Accelerating Large-Scale Sorting through Parallel Algorithms

This study explores the application of parallel algorithms to enhance large-scale sorting, focusing on the QuickSort method. Implemented in both sequential and parallel forms, the paper provides a detailed comparison of their performance. This study investigates the efficacy of both techniques through the lens of array generation and pivot selection to manage datasets of varying sizes. This study meticulously documents the performance metrics, recording 16,499.2 milliseconds for the serial implementation and 16,339 milliseconds for the parallel implementation when sorting an array by using C++ chrono library. These results suggest that while the performance gains of the parallel approach over its serial counterpart are not immediately pronounced for smaller datasets, the benefits are expected to be more substantial as the dataset size increases.

Improving path planning efficiency for underwater gravity-aided navigation based on a new depth sorting fast search algorithm

This study focuses on the improvement of path planning efficiency for underwater gravity-aided navigation.Firstly,a Depth Sorting Fast Search(DSFS)algorithm was proposed to improve the planning speed of the Quick Rapidly-exploring Random Trees*(Q-RRT*)algorithm.A cost inequality relationship between an ancestor and its descendants was derived,and the ancestors were filtered accordingly.Secondly,the underwater gravity-aided navigation path planning system was designed based on the DSFS algorithm,taking into account the fitness,safety,and asymptotic optimality of the routes,according to the gravity suitability distribution of the navigation space.Finally,experimental comparisons of the computing performance of the ChooseParent procedure,the Rewire procedure,and the combination of the two procedures for Q-RRT*and DSFS were conducted under the same planning environment and parameter conditions,respectively.The results showed that the computational efficiency of the DSFS algorithm was improved by about 1.2 times compared with the Q-RRT*algorithm while ensuring correct computational results.

Improvement of Counting Sorting Algorithm

By analyzing the internal features of counting sorting algorithm. Two improvements of counting sorting algorithms are proposed, which have a wide range of applications and better efficiency than the original counting sort while maintaining the original stability. Compared with the original counting sort, it has a wider scope of application and better time and space efficiency. In addition, the accuracy of the above conclusions can be proved by a large amount of experimental data.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

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.

Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-II

Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in-troduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated;this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.

PMS-Sorting:A New Sorting Algorithm Based on Similarity

Borda sorting algorithm is a kind of improvement algorithm based on weighted position sorting algorithm,it is mainly suitable for the high duplication of search results,for the independent search results,the effect is not very good and the computing method of relative score in Borda sorting algorithm is according to the rule of the linear regressive,but position relationship cannot fully represent the correlation changes.aimed at this drawback,the new sorting algorithm is proposed in this paper,named PMS-Sorting algorithm,firstly the position score of the returned results is standardized processing,and the similarity retrieval word string with the query results is combined into the algorithm,the similarity calculation method is also improved,through the experiment,the improved algorithm is superior to traditional sorting algorithm.

An Only-Once-Sorting Algorithm

This paper provides a new sorting algorithm called 'Only-Once-Sorting' algorithm a mathemati cal formula,this algorithm can put elements in the positions they should be stored only once,then compacts them.The algorithm completes sorting a sequence of n elements in a calculation time of O(n ).

Robust Optimization Method of Cylindrical Roller Bearing by Maximizing Dynamic Capacity Using Evolutionary Algorithms

Optimization of cylindrical roller bearings(CRBs)has been performed using a robust design.It ensures that the changes in the objective function,even in the case of variations in design variables during manufacturing,have a minimum possible value and do not exceed the upper limit of a desired range of percentage variation.Also,it checks the feasibility of design outcome in presence of manufacturing tolerances in design variables.For any rolling element bearing,a long life indicates a satisfactory performance.In the present study,the dynamic load carrying capacity C,which relates to fatigue life,has been optimized using the robust design.In roller bearings,boundary dimensions(i.e.,bearing outer diameter,bore diameter and width)are standard.Hence,the performance is mainly affected by the internal dimensions and not the bearing boundary dimensions mentioned formerly.In spite of this,besides internal dimensions and their tolerances,the tolerances in boundary dimensions have also been taken into consideration for the robust optimization.The problem has been solved with the elitist non-dominating sorting genetic algorithm(NSGA-II).Finally,for the visualization and to ensure manufacturability of CRB using obtained values,radial dimensions drawing of one of the optimized CRB has been made.To check the robustness of obtained design after optimization,a sensitivity analysis has also been carried out to find out how much the variation in the objective function will be in case of variation in optimized value of design variables.Optimized bearings have been found to have improved life as compared with standard ones.

Satellite constellation design with genetic algorithms based on system performance

Satellite constellation design for space optical systems is essentially a multiple-objective optimization problem. In this work, to tackle this challenge, we first categorize the performance metrics of the space optical system by taking into account the system tasks（i.e., target detection and tracking）. We then propose a new non-dominated sorting genetic algorithm（NSGA） to maximize the system surveillance performance. Pareto optimal sets are employed to deal with the conflicts due to the presence of multiple cost functions. Simulation results verify the validity and the improved performance of the proposed technique over benchmark methods.

A Multi-Objective Optimization for Locating Maintenance Stations and Operator Dispatching of Corrective Maintenance

In this study,we introduce a novel multi-objective optimization model tailored for modern manufacturing,aiming to mitigate the cost impacts of operational disruptions through optimized corrective maintenance.Central to our approach is the strategic placement of maintenance stations and the efficient allocation of personnel,addressing a crucial gap in the integration of maintenance personnel dispatching and station selection.Our model uniquely combines the spatial distribution of machinery with the expertise of operators to achieve a harmonious balance between maintenance efficiency and cost-effectiveness.The core of our methodology is the NSGA Ⅲ+Dispatch,an advanced adaptation of the Non-Dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ),meticulously designed for the selection of maintenance stations and effective operator dispatching.This method integrates a comprehensive coding process,crossover operator,and mutation operator to efficiently manage multiple objectives.Rigorous empirical testing,including a detailed analysis from a taiwan region electronic equipment manufacturer,validated the effectiveness of our approach across various scenarios of machine failure frequencies and operator configurations.The findings reveal that the proposed model significantly outperforms current practices by reducing response times by up to 23%in low-frequency and 28.23%in high-frequency machine failure scenarios,leading to notable improvements in efficiency and cost reduction.Additionally,it demonstrates significant improvements in oper-ational efficiency,particularly in selective high-frequency failure contexts,while ensuring substantial manpower cost savings without compromising on operational effectiveness.This research significantly advances maintenance strategies in production environments,providing the manufacturing industry with practical,optimized solutions for diverse machine malfunction situations.Furthermore,the methodologies and principles developed in this study have potential applications in various other sectors,including healthcare,transportation,and energy,where maintenance efficiency and resource optimization are equally critical.

Strengthened Dominance Relation NSGA-Ⅲ Algorithm Based on Differential Evolution to Solve Job Shop Scheduling Problem

The job shop scheduling problem is a classical combinatorial optimization challenge frequently encountered in manufacturing systems.It involves determining the optimal execution sequences for a set of jobs on various machines to maximize production efficiency and meet multiple objectives.The Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ)is an effective approach for solving the multi-objective job shop scheduling problem.Nevertheless,it has some limitations in solving scheduling problems,including inadequate global search capability,susceptibility to premature convergence,and challenges in balancing convergence and diversity.To enhance its performance,this paper introduces a strengthened dominance relation NSGA-Ⅲ algorithm based on differential evolution(NSGA-Ⅲ-SD).By incorporating constrained differential evolution and simulated binary crossover genetic operators,this algorithm effectively improves NSGA-Ⅲ’s global search capability while mitigating pre-mature convergence issues.Furthermore,it introduces a reinforced dominance relation to address the trade-off between convergence and diversity in NSGA-Ⅲ.Additionally,effective encoding and decoding methods for discrete job shop scheduling are proposed,which can improve the overall performance of the algorithm without complex computation.To validate the algorithm’s effectiveness,NSGA-Ⅲ-SD is extensively compared with other advanced multi-objective optimization algorithms using 20 job shop scheduling test instances.The experimental results demonstrate that NSGA-Ⅲ-SD achieves better solution quality and diversity,proving its effectiveness in solving the multi-objective job shop scheduling problem.

考虑交货期的双资源柔性作业车间节能调度

为解决含有机器和工人双资源约束的柔性作业车间节能调度问题,在考虑交货期的基础上,建立了以总提前和拖期惩罚值及总能耗最小为目标的双资源柔性作业车间节能调度模型。提出了一种改进的非支配排序遗传算法(improved non-dominated sorting genetic algorithmⅡ,INSGA-Ⅱ)进行求解。针对所优化的目标,设计了一种三阶段解码方法以获得高质量的可行解;利用动态自适应交叉和变异算子以获得更多优良个体;改进拥挤距离以获得收敛性和分布性更优的种群。将INSGA-Ⅱ与多种多目标优化算法进行对比分析,实验结果表明所提算法可行且有效。

基于混合遗传蚁群算法的多目标FJSP问题研究

针对多目标柔性作业车间调度问题求解过程中未综合考虑解集多样性与求解效率的问题,提出了一种混合遗传蚁群算法来求解。首先,通过改进的NSGA-Ⅱ(non-dominated sorting genetic algorithmⅡ)获取问题的较优解,以此来确定蚁群算法的初始信息素分布;其次,根据提出的自适应伪随机比例规则和改进的信息素更新规则来优化蚂蚁的遍历过程;最后,通过邻域搜索,扩大蚂蚁的搜索空间,从而提高解集的多样性。通过Kacem和BRdata算例进行实验验证,证明混合遗传蚁群算法具有更高的求解效率和更好解集多样性。

Smart Bubble Sort:A Novel and Dynamic Variant of Bubble Sort Algorithm

In the present era,a very huge volume of data is being stored in online and offline databases.Enterprise houses,research,medical as well as healthcare organizations,and academic institutions store data in databases and their subsequent retrievals are performed for further processing.Finding the required data from a given database within the minimum possible time is one of the key factors in achieving the best possible performance of any computer-based application.If the data is already sorted,finding or searching is comparatively faster.In real-life scenarios,the data collected from different sources may not be in sorted order.Sorting algorithms are required to arrange the data in some order in the least possible time.In this paper,I propose an intelligent approach towards designing a smart variant of the bubble sort algorithm.I call it Smart Bubble sort that exhibits dynamic footprint:The capability of adapting itself from the average-case to the best-case scenario.It is an in-place sorting algorithm and its best-case time complexity isΩ(n).It is linear and better than bubble sort,selection sort,and merge sort.In averagecase and worst-case analyses,the complexity estimates are based on its static footprint analyses.Its complexity in worst-case is O(n2)and in average-case isΘ(n^(2)).Smart Bubble sort is capable of adapting itself to the best-case scenario from the average-case scenario at any subsequent stages due to its dynamic and intelligent nature.The Smart Bubble sort outperforms bubble sort,selection sort,and merge sort in the best-case scenario whereas it outperforms bubble sort in the average-case scenario.

Multi-objective Optimization of Industrial Purified Terephthalic Acid Oxidation Process

Multi-objective optimization of a purified terephthalic acid (PTA) oxidation unit is carried out in this paper by using a process modei that has been proved to describe industrial process quite well. The modei is a semi-empirical structured into two series ideal continuously stirred tank reactor (CSTR) models. The optimal objectives include maximizing the yield or inlet rate and minimizing the concentration of 4-carboxy-benzaldhyde, which is the main undesirable intermediate product in the reaction process. The multi-objective optimization algorithra applied in this study is non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ). The performance of NSGA-Ⅱ is further illustrated by application to the title process.

Dual-Objective Mixed Integer Linear Program and Memetic Algorithm for an Industrial Group Scheduling Problem

Group scheduling problems have attracted much attention owing to their many practical applications.This work proposes a new bi-objective serial-batch group scheduling problem considering the constraints of sequence-dependent setup time,release time,and due time.It is originated from an important industrial process,i.e.,wire rod and bar rolling process in steel production systems.Two objective functions,i.e.,the number of late jobs and total setup time,are minimized.A mixed integer linear program is established to describe the problem.To obtain its Pareto solutions,we present a memetic algorithm that integrates a population-based nondominated sorting genetic algorithm II and two single-solution-based improvement methods,i.e.,an insertion-based local search and an iterated greedy algorithm.The computational results on extensive industrial data with the scale of a one-week schedule show that the proposed algorithm has great performance in solving the concerned problem and outperforms its peers.Its high accuracy and efficiency imply its great potential to be applied to solve industrial-size group scheduling problems.

Optimization of maintenance strategy for high-speed railwaycatenary system based on multistate model

A multi-objective optimization model considering both reliability and maintenance cost is proposed to solve the contradiction between reliability and maintenance cost in high-speed railway catenary system maintenance activities.The non-dominated sorting genetic algorithm 2(NSGA2)is applied to multi-objective optimization,and the optimization result is a set of Pareto solutions.Firstly,multistate failure mode analysis is conducted for the main devices leading to the failure of catenary,and then the reliability and failure mode of the whole catenary system is analyzed.The mathematical relationship between system reliability and maintenance cost is derived considering the existing catenary preventive maintenance mode to improve the reliability of the system.Secondly,an improved NSGA2(INSGA2)is proposed,which strengths population diversity by improving selection operator,and introduces local search strategy to ensure that population distribution is more uniform.The comparison results of the two algorithms before and after improvement on the zero-ductility transition(ZDT)series functions show that the population diversity is better and the solution is more uniform using INSGA2.Finally,the INSGA2 is applied to multi-objective optimization of system reliability and maintenance cost in different maintenance periods.The decision-makers can choose the reasonable solutions as the maintenance plans in the optimization results by weighing the relationship between the system reliability and the maintenance cost.The selected maintenance plans can ensure the lowest maintenance cost while the system reliability is as high as possible.

Evolutionary Trajectory Planning for an Industrial Robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator （AdeptOne XL robot） in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm （NSGA-II） and multi-objective differential evolution （MODE）, have been used for the optimization. Two methods （normalized weighting objective functions and average fitness factor） are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.

Research on the Optimization and Simulation of the Shortest Path Based on Algorithm of Dijkstra

Dijkstra algorithm is a theoretical basis to solve transportation network problems of the shortest path, which has a wide range of application in path optimization. Through analyzing traditional Dijkstra algorithm,on account of the insufficiency of this algorithm in path optimization,this paper uses adjacency list and circular linked list with combination to store date,and through the improved quick sorting algorithm for weight sorting, accomplish a quick search to the adjacent node,and so an improved Dijkstra algorithm is got.Then apply it to the optimal path search,and make simulation analysis for this algorithm through the example,also verify the effectiveness of the proposed algorithm.