Stochastic Optimization Strategy Research Articles

Optimizing the bidding strategy and assessing profitability of over-install renewable plants equipped with battery energy storage systems

The over-installation of renewable energy sources (RES) can enhance the profits of RES producers by increasing the total exporting energy; however, RES power curtailments must be applied under over-production of RES plants to ensure their contracted maximum export capacity limits. Battery energy storage systems (BESSs) can be used to reduce the RES curtailments and therefore enhance the profits of producers. This work develops a bidding strategy as a scenario-based stochastic optimization scheme to maximize the expected profits of producers in electricity markets considering battery degradation and maximum export capacity constraints. Using the proposed scheme, a financial analysis is performed to assess the profitability for over-installing hybrid RES plants by calculating the net present value and internal rate of return of the project under different BESS costs. Simulation results, using real data from a wind and photovoltaic plant, demonstrate the effectiveness of the proposed stochastic scheme in enhancing the profit of producers compared to the corresponding deterministic scheme. The performed financial analysis, using the net present value metric, indicates that a maximum over-installation of 150%–170% and 160%–180% for the wind and photovoltaic plant, respectively, is profitable, while the usage of a BESS is profitable when its cost is under 200,000 €/MWh.

Experimental characterization and constitutive modeling of thermoplastic polyurethane under complex uniaxial loading

This paper presents the testing and constitutive modeling of a Thermoplastic Polyurethane (TPU) compound used in commercial applications. The tested specimens were extracted directly from a TPU sphere used in check valves through water-jet cutting. The tests included tensile and compression tests under complex uniaxial loading protocols to capture different nonlinear phenomena, such as stress softening, hysteresis, relaxation, creep, and rate dependence. The material is modeled assuming a nonlinear elastic equilibrium path that may exhibit stress softening (i.e., Mullins effect), and a hysteretic viscoplastic response that presents rate dependence at three different time scales. To achieve this constitutive behavior, a Parallel Rheological Framework model is used. The nonlinear elastic equilibrium path is modeled using the generalized Yeoh hyperelastic model. The stress softening of the equilibrium path is modeled using the Ogden-Roxburgh damage model on the deviatoric response. The hysteretic viscous response is further split into three viscoplastic chains to represent time dependence at three different time scales in a decoupled way. Each viscoplastic chain is modeled using the Bergstrom-Boyce model with its standard evolution law of the creep strain. The model parameters were found using a stochastic optimization scheme to simultaneously fit all the considered tests. The outstanding agreement between the model and the experimental data across a wide range of loading scenarios provides additional insight into the time-dependent behavior and deformation mechanism of TPUs. Moreover, it shows that the mechanical behavior of these materials can be represented by decoupling the nonlinear viscoplastic behavior in different time scales.

The continuous stochastic gradient method: part II–application and numerics

In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization schemes, CSG does not discard old gradient samples from previous iterations. Instead, design dependent integration weights are calculated to form a convex combination as an approximation to the true gradient at the current design. As the approximation error vanishes in the course of the iterations, CSG represents a hybrid approach, starting off like a purely stochastic method and behaving like a full gradient scheme in the limit. In this work, the efficiency of CSG is demonstrated for practically relevant applications from topology optimization. These settings are characterized by both, a large number of optimization variables and an objective function, whose evaluation requires the numerical computation of multiple integrals concatenated in a nonlinear fashion. Such problems could not be solved by any existing optimization method before. Lastly, with regards to convergence rates, first estimates are provided and confirmed with the help of numerical experiments.

The continuous stochastic gradient method: part I–convergence theory

In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function requires some form of integration, e.g., expected values. Since approximating the integration by a fixed quadrature rule can introduce artificial local solutions into the problem while simultaneously raising the computational effort, stochastic optimization schemes have become increasingly popular in such contexts. However, known stochastic gradient type methods are typically limited to expected risk functions and inherently require many iterations. The latter is particularly problematic, if the evaluation of the cost function involves solving multiple state equations, given, e.g., in form of partial differential equations. To overcome these drawbacks, a recent article introduced the CSG method, which reuses old gradient sample information via the calculation of design dependent integration weights to obtain a better approximation to the full gradient. While in the original CSG paper convergence of a subsequence was established for a diminishing step size, here, we provide a complete convergence analysis of CSG for constant step sizes and an Armijo-type line search. Moreover, new methods to obtain the integration weights are presented, extending the application range of CSG to problems involving higher dimensional integrals and distributed data.

A hybrid heuristic-reinforcement learning-based real-time control model for residential behind-the-meter PV-battery systems

The behind-the-meter (BTM) energy management problem has recently attracted a lot of attention due to the increase in the number of residential photovoltaic (PV)-battery energy storage systems (BESSs). In this work, the use of deep reinforcement learning (DRL) combined with a novel heuristic model for real-time control of home batteries is investigated. The control problem is formulated as a finite Markov Decision Process with discrete time steps, where a proximal policy optimization (PPO) algorithm is employed to train the DRL agent with discrete action space. The agent is trained using real-world measured data to learn the policy for sequential charge/discharge tasks, aiming to minimize daily electricity costs. The battery power is calculated using an innovative heuristic model considering the agent's decision and the battery's available capacity, ensuring demand-supply balance through PV self-consumption and load demand shifting. The performance of the model is evaluated by comparing it to four RL agents and two benchmark models based on rule-based and scenario-based stochastic optimization strategies. The results confirm that the presented model outperforms its counterparts, offering €80.38 savings on electricity bills over 46 days of the test data set. This figure exceeds the savings of the rule-based and stochastic models by €15.64 and €19.38, respectively.

Optimal Placement of PV Smart Inverters With Volt-VAr Control in Electric Distribution Systems

The high R/X ratio of typical distribution systems makes the system voltage vulnerable to the active power injection from distributed energy resources (DERs). Moreover, the intermittent and uncertain nature of the DER generation brings new challenges to the voltage control. This article proposes a two-stage stochastic optimization strategy to optimally place the photovoltaic (PV) smart inverters with Volt-VAr capability for distribution systems with high PV penetration to mitigate voltage violation issues. The proposed optimization strategy enables a planning-stage guide for upgrading the existing PV inverters while considering the operation-stage characteristics of the Volt-VAr control. One advantage of this planning strategy is that it utilizes the local control capability of the smart inverter that requires no communication, thus avoiding issues related to communication delays and failures. Another advantage is that the Volt-VAr control characteristic is internally integrated into the optimization model as a set of constraints, making placement decisions more accurate. The objective of the optimization is to minimize the upgrading cost and the number of the smart inverters required while maintaining the voltage profile within the acceptable range. Case studies on an actual 12.47 kV, 9-km-long Arizona utility feeder have been conducted using OpenDSS to validate the effectiveness of the proposed placement strategy in both static and dynamic simulations.

A random optimization strategy of microgrid dispatching based on stochastic response surface method considering uncertainty of renewable energy supplies and load demands

The stochastic response of microgrid regulation under the influence of uncertainty should be considered in the day-ahead optimal dispatching. This paper focuses on the Stochastic Response Surface Method (SRSM) modelling and Second-Order Cone Programming (SOCP) optimal solution for the stochastic optimization strategy of microgrid dispatching considering the random fluctuations of renewable energy supplies and load demands. Based on the SRSM theory, the random distributions of uncertainty are converted into independent standard normal distributions by Nataf transformation, then by means of a small amount of standardized SRSM samples of random fluctuations, the Hermite Chaotic Polynomials can be formulated to describe the random response process of microgrid adjustment. And the Hermite Chaotic Matrix establishes the linear constraint functions for the probability distribution characteristics of stochastic response process of microgrid adjustment considering uncertainty. On this basis, the SRSM based stochastic optimization (SO) model with multi-objective functions are constructed for the optimal economic operation, control of cost fluctuation and lower carbon emissions. In addition, to reduce operation risk, the constraints of extreme power shortage are introduced into the model. To ensure the convexity of the optimization model, the Second-Order Cone Relaxation is applied to all the quadratic terms in the model. Thus, the proposed SO model of microgrid dispatching can be transformed into an SOCP optimization problem. And the Yalmip-Gurobi solver is adopted for the solution of the proposed SO model, which has an efficient operation speed and stability. The effectiveness of the proposed scheme is demonstrated by the case studies using Monte Carlo sampling simulation.

Optimal scheduling of ethylene plants under uncertainty: An unsupervised learning-based data-driven strategy

Ethylene cracking furnaces are core units that determine the yield of key products, and its cycle scheduling optimization is of great significance to improve the efficiency of the whole plant. However, uncertainties in cracking batch durations may lead to sub-optimal or ineffective scheduling arrangements. This paper develops a novel data-driven stochastic robust optimization strategy to achieve the optimal scheduling of cracking furnaces under uncertainty. The proposed stochastic robust optimization model applies machine learning methods to extract data information and is represented as a bilevel problem: the outer layer is a two-stage stochastic programming, where typical scenarios are clustered by a three-level data mining approach; the inner layer is robust optimization, whose uncertainty set is constructed by an efficient kernel-based approach. An actual ethylene cracking system is investigated and the results show that the proposed method achieves the highest daily profit, performing well in data coverage (92.3%) and change rate (0.826%). Moreover, the sensitivity analysis for the number of clusters and regularization parameter values is performed.

Generative and discriminative training of Boltzmann machine through quantum annealing

A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. BM are undirected graphs with a network of visible and hidden nodes where the former is used as the reading site. In contrast, the latter is used to manipulate visible states’ probability. In Generative BM, the samples of visible data imitate the probability distribution of a given data set. In contrast, the visible sites of discriminative BM are treated as Input/Output (I/O) reading sites where the conditional probability of output state is optimized for a given set of input states. The cost function for learning BM is defined as a weighted sum of Kullback-Leibler (KL) divergence and Negative conditional Log-likelihood (NCLL), adjusted using a hyper-parameter. Here, the KL Divergence is the cost for generative learning, and NCLL is the cost for discriminative learning. A Stochastic Newton-Raphson optimization scheme is presented. The gradients and the Hessians are approximated using direct samples of BM obtained through quantum annealing. Quantum annealers are hardware representing the physics of the Ising model that operates on low but finite temperatures. This temperature affects the probability distribution of the BM; however, its value is unknown. Previous efforts have focused on estimating this unknown temperature through regression of theoretical Boltzmann energies of sampled states with the probability of states sampled by the actual hardware. These approaches assume that the control parameter change does not affect the system temperature; however, this is usually untrue. Instead of using energies, the probability distribution of samples is employed to estimate the optimal parameter set, ensuring that the optimal set can be obtained from a single set of samples. The KL divergence and NCLL are optimized for the system temperature, and the result is used to rescale the control parameter set. The performance of this approach, as tested against the theoretically expected distributions, shows promising results for Boltzmann training on quantum annealers.

An Online Control Method of Reactive Power and Voltage Based on Mechanism–Data Hybrid Drive Model Considering Source–Load Uncertainty

The uncertainty brought about by the high proportion of distributed generations poses great challenges to the operational safety of novel distribution systems. Therefore, this paper proposes an online reactive power and voltage control method that integrates source–load uncertainty and a mechanism–data hybrid drive (MDHD) model. Based on the concept of a mechanism and data hybrid drive, the mechanism-driven deterministic reactive power optimization strategy and the stochastic reactive power optimization strategy are used as training data. By training the data-driven CNN–GRU network model offline, the influence of source–load uncertainty on reactive power optimization can be effectively assessed. On this basis, according to the online source and load predicted data, the proposed hybrid-driven model can be applied to quickly obtain the reactive power optimization strategy to enable fast control of voltage. As observed in the case studies, compared with the traditional deterministic and stochastic reactive power optimization models, the hybrid-driven model not only satisfies the real-time requirement of online voltage control, but also has stronger adaptability to source–load uncertainty.

Efficient optimization techniques for resource allocation in UAVs mission framework.

This paper considers the generic problem of a central authority selecting an appropriate subset of operators in order to perform a process (i.e. mission or task) in an optimized manner. The subset is selected from a given and usually large set of 'n' candidate operators, with each operator having a certain resource availability and capability. This general mission performance optimization problem is considered in terms of Unmanned Aerial Vehicles (UAVs) acting as firefighting operators in a fire extinguishing mission and from a deterministic and a stochastic algorithmic point of view. Thus the applicability and performance of certain computationally efficient stochastic multistage optimization schemes is examined and compared to that produced by corresponding deterministic schemes. The simulation results show acceptable accuracy as well as useful computational efficiency of the proposed schemes when applied to the time critical resource allocation optimization problem. Distinguishing features of this work include development of a comprehensive UAV firefighting mission framework, development of deterministic as well as stochastic resource allocation optimization techniques for the mission and development of time-efficient search schemes. The work presented here is also useful for other UAV applications such as health care, surveillance and security operations as well as for other areas involving resource allocation such as wireless communications and smart grid.

Optimizing Color of Particulate Products

AbstractOptical properties of nanoparticles largely depend on their shape and material distribution. Given any such property, e.g., a desired color, the aim is to design an optimal nanoparticle, whose properties best match these targets. The corresponding nonlinear optimization problem is challenging due to numerous difficulties: The objective function is given by a multi‐dimensional integral over wavelengths, directions of incoming light rays and nanoparticle design distributions, where the integrand depends on the extinction cross section of the nanoparticle design.Thus, classical full gradient schemes based on numerical integration prove ineffective due to their tremendous computational cost. On the other hand, known stochastic gradient descent methods cannot deal with the nonlinear fashion in which the design variables enter the objective function. Therefore, we introduce the continuous stochastic gradient (CSG) method, which does not compute a full gradient, but instead uses information from previous iterations in an optimal way to learn the exact gradient during the optimization process. Hence, CSG thematically lies in between a stochastic optimization scheme and a full gradient method, combining both the low computational cost of SG due to very few partial gradient evaluations (small “batch size”) as well as step size rules and line search techniques known from full gradient descent.

A Gramian angular field-based data-driven approach for multiregion and multisource renewable scenario generation

Scenario generation is a pivotal method for providing system operators with a reasonable quantity of power scenarios that are capable of reflecting uncertainties and spatiotemporal processes to make exact and effective decisions for power systems. Aiming at improving the forecasting performance of renewable generation and capturing uncertainty as well as dependency over renewable site groups in different regions, this paper proposes a data-driven approach for parallel scenario generation. To capture the complex spatiotemporal dynamics of renewable energy sources (RESs), the proposed approach utilizes Gramian angular field (GAF) to process time sequences and constructs style-based super-resolution models that correspond with the idea of multi-model ensembles. Thereafter, a two-stage stochastic optimization strategy is adopted to accomplish scenario forecasting using point forecasts and historical error information as input. Based on two real-world datasets from the National Renewable Energy Laboratory (NREL) and the Belgian transmission operator ELIA, the effectiveness of the proposed approach is verified by methods including statistical analysis, spatiotemporal correlations, power system scheduling, and out-of-sample evaluations. Compared with three advanced benchmarks, the proposed approach has superior forecasting performance and spatiotemporal dynamic capture capability. At a 24-h lead time, the proposed model achieves continuous ranked probability scores (CRPSs) of 4–14% over the other models with consistent performance during the economic dispatching of actual power system operations.

Coordinated day-ahead dispatch of multiple power distribution grids hosting stochastic resources: An ADMM-based framework

This work presents an optimization framework to aggregate the power and energy flexibilities in an interconnected power distribution systems. The aggregation framework is used to compute the day-ahead dispatch plans of multiple and interconnected distribution grids operating at different voltage levels. Specifically, the proposed framework optimizes the dispatch plan of an upstream medium voltage (MV) grid accounting for the flexibility offered by downstream low voltage (LV) grids and the knowledge of the uncertainties of the stochastic resources. The framework considers grid, i.e., operational limits on the nodal voltages, lines, and transformer capacity using a linearized grid model, and controllable resources' constraints. The dispatching problem is formulated as a stochastic-optimization scheme considering uncertainty on stochastic power generation and demands and the voltage imposed by the upstream grid. The problem is solved by a distributed optimization method relying on the Alternating Direction Method of Multipliers (ADMM) that splits the main problem into an aggregator problem (solved at the MV-grid level) and several local problems (solved at the MV-connected-controllable-resources and LV-grid levels). The use of distributed optimization enables a decentralized dispatch computation where the centralized aggregator is agnostic about the parameters/models of the participating resources and downstream grids. The framework is validated for interconnected CIGRE medium- and low-voltage networks hosting heterogeneous stochastic and controllable resources.

A centralized stochastic optimal dispatching strategy of networked multi-carrier microgrids considering transactive energy and integrated demand response: Application to water–energy nexus

Over a few decades, energy system operators have sought to achieve appropriate frameworks based on the water–energy nexus issues due to energy crises and the rapid growth of water demand. In this regard, multi-carrier microgrids (MCMGs) have been widely welcomed to implement water–energy nexus-related strategies to meet local energy and water demands. This paper presents a centralized stochastic optimization strategy for energy transactions in networked MCMGs to exploit the potential capabilities of the promoted energy conversion facilities in meeting electricity, thermal, and water demands at the lowest operating cost. To enhance the flexibility and operational cost of the system under severe uncertainties, the day-ahead scheduling of all individual MCMGs is carried out by a central operator with the consideration of transactive energy management (TEM) strategy and integrated demand response program (DRP). The MCMGs can purchase energy from the electricity and gas markets to supply demands and energize local generation resources, and also exchange electrical energy with each other under the TEM strategy. The uncertainties arising from the renewable power generation, energy demands, water demand, and electricity market prices are applied to the optimization model using a scenario-based method. The proposed strategy is formulated as the mixed-integer nonlinear programming problem and is solved under GAMS software. The effectiveness of the proposed strategy is validated using a test system consisting of three networked MCMGs. According to the obtained results, the central operator can reduce the total operating cost of the networked MCMGs considerably if employing the TEM strategy and integrated DRP.

Optimal economic scheduling of microgrids considering renewable energy sources based on energy hub model using demand response and improved water wave optimization algorithm

Unpredictable nature of renewable energy sources puts power system operators in different conditions in terms of maintaining the system reliability. Microgrids (MGs) can provide an effective solution for the problems of grid-connected renewable energy sources due to their tuning capability and flexibility. In this study, a stochastic optimization strategy was proposed for participating in energy market operations considering demand response (DR). The results indicated the operating cost decreased when the MG implemented DR programs. Also, DR program could shift energy consumption from on- to off-peak hours and flatten the load curve. Therefore, a scheduling model was presented for the operation of energy carriers and reserves considering security constraints of power and natural gas grids in interconnected hubs as well as responsive load participation using the developed water wave optimization (WWO) algorithm. The objective function of this model aimed to minimize the operating cost of sources to supply electrical and thermal loads applied to the proposed MG. WWO is a meta-heuristic algorithm inspired by the behavior of water waves. The waves formed on the sea surface have complex, but interesting, relationships that can be used to solve optimization problems. In this algorithm, each problem solution is encoded as a water wave and undergoes changes in the problem search space based on three behaviors of propagation, refraction, and decay of water waves or problem solutions. The simplicity of the structure of this method, elitism and the ability to escape from local points due to the existence of different search operators and the mutation of generations have led to the use of this method. The results indicated a decline in operating costs through electrical and thermal responsive load participation and thermal energy storage system. Results of the proposed model revealed a correlation between the electricity price and natural gas consumption, indicating multi-carrier energy grids should be examined and optimized simultaneously.

PSO Algorithm-Based Design of Intelligent Education Personalization System.

The application of artificial intelligence in the field of education is becoming more and more extensive and in-depth. The intelligent education system can not only solve the limitations of location, time, and resources in the traditional learning field but it can also provide learners with a convenient, real-time, and interactive learning environment and has become one of the important applications in the Internet field. Particle swarm optimization (PSO) is a swarm intelligence-enabled stochastic optimization scheme. It is derived from a model of bird population foraging behavior. Because of its benefits of ease of implementation, high accuracy, and quick convergence, this algorithm has gained the attention of academics, and it has demonstrated its supremacy in addressing real issues. This paper aims to study the optimization of PSO in the field of computational intelligence, improve the matching degree of learning resource recommendation and learning path optimization, and improve the learning efficiency of online learners. This paper suggests intelligent education as the center, takes the PSO algorithm as the main research object, and expounds the related concepts of intelligent education and PSO algorithm. It uses swarm intelligence algorithms for intelligent education personalized services. He focuses on PSO algorithm and its work in intelligent education recommendation and learning path planning. Experiments show that the average value of the difference between the two obtained by the NBPSO algorithm is 1.13E + 02 and the variance 1.88E + 02 is the smallest. Therefore, PSO aids in improving the quality and consistency of online course resource development. In conclusion, the research results of this paper further demonstrate the advantages of PSO algorithm in solving the problem of personalized service in intelligent education. It can promote the in-depth application of swarm intelligence optimization algorithms in intelligent online learning systems. This effectively enhances the intelligent service level of the online learning system and increases the efficiency of online learning.

Stochastic optimization for the scheduling of a grid-connected microgrid with a hybrid energy storage system considering multiple uncertainties

The deployment of a microgrid with renewable energy sources (RESs) generally considers two aspects i.e., the need for the energy storage and the presence of many uncertainties due to the intermittent nature of several RESs and the load demand variability. The latter justifies the use of stochastic optimization for the scheduling purpose. Therefore, this paper aims to investigate the optimal stochastic scheduling and evaluate the expected performance of a microgrid in grid-connected mode with a hybrid energy storage system consisting of a battery and a supercapacitor. The proposed optimization approach is formulated as a stochastic mixed-integer linear programming (MILP) problem and applied to a modified ORNL-DECC microgrid test system. The system uncertainties are associated with wind power, solar power, and load demand, which are represented by Gaussian distributed scenarios with standard deviations of 10%, 5%, and 3%, respectively. To investigate the effect of supercapacitor addition on the scheduling stochastic performance, the power rating of supercapacitor is varied between 0 and 20 kW. The analysis is performed based on the results of scheduling using the deterministic and the stochastic optimization schemes. In the deterministic scheme, the addition of supercapacitor is reviewed based on the achieved total cost. In the stochastic optimization scheme, we use the expected value of perfect information (EVPI) to observe the stochastic performance in addition to the expected total cost. The results are beneficial when assessing the advantage and disadvantage of supercapacitor deployment in a microgrid scheduling.

A Multiobjective Stochastic Optimization Scheme for the Problem of Chemical Production for Sugarcane Companies


 
 
 
 This paper presents a multiobjective optimization stochastic scheme for production planning for sugarcane companies under uncertainty. The proposed approach considers three stages. The first stage comprises the mass and energy balances for determining process flows. The second stage considers the formulation of a Multiobjective Deterministic Model (MODM) by considering two objective functions: maximizing the gross margin and minimizing the environmental impact. The MODM is given by different production plans that respond differently to the parameters’ variability under uncertainty. Finally, the last stage considers stochastic elements (i.e., product prices, demands, and costs) within the deterministic scheme to obtain a Multiobjective Stochastic Model (MOSM). A case study’s computational results based on the Colombian sugarcane industry show the proposed scheme’s effectiveness. Results include the investment strategy for optimal production planning with an analysis of the parameters’ uncertainty on the economic performance of the planning production configurations.
 
 
 

Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach

Compartmental pandemic models have become a significant tool in the battle against disease outbreaks. Despite this, pandemic models sometimes require extensive modification to accurately reflect the actual epidemic condition. The Susceptible-Infectious-Removed (SIR) model, in particular, contains two primary parameters: the infectious rate parameter ß and the removal rate parameter y, in addition to additional unknowns such as the initial infectious population. Adding to the complexity, there is an obvious challenge to track the evolution of these parameters, especially ß and y, over time which leads to the estimation of the reproduction number for the particular time window, R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> . This reproduction number may provide better understanding on the effectiveness of isolation or control measures. The changing RT values (evolving over time window) will lead to even more possible parameter scenarios. Given the present Coronavirus Disease 2019 (COVID-19) pandemic, a stochastic optimization strategy is proposed to fit the model on the basis of parameter changes over time. Solutions are encoded to reflect the changing parameters of ß <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</inf> and γt, allowing the changing RT to be estimated. In our approach, an Adaptive Differential Evolution (ADE) and Particle Swarm Optimization (PSO) are used to fit the curves into previously recorded data. ADE eliminates the need to tune the parameters of the Differential Evolution (DE) to balance the exploitation and exploration in the solution space. Results show that the proposed optimized model can generally fit the curves well albeit high variance in the solutions.