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 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 Fast Clustering Based Evolutionary Algorithm for Super-Large-Scale Sparse Multi-Objective Optimization

During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.

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-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.

Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems

Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

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.

Optimizing Deep Learning for Computer-Aided Diagnosis of Lung Diseases: An Automated Method Combining Evolutionary Algorithm, Transfer Learning, and Model Compression

Recent developments in Computer Vision have presented novel opportunities to tackle complex healthcare issues,particularly in the field of lung disease diagnosis.One promising avenue involves the use of chest X-Rays,which are commonly utilized in radiology.To fully exploit their potential,researchers have suggested utilizing deep learning methods to construct computer-aided diagnostic systems.However,constructing and compressing these systems presents a significant challenge,as it relies heavily on the expertise of data scientists.To tackle this issue,we propose an automated approach that utilizes an evolutionary algorithm(EA)to optimize the design and compression of a convolutional neural network(CNN)for X-Ray image classification.Our approach accurately classifies radiography images and detects potential chest abnormalities and infections,including COVID-19.Furthermore,our approach incorporates transfer learning,where a pre-trainedCNNmodel on a vast dataset of chest X-Ray images is fine-tuned for the specific task of detecting COVID-19.This method can help reduce the amount of labeled data required for the task and enhance the overall performance of the model.We have validated our method via a series of experiments against state-of-the-art architectures.

Enhancing Cancer Classification through a Hybrid Bio-Inspired Evolutionary Algorithm for Biomarker Gene Selection

In this study,our aim is to address the problem of gene selection by proposing a hybrid bio-inspired evolutionary algorithm that combines Grey Wolf Optimization(GWO)with Harris Hawks Optimization(HHO)for feature selection.Themotivation for utilizingGWOandHHOstems fromtheir bio-inspired nature and their demonstrated success in optimization problems.We aimto leverage the strengths of these algorithms to enhance the effectiveness of feature selection in microarray-based cancer classification.We selected leave-one-out cross-validation(LOOCV)to evaluate the performance of both two widely used classifiers,k-nearest neighbors(KNN)and support vector machine(SVM),on high-dimensional cancer microarray data.The proposed method is extensively tested on six publicly available cancer microarray datasets,and a comprehensive comparison with recently published methods is conducted.Our hybrid algorithm demonstrates its effectiveness in improving classification performance,Surpassing alternative approaches in terms of precision.The outcomes confirm the capability of our method to substantially improve both the precision and efficiency of cancer classification,thereby advancing the development ofmore efficient treatment strategies.The proposed hybridmethod offers a promising solution to the gene selection problem in microarray-based cancer classification.It improves the accuracy and efficiency of cancer diagnosis and treatment,and its superior performance compared to other methods highlights its potential applicability in realworld cancer classification tasks.By harnessing the complementary search mechanisms of GWO and HHO,we leverage their bio-inspired behavior to identify informative genes relevant to cancer diagnosis and treatment.

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.

Tourism Route Recommendation Based on A Multi-Objective Evolutionary Algorithm Using Two-Stage Decomposition and Pareto Layering

Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.

Hybrid Hierarchical Particle Swarm Optimization with Evolutionary Artificial Bee Colony Algorithm for Task Scheduling in Cloud Computing

Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.

Optimal Location and Sizing ofMulti-Resource Distributed Generator Based onMulti-Objective Artificial Bee Colony Algorithm

Distribution generation(DG)technology based on a variety of renewable energy technologies has developed rapidly.A large number of multi-type DG are connected to the distribution network(DN),resulting in a decline in the stability of DN operation.It is urgent to find a method that can effectively connect multi-energy DG to DN.photovoltaic(PV),wind power generation(WPG),fuel cell(FC),and micro gas turbine(MGT)are considered in this paper.A multi-objective optimization model was established based on the life cycle cost(LCC)of DG,voltage quality,voltage fluctuation,system network loss,power deviation of the tie-line,DG pollution emission index,and meteorological index weight of DN.Multi-objective artificial bee colony algorithm(MOABC)was used to determine the optimal location and capacity of the four kinds of DG access DN,and compared with the other three heuristic algorithms.Simulation tests based on IEEE 33 test node and IEEE 69 test node show that in IEEE 33 test node,the total voltage deviation,voltage fluctuation,and system network loss of DN decreased by 49.67%,7.47%and 48.12%,respectively,compared with that without DG configuration.In the IEEE 69 test node,the total voltage deviation,voltage fluctuation and system network loss of DN in the MOABC configuration scheme decreased by 54.98%,35.93%and 75.17%,respectively,compared with that without DG configuration,indicating that MOABC can reasonably plan the capacity and location of DG.Achieve the maximum trade-off between DG economy and DN operation stability.

A Novel Collaborative Evolutionary Algorithm with Two-Population for Multi-Objective Flexible Job Shop Scheduling

Job shop scheduling(JS)is an important technology for modern manufacturing.Flexible job shop scheduling(FJS)is critical in JS,and it has been widely employed in many industries,including aerospace and energy.FJS enables any machine from a certain set to handle an operation,and this is an NP-hard problem.Furthermore,due to the requirements in real-world cases,multi-objective FJS is increasingly widespread,thus increasing the challenge of solving the FJS problems.As a result,it is necessary to develop a novel method to address this challenge.To achieve this goal,a novel collaborative evolutionary algorithmwith two-population based on Pareto optimality is proposed for FJS,which improves the solutions of FJS by interacting in each generation.In addition,several experimental results have demonstrated that the proposed method is promising and effective for multi-objective FJS,which has discovered some new Pareto solutions in the well-known benchmark problems,and some solutions can dominate the solutions of some other methods.

Dose reconstruction with Compton camera during proton therapy via subset-driven origin ensemble and double evolutionary algorithm

Compton camera-based prompt gamma(PG) imaging has been proposed for range verification during proton therapy. However, a deviation between the PG and dose distributions, as well as the difference between the reconstructed PG and exact values, limit the effectiveness of the approach in accurate range monitoring during clinical applications. The aim of the study was to realize a PG-based dose reconstruction with a Compton camera, thereby further improving the prediction accuracy of in vivo range verification and providing a novel method for beam monitoring during proton therapy. In this paper, we present an approach based on a subset-driven origin ensemble with resolution recovery and a double evolutionary algorithm to reconstruct the dose depth profile(DDP) from the gamma events obtained by a cadmium-zinc-telluride Compton camera with limited position and energy resolution. Simulations of proton pencil beams with clinical particle rate irradiating phantoms made of different materials and the CT-based thoracic phantom were used to evaluate the feasibility of the proposed method. The results show that for the monoenergetic proton pencil beam irradiating homogeneous-material box phantom,the accuracy of the reconstructed DDP was within 0.3 mm for range prediction and within 5.2% for dose prediction. In particular, for 1.6-Gy irradiation in the therapy simulation of thoracic tumors, the range deviation of the reconstructed spreadout Bragg peak was within 0.8 mm, and the relative dose deviation in the peak area was less than 7% compared to the exact values. The results demonstrate the potential and feasibility of the proposed method in future Compton-based accurate dose reconstruction and range verification during proton therapy.

Design and optimization of diffraction-limited storage ring lattices based on many-objective evolutionary algorithms

Multi-objective evolutionary algorithms(MOEAs) are typically used to optimize two or three objectives in the accelerator field and perform well. However, the performance of these algorithms may severely deteriorate when the optimization objectives for an accelerator are equal to or greater than four. Recently, many-objective evolutionary algorithms(MaOEAs)that can solve problems with four or more optimization objectives have received extensive attention. In this study, two diffraction-limited storage ring(DLSR) lattices of the Extremely Brilliant Source(ESRF-EBS) type with different energies were designed and optimized using three MaOEAs and a widely used MOEA. The initial population was found to have a significant impact on the performance of the algorithms and was carefully studied. The performances of the four algorithms were compared, and the results demonstrated that the grid-based evolutionary algorithm(GrEA) had the best performance.Ma OEAs were applied in many-objective optimization of DLSR lattices for the first time, and lattices with natural emittances of 116 and 23 pm·rad were obtained at energies of 2 and 6 GeV, respectively, both with reasonable dynamic aperture and local momentum aperture(LMA). This work provides a valuable reference for future many-objective optimization of DLSRs.

Design of S-band photoinjector with high bunch charge and low emittance based on multi-objective genetic algorithm

High-brightness electron beams are required to drive LINAC-based free-electron lasers(FELs)and storage-ring-based synchrotron radiation light sources.The bunch charge and RMS bunch length at the exit of the LINAC play a crucial role in the peak current;the minimum transverse emittance is mainly determined by the injector of the LINAC.Thus,a photoin-jector with a high bunch charge and low emittance that can simultaneously provide high-quality beams for 4th generation synchrotron radiation sources and FELs is desirable.The design of a 1.6-cell S-band 2998-MHz RF gun and beam dynamics optimization of a relevant beamline are presented in this paper.Beam dynamics simulations were performed by combining ASTRA and the multi-objective genetic algorithm NSGA II.The effects of the laser pulse shape,half-cell length of the RF gun,and RF parameters on the output beam quality were analyzed and compared.The normalized transverse emittance was optimized to be as low as 0.65 and 0.92 mm·mrad when the bunch charge was as high as 1 and 2 nC,respectively.Finally,the beam stability properties of the photoinjector,considering misalignment and RF jitter,were simulated and analyzed.

Evolutionary Multitasking With Global and Local Auxiliary Tasks for Constrained Multi-Objective Optimization

Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.

Do Search and Selection Operators Play Important Roles in Multi-Objective Evolutionary Algorithms:A Case Study

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.