Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method 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 the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

一种工业机器人多目标轨迹优化算法

为解决工业机器人工作效率低、能耗损失严重和关节冲击磨损较大的问题,提出了一种基于布谷鸟搜索（cuckoo search,CS）算法和非支配排序遗传算法-Ⅱ(non-dominated sorting genetic algorithm-Ⅱ,NSGA-Ⅱ)的混合算法（简称为CSNSGA-Ⅱ）,用于机器人的轨迹优化。采用5次非均匀有理B样条（non-uniform rational B-splines,NURBS）曲线作为工业机器人的轨迹规划曲线,同时以运动时间、能耗和冲击磨损为优化目标构建相应的多目标轨迹优化模型,并在速度、加速度和加加速度的约束下采用CSNSGA-Ⅱ进行轨迹优化。CSNSGA-Ⅱ以Tent混沌映射初始化时间序列,采用不可行度算法将解分为可行解与不可行解,并利用改进的CS算法对不可行解进行处理。利用MATLAB软件对6R勃朗特机器人进行建模仿真,并对得到的非支配解集和归一化加权迭代最优值进行对比分析。仿真结果表明,相比于NSGA-Ⅱ、多目标粒子群优化（multi-objective particle swarm optimization,MOPSO）算法,所提出的CSNS...     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

A hybrid multi-objective particle swarm algorithm for a mixed-model assembly line sequencing problem

Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management where diversified customers' demands exist. In this article, three major goals are considered: (i) total utility work, (ii) total production rate variation and (iii) total setup cost. Due to the complexity of the problem, a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) is devised to obtain the locally Pareto-optimal frontier where simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed algorithm in terms of solution quality and diversity level, the algorithm is applied to various test problems and its reliability, based on different comparison metrics, is compared with three prominent multi-objective genetic algorithms, PS-NC GA, NSGA-II and SPEA-II. The computational results show that the proposed hybrid algorithm significantly outperforms existing genetic algorithms in large-sized problems.     

Performance-based multi-objective optimization of large steel structures

In recent years, the importance of economical considerations in the field of structures has motivated many researchers to propose new methods for minimizing the initial and life cycle cost of the structures subjected to seismic loading. In this paper, a new framework is presented to solve the performance-based multi-objective optimization problem considering the initial and life cycle cost of large structures. In order to solve this problem, a non-dominated sorting genetic algorithm (NSGA-II) using differential evolution operators is employed to solve the optimization problem, while a specific meta-model is utilized for reducing the number of fitness function evaluations. The required computational time for pushover analysis is decreased by a simple numerical method. The constraints of the optimization problem are based on the FEMA codes. The presented results for application of the proposed framework demonstrate its capability in solving the present complex multi-objective optimization problem.     

原油一次加工过程的多目标调度优化

在制定原油一次加工过程详细调度时,往往需要考虑多个优化目标。本文提出一种基于改进的骨干粒子群算法和II代非支配遗传算法协同进化的双种群算法,并通过Pareto差熵控制种群的交流,优化了供油罐使用成本、供油罐的切换成本、管道中原油混合成本以及供油罐罐底混合成本4个目标。通过一个工业实例,将本文算法与现有的几种具有代表性的进化多目标优化算法进行对比,验证本文算法的可行性和有效性。     

Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm

The integration of process planning and scheduling is considered as a critical component in manufacturing systems. In this paper, a multi-objective approach is used to solve the planning and scheduling problem. Three different objectives considered in this work are minimisation of makespan, machining cost and idle time of machines. To solve this integration problem, we propose an improved controlled elitist non-dominated sorting genetic algorithm (NSGA) to take into account the computational intractability of the problem. An illustrative example and five test cases have been taken to demonstrate the capability of the proposed model. The results confirm that the proposed multi-objective optimisation model gives optimal and robust solutions. A comparative study between proposed algorithm, controlled elitist NSGA and NSGA-II show that proposed algorithm significantly reduces scheduling objectives like makespan, cost and idle time, and is computationally more efficient.     

基于分布式猴群算法的传感器优化布置方法研究

建立了针对具有较多自由度的大型结构传感器优化布置的分布式猴群算法。通过引入双重编码的方式, 克服了原猴群算法只能解决连续变量的缺陷;针对单个猴群全局搜索能力较弱的问题, 提出了一种将初始化产生的大量猴子个体按照指定的方式分配到多个猴群进行同步并行搜索的方法;考虑原猴群算法能够跳出局部最优的特点以及和声算法较强的局部搜索能力, 提出将每个猴群得到的初步最优解作为初始和声记忆库, 采用基本和声算法进行二次搜索的方法, 来获取传感器的最终布设方案。文末以大连国贸大厦为例, 进行了参数敏感性分析以及传感器优化布置方案的选择, 结果表明分布式猴群算法具有较强的全局寻优能力, 非常适用于具有较多自由度的大型结构传感器优化布置。     

Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.     

Improved imperialist competitive algorithms for rebalancing multi-objective two-sided assembly lines with space and resource constraints

In this paper, a mathematical model and an improved imperial competition algorithm (IICA) are proposed to solve the multi-objective two-sided assembly line rebalancing problem with space and resource restrictions (MTALRBP-SR). The aim is to find lines’ rebalance with the trade-off between efficiency, rebalancing cost and smoothing after reconfiguration. IICA utilises a new initialisation heuristic procedure based on classic heuristic rules to generate feasible initial solutions. A novel heuristic assimilation method is developed to vigorously conduct local search. In addition, a group-based decoding heuristic procedure is developed to fulfil the final task reassignment with the additional restrictions. To investigate the performance of the proposed algorithm, it is first tested on MTALRBP of benchmark problems and compared with some existing algorithms such as genetic algorithm, variable neighbourhood search algorithm, discrete artificial bee colony algorithm, and two iterated greedy algorithms. Next, the efficiency of the proposed IICA for solving MTALRBP-SR is revealed by comparison with a non-dominated sorting genetic algorithm (NSGA-II) and two versions of original ICA. Computational results and comparisons show the efficiency and effectiveness of IICA. Furthermore, a real-world case study is conducted to validate the proposed algorithm.     

On the integrated charge planning with flexible jobs in primary steelmaking processes

The integrated charge planning (ICP) problem based on flexible jobs in an integrated steel plant is extremely difficult and valuable. The purpose of this paper is to improve the efficiency and feasibility of planning by minimising the number of charges, minimising the total production costs and maximising the total throughput, considering the hard constraints and soft constraints. A multi-objective mathematical programming model for the problem is formulated, and it is shown that the problem is NP-hard. Two new meta-heuristics are designed, one is guided variable neighbourhood search (GVNS) combined with harmony search, and the other is GVNS combined with simulated annealing. Compared with enumeration algorithm, tabu search, variable neighbourhood search (VNS), harmony search, extend next fit decreasing (ENFD) and skewed VNS (SVNS), variable neighbourhood descent (VND), the numerical results by actual production data have shown that the proposed model and GVNHS are feasible and effective for ICP.     

Two efficient algorithms for constructing almost even approximations of the Pareto front in multi-objective optimization problems

In this article, two algorithms are proposed for constructing almost even approximations of the Pareto front of multi-objective optimization problems. The first algorithm is a hybrid of the ε-constraint and Pascoletti–Serafini scalarization methods for solving bi-objective problems. The second is a modification of the successive Pareto optimization (SPO) algorithm for solving three-objective problems. In these algorithms, the MATLAB fmincon solver is used to solve single-objective optimization problems, which returns a local optimal solution. Some metrics are considered to evaluate the quality of approximations obtained by the suggested algorithms on six test problems, and their results are compared with other algorithms (normal constraint, weighted constraint, SPO, differential evolution, multi-objective evolutionary algorithm/decomposition–differential evolution, non-dominated sorting genetic algorithm-II and S-metric selection evolutionary multi-objective algorithm). Experimental results show that the proposed algorithms provide almost even approximations of the whole Pareto front, and better quality of approximation and CPU time compared with established algorithms.     

An evolutionary algorithm for a new multi-objective location-inventory model in a distribution network with transportation modes and third-party logistics providers

This paper proposes a multi-objective optimisation algorithm for solving the new multi-objective location-inventory problem (MOLIP) in a distribution centre (DC) network with the presence of different transportation modes and third-party logistics (3PL) providers. 3PL is an external company that performs all or part of a company’s logistics functions. In order to increase the efficiency and responsiveness in a supply chain, it is assumed that 3PL is responsible to manage inventory in DCs and deliver products to customers according to the provided plan. DCs are determined so as to simultaneously minimise three conflicting objectives; namely, total costs, earliness and tardiness, and deterioration rate. In this paper, a non-dominated sorting genetic algorithm (NSGA-II) is proposed to perform high-quality search using two-parallel neighbourhood search procedures for creating initial solutions. The potential of this algorithm is evaluated by its application to the numerical example. Then, the obtained results are analysed and compared with multi-objective simulated annealing (MOSA). It is concluded that this algorithm is capable of generating a set of alternative DCs considering the optimisation of multiple objectives, significantly improving the decision-making process involved in the distribution network design.     

Explicit consideration of multiple objectives in cellular manufacturing

Although many methodologies have been proposed for solving the cell-formation problem, few of them explicitly consider the existence of multiple objectives in the design process. In this article, the development of multi-objective genetic programming single-linkage cluster analysis (GP-SLCA), an evolutionary methodology for the solution of the multi-objective cell-formation problem, is described. The proposed methodology combines an existing algorithm for the solution of single-objective cell-formation problems with NSGA-II, an elitist evolutionary multi-objective optimization technique. Multi-objective GP-SLCA is able to generate automatically a set of non-dominated solutions for a given multi-objective cell-formation problem. The benefits of the proposed approach are illustrated using an example test problem taken from the literature and an industrial case study.     

Optimization of aluminium sheet hot stamping process using a multi-objective stochastic approach

This article aims to investigate the means to obtain optimal hot stamping process parameters and the influence of the stochastic variability of these parameters on forming quality. A multi-objective stochastic approach, integrating response surface methodology (RSM), multi-objective genetic algorithm optimization non-dominated sorting genetic algorithm II (NSGA-II) and the Monte Carlo simulation (MCS) method is proposed in this article to achieve this goal. RSM was used to establish the relationship between the process parameters and forming quality indices. NSGA-II was utilized to obtain a Pareto frontier, which consists of a series of optimal process parameters. The MCS method was employed to study and reduce the influence of a stochastic property of these process parameters on forming quality. The results confirmed the efficiency of the proposed multi-objective stochastic approach during optimization of the hot stamping process. Robust optimal process parameters guaranteeing good forming quality were also obtained using this approach.     

Multi-objective integrated acyclic crew rostering and vehicle assignment problem in public bus transportation

In this study, we try to solve a real planning problem faced in public bus transportation. It is a multi-objective integrated crew rostering and vehicle assignment problem. We model this problem as a multi-objective set partitioning problem. Most of the time, crew rostering problem with a single-objective function is considered, and the output may not satisfy some transport companies. To minimize the cost and maximize the fairness of the workload among the drivers, we define many criteria. Although crew rostering problem and its integrated versions appear in the literature, it is the first time these two problems are integrated. We propose a new multi-objective tabu search algorithm to obtain near Pareto-optimal solutions. The algorithm works with a set of solutions using parallel search. We test our algorithm for the case with ten objectives and define a method to choose solutions from the approximated efficient frontier to present to the user. We discuss the performance of our meta-heuristic approach.

     

云环境下大规模定制中资源配置研究

针对传统大规模定制生产模式无法满足日益个性化的产品市场变化,导致产品无法形成生产批量,在生产过程中增加成本和时间的问题,结合云制造的背景环境,提出云环境下大规模定制产品的生产模式,并通过建立包含生产总时间、生产总成本和产品总质量的多目标优化函数模型,使用NSGA-Ⅱ算法对所建模型进行求解,对模式运行中的资源配置问题进行研究。最后通过航模发动机进行算例验证,证明所建模型可以得到解决云环境下大规模定制产品生产过程中资源优化配置问题的最优生产方案。     

基于Pareto最优解的零件制作方向优化研究

分析了快速成型工艺中零件制作方向对制件表面质量、所需支撑面积和零件制造时间的影响,分别建立了它们的优化数学模型。采用了基于Pareto最优解的多目标优化遗传算法NSGA-II进行优化计算,通过与单目标优化方法求得最优结果的对比,表明用多目标优化方法进行零件制作方向的优化计算,不仅可以求出比单目标方法更优的解,而且通过一次优化计算就可得到多个较优的零件制作方向。     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.