Differential Evolution For Multi-objective Optimization Research Articles

Decomposition–based multi-objective differential evolution for extractive multi-document automatic text summarization

The central challenge in Automatic Text Summarization (ATS) involves efficiently generating machine-generated text summaries through optimization algorithms. An ATS is a critical component for systems dealing with textual information processing. However, the current approach faces a significant hurdle due to the computational intensity of the process, particularly when employing complex optimization techniques like swarm intelligence optimization alongside a costly ATS repair operator. While the current approach yields impressive Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metrics for the generated summary, it struggles with inefficiencies, mainly attributed to the substantial optimization time consumed by the ATS repair operator scheme. In order to address this, a novel solution called Decomposition-based Multi-Objective Differential Evolution (MODE/D) is proposed. It is built upon the foundation of Differential Evolution for Multi-Objective Optimization (DEMO) and the weighted sum method (WS), coupled with an innovative ATS repair operator scheme. Through experimentation on Document Understanding Conferences (DUC) datasets, the novel approach of MODE/D – WS is validated by evaluating the results using ROUGE metrics. The outcomes are twofold: a remarkable reduction in serial execution time and a noteworthy enhancement over existing techniques in the scholarly domain, as evidenced by improved ROUGE-1, ROUGE-2, and ROUGE-L scores.

Multi-objective topology optimization design of truss structures based on evidence theory under limited information

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.

Optimization of hyperthermia process applied to cancer treatment using multi-objective optimization differential evolution

Due to the number of cancer cases diagnosed each year and the fatality rate resulting from some more severe types, the improvement of less invasive and more efficient treatment techniques is of great importance. In this context, hyperthermia is a medical procedure in which the tumor region is heated by using an applicator for a certain period, aiming to destroy pathological cells. Computational models can be used to simulate the heating effect of tumors and adjacent cells. In general, the solution to an optimization problem considering factors such as heating temperature, applicator position, and the time in which the region will be subjected to heating can provide important information about the procedure. Traditionally, this type of problem has been addressed in a single objective context, focusing on minimizing the destruction of adjacent healthy tissue considering the area of the applicator constant. Our fundamental objective is to propose a multi-objective design problem considering the minimization of the area subject to the procedure and the time required for the process of hyperthermia in a breast cancer treatment. The problem is constrained by the degree of tissue destruction and by a partial differential equation that describes the phenomenon of heat transfer in both healthy and tumor tissues. The results obtained demonstrate that a point with a good compromise between the objectives can be chosen in such a way that a particular strategy can be defined for each patient.

Multi-objective optimization of frequency and damping of vertical stabilizer skin structure placed with variable-angle tows

The vibration characteristics of composite vertical stabilizer skin structures play a critical role in damping effects designed for overcoming the air disturbances experienced by aircraft structural components during flight. The first-order fundamental frequencies and their corresponding damping characteristics of the vertical stabilizer skin structure tow-steered by automatic fiber placement technique were optimized with the parameterized trajectories and plies as design variables. Firstly, the vibration and damping numerical models were derived based on Kirchhoff laminate theory, the Rayleigh-Ritz method, and the Strain Energy Method. Then the optimization model was developed by adopting the self-adaptive Differential Evolution Multi-objective optimization algorithm and incorporating the solution method of Pareto Front. The constraints of this optimization model considered the experimentally obtained minimum turning radius of prepregs tow-steered in automatic fiber placement process obtained from experimental tests. Finally, the comparison of numerical simulation results was conducted for the optimized trajectories and the conventional straight trajectories under various boundary conditions, and the numerical results were partially validated through damping and frequency tests. The results indicate the vibration characteristics of the composite vertical stabilizer skin structure can be enhanced to a large extent by optimizing fiber trajectories, and the enhancement percentage is affected by the boundary conditions of the actual structure.

Economic-effectiveness analysis of micro-fins helically coiled tube heat exchanger and optimization based on multi-objective differential evolution algorithm

In this study, the heat transfer characteristics and hydrodynamics of a new type of micro-fin helically coiled tube (MF-HCT) are modelled and compared with those of typical smooth helically coiled tubes (HCTs). Calculation models are developed and compared for both helically coiled tube heat exchangers (HCTHEXs) and micro-fin helically coiled tube heat exchangers (MF-HCTHEXs). The total cost and effectiveness are selected as the objective functions, and five independent structural parameters are selected for each type of HCTHEX. Subsequently, an adaptive multi-objective optimization differential evolution algorithm is implemented for both of them, and the results are compared. The results indicate that, for Reynolds numbers smaller than 22,000, the MF-HCT performs better than the HCT, and the total cost of the MF-HCTHEX is lower than that of the HCTHEX under the same effectiveness. The difference between their total cost increases with their effectiveness and can be up to 79,000 €. For both the HCTHEX and MF-HCTHEX, when the effectiveness is less than 0.9, it is more appropriate to select a larger winding angle, layer spacing, and tube spacing.

Application of Intelligent Optimization Techniques to Spectral and Energy Efficiencies in Massive MIMO Systems at Different Circuit Power Levels

In cellular communications, whose usage continues to increase day by day, it is seen as a necessity to increase the area throughput in order to avoid data traffic density problems. For this, it is aimed to increase spectral efficiency by using massive multi-input multi-output systems and also to keep energy efficiency high. It is known that spectral and energy efficiencies can increase with different number of user equipments served in the cell, number of active antennas and values of the transmission power. By using intelligent optimization techniques, optimum combinations of these three variables can be determined and samples with both high spectral and energy efficiencies at the same time can be obtained. In this paper, multi-objective genetic algorithm, multi-objective particle swarm optimization and multi-objective differential evolution algorithm are applied on three different circuit power sets and then results obtained are evaluated.

A Comprehensive Assessment of Large-scale Battery Integrated Hybrid Renewable Energy System to Improve Sustainability of a Smart City

ABSTRACT Hybrid renewable energy systems (HRES) must be leveraged to an extent that curtailment of fossil fuel does not hinder economic growth. However, owing to their intermittency, HRES must be supported with energy storage systems (ESS) that are quite expensive. Hence, optimal sizing of such systems is advisable to improve utilization and efficiency. In this paper, a comprehensive assessment and optimal sizing of HRES, consisting of floating and rooftop solar energy, wind energy systems, and battery-energy storage system (BESS) is presented and evaluated for a smart city, Visakhapatnam, India. Open-source tools such as web-based Bhuvan GIS, the polygon tool in Google Earth and Sketch Up are used identify the potential areas and for a realistic assessment of these renewable energy technologies. It is estimated that the proposed location has a potential of 105 MW of floating solar with 20% utilization of water bodies, 260 MW of rooftop bifacial PV system with an assumed acceptance rate of 5%. In addition, 62 MW of wind energy is estimated over shorelines and hilltops. With the upper limits of HRES, various multi-objective optimization techniques, differential evolution, mutation-based PSO, Quantum-behaved PSO, and mutation-based QPSO, are applied to minimize reliability indices like Levelized cost of energy (LCoE), loss of power supply probability (LPSP), and Life Cycle Emissions (LCE). Sensitivity analysis is performed to assess the impact of techno-economic changes, such as load appreciation, damage to batteries, and price changes. The results show that the proposed hybrid structure helps in combating carbon emissions with LPSP in acceptable limits of 0.285% to 0.3% while LCoE is in between 0.9 $/kW and 0.11 $/kW.

Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment

Background and objectiveFor decades, mathematical models have been used to predict the behavior of physical and biological systems, as well as to define strategies aiming at the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of the novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the objective is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. Two optimal control problems (mono- and multi-objective) to determine a strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment. MethodsAn inverse problem is formulated and solved in order to determine the parameters of the compartmental Susceptible-Infectious-Removed model. The solutions for both optimal control problems proposed are obtained by using Differential Evolution and Multi-objective Optimization Differential Evolution algorithms. ResultsA comparative analysis on the influence related to the inclusion of a control strategy in the population subject to the epidemic is carried out, in terms of the compartmental model and its control parameters. The results regarding the proposed optimal control problems provide information from which an optimal strategy for vaccine administration can be defined. ConclusionsThe solution of the optimal control problem can provide information about the effect of vaccination of a population in the face of an epidemic, as well as essential elements for decision making in the economic and governmental spheres.

Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.

Optimal Sizing of Standalone Photovoltaic System Using Improved Performance Model and Optimization Algorithm

A standalone photovoltaic system mainly consists of photovoltaic panels and battery bank. The use of such systems is restricted mainly due to their high initial costs. This problem is alleviated by optimal sizing as it results in reliable and cost-effective systems. However, optimal sizing is a complex task. Artificial intelligence (AI) has been shown to be effective in PV system sizing. This paper presents an AI-based standalone PV system sizing method. Differential evolution multi-objective optimization is used to find the optimal balance between system’s reliability and cost. Two objective functions are minimized, the loss of load probability and the life cycle cost. A numerical algorithm is used as a benchmark for the proposed method’s speed and accuracy. Results indicate that the AI algorithm can be successfully used in standalone PV systems sizing. The proposed method was roughly 27 times faster than the numerical method. Due to AI algorithm’s random nature, the proposed method resulted in the exact optimal solution in 6 out of 12 runs. Near-optimal solutions were found in the other six runs. Nevertheless, the nearly optimal solutions did not introduce major departure from optimal system performance, indicating that the results of the proposed method are practically optimal at worst.

Design of high performance thickener hydrocyclones using robust optimization

In the literature, a large number of works about the hydrocyclones geometry optimization to obtain high performance separators can be found. However, in these works, during the optimization process, no uncertainties in model, design variables and/or parameters are considered. In these cases, a small variation in the design variable vector can result in a meaningful change on the theoretical optimal design as represented by the minimization of the corresponding vector of objective functions. In this contribution, the Effective Mean Concept is associated with the Multi-Objective Optimization Differential Evolution to obtain solutions less sensitive to perturbations in the design variables during the thickener hydrocyclones design. For this purpose, the proposed multi-objective optimization problem considers the determination of geometric variables to maximize hydrocyclone's total efficiency (η), to minimize the underflow-to-throughput ratio (RL) and to minimize the Euler number (Eu). The robust results are compared with those obtained considering nominal context (without robustness). The results showed that the tested hydrocyclones present good thickener equipment and that the robust Pareto's curve presents less diversity in comparison with the nominal solution.

Design, Optimization, and Analysis of Supersonic Radial Turbines

Abstract New compact engine architectures such as pressure gain combustion require ad hoc turbomachinery to ensure an adequate range of operation with high performance. A critical factor for supersonic turbines is to ensure the starting of the flow passages, which limits the flow turning and airfoil thickness. Radial outflow turbines inherently increase the cross section along the flow path, which holds great potential for high turning of supersonic flow with a low stage number and guarantees a compact design. First, the preliminary design space is described. Afterward a differential evolution multi-objective optimization with 12 geometrical design parameters is deducted. With the design tool autoblade 10.1, 768 geometries were generated and hub, shroud, and blade camber line were designed by means of Bezier curves. Outlet radius, passage height, and axial location of the outlet were design variables as well. Structured meshes with around 3.7 × 106 cells per passage were generated. Steady three-dimensional (3D) Reynolds-averaged Navier–Stokes (RANS) simulations, enclosed by the k-omega shear stress transport turbulence model were solved by the commercial solver CFD++. The geometry was optimized toward low entropy and high-power output. To prove the functionality of the new turbine concept and optimization, a full wheel unsteady RANS simulation of the optimized geometry exposed to a nozzled rotating detonation combustor (RDC) has been performed and the advantageous flow patterns of the optimization were also observed during transient operation.

Optimization Control for Flapping Load Mitigation and Output Power Levelling of Wind Turbine

Fatigue load affects the secure and stability of wind turbine operation. Flapping load is the main source of fatigue load endured by wind turbine operating above the rated wind speed. In this paper, a novel optimization control method for wind turbine flapping load mitigation and output power leveling is proposed. At first, wind turbine flapping load is analyzed and its calculation model is presented. Secondly, principle of the proposed control method is presented. Considering on coupling between flapping load and output power, a multi-objective optimization model and differential evolution based flapping load optimization controller are then designed. Additional PID-based output power leveling controller is employed to keep the output power leveling around the rated power. Finally, the effectiveness of the proposed control method is demonstrated by NREL 5MW wind turbine simulations.

Study on the Three Gorges reservoir flood control operation chart considering comprehensive utilization requirements

This paper constructs a multi-objective flood forecasting optimization operation model based on inflow forecasting information considering flood control, power generation, and navigation. The optimization-simulation-test algorithm and modified differential evolution for multi-objective optimization (DEMO) were used. Some non-dominated solutions were derived from optimization of the inflow data of 126 years (1882-2007) and test by 1000-year design floods. The solutions were distributed uniformly and the algorithm was efficient. The flood during August 2009 was also used to test the selected solution. The results show that the optimal schemes can generate extra hydropower energy, and save great flood water resources. The navigation days for all types of ships are also increased greatly. To maximize comprehensive utilization benefits on the premise of flood control safety, the traditional design flood routing method is well combined with the optimization method by reservoir operation chart for flood control based on inflow forecasting, which provides a new way for reservoir flood control operation by considering the comprehensive utilization benefits.

Domestic load management based on integration of MODE and AHP-TOPSIS decision making methods

The increasing in energy demand leads to wide range of blackout crises around the worldwide. Load management is represented as one of the most important solutions to balance the energy demand with the available generation resource. Dynamic and adaptive method is required to sort all multi-objective sets of optimal solutions of customer load scheduling. A multi-objective optimization differential evolution (MODE) algorithm in this paper is used to obtain a set of optimal customer load management by minimizing the energy cost and customer’s inconvenience simultaneously. The obtained optimal set of solutions are sorted from the best to the worst using multi-criteria decision making (MCDM) methods. An integration of analytic hierarchy process (AHP) and technique for order preferences by similarity to ideal solution (TOPSIS) are used as MCDM methods. The effect of different time slots on the given optimal solutions are addressed for real customer’s data of a typical household. Results of simulation indicate that the proposed method manages to realize energy cost saving of 44%, 44% and 32% for 1, 5 and 10 min time slots, respectively. Moreover, the peak load savings are 42%, 31% and 41% for 1, 5 and 10 min time slots, respectively. Furthermore, the results are validated by other approaches presented earlier in literature to support the findings of the proposed method. The proposed method provides superior saving for energy cost and peak consumption as well as maintains an acceptable range of customer inconvenience.

Improvement of Differential Evolution Multiobjective Optimization Algorithm Based on Decomposition

Multi-objective optimization problem (MOP) is a challenging field of scientific research in real-life. The effective way to solve multi-objective optimization problems is Multi-objective Evolutionary Algorithm (MOEA). In this paper, enhancements to a Multi-objective Evolutionary algorithm MOEA/D-DE are proposed. The proposed improvement points help to improve both population distribution and algorithmic local search capabilities. In an existing study, in order to better distribute the population, the Monte Carlo method was used for population initialization. Adaptive differential evolution operators are used to improve the local search ability of the algorithm. The algorithm was tested on widely used ZDT and DTLZ family test problems. The experimental results show that the proposed algorithm is better than MOEA/D-DE and has better performance than other excellent multi-objective algorithms.

Optimal Home Energy Demand Management Based Multi-Criteria Decision Making Methods

From the growth of residential energy demands has emerged new approaches for load scheduling to realize better energy consumption by shifting the required demand in response to cost changes or incentive offers. In this paper, a hybrid method is proposed to optimize the load scheduling problem for cost and energy saving. The method comprises a multi-objective optimization differential evolution (MODE) algorithm to obtain a set of optimal solutions by minimizing the cost and peak of a load simultaneously, as a multi-objective function. Next, an integration of the analytic hierarchy process (AHP) and a technique for order preferences by similarity to ideal solution (TOPSIS) methods are used as multi-criteria decision making (MCDM) methods for sorting the optimal solutions’ set from the best to the worst, to enable the customer to choose the appropriate schedule time. The solutions are sorted based on the load peak and energy cost as multi-criteria. Data are for ten appliances of a household used for 24 h with a one-minute time slot. The results of the proposed method demonstrate both energy and cost savings of around 47% and 46%, respectively. Furthermore, the results are compared with other recent methods in the literature to show the superiority of the proposed method.

NARMAX Model Identification Using Multi-Objective Optimization Differential Evolution

Multi-objective optimization differential evolution (MOODE) algorithm has demonstrated to be an effective algorithm for selecting the structure of nonlinear auto-regressive with exogeneous input (NARX) model in dynamic system modeling. This paper presents the expansion of the MOODE algorithm to obtain an adequate and parsimonious nonlinear auto-regressive moving average with exogenous input (NARMAX) model. A simple methodology for developing the MOODE-NARMAX model is proposed. Two objective functions were considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. Two simulated systems and two real systems data were considered for testing the effectiveness of the algorithm. Model validity tests were applied to the set of solutions called the Pareto-optimal set that was generated from the MOODE algorithm in order to select an optimal model. The results show that the MOODE-NARMAX algorithm is able to correctly identify the simulated examples and adequately model real data structures.

Two-Level Surrogate-Assisted Differential Evolution Multi-Objective Optimization of Electric Machines Using 3-D FEA

A two-level surrogate-assisted optimization algorithm is proposed for electric machine design using 3-D finite-element analysis (FEA). The algorithm achieves the optima with much fewer FEA evaluations than conventional methods. It is composed of interior and exterior levels. The exploration is performed mainly in the interior level, which evaluates hundreds of designs employing affordable kriging models. Then, the most promising designs are evaluated in the exterior loop with expensive 3-D FEA models. The sample pool is constructed in a self-adjustable and dynamic way. A hybrid stopping criterion is used to avoid unnecessary expensive function evaluations.

Wind turbine blade geometry design based on multi-objective optimization using metaheuristics

The application of evolutionary algorithms to wind turbine blade design can be interesting, by reducing the number of aerodynamic-to-structural design loops in the conventional design process, hence reducing the design time and cost. Recent developments showed satisfactory results with this approach, mostly combining genetic algorithms with the blade element momentum theory. The general objective of the present work is to define and evaluate a design methodology for the rotor blade geometry in order to maximize the energy production of wind turbines and minimize the mass of the blade itself, using for that purpose stochastic multi-objective optimization methods. An optimization benchmark problem was proposed, which represents the wind conditions and present wind turbine concepts found in Brazil. A variable speed pitch-controlled 2.5 MW direct-drive synchronous generator turbine with a rotor diameter of 120 m was chosen as concept. Four different multi-objective evolutionary algorithms were selected for evaluation in solving this benchmark problem: Non-dominated Sorting Genetic Algorithm version II (NSGA-II), Quantum-inspired Multi-objective Evolutionary Algorithm (QMEA), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multi-objective Optimization Differential Evolution Algorithm (MODE). Detailed analysis of the best compromise blade design showed that the output of the design methodology is feasible for manufacturing.