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 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.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

Integrated building design is inherently a multi-objective optimization problem where two or more conflicting objectives must be minimized and/or maximized concurrently.Many multi-objective optimization algorithms have been developed;however few of them are tested in solving building design problems.This paper compares performance of seven commonly-used multi-objective evolutionary optimization algorithms in solving the design problem of a nearly zero energy building(n ZEB) where more than 1.610 solutions would be possible.The compared algorithms include a controlled non-dominated sorting genetic algorithm witha passive archive(p NSGA-II),a multi-objective particle swarm optimization(MOPSO),a two-phase optimization using the genetic algorithm(PR_GA),an elitist non-dominated sorting evolution strategy(ENSES),a multi-objective evolutionary algorithm based on the concept of epsilon dominance(ev MOGA),a multi-objective differential evolution algorithm(sp MODE-II),and a multi-objective dragonfly algorithm(MODA).Several criteria was used to compare performance of these algorithms.In most cases,the quality of the obtained solutions was improved when the number of generations was increased.The optimization results of running each algorithm20 times with gradually increasing number of evaluations indicated that the PR_GA algorithm had a high repeatability to explore a large area of the solution-space and achieved close-to-optimal solutions with a good diversity,followed by the p NSGA-II,ev MOGA and sp MODE-II.Uncompetitive results were achieved by the ENSES,MOPSO and MODA in most running cases.The study also found that 1400-1800 were minimum required number of evaluations to stabilize optimization results of the building energy model.

Cooperative task allocation for heterogeneous multi-UAV using multi-objective optimization algorithm

The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.

An improved multi-objective optimization algorithm for solving flexible job shop scheduling problem with variable batches

In order to solve the flexible job shop scheduling problem with variable batches,we propose an improved multiobjective optimization algorithm,which combines the idea of inverse scheduling.First,a flexible job shop problem with the variable batches scheduling model is formulated.Second,we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method.Moreover,in order to increase the diversity of the population,two methods are developed.One is the threshold to control the neighborhood updating,and the other is the dynamic clustering algorithm to update the population.Finally,a group of experiments are carried out.The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively,and has effective performance in solving the flexible job shop scheduling problem with variable batches.

Interactive Evolutionary Multi-Objective Optimization Algorithm Using Cone Dominance

As the number of objectives increases,the performance of the Pareto dominance-based Evolutionary Multi-objective Optimization( EMO) algorithms such as NSGA-II,SPEA2 severely deteriorates due to the drastic increase in the Pareto-incomparable solutions. We propose a sorting method which classifies these incomparable solutions into several ordered classes by using the decision maker's( DM) preference information.This is accomplished by designing an interactive evolutionary algorithm and constructing convex cones. This method allows the DMs to drive the search process toward a preferred region of the Pareto optimal front. The performance of the proposed algorithm is assessed for two,three,and four-objective knapsack problems. The results demonstrate the algorithm ' s ability to converge to the most preferred point. The evaluation and comparison of the results indicate that the proposed approach gives better solutions than that of NSGA-II. In addition,the approach is more efficient compared to NSGA-II in terms of the number of generations required to reach the preferred point.

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.

Constructal design of printed circuit recuperator for S-CO_(2)cycle via multi-objective optimization algorithm

Based on a constructal theory,the structure design of a printed circuit recuperator with a semicircular heat transfer channel for supercritical CO_(2)cycle is carried out.First,a complex function composed of weighted sum of the reciprocal of total heat transfer rate and total pumping power consumption is regarded as an optimization objective,and total volumes of the recuperator and heat transfer channel are regarded as constraints.The optimal heat transfer channel radius and minimum complex function of the recuperator are obtained.It turns out that heat transfer rate,pumping power consumption,and complex function under the optimal construct of recuperator are reduced by 15.10%,82.44%,and 32.33%,respectively.There exists the optimal single plate channel number which results in the double minimum complex function.Second,for the purpose of minimizing the reciprocal of heat transfer rate and pumping power consumption,NSGA-II algorithm is used to achieve multi-objective optimization,and the minimum deviation index derived by the decision-making methods is 0.076,which can be taken as multi-objective optimal design scheme for printed circuit recuperator with semicircular heat transfer channels.The findings presented here can serve as theoretical recommendations for the structure design of printed circuit recuperator.

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.

Enhancing Evolutionary Algorithms With Pattern Mining for Sparse Large-Scale Multi-Objective Optimization Problems

Sparse large-scale multi-objective optimization problems(SLMOPs)are common in science and engineering.However,the large-scale problem represents the high dimensionality of the decision space,requiring algorithms to traverse vast expanse with limited computational resources.Furthermore,in the context of sparse,most variables in Pareto optimal solutions are zero,making it difficult for algorithms to identify non-zero variables efficiently.This paper is dedicated to addressing the challenges posed by SLMOPs.To start,we introduce innovative objective functions customized to mine maximum and minimum candidate sets.This substantial enhancement dramatically improves the efficacy of frequent pattern mining.In this way,selecting candidate sets is no longer based on the quantity of nonzero variables they contain but on a higher proportion of nonzero variables within specific dimensions.Additionally,we unveil a novel approach to association rule mining,which delves into the intricate relationships between non-zero variables.This novel methodology aids in identifying sparse distributions that can potentially expedite reductions in the objective function value.We extensively tested our algorithm across eight benchmark problems and four real-world SLMOPs.The results demonstrate that our approach achieves competitive solutions across various challenges.

Multi-objective Design of Blending Fuel by Intelligent Optimization Algorithms

Fuel design is a complex multi-objective optimization problem in which facile and robust methods are urgently demanded.Herein,a complete workflow for designing a fuel blending scheme is presented,which is theoretically supported,efficient,and reliable.Based on the data distribution of the composition and properties of the blending fuels,a model of polynomial regression with appropriate hypothesis space was established.The parameters of the model were further optimized by different intelligence algorithms to achieve high-precision regression.Then,the design of a blending fuel was described as a multi-objective optimization problem,which was solved using a Nelder–Mead algorithm based on the concept of Pareto domination.Finally,the design of a target fuel was fully validated by experiments.This study provides new avenues for designing various blending fuels to meet the needs of next-generation engines.

Hybrid Prairie Dog and Beluga Whale Optimization Algorithm for Multi-Objective Load Balanced-Task Scheduling in Cloud Computing Environments

The cloud computing technology is utilized for achieving resource utilization of remotebased virtual computer to facilitate the consumers with rapid and accurate massive data services.It utilizes on-demand resource provisioning,but the necessitated constraints of rapid turnaround time,minimal execution cost,high rate of resource utilization and limited makespan transforms the Load Balancing(LB)process-based Task Scheduling(TS)problem into an NP-hard optimization issue.In this paper,Hybrid Prairie Dog and Beluga Whale Optimization Algorithm(HPDBWOA)is propounded for precise mapping of tasks to virtual machines with the due objective of addressing the dynamic nature of cloud environment.This capability of HPDBWOA helps in decreasing the SLA violations and Makespan with optimal resource management.It is modelled as a scheduling strategy which utilizes the merits of PDOA and BWOA for attaining reactive decisions making with respect to the process of assigning the tasks to virtual resources by considering their priorities into account.It addresses the problem of pre-convergence with wellbalanced exploration and exploitation to attain necessitated Quality of Service(QoS)for minimizing the waiting time incurred during TS process.It further balanced exploration and exploitation rates for reducing the makespan during the task allocation with complete awareness of VM state.The results of the proposed HPDBWOA confirmed minimized energy utilization of 32.18% and reduced cost of 28.94% better than approaches used for investigation.The statistical investigation of the proposed HPDBWOA conducted using ANOVA confirmed its efficacy over the benchmarked systems in terms of throughput,system,and response time.

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.

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.

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.

Multi-objective optimization and evaluation of supercritical CO_(2) Brayton cycle for nuclear power generation

The supercritical CO_(2) Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout,compact structure,and high cycle efficiency.Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy.Parametric analysis,multi-objective optimizations,and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes.Results show that for the same design thermal power scale of reactors,the higher the core’s exit temperature,the better the Brayton cycle’s thermo-economic performance.Among the four-cycle layouts,the recompression cycle(RC)has the best overall performance,followed by the simple recuperation cycle(SR)and the intercooling cycle(IC),and the worst is the reheating cycle(RH).However,RH has the lowest total cost of investment(C_(tot))of$1619.85 million,and IC has the lowest levelized cost of energy(LCOE)of 0.012$/(kWh).The nuclear Brayton cycle system’s overall performance has been improved due to optimization.The performance of the molten salt reactor combined with the intercooling cycle(MSR-IC)scheme has the greatest improvement,with the net output power(W_(net)),thermal efficiencyη_(t),and exergy efficiency(η_(e))improved by 8.58%,8.58%,and 11.21%,respectively.The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_(tot) by 27.78%.In comparison,the internal rate of return(IRR)increased by only 7.8%,which is not friendly to investors with limited funds.For the nuclear Brayton cycle,the molten salt reactor combined with the recompression cycle scheme should receive priority,and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

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.

Hybrid Operator and Strengthened Diversity Improving for Multimodal Multi-Objective Optimization

Multimodal multi-objective optimization problems(MMOPs)contain multiple equivalent Pareto subsets(PSs)corresponding to a single Pareto front(PF),resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these PSs.Widely used to solve MMOPs,evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the solutions.To enhance performance in solving MMOPs,this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity improving.Specifically,a hybrid operator mechanism is devised to ensure the exploration of the decision space in the early stage and approximation to the optima in the latter stage.Moreover,an elitist-assisted differential evolution mechanism is designed for the early exploration stage.In addition,a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and PSs.Experimental studies on 11 widely used benchmark instances from a test suite verify the superiority or at least competitiveness of the proposed methods compared to five state-of-the-art algorithms tailored for MMOPs.

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.

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.