DeepSurNet-NSGA II:Deep Surrogate Model-Assisted Multi-Objective Evolutionary Algorithm for Enhancing Leg Linkage in Walking Robots

This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.

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.

Multi-objective Evolutionary Algorithms for MILP and MINLP in Process Synthesis

Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.

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.

EFFICIENT MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM FOR JOB SHOP SCHEDULING

A new representation method is first presented based on priority roles. According to this method, each entry in the chromosome indicates that in the procedure of the Giffler and Thompson （GT） algorithm, the conflict occurring in the corresponding machine is resolved by the corresponding priority role. Then crowding-measure multi-objective evolutionary algorithm （CMOEA） is designed, in which both archive maintenance and fitness assignment use crowding measure. Finally the comparisons between CMOEA and SPEA in solving 15 scheduling problems demonstrate that CMOEA is suitable to job shop scheduling.

Solving material distribution routing problem in mixed manufacturing systems with a hybrid multi-objective evolutionary algorithm

The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.

Optimal setting and placement of FACTS devices using strength Pareto multi-objective evolutionary algorithm

This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems.

A Hybrid Multi-Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.

Synergetic Optimization of Missile Shapes for Aerodynamic and Radar Cross-Section Performance Based on Multi-objective Evolutionary Algorithm

A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set using interactive preference articulation. There are two objective functions, to maximize ratio of lift to drag and to minimize radar cross-section (RCS) value. 3D computational electromagnetic solver was used to evaluate RCS, electromagnetic performance. 3D Navier-Stokes flow solver was adopted to evaluate aerodynamic performance. A flight mechanics solver was used to analyze the stability of the missile. Based on the MOEA, a synergetic optimization of missile shapes for aerodynamic and radar cross-section performance is completed. The results show that the proposed approach can be used in more complex optimization case of flight vehicles.

Multi-objective Evolutionary Algorithm Based on Target Space Partitioning Method

Considering the defects of conventional optimization methods, a novel optimization algorithm is introduced in this paper. Target space partitioning method is used in this algorithm to solve multi-objective optimization problem, thus achieve the coherent solution which can meet the requirements of all target functions, and improve the population's overall evolution level. The algorithm which guarantees diversity preservation and fast convergence to the Pareto set is applied to structural optimization problems. The empirical analysis supports the algorithm and gives an example with program.

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-Robot Task Allocation Using Multimodal Multi-Objective Evolutionary Algorithm Based on Deep Reinforcement Learning

The overall performance of multi-robot collaborative systems is significantly affected by the multi-robot task allocation.To improve the effectiveness,robustness,and safety of multi-robot collaborative systems,a multimodal multi-objective evolutionary algorithm based on deep reinforcement learning is proposed in this paper.The improved multimodal multi-objective evolutionary algorithm is used to solve multi-robot task allo-cation problems.Moreover,a deep reinforcement learning strategy is used in the last generation to provide a high-quality path for each assigned robot via an end-to-end manner.Comparisons with three popular multimodal multi-objective evolutionary algorithms on three different scenarios of multi-robot task allocation problems are carried out to verify the performance of the proposed algorithm.The experimental test results show that the proposed algorithm can generate sufficient equivalent schemes to improve the availability and robustness of multi-robot collaborative systems in uncertain environments,and also produce the best scheme to improve the overall task execution efficiency of multi-robot collaborative systems.

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.

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.

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.

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.

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.

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 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.