Multi-Objective Optimization Algorithm for Grouping Decision Variables Based on Extreme Point Pareto Frontier

The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Multi-Objective Optimization of Multi-Product Parallel Disassembly Line Balancing Problem Considering Multi-Skilled Workers Using a Discrete Chemical Reaction Optimization Algorithm

This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers.A mathematical model for the parallel disassembly line is established to achieve maximized disassembly profit and minimized workstation cycle time.Based on a product’s AND/OR graph,matrices for task-skill,worker-skill,precedence relationships,and disassembly correlations are developed.A multi-objective discrete chemical reaction optimization algorithm is designed.To enhance solution diversity,improvements are made to four reactions:decomposition,synthesis,intermolecular ineffective collision,and wall invalid collision reaction,completing the evolution of molecular individuals.The established model and improved algorithm are applied to ball pen,flashlight,washing machine,and radio combinations,respectively.Introducing a Collaborative Resource Allocation(CRA)strategy based on a Decomposition-Based Multi-Objective Evolutionary Algorithm,the experimental results are compared with four classical algorithms:MOEA/D,MOEAD-CRA,Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ),and Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ).This validates the feasibility and superiority of the proposed algorithm in parallel disassembly production lines.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme

In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.

A Discrete Multi-Objective Squirrel Search Algorithm for Energy-Efficient Distributed Heterogeneous Permutation Flowshop with Variable Processing Speed

In the manufacturing industry,reasonable scheduling can greatly improve production efficiency,while excessive resource consumption highlights the growing significance of energy conservation in production.This paper studies the problem of energy-efficient distributed heterogeneous permutation flowshop problem with variable processing speed(DHPFSP-VPS),considering both the minimum makespan and total energy consumption(TEC)as objectives.A discrete multi-objective squirrel search algorithm(DMSSA)is proposed to solve the DHPFSPVPS.DMSSA makes four improvements based on the squirrel search algorithm.Firstly,in terms of the population initialization strategy,four hybrid initialization methods targeting different objectives are proposed to enhance the quality of initial solutions.Secondly,enhancements are made to the population hierarchy system and position updating methods of the squirrel search algorithm,making it more suitable for discrete scheduling problems.Additionally,regarding the search strategy,six local searches are designed based on problem characteristics to enhance search capability.Moreover,a dynamic predator strategy based on Q-learning is devised to effectively balance DMSSA’s capability for global exploration and local exploitation.Finally,two speed control energy-efficient strategies are designed to reduce TEC.Extensive comparative experiments are conducted in this paper to validate the effectiveness of the proposed strategies.The results of comparing DMSSA with other algorithms demonstrate its superior performance and its potential for efficient solving of the DHPFSP-VPS problem.

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

With the increasing demand for electrical services,wind farm layout optimization has been one of the biggest challenges that we have to deal with.Despite the promising performance of the heuristic algorithm on the route network design problem,the expressive capability and search performance of the algorithm on multi-objective problems remain unexplored.In this paper,the wind farm layout optimization problem is defined.Then,a multi-objective algorithm based on Graph Neural Network(GNN)and Variable Neighborhood Search(VNS)algorithm is proposed.GNN provides the basis representations for the following search algorithm so that the expressiveness and search accuracy of the algorithm can be improved.The multi-objective VNS algorithm is put forward by combining it with the multi-objective optimization algorithm to solve the problem with multiple objectives.The proposed algorithm is applied to the 18-node simulation example to evaluate the feasibility and practicality of the developed optimization strategy.The experiment on the simulation example shows that the proposed algorithm yields a reduction of 6.1% in Point of Common Coupling(PCC)over the current state-of-the-art algorithm,which means that the proposed algorithm designs a layout that improves the quality of the power supply by 6.1%at the same cost.The ablation experiments show that the proposed algorithm improves the power quality by more than 8.6% and 7.8% compared to both the original VNS algorithm and the multi-objective VNS algorithm.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

Discrete Optimization on Unsteady Pressure Fluctuation of a Centrifugal Pump Using ANN and Modified GA

Pressure fluctuation due to rotor-stator interaction in turbomachinery is unavoidable,inducing strong vibration in the equipment and shortening its lifecycle.The investigation of optimization methods for an industrial centrifugal pump was carried out to reduce the intensity of pressure fluctuation to extend the lifecycle of these devices.Considering the time-consuming transient simulation of unsteady pressure,a novel optimization strategy was proposed by discretizing design variables and genetic algorithm.Four highly related design parameters were chosen,and 40 transient sample cases were generated and simulated using an automatic program.70%of them were used for training the surrogate model,and the others were for verifying the accuracy of the surrogate model.Furthermore,a modified discrete genetic algorithm(MDGA)was proposed to reduce the optimization cost owing to transient numerical simulation.For the benchmark test,the proposed MDGA showed a great advantage over the original genetic algorithm regarding searching speed and effectively dealt with the discrete variables by dramatically increasing the convergence rate.After optimization,the performance and stability of the inline pump were improved.The efficiency increased by more than 2.2%,and the pressure fluctuation intensity decreased by more than 20%under design condition.This research proposed an optimization method for reducing discrete transient characteristics in centrifugal pumps.

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.

STUDIFS ON OPTIMAL TOPOLOGY DES IGN OF STRUCTURES WITH DISCRETE VARIABLES

Some problems in the optimal topology design of structures with discrete variables are studied in this paper.The problem of a model of discrete optimization is discussed and a neglected fact that discrete optimum design may be controlled by the discreteness of sizing variables and global con- straints is pointed out.A heuristic algorithm for solving discrete topology optimization problems of trusses and frames is proposed.

Long-term operation optimization of circulating cooling water systems under fouling conditions

Fouling caused by excess metal ions in hard water can negatively impact the performance of the circulating cooling water system(CCWS)by depositing ions on the heat exchanger's surface.Currently,the operation optimization of CCWS often prioritizes short-term flow velocity optimization for minimizing power consumption,without considering fouling.However,low flow velocity promotes fouling.Therefore,it's crucial to balance fouling and energy/water conservation for optimal CCWS long-term operation.This study proposes a mixed-integer nonlinear programming(MINLP)model to achieve this goal.The model considers fouling in the pipeline,dynamic concentration cycle,and variable frequency drive to optimize the synergy between heat transfer,pressure drop,and fouling.By optimizing the concentration cycle of the CCWS,water conservation and fouling control can be achieved.The model can obtain the optimal operating parameters for different operation intervals,including the number of pumps,frequency,and valve local resistance coefficient.Sensitivity experiments on cycle and environmental temperature reveal that as the cycle increases,the marginal benefits of energy/water conservation decrease.In periods with minimal impact on fouling rate,energy/water conservation can be achieved by increasing the cycle while maintaining a low fouling rate.Overall,the proposed model has significant energy/water saving effects and can comprehensively optimize the CCWS through its incorporation of fouling and cycle optimization.

Multi-Objective Optimization of VBHF in Deep Drawing Based on the Improved QO-Jaya Algorithm

Blank holder force(BHF)is a crucial parameter in deep drawing,having close relation with the forming quality of sheet metal.However,there are different BHFs maintaining the best forming effect in different stages of deep drawing.The variable blank holder force(VBHF)varying with the drawing stage can overcome this problem at an extent.The optimization of VBHF is to determine the optimal BHF in every deep drawing stage.In this paper,a new heuristic optimization algorithm named Jaya is introduced to solve the optimization efficiently.An improved“Quasi-oppositional”strategy is added to Jaya algorithm for improving population diversity.Meanwhile,an innovated stop criterion is added for better convergence.Firstly,the quality evaluation criteria for wrinkling and tearing are built.Secondly,the Kriging models are developed to approximate and quantify the relation between VBHF and forming defects under random sampling.Finally,the optimization models are established and solved by the improved QO-Jaya algorithm.A VBHF optimization example of component with complicated shape and thin wall is studied to prove the effectiveness of the improved Jaya algorithm.The optimization results are compared with that obtained by other algorithms based on the TOPSIS method.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

Aerodynamic/stealth design of S-duct inlet based on discrete adjoint method

It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.

Genetic Optimization via Diverse Crossover Intelligence

An intelligent crossover methodology within the genetic algorithm (GA) is explored within both mathematical and finite element arenas improving both design and solution convergence time. This improved intelligent crossover outperforms the traditional genetic algorithm combined with a rule-based approach utilizing domain specific knowledge developed by Webb, et al. [1]. The encoding of the improved crossover consists of two chromosome strings within the genetic algorithm where the first string represents the design or solution string, and the second string represents chromosome crossover string intelligence. This improved crossover methodology saves the best population members or designs evaluated from each generation and applies crossover chromosome intelligence to the best saved population members paired with globally selected parents. Enhanced features of this crossover methodology employ the random selection of the best designs from the prior generation as a potential parent coupled with alternating intelligence pairing methods. In addition to this approach, two globally selected parents possess the ability to mate utilizing crossover chromosome string intelligence maintaining the integrity of a global GA search. Overall, the final population following crossover employs both global and best generation design chromosome strings to maximize creativity while enhancing the solution search. This is a modification to a conventional GA that can be translated into GA encoding. This technique is explored initially through a Base 10 mathematical application followed by the examination of plate structural optimization considering stress and displacement constraints. Results from crossover intelligence are compared with the conventional genetic algorithm and from Webb, et al. [1] which illustrates the outcome of a two phase genetic optimization algorithm.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

Discrete GWO Optimized Data Aggregation for Reducing Transmission Rate in IoT

The conventional hospital environment is transformed into digital transformation that focuses on patient centric remote approach through advanced technologies.Early diagnosis of many diseases will improve the patient life.The cost of health care systems is reduced due to the use of advanced technologies such as Internet of Things(IoT),Wireless Sensor Networks(WSN),Embedded systems,Deep learning approaches and Optimization and aggregation methods.The data generated through these technologies will demand the bandwidth,data rate,latency of the network.In this proposed work,efficient discrete grey wolf optimization(DGWO)based data aggregation scheme using Elliptic curve Elgamal with Message Authentication code(ECEMAC)has been used to aggregate the parameters generated from the wearable sensor devices of the patient.The nodes that are far away from edge node will forward the data to its neighbor cluster head using DGWO.Aggregation scheme will reduce the number of transmissions over the network.The aggregated data are preprocessed at edge node to remove the noise for better diagnosis.Edge node will reduce the overhead of cloud server.The aggregated data are forward to cloud server for central storage and diagnosis.This proposed smart diagnosis will reduce the transmission cost through aggrega-tion scheme which will reduce the energy of the system.Energy cost for proposed system for 300 nodes is 0.34μJ.Various energy cost of existing approaches such as secure privacy preserving data aggregation scheme(SPPDA),concealed data aggregation scheme for multiple application(CDAMA)and secure aggregation scheme(ASAS)are 1.3μJ,0.81μJ and 0.51μJ respectively.The optimization approaches and encryption method will ensure the data privacy.

ANALYSIS AND DISCRETIZATION FOR AN OPTIMAL CONTROL PROBLEM OF A VARIABLE-COEFFICIENT RIESZ-FRACTIONAL DIFFUSION EQUATION WITH POINTWISE CONTROL CONSTRAINTS

We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion equation.Due to the impact of the variable diffusivity coefficient,existing regularity results for their constantcoefficient counterparts do not apply,while the bilinear forms of the state(adjoint)equation may lose the coercivity that is critical in error estimates of the finite element method.We reformulate the state equation as an equivalent constant-coefficient fractional diffusion equation with the addition of a variable-coefficient low-order fractional advection term.First order optimality conditions are accordingly derived and the smoothing properties of the solutions are analyzed by,e.g.,interpolation estimates.The weak coercivity of the resulting bilinear forms are proven via the Garding inequality,based on which we prove the optimal-order convergence estimates of the finite element method for the(adjoint)state variable and the control variable.Numerical experiments substantiate the theoretical predictions.