Multi-objective optimization design of anti-roll torsion bar using improved beluga whale optimization algorithm

Purpose – This study aims to reduce the redundant weight of the anti-roll torsion bar brought by thetraditional empirical design and improving its strength and stiffness.Design/methodology/approach – Based on the finite element approach coupled with the improved belugawhale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the designof the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar weredefined as random variables, and the torsion bar’s mass and strength were investigated using finite elements.Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whaleoptimization (BWO) algorithm and run case studies.Findings – The findings demonstrate that the IBWO has superior solution set distribution uniformity,convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimizethe anti-roll torsion bar design. The error between the optimization and finite element simulation results wasless than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress wasreduced by 35% and the stiffness was increased by 1.9%.Originality/value – The study provides a methodological reference for the simulation optimization process ofthe lateral anti-roll torsion bar.

Interactive Multi-objective Optimization Design for the Pylon Structure of an Airplane

The pylon structure of an airplane is very complex, and its high-fidelity analysis is quite time-consuming. If posterior preference optimization algorithm is used to solve this problem, the huge time consumption will be unacceptable in engineering practice due to the large amount of evaluation needed for the algorithm. So, a new interactive optimization algorithm-interactive multi-objective particle swarm optimization （IMOPSO） is presented. IMOPSO is efficient, simple and operable. The decision-maker can expediently determine the accurate preference in IMOPSO. IMOPSO is used to perform the pylon structure optimization design of an airplane, and a satisfactory design is achieved after only 12 generations of IMOPSO evolutions. Compared with original design, the maximum displacement of the satisfactory design is reduced, and the mass of the satisfactory design is decreased for 22%.

Multi-objective Optimization Design of Vented Cylindrical Airbag Cushioning System for Unmanned Aerial Vehicle

Multi-objective optimization design of the gas-filled bag cushion landing system is investigated.Firstly,the landing process of airbag is decomposed into a adiabatic compression and a release of landing shock energy,and the differential equation of cylindrical gas-filled bag is presented from a theoretical perspective based on the ideal gas state equation and dynamic equation.Then,the effects of exhaust areas and blasting pressure on buffer characteristics are studied,taking those parameters as design variable for the multiobjective optimization problem,and the solution can be determined by comparing Pareto set,which is gained by NSGA-Ⅱ.Finally,the feasibility of the design scheme is verified by experimental results of the ground test.

Multi-Objective Optimization Design through Machine Learning for Drop-on-Demand Bioprinting

Drop-on-demand (DOD) bioprinting has been widely used in tissue engineering due to its highthroughput efficiency and cost effectiveness. However, this type of bioprinting involves challenges such as satellite generation, too-large droplet generation, and too-low droplet speed. These challenges reduce the stability and precision of DOD printing, disorder cell arrays, and hence generate further structural errors. In this paper, a multi-objective optimization (MOO) design method for DOD printing parameters through fully connected neural networks (FCNNs) is proposed in order to solve these challenges. The MOO problem comprises two objective functions: to develop the satellite formation model with FCNNs;and to decrease droplet diameter and increase droplet speed. A hybrid multi-subgradient descent bundle method with an adaptive learning rate algorithm (HMSGDBA), which combines the multisubgradient descent bundle (MSGDB) method with Adam algorithm, is introduced in order to search for the Pareto-optimal set for the MOO problem. The superiority of HMSGDBA is demonstrated through comparative studies with the MSGDB method. The experimental results show that a single droplet can be printed stably and the droplet speed can be increased from 0.88 to 2.08 m·s^-1 after optimization with the proposed method. The proposed method can improve both printing precision and stability, and is useful in realizing precise cell arrays and complex biological functions. Furthermore, it can be used to obtain guidelines for the setup of cell-printing experimental platforms.

The Coalition Cooperative Game Method and Its Application in Multi-objective Optimization Design

This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors and fuzzy clustering, the design variables are divided into different strategic spaces which belong to each player, then it constructs a payoff function based on the coalition mechanism. Each game player takes its own revenue function as a target and obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. A multi-objective optimization example of the luff mechanism of compensative sheave block shows the effectiveness of the coalition cooperative game method.

Multi-objective optimization design of radar absorbing sandwich structure

By introducing a dimensionless parameter to couple the two objectives, weight and radar absorbing performance, into a single objective function, a multi-objective optimization procedure for the radar absorbing sandwich structure （RASS） with a cellular core is proposed. The optimization models considered are one-side clamped sandwich panels with four kinds of cores subject to uniformly distributed loads. The average specular reflectivity calculated with the transfer matrix method and the periodic moment method is utilized to characterize the radar absorbing performance, while the mechanical constraints include the facesheet yielding, core shearing, and facesheet wrinkling. The optimization analysis indicates that the sandwich structure with a two-dimensional （2D） composite lattice core filled with ultra-lightweight sponge may be a better candidate of lightweight RASS than those with cellular foam or hexagonal honeycomb cores. The 2D Kagome lattice is found to outperform the square lattice with respect to radar absorbing.

Multi-objective optimization design of deviation-correction trajectory considering the production loss in shale gas cluster well

In shale gas mining,the inter-fracture interference effect will significantly occur if the actual well deviates from the planned trajectory.To reduce production loss,operators want to get back on the planned trajectory economically and safely.Based on this,a multi-objective optimization model of deviationcorrection trajectory is established considering the production loss evaluation.Firstly,the functional relationship between the production envelope and the fracturing depth is constructed,and the production loss is obtained by combining the calculation method of volume flow.Based on the proposed“double-arc”trajectory design method,the production loss of the fracture on the deviation-correction trajectory is obtained.Finally,combined with the well profile energy evaluation,a new optimization model of deviation-correction trajectory is established.The results demonstrate that after optimizing the fracturing depth,the production loss of the deviation-correction trajectory is reduced by 13.2%.The maximum curvature value results in a trajectory with a minimum production loss yet a maximum well profile energy.The proposed model reduces the well profile energy by 15.6%compared with the existing model.It is proved that the proposed model can reduce the probability of drilling accidents and achieve high gas production in the later mining stage.This study fully considers various factors affecting horizontal wells in the fracturing area,which can provide theoretical guidance for the design of deviationcorrection trajectory.

Multi-objective optimization design for leg mechanism of hydraulic-actuated quadruped robot

In order to improve the robot＇ s abilities of bearing heavy burdens and transporting in complex terrains, the multi-objective optimization design for leg mechanism of the quadruped robot with hydraulic actuated is studied in this paper. The kinematics and dynamics of the robot are ana- lyzed and the two-dimensional linear inverted pendulum model is adopted in planning the trajectories of joints. Then the mathematical model of valve-controlled asymmetric cylinder and control model of single leg are proposed respectively. In the end, NSGA-Ⅱ algorithm is used to achieve the multi^ob- jective optimization design of parameters concerning single leg mechanism and PD torque control. The results prove that the optimized leg mechanism can significantly reduce the required maximum power of hydraulic system, thus decrease its own weight and lead to the obtaining of good dynamic performance.

Multi-objective Optimization Design of Magnesium Alloy Wheel Based on Topology Optimization

Lightweight of automatic vehicle is a significant application trend,using topology optimization and magnesium alloy materials is a valuable way.This article designs a new model of automobile wheel and optimizes the structure for lightweight.Through measuring and analyzing designed model under static force,clear and useful topology optimization results were obtained.Comparing wheel performance before and after optimization,the optimized wheel structure compliance with conditions such as strength can be obtained.Considering three different materials namely magnesium alloy,aluminum alloy and steel,the stress and strain performances of each materials can be obtained by finite element analysis.The reasonable and superior magnesium alloy wheels for lightweight design were obtained.This research predicts the reliability of the optimization design,some valuable references are provided for the development of magnesium alloy wheel.

Crashworthiness Design and Multi-Objective Optimization of Bionic Thin-Walled Hybrid Tube Structures

Thin-walled structures are widely used in cars due to their lightweight construction and energy-absorbing properties.However,issues such as high initial stress and lowenergy-absorbing efficiency arise.This study proposes a novel energy-absorbing structure inwhich a straight tube is combinedwith a conical tube and a bamboo-inspired bulkhead structure is introduced.This configuration allows the conical tube to flip outward first and then fold together with the straight tube.This deformation mode absorbs more energy and less peak force than the conical tube sinking and flipping inward.Through finite element numerical simulation,the specific energy absorption capacity of the structure is increased by 26%compared to that of a regular circular cross-section tube.Finally,the impact resistance of the bionic straight tapered tube structure is further improved through multi-objective optimization,promoting the engineering application and lightweight design of hybrid cross-section tubes.

Multi-Objective Optimization of Aluminum Alloy Electric Bus Frame Connectors for Enhanced Durability

The widespread adoption of aluminumalloy electric buses,known for their energy efficiency and eco-friendliness,faces a challenge due to the aluminum frame’s susceptibility to deformation compared to steel.This issue is further exacerbated by the stringent requirements imposed by the flammability and explosiveness of batteries,necessitating robust frame protection.Our study aims to optimize the connectors of aluminum alloy bus frames,emphasizing durability,energy efficiency,and safety.This research delves into Multi-Objective Coordinated Optimization(MCO)techniques for lightweight design in aluminum alloy bus body connectors.Our goal is to enhance lightweighting,reinforce energy absorption,and improve deformation resistance in connector components.Three typical aluminum alloy connectors were selected and a design optimization platform was built for their MCO using a variety of software and methods.Firstly,through three-point bending experiments and finite element analysis on three types of connector components,we identified optimized design parameters based on deformation patterns.Then,employing Optimal Latin hypercube design(OLHD),parametric modeling,and neural network approximation,we developed high-precision approximate models for the design parameters of each connector component,targeting energy absorption,mass,and logarithmic strain.Lastly,utilizing the Archive-based Micro Genetic Algorithm(AMGA),Multi-Objective Particle Swarm Optimization(MOPSO),and Non-dominated SortingGenetic Algorithm(NSGA2),we explored optimized design solutions for these joint components.Subsequently,we simulated joint assembly buckling during bus rollover crash scenarios to verify and analyze the optimized solutions in three-point bending simulations.Each joint component showcased a remarkable 30%–40%mass reduction while boosting energy absorption.Our design optimization method exhibits high efficiency and costeffectiveness.Leveraging contemporary automation technology,the design optimization platform developed in this study is poised to facilitate intelligent optimization of lightweight metal components in future applications.

A modified back analysis method for deep excavation with multi-objective optimization procedure

Real-time prediction of excavation-induced displacement of retaining pile during the deep excavation process is crucial for construction safety.This paper proposes a modified back analysis method with multi-objective optimization procedure,which enables a real-time prediction of horizontal displacement of retaining pile during construction.As opposed to the traditional stage-by-stage back analysis,time series monitoring data till the current excavation stage are utilized to form a multi-objective function.Then,the multi-objective particle swarm optimization (MOPSO) algorithm is applied for parameter identification.The optimized model parameters are immediately adopted to predict the excavation-induced pile deformation in the continuous construction stages.To achieve efficient parameter optimization and real-time prediction of system behavior,the back propagation neural network (BPNN) is established to substitute the finite element model,which is further implemented together with MOPSO for automatic operation.The proposed approach is applied in the Taihu tunnel excavation project,where the effectiveness of the method is demonstrated via the comparisons with the site monitoring data.The method is reliable with a prediction accuracy of more than 90%.Moreover,different optimization algorithms,including non-dominated sorting genetic algorithm (NSGA-II),Pareto Envelope-based Selection Algorithm II (PESA-II) and MOPSO,are compared,and their influences on the prediction accuracy at different excavation stages are studied.The results show that MOPSO has the best performance for high dimensional optimization task.

Multi-Strategy Assisted Multi-Objective Whale Optimization Algorithm for Feature Selection

In classification problems,datasets often contain a large amount of features,but not all of them are relevant for accurate classification.In fact,irrelevant features may even hinder classification accuracy.Feature selection aims to alleviate this issue by minimizing the number of features in the subset while simultaneously minimizing the classification error rate.Single-objective optimization approaches employ an evaluation function designed as an aggregate function with a parameter,but the results obtained depend on the value of the parameter.To eliminate this parameter’s influence,the problem can be reformulated as a multi-objective optimization problem.The Whale Optimization Algorithm(WOA)is widely used in optimization problems because of its simplicity and easy implementation.In this paper,we propose a multi-strategy assisted multi-objective WOA(MSMOWOA)to address feature selection.To enhance the algorithm’s search ability,we integrate multiple strategies such as Levy flight,Grey Wolf Optimizer,and adaptive mutation into it.Additionally,we utilize an external repository to store non-dominant solution sets and grid technology is used to maintain diversity.Results on fourteen University of California Irvine(UCI)datasets demonstrate that our proposed method effectively removes redundant features and improves classification performance.The source code can be accessed from the website:https://github.com/zc0315/MSMOWOA.

MOALG: A Metaheuristic Hybrid of Multi-Objective Ant Lion Optimizer and Genetic Algorithm for Solving Design Problems

This study proposes a hybridization of two efficient algorithm’s Multi-objective Ant Lion Optimizer Algorithm(MOALO)which is a multi-objective enhanced version of the Ant Lion Optimizer Algorithm(ALO)and the Genetic Algorithm(GA).MOALO version has been employed to address those problems containing many objectives and an archive has been employed for retaining the non-dominated solutions.The uniqueness of the hybrid is that the operators like mutation and crossover of GA are employed in the archive to update the solutions and later those solutions go through the process of MOALO.A first-time hybrid of these algorithms is employed to solve multi-objective problems.The hybrid algorithm overcomes the limitation of ALO of getting caught in the local optimum and the requirement of more computational effort to converge GA.To evaluate the hybridized algorithm’s performance,a set of constrained,unconstrained test problems and engineering design problems were employed and compared with five well-known computational algorithms-MOALO,Multi-objective Crystal Structure Algorithm(MOCryStAl),Multi-objective Particle Swarm Optimization(MOPSO),Multi-objective Multiverse Optimization Algorithm(MOMVO),Multi-objective Salp Swarm Algorithm(MSSA).The outcomes of five performance metrics are statistically analyzed and the most efficient Pareto fronts comparison has been obtained.The proposed hybrid surpasses MOALO based on the results of hypervolume(HV),Spread,and Spacing.So primary objective of developing this hybrid approach has been achieved successfully.The proposed approach demonstrates superior performance on the test functions,showcasing robust convergence and comprehensive coverage that surpasses other existing algorithms.

Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

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.

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.

Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection

Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.