, take-off distance and landing distance are improved by 0.36%, 26.02%, 10.12%, 4.48%, 27.24%, 13.13% and 9.2% respectively. At the end, the paper provides a clear statement on the managerial perceptions and future insights for the upcoming challenges towards sustainable design.

Optimizing the performance of the ZnO-based varistors using the neural networks technique

This study aimed to propose a scientific method depending on neural networks technique to determine the optimal proportions of some impurities (Bi2O3, Nb2O5, MnO2, Co3O4, Cr2O3, NiO, La2O3, Ce2O3) used in manufacturing the ZnO-based varistors. The technique enables obtaining varistors with high structural homogeneity, high performance, and surge energy absorption capability. A nonlinear neural model between the nonlinear coefficient and the proportion of each impurity was accurately created. Subsequently, the neural models have been trained to approximate the correlation factor to the optimum value (R = 1), which proves the accuracy of the models. Then, using the optimization toolbox in MATLAB, the proportion of each impurity producing the highest nonlinear coefficient was determined. Afterwards, a nonlinear neural model representing the relationship between the most influential impurities combined (MnO2, NiO, Ce2O3, La2O3) and the nonlinear coefficient was built. Through training the neural model, the correlation factor was R = 0.99516, and the mean square error was MSE = 0.1078, proving the model's accuracy. Depending on the optimal solutions based on the Lagrange-Newton algorithm in MATLAB, the optimal proportions of impurities combined corresponding to the highest value of the nonlinear coefficient were determined. The accuracy of the proposed method was practically confirmed by preparing a varistor according to the optimal proportions and performing the measurements. The relative error between the theoretical value (α = 99.7522) and the practical value (α = 99.41) of the nonlinear coefficient was RE = 0.0035. That confirms that the proposed method has high reliability and accuracy to be adopted.

Dynamic simulation of a triple-mode multi-generation system assisted by heat recovery and solar energy storage modules: Techno-economic optimization using machine learning approaches

Intelligent design and operation optimization allow energy systems to take advantage of the flexibility that multi-generation provides. This study proposes a basic solar-driven system integrated with thermal energy storage for round-the-clock energy harvesting. A modified configuration is then designed incorporating innovative multi-heat recovery approaches to increase the capacity and product diversity of the basic system. The modified system is able to cover vital urban utilities such as electricity, fresh water, cooling, and hydrogen throughout the day. To overcome the time-consuming procedure of dynamic techno-economic simulation as well as the limitation of commercial engineering equation solvers for tri-objective optimization, a deep learning approach is developed to reduce the computational complexity and improve the analysis accuracy. In this regard, the trained neural networks play an intermediary role in coupling the developed code with the MATLAB optimization toolbox. A comparison between the modified and conventional configurations indicates that implementing the multi-heat recovery approach results in a 29% increase in power generation while only increasing the overall system cost by 1.97%. From an economic perspective, the Sankey diagram depicts that the storage unit with a cost rate of 12.25 $/h accounts for 6.77% of the plant's cost rate, which enables the system to operate continuously. According to the sensitivity analysis and contour plots, the number of collectors significantly affects the total cost rate and fresh water production capacity while it has no tangible effect on the exergy efficiency.

Multi-level Reliability-Based Design Optimization (RBDO) study for electronic cooling: Application of heat sink based on multiple phase change materials enhanced with carbon nanoparticles

Phase change materials represent efficient performances in the thermal management field. However, the low thermal conductivity poses a serious restraint for electronic cooling applications. Recently, the use of multiple phase change materials and the dispersion of nanoparticles are the most recommended techniques to improve the performance of the heat sink. In this study, a developed heat sink filled with multiple phase change materials (PCMs) enhanced with carbon nanoparticles was proposed. First, a parametric study was carried out to determine the optimal pair of phase change materials and nanoparticles. Then, deterministic design optimization and various reliability-based design optimization methods are performed. The optimization and reliability problems are solved by coupling the MATLAB optimization toolbox and the ANSYS Finite Element Model. The optimization-reliability results prove the efficiency of the Robust Hybrid Method in proposing a reliable and optimal heat sink design filled with multiple nano-enhanced phase change materials. The temperature is reduced by 25 % (16,5 °C) and the discharge time is reduced by 8,69 % (14 min) compared to the baseline heat sink.

Determination of the space-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer

PurposeWhen modeling heat propagation in biological bodies, a non-negligible relaxation time (typically between 15-30 s) is required for the thermal waves to accumulate and transfer, i.e. thermal waves propagate at a finite velocity. To accommodate for this feature that is characteristic to heat transfer in biological bodies, the classical Fourier's law has to be modified resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the space-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from final time temperature measurements.Design/methodology/approachThe non-linear and ill-posed blood perfusion coefficient identification problem is reformulated as a non-linear minimization problem of a Tikhonov regularization functional subject to lower and upper simple bounds on the unknown coefficient. For the numerical discretization, an unconditionally stable direct solver based on the Crank–Nicolson finite difference scheme is developed. The Tikhonov regularization functional is minimized iteratively by the built-in routine lsqnonlin from the MATLAB optimization toolbox. Both exact and numerically simulated noisy input data are inverted.FindingsThe reconstruction of the unknown blood perfusion coefficient for three benchmark numerical examples is illustrated and discussed to verify the proposed numerical procedure. Moreover, the proposed algorithm is tested on a physical example which consists of identifying the blood perfusion rate of a biological tissue subjected to an external source of laser irradiation. The numerical results demonstrate that accurate and stable solutions are obtained.Originality/valueAlthough previous studies estimated the important thermo-physical blood perfusion coefficient, they neglected the wave-like nature of heat conduction present in biological tissues that are captured by the more accurate thermal-wave model of bio-heat transfer. The originalities of the present paper are to account for such a more accurate thermal-wave bio-heat model and to investigate the possibility of determining its space-dependent blood perfusion coefficient from temperature measurements at the final time.

A Rheological Model with Integer and Non-Integer Orders Nonlinearities for Predicting Stress Relaxation Behavior in Viscoelastic Materials

Viscoelastic materials are widely used as devices for vibration control in modern engineering applications. They exhibit both viscous and elastic characteristic when undergoing deformation. They are mainly characterized by three time-dependent mechanical properties such as creep, stress relaxation and hysteresis. Among them, stress relaxation is one of the most important features in the characterization of viscoelastic materials. This phenomenon is defined as a time-dependent decrease in stress under a constant strain. Due to the inherent nonlinearity shown by the material response over a certain range of strain when viscoelastic materials are subjected to external loads, nonlinear rheological models are needed to better describe the experimental data. In this study, a singlenonlinear differential constitutive equation is derived froma nonlinear rheological model composed of a generalized nonlinear Maxwell fluid model in parallel with a nonlinear spring obeying a power law for the prediction of the stress relaxation behavior in viscoelastic materials. Under a constant strain-history, the time-dependent stress is analytically derived in the cases where the positive power law exponent, α ˂ 1 and α ˃1. The Trust Region Method available in MATLAB Optimization Toolbox is used to identify the material parameters. Significant correlations are found between the experimental relaxation data taken from literature and exact analytical predictions. The obtained results show that the developed rheological model with integer and non-integer orders nonlinearities accurately describes the experimental relaxation data of some viscoelastic materials.

Accurate Base Station Placement in 4G LTE Networks Using Multiobjective Genetic Algorithm Optimization

Cellular mobile communication network planning and optimization involve a complex engineering process that deals with network fundamentals, radio resource elements, and critical decision variables. The continuous evolution of radio access technologies provides new challenges that necessitate efficient radio planning and optimization. Therefore, the planning and optimization algorithms should be highly efficient, advanced, and robust. An important component of 4G LTE network planning is the proper placement of evolved node base stations (eNodeBs) and the configuration of their antenna elements. This contribution proposes a multiobjective genetic algorithm that integrates network coverage, capacity, and power consumption for optimal eNodeB placement in an operational 4G LTE network. The multi-objective-based genetic algorithm optimization has been achieved using the optimization toolbox in MATLAB. By leveraging the proposed method, the effect of different population sizes on the cost of placing the eNodeBs and the percentage coverage of the eNodeBs in a given cell is determined. As a result, the optimal selection technique that minimizes the total network cost without compromising the desired coverage and capacity benchmarks is achieved. The proposed automatic eNodeB antenna placement method can be explored to optimize 4G LTE cellular network planning in related wireless propagation environments.

Quadrotor Path Planning and Polynomial Trajectory Generation Using Quadratic Programming for Indoor Environments

This study considers the problem of generating optimal, kino-dynamic-feasible, and obstacle-free trajectories for a quadrotor through indoor environments. We explore methods to overcome the challenges faced by quadrotors for indoor settings due to their higher-order vehicle dynamics, relatively limited free spaces through the environment, and challenging optimization constraints. In this research, we propose a complete pipeline for path planning, trajectory generation, and optimization for quadrotor navigation through indoor environments. We formulate the trajectory generation problem as a Quadratic Program (QP) with Obstacle-Free Corridor (OFC) constraints. The OFC is a collection of convex overlapping polyhedra that model tunnel-like free connecting space from current configuration to goal configuration. Linear inequality constraints provided by the polyhedra of OFCs are used in the QP for real-time optimization performance. We demonstrate the feasibility of our approach, its performance, and its completeness by simulating multiple environments of differing sizes and varying obstacle densities using MATLAB Optimization Toolbox. We found that our approach has higher chances of convergence of optimization solver as compared to current approaches for challenging scenarios. We show that our proposed pipeline can plan complete paths and optimize trajectories in a few hundred milliseconds and within approximately ten iterations of the optimization solver for everyday indoor settings.

Energy-Performance Evaluation with Revit Analysis of Mathematical-Model-Based Optimal Insulation Thickness

This study investigates the optimum insulation thickness value using MATLAB Optimization Toolbox based on a mathematical model for sandwich walls that are formed with different insulation-building materials by different fuel types for a particular city located in the second climatic region of Turkey. In the second stage of study, using the BIM-based Revit simulation program, a building was designed with the same building-insulation materials under the same climate conditions. The six different wall performances were compared for the designed building. The study proposes a comprehensive approach by combining technical and economic factors in the sustainable design of buildings. The computational results indicate that using different energy alternatives has a significant impact on the air quality in residential areas. The lowest value is reached when natural gas is used. The energy cost savings change from 7.56 to 14.12 TRY/m2 for external walls. While payback periods vary between 2.15 and 3.76 years for external walls, the lowest period for all wall types is obtained for electricity, which has a high cost. The optimum insulation thickness for 10 years of lifetime varies between 0.02 and 0.16 m. This study reflects that the highest optimal insulating thickness is reached when electricity is utilized as the energy source for all wall types. According to the Revit analysis, the lowest energy consumption of 21,677 kWh during one year using natural gas was obtained for a building material of porous light brick and an insulation material of glass wool.