Modified Differential Evolution Algorithm Research Articles

Assessment of Femoral Head Sphericity Using Coordinate Data through Modified Differential Evolution Approach

Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is applied to assess the form error. Since the traditional least-squares approach is susceptible to overestimation, it leads to unreasonable rejections. This paper implements a modified differential evolution (DE) algorithm to estimate the minimum zone femoral head sphericity. In this algorithm, opposition-based learning is considered for population initialization, and an adaptive scheme is enacted for scaling factor and crossover probability. The coefficients of the correlation factor and the uncertainty propagation are also measured so that the result’s uncertainty can be determined. Undoubtedly, the credibility and plausibility of inspection outcomes are strengthened by evaluating measurement uncertainty. Several data sets are used to corroborate the outcome of the DE algorithm. CMM validation shows that the modified DE algorithm can measure sphericity with high precision and consistency. This algorithm allows for an adequate initial solution and adaptability to address a wide range of industrial problems. It ensures a proper balance between exploitation and exploration capabilities. Thus, the suggested methodology, based on the computational results, is feasible for the online deployment of the sphericity evaluation. The adopted DE strategy is simple to use, has few controlling variables, and is computationally less expensive. It guarantees a robust solution and can be used to compute different form errors.

Innovative integrated workflow for data-driven production forecasting and well completion optimization: A Montney Formation case study

With the use of advanced data analytics and machine learning (ML) techniques, the oil and gas industry has transformed significantly in recent years. These innovations have opened new opportunities in reservoir engineering, allowing engineers to leverage data for better decision-making and well completion optimization. A key challenge in hydrocarbon exploration and production is forecasting gas production rates from unconventional sources. This is a crucial factor that affects how resources are allocated and decisions are made, requiring the application of novel techniques to enhance hydrocarbon production. Here, a novel and comprehensive automated workflow is introduced covering data collection, data preparation, feature selection, ML model development, and operational parameter optimization. The workflow uses various ML and optimization methods, including a modified Differential Evolution (MDE) algorithm, to improve gas production forecasting and optimize well completion parameters. We applied the proposed workflow to 3144 horizontal gas wells in the Montney Formation, British Columbia (BC), Canada, to assess its performance. The results showed the advantages of incorporating the initial 24 months of cumulative gas production data alongside well and completion data. Also, following the fine-tuning of hyperparameters for the ML algorithms, we identified the most effective model for forecasting cumulative gas production within the Montney Formation as a two-layer Artificial Neural Network (ANN) model. Moreover, using the MDE algorithm, the optimization results revealed the possibility of increasing gas production by more than 10% for about 47% of the wells. This research makes a significant contribution to the field of unconventional gas exploration by introducing an automated workflow that simplifies data processing, model development, and decision-making processes. It also offers valuable insights for optimizing unconventional gas production in the Montney Formation and similar reservoirs, as the energy industry moves towards more sustainable and efficient practices.

Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure

This article aims to improve the synthesis efficiency and radiation performance of large ultra-wideband (UWB) rotationally symmetric sparse circular planar arrays by using a modified differential evolution algorithm (MDEA). In the proposed MDEA, we adopt a new encoding mechanism in which an individual represents an element position expressed in polar coordinates. Importantly, such an encoding mechanism can facilitate the multiplication calculation for the array factor in the individual being updated while making it easier to meet the given minimum element spacing constraint. Moreover, to cater to the new encoding mechanism, some low-dimensional evolution operators are introduced to avoid the prematurity. In particular, the UWB rotationally symmetric sparse planar array synthesis problem is transformed into the sidelobe suppression problem of the array pattern at the highest frequency under the given array aperture, and the minimum spacing constraints is used to guarantee enough space to place physical UWB antenna elements. Two synthesis examples of UWB sparse planar arrays based on rotationally symmetric structures are presented. The results show that the peak sidelobe level (PSL) obtained by the proposed MDEA is significantly lower than the results obtained by some existing algorithms in an acceptable CPU time, which proves the effectiveness and superiority of the proposed MDEA.

Frequency Management of an Interconnected Power System using Modified Differential Evolution Algorithm

Frequency Management of an Interconnected Power System using Modified Differential Evolution Algorithm

Reactive power management by using a modified differential evolution algorithm

AbstractIn this article, a modified differential evolution (MDE) algorithm is proposed and applied to provide the solution for reactive power management by incorporating the flexible alternating current transmission systems (FACTS) controllers. The proper siting of FACTS controller has been achieved with an objective to minimize the losses and to improve the loading capability. The power flow analysis is performed to determine the optimal position for FACTS controllers. These controllers are incorporated in the most heavily loaded lines and hence controls the power flow in that particular line and allow more power to be transmitted in the remaining lines. The proposed MDE algorithm uses a novel DE/best3/1/bin mutation operator to produce three temporary mutant vectors which are averaged to obtain the mutant vector. Hence, the decision vectors of a generation simultaneously move toward the three best decision vectors of the population thereby maintains a better trade between exploration and exploitation. The proposed MDE algorithm is applied on different standard test bus (i.e., IEEE30, IEEE57, and IEEE118) systems with varying active and reactive loading (i.e., 100%, 110%, and 120%). The proposed method's performance is compared to those obtained from some well‐known meta‐heuristic algorithms. The proposed MDE algorithm optimized FACTS controllers reduce transmission loss by 60.90% in IEEE30 bus, 49.72% in IEEE57 bus and 8.37% in IEEE118 bus test system under base loading. The statistical analysis of the obtained results is carried out using the Wilcoxon signed rank test and the Friedman and Nemenyi hypothesis test, which ensures the reliability and robustness of the proposed method.

Implementation of Modified Differential Evolution Algorithm for Hybrid Renewable Energy System

A hybrid renewable energy system, which could provide a reliable energy alternative for conventional Battery systems is implemented in this paper. The primary requirement is that the hybrid energy system should be cost-effective while meeting the energy demand. The hybrid system is implemented to a area located in Uttarakhand, India using solar photovoltaic cells to supply power during hot and humid conditions and using wind turbine generators to supply power during windy conditions. The wind turbine generators and photovoltaic cells are used in a combined manner along with the diesel generators as in case if it fails to meet the demand. In order to meet the requirements, modified Differential Evolution (DE) Algorithm is being implemented. Moreover, the effectiveness of the performance is evaluated by comparing the results obtained from modified DE with other optimization algorithms. In comparison with other optimization algorithms, results indicate that the implementation of the modified DE algorithm helps in obtaining the best cost effective solution for the system along with meeting the energy demand.

Design and Optimization of a Vibrating Ring Gyroscope With High Shock Resistance by Differential Evolution

In this paper, a mode order optimized vibrating ring gyroscope (VRG) with high shock resistance is designed, and the improved optimization algorithm is proposed to optimize the structure design. The mode order of n=2 mode of the proposed VRG can be the first by structure design, which helps to enhance the anti-shock ability by increasing the translational mode frequency and avoid the excessive large n=2 mode frequency at the same time. The optimization method based on the differential evolution (DE) algorithm is developed to maximize the anti-shock ability of the VRG. At first, the shock response of VRG is analyzed. After representing the working principle and specific design of the designed VRG, the effect of the structural parameter of VRG on mode orders and frequencies of the n=2 mode and the translational mode as well as the shock response is simulated and analyzed. Finally, the structural design of VRG is transformed into a constrained optimization problem, and a modified DE algorithm integrated with the infeasible solution handling mechanism and the diversity enhancement strategy is applied to find feasible optimized structural parameters to maximize the shock resistance. The displacement and stress of optimized VRG structures under 10,000 g shock are small, which indicates the validity of the improved DE algorithm. Overall, the structure design and the optimization method in this paper can be a reference for other micromachined structure designs.

A systematic identification approach for biaxial piezoelectric stage with coupled Duhem-type hysteresis

PurposeThe problem of parameter identification for biaxial piezoelectric stages is still a challenging task because of the existing hysteresis, dynamics and cross-axis coupling. This study aims to find an accurate and systematic approach to tackle this problem.Design/methodology/approachFirst, a dual-input and dual-output (DIDO) model with Duhem-type hysteresis is proposed to depict the dynamic behavior of the biaxial piezoelectric stage. Then, a systematic identification approach based on a modified differential evolution (DE) algorithm is proposed to identify the unknown parameters of the Duhem-type DIDO model for a biaxial piezostage. The randomness and parallelism of the modified DE algorithm guarantee its high efficiency.FindingsThe experimental results show that the characteristics of the biaxial piezoelectric stage can be identified with adequate accuracy based on the input–output data, and the peak-valley errors account for 2.8% of the full range in the X direction and 1.5% in the Y direction. The attained results validated the correctness and effectiveness of the presented identification method.Originality/valueThe classical DE algorithm has many adjustment parameters, which increases the inconvenience and difficulty of using in practice. The parameter identification of Duhem-type DIDO piezoelectric model is rarely studied in detail and its successful application based on DE algorithm on a biaxial piezostage is hitherto unexplored. To close this gap, this work proposed a modified DE-based systematic identification approach. It not only can identify this complicated model with more parameters, but also has little tuning parameters and thus is easy to use.

Modified Differential Evolution Algorithm for Time-Modulated Linear Array Antenna

A modified differential evolution (MDE) algorithm based on a novel mutation strategy and adaptive adjustment strategy of parameter crossover rate (CR) is proposed to improve the population diversity and to avoid frapping in local optima. Also the simplified quadratic interpolation is employed to accelerate the convergence rate. Benchmark functions have been provided to verify the MDE algorithm. Compared with other improved evolutionary algorithms, experiment results reveal that the MDE has a promising performance in the convergence rate and the exploration ability. Finally, the proposed algorithm is proved to realize accelerating the optimization of time-modulated arrays (TMA).

Auto-Tuning Parameters of Fractional PID Controller Design for Air-Conditioning Fan Coil Unit

The traditional integer order PID controller manipulates the air-conditioning fan coil unit (FCU) that offers cooling and heating loads to each air-conditioning room in summer and winter, respectively. In order to maintain a steady indoor temperature in summer and winter, the control quality cannot meet the related requirements of air-conditioning automation, such as large overshoot, large steady state error, long regulating time, etc. In view of these factors, this paper develops a fractional order PID controller to deal with such problem associated with FCU. Then, by varying mutation factor and crossover rate of basic differential evolution algorithm adaptively, a modified differential evolution algorithm (MDEA) is designed to tune the satisfactory values of five parameters of indoor temperature fractional order PID controller. This fractional order PID control system is configured and the corresponding numerical simulation is conducted by means of MATLAB software. The results indicate that the proposed fractional order PID control system and MDEA are reliable and the related control performance indexes meet with the related requirements of comfortable air-conditioning design and control criteria.

Modified differential evolution and heuristic algorithms for dump tippler machine allocation in a typical sugar mill in Thailand

This paper focuses on a computational tool for scheduling and sequencing sugarcane vehicles for dump tippler machines at the mill yard of a sugar mill, which can be represented as an NP-hard problem for parallel capacitated machines with machine restrictions, job grouping, and sequencing independent setup time. This research aims to determine the optimal sequencing of jobs, i.e. minimizing the makespan by considering machine restrictions, capacitated machines, group size, number of jobs, and the constraints of the sugar mill. In the considered problem machines alternatively operate, that distinguishes it from a general parallel machine problem. The mixed integer linear programing model is developed for solving the small-scale problem instances. Large-scale instances are handled by four heuristics, and four differential evolution (DE) metaheuristics. In order to improve the computational results, solution quality and computation time were considered. In addition, modified DE algorithms were used in encoding operation (initial solution), mutation and local search operation. The computational results revealed that the modified DE algorithms had higher relative improvement on the makespan. Furthermore, this decision-making support tool was implemented as a prototype in the sector of cane and sugar industry in Thailand and extended to other similar industries.

Optimization of Dynamic Systems: A Comparative Study of Two Modified Differential Evolution Algorithms

Differential Evolution (DE) is a novel, efficient, effective and robust evolutionary optimization technique. DE algorithm is gaining popularity for solving complex optimization problems encountered in many engineering disciplines. This paper deals with the application and performance evaluation of two modified versions of DE [named as Modified Differential Evolution (MDE) and Trigonometric Differential Evolution (TDE)]. Three algorithms have been used for solving five dynamic optimization problems encountered in chemical engineering. Results indicate that MDE algorithm outperformed DE and TDE algorithms for solving problems with small number of control stages. But TDE algorithm is found to be faster and efficient than MDE and DE algorithms particularly for problems involving large number of control stages.

Techno-economic assessment of consumers' participation in the demand response program for optimal day-ahead scheduling of virtual power plants

In this paper, the consumers' participation in the demand response program for virtual power plant (VPP) is proposed. A proposed price-based scheduling strategy for optimal day-ahead scheduling of VPP is investigated to maximize the profit of the VPP composed of a set of distributed generation, dispatchable load, and wind turbines. For solving the optimal scheduling problem, a modified differential evolution algorithm (MDEA) is proposed. To achieve the work target, 33-kV, 18-bus test system is selected as a test system. The proposed algorithm leads to effective scheduling of VPP resources, especially for reserve power. To investigate the proposed methodology, the load is increased and the scheduling of VPP is investigated at the best and worst boundaries of VPP resources uncertainty. The best case happens at maximum load, high prices and maximum energy from renewables, while the worst scenario occurs at minimum load, low prices and minimum energy from renewables. In addition, the algorithm ensures the importance of VPP in playing a dual role as a demand/generation unit from the perspective of the upstream network in some time periods and highlights the vital effect of dispatchable loads on the management process at different conditions of the dispatchable load.

Modified Differential Evolution Algorithm for a Transportation Software Application

This research developed a solution approach that is a combination of a web application and the modified differential evolution (MDE) algorithm, aimed at solving a real-time transportation problem. A case study involving an inbound transportation problem in a company that has to plan the direct shipping of a finished product to be collected at the depot where the vehicles are located is presented. In the newly designed transportation plan, a vehicle will go to pick up the raw material required by a certain production plant from the supplier to deliver to the production plant in a manner that aims to reduce the transportation costs for the whole system. The reoptimized routing is executed when new information is found. The information that is updated is obtained from the web application and the reoptimization process is executed using the MDE algorithm developed to provide the solution to the problem. Generally, the original DE comprises of four steps: (1) randomly building the initial set of the solution, (2) executing the mutation process, (3) executing the recombination process, and (4) executing the selection process. Originally, for the selection process in DE, the algorithm accepted only the better solution, but in this paper, four new selection formulas are presented that can accept a solution that is worse than the current best solution. The formula is used to increase the possibility of escaping from the local optimal solution. The computational results show that the MDE outperformed the original DE in all tested instances. The benefit of using real-time decision-making is that it can increase the company’s profit by 5.90% to 6.42%.

Antenna Array Pattern Nulling by Phase Perturbations using Modified Differential Evolution Algorithm

Antenna Array Pattern Nulling by Phase Perturbations using Modified Differential Evolution Algorithm

Modified differential evolution algorithms for multi-vehicle allocation and route optimization for employee transportation

ABSTRACTThis research aims to develop decision making on how to provide employees with a transportation service that is fast, cost effective and timely. This work is different from previous research in that it integrates the bus stop determination, bus assignment and the bus route design sub-problems of an employee transportation service for a large-scale company. The objective of this article is to minimize total travelling costs and the total rental costs of the heterogeneous fleet capacitated vehicles. A mathematical model is applied to solve for small-size problems. Additionally, for large-size problems, five modified differential evolution (MDE) algorithms are developed to solve the three sub-problems simultaneously. New rules used in the mutation process of the MDE algorithms and an advanced design of the encoding and decoding method are presented in this article. The results demonstrate that the MDE is an efficient transportation management system for any organization.

Forward and inverse nonlinear heat transfer analysis for optimization of a constructal T-shape fin under dry and wet conditions

This work deals with direct and inverse analysis of T-shaped dry and wet fins. Direct analysis is done to study heat transfer performance, whereas inverse analysis is performed to simultaneously estimate five optimum geometric parameters satisfying a prescribed fin volume. The modified differential evolution (MDE) search algorithm is used to explore the required geometrical parameters pertaining to the stem and the flange parts of the fin. In the present MDE, the mutant is generated using five distinct vectors instead of three as conventionally practiced. Due to the existence of multiple solutions, the selection criterion is based upon the fulfilment of different performance parameters. These involve individual maximization of heat transfer rate, fin efficiency and fin effectiveness. Since the application of the differential transformation method (DTM) is not yet demonstrated for nonlinear heat transfer analysis of T-shaped wet fins, thus, for generating the heat transfer parameters using the inversely estimated geometric parameters, a forward approach based on the DTM is used here. Parametric variations along with necessary validations of the direct method are presented. Furthermore, a comparison of the present MDE search-based inverse algorithm is done with a classical gradient-based optimization technique. It can be highlighted from the present study that only when at-least three geometrical parameters are known, then the classical method successfully yields heat transfer performance parameters comparable with the MDE algorithm. From the optimization study, it is found that a particular value of fin performance (heat transfer rate, efficiency, effectiveness) can be acquired with various values of surface area and even at a given surface area, different fin performances can be obtained. However, a single and distinct operating point is revealed where the performance index of the fin is maximized. For ensuring maximum possible performance from constructal T-shape wet fins, it is recommended that for the present type of problem, the present stochastic optimization method such as MDE must be used where the classical deterministic methods suffer from inherent limitations on multi-variables optimization.

Solving a Special Case of the Generalized Assignment Problem Using the Modified Differential Evolution Algorithms: A Case Study in Sugarcane Harvesting

We proposed and created a methodology to solve a real-world problem, which is a special case of the generalized assignment problem. The problem consists of assigning drivers to harvesters, which will then be assigned to harvest sugarcane in order to maximize daily profit. A set of drivers have various levels of experience. Therefore, a different capability to harvest sugarcane leads to a range of daily wages. Each harvester has different operating years and engine size, which affects its fuel consumption rate and capacity to harvest sugarcane, respectively. Assigning a worker to a harvester can improve the fuel consumption and efficiency of the harvester. We developed a mathematical model to reflect this problem and to solve it to find the maximum outcome using Lingo v.11 commercial optimization software. Since Lingo v.11 is limited to solving only small-size test instances, for medium to large test instances, four modified differential evolution (MDE) algorithms were used to solve the problem: MDE-1, MDE-2, MDE-3, and MDE-4. MDE-2 was found to be the best proposed heuristics because it has intensification and diversification ability. MDE has been tested with the case study. We tried to increase the daily profit by implementing three strategies: (1) change all harvesters that are more than five years old, (2) train drivers to reach maximum capacity, and (3) a combination of 1 and 2. Each strategy has a different investment. The breakeven point (number of days) to return the investment was calculated from the increase of daily profit. The computational results show that strategy 2 is the best because it has the quickest rate of investment return rate. However, this strategy has a disadvantage, since it is possible that drivers may leave the company if they have been highly trained. Moreover, strategy 1 has an acceptable break-even point at 392 days.

Fog Computing for Internet of Things (IoT)-Aided Smart Grid Architectures

The fast-paced development of power systems necessitates the smart grid (SG) to facilitate real-time control and monitoring with bidirectional communication and electricity flows. In order to meet the computational requirements for SG applications, cloud computing (CC) provides flexible resources and services shared in network, parallel processing, and omnipresent access. Even though CC model is considered to be efficient for SG, it fails to guarantee the Quality-of-Experience (QoE) requirements for the SG services, viz. latency, bandwidth, energy consumption, and network cost. Fog Computing (FC) extends CC by deploying localized computing and processing facilities into the edge of the network, offering location-awareness, low latency, and latency-sensitive analytics for mission critical requirements of SG applications. By deploying localized computing facilities at the premise of users, it pre-stores the cloud data and distributes to SG users with fast-rate local connections. In this paper, we first examine the current state of cloud based SG architectures and highlight the motivation(s) for adopting FC as a technology enabler for real-time SG analytics. We also present a three layer FC-based SG architecture, characterizing its features towards integrating massive number of Internet of Things (IoT) devices into future SG. We then propose a cost optimization model for FC that jointly investigates data consumer association, workload distribution, virtual machine placement and Quality-of-Service (QoS) constraints. The formulated model is a Mixed-Integer Nonlinear Programming (MINLP) problem which is solved using Modified Differential Evolution (MDE) algorithm. We evaluate the proposed framework on real world parameters and show that for a network with approximately 50% time critical applications, the overall service latency for FC is nearly half to that of cloud paradigm. We also observed that the FC lowers the aggregated power consumption of the generic CC model by more than 44%.

Optimal planning of energy storage system using modified differential evolution algorithm

In smart distribution network, optimal planning of Energy Storage Systems (ESS) can lead to voltage profile improvement, network loss reduction and increasing the profit of distribution company (DISCO). This paper proposes the application of Modified Differential Evolution Algorithm (MDEA) which is very strong global search capability for maximizing the DISCO profit over the planning. The objective function is the difference between the benefit which is the energy arbitrage in a deregulated market and the costs which are investment cost, operation and maintenance cost. The implementation of MDEA is performed on a 30-bus radial distribution network. The simulation results demonstrate that the proposed MDEA application significantly increases the profit without any violation of network constraints.