Multi-objective Optimization Problem Research Articles

Reliability design involving optimization with multiple objectives by means of probabilistic multi-objective optimization

AbstractAlthough there have been many achievements on single—objective models, the reliability research involving multi-objective optimization problems has not obtained satisfactory research results. In this paper, the reliability design involving optimization with multiple objectives is developed by means of probabilistic multi-objective optimization (PMOO), which considers the simultaneity of optimization of multiple objectives and treats both beneficial type of utility indexes and unbeneficial type of utility indexes of performance indicators equivalently and conformably. Three cases of reliability design concerning multi—objective optimization, i.e., reliability requirement as the additional constraint condition, reliability assessment as an additional optimized objective, and the mixture of these two cases, are formulated by means of PMOO, respectively. Furthermore, a typical example is given to show the procedure of the approach for reliability assessment involving multiple objectives by means of PMOO, which exhibits the validity of the present approach. The approach is objective without any subjective factors.

Research on Frequency Regulation with Dynamic Trajectory Planning of Participation Factors

The energy transformation has led to a high proportion of new energy entering the grid. New energy has high randomness, which challenges the frequency stability of the power system. A new approach to improve frequency based on dynamic trajectory planning of participation factors is proposed in this work. In the frequency regulation interval, the trajectory and termination time of participation factors are regarded as the variables to be optimized. Then, taking the frequency regulation performance and economy as the goals, a multi-objective optimization problem is constructed. The participation factors are used to dispatch the output power of different units, which breaks the constraint that the output characteristics of different units are consistent in the original regulation process. Therefore, the generator units with different regulation characteristics in the system achieve complementary coordination on the second time scale. In simulation cases, frequency oscillation is reduced, while the overall economy of the system is improved. The numerical evaluation results show that the frequency performance is improved by 2.7% at most and 2.9% of the economy is improved at most simultaneously. The above results demonstrate the effectiveness of the proposed approach.

On conjugate direction-type method for interval-valued multiobjective quadratic optimization problems

On conjugate direction-type method for interval-valued multiobjective quadratic optimization problems

An assistance technology towards maintaining efficient driving strategies of electric vehicle

ABSTRACT In order to overcome the problems of electric vehicle (EV) range anxiety and inadequate charging station, a driver assistance technology is presented here. The proposed technology assists a driver to maintain an efficient driving strategy (EDS) that minimizes energy consumption toward increasing the driving range. Additionally, it provides an anticipated range of EV corresponding to its current battery charge which alerts the driver to take a decision for required charging. EDS is determined by solving a multi-objective optimization problem corresponding to the current route characteristics. Optimization problem considers three primary objectives, minimization of energy consumption and travel time and maximize journey comfort, and follows an EV drive model. Effectiveness of the proposed technology is identified by analyzing the effect of adopting EDS in a micro-trip planning with an E-bus based on experimental drive data. A drive model for the E-bus is formulated and validated through comparative analysis of speed, motor current, and voltage that are obtained in simulation and experimentation. Such analysis was performed independently in four micro-trips identified from E-bus drive data following a typical route. It was found that the driver assistance technology reduces both energy consumption and travel time than that found by following a random driving strategy.

Optimal siting and sizing of battery energy storage systems in unbalanced distribution systems: A multi objective problem under uncertainty

In this paper the siting and sizing problem of battery energy storage systems in unbalanced active distribution systems is formulated as a mixed-integer, non-linear, constrained multi objective (MO) optimization problem under uncertainties. The problem is cumbersome from the computational point of view due to the presence of intertemporal constraints, a great number of state variables and the presence of uncertainties in the problem input data. A new approach based on the trade-off/risk analysis is proposed to obtain with acceptable computational efforts a solution that may not be the optimal solution but represents a reasonable and robust compromise. We use the trade-off/risk analysis, because it was specifically developed for power system planning problems in which we deal with a wide range of options, with possible conflicting objectives, and with uncertainty and risk. The proposed approach includes new procedures to select an adequate set of planning alternatives to be considered in the trade-off/risk analysis framework and to assist the planning engineer when difficulties arise in setting probabilities of the input data. Numerical applications to an IEEE unbalanced test system demonstrate the effectiveness of the proposed procedure and indicate the best alternatives of storage systems in the range from 450 kW to 600 kW globally installed in a reduced set of nodes.

A Design Method for Road Vehicles with Autonomous Driving Control

The past three decades have witnessed extensive studies on motion-planning and tracking-control for autonomous vehicles (AVs). There is, however, a lack of studies on effective design methods for AVs, which consist of the subsystems of the mechanical vehicle, tracking-control, motion-planning, etc. To tackle this problem, this paper proposes a design approach for AVs. The proposed method features a design framework with two layers: at the upper layer, a particle swarm optimization (PSO) algorithm serves as a solver to a multi-objective optimization problem for desired AV trajectory-tracking performance; at the lower layer, a coupled dynamic analysis is conducted among the three subsystems, i.e., a nonlinear model for the mechanical vehicle, a motion-planning module, and a controller based on nonlinear model predictive control (NLMPC) for direction control. The simulation results demonstrate that the proposed method can effectively determine the desired design variables for the NLMPC controller and the mechanical vehicle to achieve optimal trajectory-tracking performance. The research findings from this work provide guidelines for designing AVs.

An enhanced competitive swarm optimizer with strongly robust sparse operator for large-scale sparse multi-objective optimization problem

In the real world, the decision variables of large-scale sparse multi-objective problems are high-dimensional, and most Pareto optimal solutions are sparse. The balance of the algorithms is difficult to control, so it is challenging to deal with such problems in general. Therefore, An Enhanced Competitive Swarm Optimizer with Strongly Robust Sparse Operator (SR-ECSO) algorithm is proposed. Firstly, the strongly robust sparse functions which accelerate particles in the population better sparsity in decision space, are used in high-dimensional decision variables. Secondly, the diversity of sparse solutions is maintained, and the convergence balance of the algorithm is enhanced by the introduction of an adaptive random perturbation operator. Finally, the state of the particles is updated using a swarm optimizer to improve population competitiveness. To verify the proposed algorithm, we tested eight large-scale sparse benchmark problems, and the decision variables were set in three groups with 100, 500, and 1000 as examples. Experimental results show that the algorithm is promising for solving large-scale sparse optimization problems.

Determining method of optimal process parameters using Taguchi method and technique for order preference by similarity to ideal solution in plastic injection molding

Many plastic injection molding (PIM) process optimization problems are multi-objective optimization problems that optimize multiple mechanical properties. This paper proposed a determining method of optimal process parameters and their effect ranks using Taguchi method and TOPSIS in the PIM. TOPSIS was used to convert multiple mechanical properties into single comprehensive response. It was selected as a reasonable multi-attribute decision-making (MADM) method from among some well-known MADM methods based on mean rank correlation coefficient and mean absolute rank deviation. Taguchi method was used to design experiment and find the optimal process parameters. The proposed method was applied to determine the optimal values of the process parameters: melt temperature (MT), packing pressure (PP), cooling time (CT), and injection pressure (IP) for improving tensile strength, elasticity module, flexural modulus, and impact strength in the PIM with Acrylonitrile-Butadiene-Styrene compound as plastic materials and AISI 1020 as mold materials. The optimal values of the process parameters were MT of 280°C, PP of 28 MPa, CT of 22 s, and IP of 50 MPa, and their effect ranking was IP (51.941%), PP (32.280%), CT (9.045%), and MT (6.734%). The method could be widely applied to not only the PIM process optimization but also various manufacturing process optimization problems.

Generating optimal reloading patterns for CNPGS Unit-3 core using multi-objective elitist teaching-learning-based optimizer

Pressurized Water Reactors (PWRs) management presents the core reloading pattern optimization as a significant problem that contributes to the improvement of reactor productivity and optimal fuel utilization with considering safety conditions. In present study, Multi-Objective Elitist Teaching-Learning-Based Optimization (MO-ETLBO) technique is suggested to cope up the multi-objective reloading optimization problem of the Chashma Nuclear Power Generating Station (CNPGS) unit-3 core. A multivariable objective function is designed to evaluate the quality of each loading pattern while maximizing critical boron concentration (CBC), minimizing the power peaking factor (PPF), and optimally enhancing the cycle length while ensuring adequate safety margins and design limits. It has been found that the equilibrium cycle can be extended to 16.07 extended full power days (EFPDs) while maintaining the PPF and CBC within design limits. To validate the effectiveness of TLBO, the optimized loading pattern of the equilibrium core was evaluated using the deterministic computer code DONJON5, for neutronic parameter analysis. The results show that the algorithm proposed in this study is a promising approach for reloading pattern optimization in CNPGS unit-3, offering potential improvements in reactor cycle length while ensuring safety and enhancing overall performance.

Strategy for obtaining robust solutions in multi-objective design with uncertainties

This paper proposes a novel definition of robustness for multi-objective optimization problems. This definition underpins an innovative strategy for obtaining robust solutions in the presence of uncertainty; it involves formulating the cost function under uncertainties as conflicting objectives during optimization. This approach aims to define the decision vectors that are not dominated in all scenarios simultaneously by any other. These solutions exhibit both optimality and robustness properties, aligning with conventional and unconventional multi-objective methods. This approach enables the implicit definition of the Pareto-optimal solutions for each scenario and robust solutions that optimize performance in worst-case scenarios. Additionally, the set of robust solutions that optimize the global performance concerning the utopian points of all uncertainty scenarios is also defined.To demonstrate the effectiveness of this method, this paper addresses two control design problems. The first example, a first-order process, illustrates the advantages and aspects of the optimization strategy. The second problem, multi-loop temperature control design of a proton exchange membrane fuel cell stack, is a more complex engineering problem involving results from previous research.

Learnable self-supervised support vector machine based individual selection strategy for multimodal multi-objective optimization

Multimodal multi-objective optimization problem (MMOP) is a frontier research problem, which can provide decision makers with more choices without making trade-offs. Many multimodal multi-objective evolutionary algorithms (MMOEAs) have been proposed to solve MMOP. However, most MMOEAs tend to prioritize the objective dominance of individuals in the process of individual selection, and only individuals with the same objective dominance will be considered the diversity, which leads to the loss of many promising solutions. To solve the above problem, this paper proposes a learnable self-supervised support vector machine (SVM) based multimodal multi-objective optimization algorithm (SVMEA). Support vector machine can learn the knowledge about distinguishing the advantages and disadvantages of individuals from the data in the existing training set and select individuals, in which the objective dominance of individuals is as important as diversity. Moreover, a crowding distance calculation method based on Manhattan distance is designed. Compared with the traditional method using Euclidean distance to calculate crowding distance, it can better evaluate the diversity of individuals in the decision space and assist the selection of elite solutions. Experimental results show that the proposed SVMEA is competitive with seven other advanced MMOEAs on 34 benchmark problems and a practical application problem.

Multi-faceted sustainability improvement in low voltage power distribution network employing DG and capacitor bank

Efficient distribution of active and reactive power in distribution networks is crucial for ensuring that consumer demand is met and that electrical power quality is maintained. This requires careful planning, particularly in terms of optimally placing and sizing distributed generator (DG) and capacitor bank (CB) units. These units play a key role in minimizing power losses and voltage fluctuations within the network. However, implementing DG and CB units in unbalanced distribution networks presents unique challenges due to inherent system unbalances. To address these challenges, this article proposes a method for allocating and sizing DG and CB units in unbalanced distribution networks. The approach accounts for the network's unbalance and targets multiple objectives, such as reducing power losses, improving multi-phase voltage stability, and minimizing phase-to-phase voltage unbalance. The fast and flexible radial power flow (FFRPF) technique is employed to model complex interactions and constraints within the network, leading to a multi-objective optimization problem. This optimization problem is solved using the weight aggregated particle swarm optimization (WA-PSO) method, a variant of particle swarm optimization tailored for multi-objective functions. WA-PSO simplifies the process by combining multiple objectives into a single function using weighted aggregation. The efficacy of this approach is validated on 19, 34, and 123-node unbalanced radial distribution networks (URDNs). The results show significant improvements in power delivery efficiency across all tested networks, especially when DG and CB units are operated simultaneously. Specifically, DG and CB integration led to a reduction in system losses by 89.90 %, 88.42 %, and 86.87 %, and a decrease in three-phase voltage unbalance indices by 88.75 %, 81.68 %, and 39.05 %, for the 19, 34, and 123-node systems, respectively, while maintaining voltage stability within acceptable limits. Additionally, CO2 emissions were reduced by 52 %, 62 %, and 53 % when microturbines were utilized instead of coal-based thermal power plants, further highlighting the environmental benefits of the proposed approach.

Validation of a Model Predictive Control Strategy on a High Fidelity Building Emulator

In recent years, advanced controllers, including Model Predictive Control (MPC), have emerged as promising solutions to improve the efficiency of building energy systems. This paper explores the capabilities of MPC in handling multiple control objectives and constraints. A first MPC controller focuses on the task of ensuring thermal comfort in a residential house served by a heat pump while minimizing the operating costs when subject to different pricing schedules. A second MPC controller working on the same system tests the ability of MPC to deal with demand response events by enforcing a time-varying maximum power usage limitation signal from the electric grid. Furthermore, multiple combinations of the control parameters are tested in order to assess their influence on the controller performance. The controllers are tested on the BOPTEST framework, which offers standardized test cases in high-fidelity emulation models, and pre-defined baseline control strategies to allow fair comparisons also across different studies. Results show that MPC is able to handle multi-objective optimal control problems, reducing thermal comfort violations by between 66.9% and 82% and operational costs between 15.8% up to 20.1%, depending on the specific scenario analyzed. Moreover, MPC proves its capability to exploit the building thermal mass to shift heating power consumption, allowing the latter to adapt its time profile to time-varying constraints. The proposed methodology is based on technologically feasible steps that are intended to be easily transferred to large scale, in-field applications.

An archive-assisted multi-modal multi-objective evolutionary algorithm

The multi-modal multi-objective optimization problems (MMOPs) pertain to characteristic of the decision space that exhibit multiple sets of Pareto optimal solutions that are either identical or similar. The resolution of these problems necessitates the utilization of optimization algorithms to locate multiple Pareto sets (PSs). However, existing multi-modal multi-objective evolutionary algorithms (MMOEAs) encounter difficulties in concurrently enhancing solution quality in both decision space and objective space. In order to deal with this predicament, this paper presents an Archive-assisted Multi-modal Multi-objective Evolutionary Algorithm, called A-MMOEA. This algorithm maintains a main population and an external archive, which is leveraged to improve the fault tolerance of individual screening. To augment the quality of solutions in the archive, an archive evolution mechanism (AEM) is formulated for updating the archive and an archive output mechanism (AOM) is used to output the final solutions. Both mechanisms incorporate a comprehensive crowding distance metric that employs objective space crowding distance to facilitate the calculation of decision space crowding distance. Besides, a data screening method is employed in the AOM to alleviate the negative impact on the final results arising from undesirable individuals resulting from diversity search. Finally, in order to enable individuals to effectively escape the limitation of niches and further enhance diversity of population, a diversity search method with level-based evolution mechanism (DSMLBEM) is proposed. The proposed algorithm’s performance is evaluated through extensive experiments conducted on two distinct test sets. Final results indicate that, in comparison to other commonly used algorithms, this approach exhibits favorable performance.

A method for optimizing different geometric shields of D-T neutron generators by combining BP neural network and Analytic Hierarchy Process

In this paper, an optimization of shielding structures with different geometries is established for the D-T neutron generator system by combining Back Propagation (BP) neural network and Analytic Hierarchy Process (AHP). The D-T neutron generator (Model NG-9) used in the system was developed independently by Northeast Normal University. After investigating the rule of shielding performance among spherical, cylindrical and cubic geometries, the spherical shield is selected for BP neural network prediction to determine the total dose rate through it. Information about spherical multilayer-shielding structures and properties calculated by MCNP code is used to train the neural network. The predicted result serves as a parameter of the evaluation function, which provides a comprehensive assessment of the dose rate penetrated the shield, the shielding mass, and the shielding volume. Together with AHP, the weight factors are determined for all the optimization objectives to construct the evaluation function. By comparing its values, the optimal shielding structures for spherical, cylindrical and cubic materials are found. Against MCNP simulated values, the total dose rates’ errors of the optimal shielding structures for the sphere, cylinder, and cube are 1.72 %, -4.94 %, and -5.17 %, respectively. This result demonstrates that the combination of BP neural network and AHP is more effective in addressing multi-objective optimization problems related to the design of radiation shielding for various geometries.

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

A Novel Approach for Power Quality Improvement Using D-STATCOM in Wind Integrated Distribution System

Objectives: The major goal of the proposed article is to enhance the power quality of a wind-integrated radial distribution network utilizing D-STATCOM. It is done by the appropriate allocation of wind turbine-based DGs and D-STATCOM. Methods: The multi-objective optimization problem is implemented using a novel and effective Prairie Dog Optimization (PDO) to attain the best-compromised solutions. This optimization tool is well suited for solving complex, non-linear voltage stability problems. The proposed approach is validated for the modified IEEE-13 bus highly unbalanced system using MATLAB. Findings: The findings indicate enhancements in the voltage profile, system losses, and total harmonic distortion (THD). The THD for the load current is 18%, while the THD for the source current is 2.54% for nonlinear loads using the proposed methodology. The voltage profile of 3.25% is enhanced as compared with the existing method, which is 2.15% better than the other obtainable method. Novelty: Prairie Dog Optimization (PDO) was chosen over traditional algorithms for its nature-inspired approach, simplicity, and efficacy in exploring complicated search fields. Its robust exploration and exploitation skills make it excellent for multi-modal optimization challenges. Keywords: Radial distribution system (RDS), D-STATCOM, Power quality, Prairie Dog Optimization, THD

Multi-Objective Optimization of the Forming Process Parameters of Disc Forgings Based on Grey Correlation Analysis and the Response Surface Method

This paper introduces a multi-objective optimization problem (MPO) for the forming process parameters of disc forgings using grey relational analysis (GRA) and the response surface methodology (RSM). Firstly, an experimental design based on the Box–Behnken design (BBD) principle was established, and simulations were performed in Deform to obtain response data. Secondly, GRA was used to transform the MPO into a grey relational degree (GRD) problem, and the entropic weight method was integrated to ascertain the influence weights of each variable on GRD. Then, a quadratic polynomial prediction model based on the RSM was constructed, and its accuracy was ensured through model validation. Finally, the optimal process parameter combination was determined through the particle swarm optimization algorithm, which included a friction coefficient of 0.3, an initial temperature of 1250 °C, and a downward pressing speed of 7.5 mm/s. The results of the experimental investigation indicate that optimized process parameters significantly reduce the forming load, equivalent stress, and damage value, effectively enhancing the overall quality of forged parts.

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

A staged fuzzy evolutionary algorithm for constrained large-scale multiobjective optimization

Constrained multiobjective optimization problems (CMOPs) are prevalent in practical applications, where constraints play a significant role. Building on techniques from constrained single-objective optimization, classical methods such as the constrained dominance principle have been extended to CMOPs. However, these methods struggle with CMOPs characterized by complex infeasible regions. Furthermore, as the number of decision variables increases, the search efficiency of algorithms deteriorates dramatically. To solve those issues, we propose a staged fuzzy evolutionary algorithm (i.e., SFEA) for constrained large-scale problems. To balance exploration and exploitation, a fuzzy stage adjustment strategy based on the sigmoid function is proposed. Furthermore, this article develops an improved fuzzy operator to perform fuzzy operations on various vectors (e.g., solutions or constraint violations). Computational experiments were conducted on CMOP test suites with up to 500 decision variables and a series of real-world applications. The experimental results demonstrate that, compared to existing peer algorithms, our algorithm exhibits superior or competitive performance.