Solving conflicting bi-objective facility location problem by NSGA II evolutionary algorithm

This paper focuses on the facility location problem with two conflicting objectives. We observe that minimization of the total cost of a particular echelon may lead to the increase in the total cost of a supply chain as a whole. Thus, these conflicting objectives are required to be met together from a supply chain perspective. We have solved the problem formulated in mixed nonlinear programming by a multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting algorithm, or NSGA II in short. Numerical example is provided to show the effect of the algorithm on the solution.     

Secondary population implementation in multi-objective evolutionary algorithm for scheduling of FMS

Any practical implementation of any multi-objective evolutionary algorithm (MOEA) must include a secondary population composed of all Pareto-optimal solutions found during its search process. Such an implementation with an active participation of solutions from the secondary population into the generational population of the genetic cycle is expected to improve the effectiveness of the MOEA. In this work, two kinds of secondary population, one with set of non-dominated solutions and another with a set of inferior solutions, accrued out of the generation cycles are constructed, and with different combinations of feeding of solutions from these two secondary populations, seven different implementation schemes are designed with an aim of intensifying the convergence and diversification capabilities of the genetic process of MOEA. All the schemes were implemented in a genetic algorithm-based MOEA designed to solve the scheduling problem with dual objectives for a flexible manufacturing system and tested with common experimental data. The performances of the schemes are compared, and the most appropriate implementation scheme is proposed.     

A new multi-objective ant colony algorithm for solving the disassembly line balancing problem

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing.     

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.     

A novel hybrid multi-objective shuffled frog-leaping algorithm for a bi-criteria permutation flow shop scheduling problem

This paper investigates a novel multi-objective model for a permutation flow shop scheduling problem that minimizes both the weighted mean earliness and the weighted mean tardiness. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, a new hybrid multi-objective algorithm based on shuffled frog-leaping algorithm (SFLA) and variable neighborhood search (VNS) is devised to find Pareto optimal solutions for the given problem. To validate the performance of the proposed hybrid multi-objective shuffled frog-leaping algorithm (HMOSFLA) in terms of solution quality and diversity level, various test problems are examined. Further, the efficiency of the proposed algorithm, based on various salient metrics, is compared against two well-known multi-objective genetic algorithms: NSGA-II and SPEA-II. Our computational results suggest that the proposed HMOSFLA outperforms the two foregoing algorithms, especially for large-sized problems.     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

Multi-objective dynamic optimal trajectory planning of robot manipulators in the presence of obstacles

In this paper, a real-world test problem is presented and made available for the use of evolutionary multi-objective community. The generation of manipulator trajectories by considering multiple objectives and obstacle avoidance is a non-trivial optimisation problem. In this paper two multi-objective evolutionary algorithms viz., elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm are proposed to address this problem. Multiple criteria are optimised to two simultaneous objectives. Simulations results are presented for industrial robots with two degrees of freedom (Cartesian robot (PP) with two prismatic joints) and six degrees of freedom (PUMA 560 robot), by considering two objectives optimisation. Two methods (normalized weighting objective functions and average fuzzy membership function) are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.     

Performance enhancement of axial fan blade through multi-objective optimization techniques

This paper presents an axial fan blade design optimization method incorporating a hybrid multi-objective evolutionary algorithm (hybrid MOEA). In flow analyses, Reynolds-averaged Navier-Stokes (RANS) equations were solved using the shear stress transport turbulence model. The numerical results for the axial and tangential velocities were validated by comparing them with experimental data. Six design variables relating to the blade lean angle and the blade profile were selected through Latin hypercube sampling of design of experiments (DOE) to generate design points within the selected design space. Two objective functions, namely, total efficiency and torque, were employed, and multi-objective optimization was carried out, to enhance the performance. A surrogate model, Response Surface Approximation (RSA), was constructed for each objective function based on the numerical solutions obtained at the specified design points. The Non-dominated Sorting of Genetic Algorithm (NSGA-II) with local search was used for multi-objective optimization. The Pareto-optimal solutions were obtained, and a trade-off analysis was performed between the two conflicting objectives in view of the design and flow constraints. It was observed that, by the process of multi-objective optimization, the total efficiency was enhanced and the torque reduced. The mechanisms of these performance improvements were elucidated by analysis of the Pareto-optimal solutions.     

基于机器学习和多目标算法的钛合金插铣优化

针对钛合金的插铣加工过程开展试验和优化研究。以材料去除率和切削力为目标，采用机器学习和多目标优化算法相结合的方法来优化插铣切削参数；以主轴转速、径向切削宽度、切削步距和每齿进给量为试验变量，采用田口方法对试验变量组进行缩减。将机器学习方法与传统一阶和二阶回归方法比较，发现机器学习有很好的预测精度且解集分布更合理。分别采用MOEA/D、NSGA-Ⅱ、SPEA2、NSPSO算法对问题进行求解，并比较它们的性能，结果表明NSGA-Ⅱ综合表现最佳。最后将优化结果与初始参照进行比较，发现优化结果可以显著提高材料去除率并减小切削力，达到了高效稳定加工的目的。     

基于多目标遗传算法的水陆两栖可变形机器人结构参数设计方法

水陆两栖可变形机器人是一种兼具变形能力与两栖环境适应能力的新型移动机器人。在其机构设计中,结构参数直接影响该机器人在任务环境中的各项机动性能。针对水陆两栖可变形机器人工作环境复杂性和任务多变性,提出一种基于多目标遗传算法的机器人结构参数设计方法,以得到该型机器人在两栖环境中的最优的综合性能。在水陆两栖可变形机器人陆地环境和水环境中运动学和动力学模型基础上,建立两栖环境中机器人的机动性能指标函数与结构参数的映射关系,并在此基础之上构建面向水陆两栖可变形机器人的结构参数设计的多目标优化问题。利用多目标遗传算法得到该多目标机构参数设计问题的Pareto最优解集,并且通过组合赋权方法确定各目标决策属性的权重,从Pareto最优解集中得到符合设计要求的水陆两栖可变形机器人的各项机构参数最优解,进而指导机器人最终结构参数设计。根据最终得到的结构参数研制出水陆两栖可变形机器人样机Amoeba-II,并在两栖环境下进行样机的各项性能试验,最终验证了基于多目标遗传算法的机器人结构参数设计方法的有效性以及在机器人设计中的适用性。     

Scheduling multi-objective open shop scheduling using a hybrid immune algorithm

Despite their importance, hardly ever have multi-objective open shop problems been the topic of researches. This paper studies the mentioned problem and proposes some novel multi-objective solution methods centered on the idea behind artificial immune and simulated annealing algorithms incorporating with powerful and fast local search engines. First, the algorithms are tuned and then carefully evaluated for their performance by means of multi-objective performance measures and statistical tools. An available ant colony optimization is also brought into the experiment. Among the proposed algorithms, the results show that the variant of enhanced artificial immune algorithm outperforms the others.     

A parallel computing application of the genetic algorithm for lubrication optimization

This study investigated the performance of parallel optimization by means of a genetic algorithm (GA) for lubrication analysis. An air-bearing design was used as the illustrated example and the parallel computation was conducted in a single system image (SSI) cluster, a system of loosely network-connected desktop computers. The main advantages of using GAs as optimization tools are for multi-objective optimization, and high probability of achieving global optimum in a complex problem. To prevent a premature convergence in the early stage of evolution for multi-objective optimization, the Pareto optimality was used as an effective criterion in offspring selections. Since the execution of the genetic algorithm (GA) in search of optimum is population-based, the computations can be performed in parallel. In the cases of uneven computational loads a simple dynamic load-balancing scheme is proposed for optimizing the parallel efficiency. It is demonstrated that the huge amount of computing demand of the GA for complex multi-objective optimization problems can be effectively dealt with by parallel computing in an SSI cluster.     

考虑外包的平行机调度问题的多目标遗传算法

研究了一类考虑外包的平行机调度问题,目标是使作业外包总成本与最大完工时间同时最小化。通过对该类问题进行形式化描述与分析,设计了一种数字串形式的解的表示方法,其中每位数字表示固定作业对应的机器编号,该方法能够有效缩小解空间,从而提高搜索效率。进而构建了一种带精英策略的非支配遗传算法PD-NSGA-Ⅱ,为该类多目标调度问题提供Pareto最优解集。大量数据实验结果表明,所构造的PD-NSGA-Ⅱ算法能够在合理的时间内有效求解该类调度问题,其解的质量与计算效率均优于SPEA算法。     

多方案经营过程模型选择策略

经营过程建模的目的是为了经营过程的分析及重构。在经营过程中，由于存在约束、不确定性和不可精确估量等因素，其评价值常常是模糊的，评价目标不单一。因而存在一个对各种方案过程模型选择的问题，这个问题可以转化为多目标模糊最短路的问题。讨论了多目标模糊最短路径的算法与Pareto解空间问题，提出了基于模糊推理引擎选择多个Pareto解的策略。提出了经营过程设计框架，从而解决了企业内、企业间经营过程及供应链优化设计问题。     

Multi-objective path planning for unmanned surface vehicle with currents effects

This paper investigates the path planning problem for unmanned surface vehicle (USV), wherein the goal is to find the shortest, smoothest, most economical and safest path in the presence of obstacles and currents, which is subject to the collision avoidance, motion boundaries and velocity constraints. We formulate this problem as a multi-objective nonlinear optimization problem with generous constraints. Then, we propose the dynamic augmented multi-objective particle swarm optimization algorithm to achieve the solution. With our approach, USV can select the ideal path from the Pareto optimal paths set. Numerical simulations verify the effectiveness of our formulated model and proposed algorithm.     

Multi-objective optimization of drive gears for power split device using surrogate models

Power split device (PSD) is a key component in the energy coupling and decoupling of parallel-series hybrid electric vehicle. This paper proposes a multi-objective optimization method to achieve optimal balance solution among the volume, contact stress, and frictional energy dissipation of PSD drive gears, some of which are implicit with respect to design variables. To avoid the time-consuming problem of finite element analysis used to solve nonlinear responses, surrogate models are adopted to generate approximate expressions of design variables. Pareto-optimal solutions of PSD are obtained using multi-island genetic algorithm (MIGA), non-dominated sorting GA-II (NSGA-II), and multi-objective particle swarm optimization algorithm. The performances of PSD before and after optimization are compared. Results indicate that the proposed method is effective, and NSGA-II achieves higher optimizing efficiency in solving the multiobjective optimization problem of PSD than the other algorithms.     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

混合离散蝙蝠算法求解多目标柔性作业车间调度

针对以最大完工时间、生产成本和生产质量为目标的柔性作业车间调度问题,在研究和分析蝙蝠算法的基础上,提出一种混合离散蝙蝠算法。为了提高求解多目标柔性作业车间调度问题的混合离散蝙蝠算法的初始种群质量,在通过分析初始选择的机器与每道工序调度完工时间两者关系的基础上,提出一种优先指派规则策略产生初始种群,提高了算法的全局搜索能力。同时采用位置变异策略来使得算法在较短的时间内尽可能多地搜索到最优位置,有效地避免了算法早熟收敛。在计算问题的目标值上面,首次提出时钟算法。针对具体实例进行测试,试验数据表明,该算法在求解柔性作业车间调度问题上有很好的性能,是一种有效的调度算法,从而为解决这类问题提供了新的途径和方法。     

扇形采样约束多目标差分进化算法及工程应用

工程实践中存在大量约束多目标优化问题(Constrained multi-objective optimization problems, CMOPs),多目标进化算法是求解这类问题的一类有效方法。引入扇形采样技术,将二次变异双种群差分进化算法和约束处理方法相结合,设计求解CMOPs的进化算法——基于扇形采样的约束多目标差分进化算法(Sector-sampling-based constrained multi-objective differential evolution algorithm, SS-CMODE)。扇形采样可避免耗时的非劣操作,且能保证Pareto最优解集的良好逼近性和多样性。通过3个典型CMOPs的对比测试,表明SS-CMODE的解集均匀性和计算效率明显优于对比算法。以J23-80机械压力机使用的双曲柄串联机构多目标优化为例,研究新算法求解工程问题的有效性。以锻冲工作阶段平均速度波动最小和力传动性能最优为目标,建立机构的约束多目标优化模型,再应用SS-CMODE求解该问题。结果表明,该算法能求出多组满足约束条件的Pareto最优解,且解集均匀性良好。     

A machine cell formation algorithm for simultaneously minimising machine workload imbalances and inter-cell part movements

This paper considers a multi-objective machine cell problem, in which part types have several alternative part routings and the expected annual demand of each part type is known. This problem is characterised as optimally determining part type (routing) sets and corresponding machine cells such that total inter-cell part movements and total machine workload imbalances are simultaneously minimised. Due to the complexity of the problem, a two-stage heuristic algorithm is proposed, and computational experiments were conducted to verify the performance of the algorithm.