Reliability-based robust design optimization: A general methodology using genetic algorithm

In this paper, we present an improved general methodology including four stages to design robust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simultaneously to propose the new formulation of reliability-based robust design optimization (RBRDO) problems. In order to generate reliable and robust Pareto-optimal solutions, the combination of genetic algorithm with reliability assessment loop based on the performance measure approach is applied as the second stage. Next, we develop two criteria to select a solution from obtained Pareto-optimal set to achieve the best possible implementation. Finally, the result verification is performed with Monte Carlo Simulations and also the quality improvement during manufacturing process is considered by identifying and controlling the critical variables. The effectiveness and applicability of this new proposed methodology is demonstrated through a case study.     

Goal programming approach to solving network design problem with multiple objectives and demand uncertainty

The transportation network design problem (NDP) with multiple objectives and demand uncertainty was originally formulated as a spectrum of stochastic multi-objective programming models in a bi-level programming framework. Solving these stochastic multi-objective NDP (SMONDP) models directly requires generating a family of optimal solutions known as the Pareto-optimal set. For practical implementation, only a good solution that meets the goals of different stakeholders is required. In view of this, we adopt a goal programming (GP) approach to solve the SMONDP models. The GP approach explicitly considers the user-defined goals and priority structure among the multiple objectives in the NDP decision process. Considering different modeling purposes, we provide three stochastic GP models with different philosophies to model planners’ NDP decision under demand uncertainty, i.e., the expected value GP model, chance-constrained GP model, and dependent-chance GP model. Meanwhile, a unified simulation-based genetic algorithm (SGA) solution procedure is developed to solve all three stochastic GP models. Numerical examples are also presented to illustrate the practicability of the GP approach in solving the SMONDP models as well as the robustness of the SGA solution procedure.     

A genetic algorithm approach for multi-objective optimization of supply chain networks

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management. It is an important and strategic operations management problem in supply chain management, and usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective SCN design problem. To deal with multi-objective and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. An experimental study using actual data from a company, which is a producer of plastic products in Turkey, is carried out into two stages. While the effects of weight approaches on the performance of proposed solution procedure are investigated in the first stage, the proposed solution procedure and simulated annealing are compared according to quality of Pareto-optimal solutions in the second stage.     

Machining scheme selection of digital manufacturing based on genetic algorithm and AHP

The selection of machining scheme for a part is an important and strategic problem. It involves multiple and conflicting objectives such as cost, time, quality, service level, resource utilization, etc. The selection is always affected by subjective factors such as the knowledge and experiences of decision maker in conventional machining. This paper proposes a method based on genetic algorithms (GA) to find out the set of Pareto-optimal solutions for multi-objective digital machining scheme selection. To deal with multi-objective and enable the engineer to make decision on different demands, an analytic hierarchy process (AHP) is implemented in the proposed procedure to determine the weight value of evaluation indexes. Three conflicting objectives: cost, quality and operation time are simultaneously optimized. An application sample is developed and its results are analyzed. The optimization results show that the hybrid algorithm is reliable and robust.     

基于正交设计的多目标演化算法

提出一种基于正交设计的多目标演化算法以求解多目标优化问题(MOPs)．它的特点在于：(1)用基于正交数组的均匀搜索代替经典EA的随机性搜索,既保证了解分布的均匀性,又保证了收敛的快速性;(2)用统计优化方法繁殖后代,不仅提高了解的精度,而且加快了收敛速度;(3)实验结果表明,对于双目标的MOPs,新算法在解集分布的均匀性、多样性与解精确性及算法收敛速度等方面均优于SPEA;(4)用于求解一个带约束多目标优化工程设计问题,它得到了最好的结果——Pareto最优解,在此之前,此问题的Pareto最优解是未知的．     

On decomposition methods in interactive user-preference based optimization

Evolutionary multi-objective optimization (EMO) methodologies have been widely applied to find a well-distributed trade-off solutions approximating to the Pareto-optimal front in the past decades. However, integrating the user-preference into the optimization to find the region of interest (ROI) [1] or preferred Pareto-optimal solutions could be more efficient and effective for the decision maker (DM) straightforwardly. In this paper, we propose several methods by combining preference-based strategy (like the reference points) with the decomposition-based multi-objective evolutionary algorithm (MOEA/D) [2], and demonstrate how preferred sets or ROIs near the different reference points specified by the DM can be found simultaneously and interactively. The study is based on the experiments conducted on a set of test problems with objectives ranging from two to fifteen objectives. Experiments have proved that the proposed approaches are more efficient and effective especially on many-objective problems to provide a set of solutions to the DM's preference, so that a better and a more reliable decision can be made.     

Introducing robustness in multi-objective optimization

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.     

一类新型动态多目标鲁棒进化优化方法

传统动态多目标优化问题（Dynamic multi-objective optimization problems,DMOPs）的求解方法,通常需要在新环境下,通过重新激发寻优过程,获得适应该环境的Pareto最优解.这可能导致较高的计算代价和资源成本,甚至无法在有限时间内执行该优化解.由此,提出一类寻找动态鲁棒Pareto最优解集的进化优化方法.动态鲁棒Pareto解集是指某一时刻下的Pareto较优解可以以一定稳定性阈值,逼近未来多个连续动态环境下的真实前沿,从而直接作为这些环境下的Pareto解集,以减小计算代价.为合理度量Pareto解的环境适应性,给出了时间鲁棒性和性能鲁棒性定义,并将其转化为两类鲁棒优化模型.引入基于分解的多目标进化优化方法和无惩罚约束处理方法,构建了动态多目标分解鲁棒进化优化方法.特别是基于移动平均预测模型实现了未来动态环境下适应值的多维时间序列预测.基于提出的两类新型性能评价测度,针对8个典型动态测试函数的仿真实验,结果表明该方法得到满足决策者精度要求,且具有较长平均生存时间的动态鲁棒Pareto最优解.     

Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Most existing multiobjective evolutionary algorithms aim at approximating the Pareto front (PF), which is the distribution of the Pareto-optimal solutions in the objective space. In many real-life applications, however, a good approximation to the Pareto set (PS), which is the distribution of the Pareto-optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of multiobjective optimization problems (MOPs), in which the dimensionalities of the PS and the PF manifolds are different so that a good approximation to the PF might not approximate the PS very well. It proposes a probabilistic model-based multiobjective evolutionary algorithm, called MMEA, for approximating the PS and the PF simultaneously for an MOP in this class. In the modeling phase of MMEA, the population is clustered into a number of subpopulations based on their distribution in the objective space, the principal component analysis technique is used to estimate the dimensionality of the PS manifold in each subpopulation, and then a probabilistic model is built for modeling the distribution of the Pareto-optimal solutions in the decision space. Such a modeling procedure could promote the population diversity in both the decision and objective spaces. MMEA is compared with three other methods, KP1, Omni-Optimizer and RM-MEDA, on a set of test instances, five of which are proposed in this paper. The experimental results clearly suggest that, overall, MMEA performs significantly better than the three compared algorithms in approximating both the PS and the PF.     

A systematic methodology for the creation of Six Sigma projects: A case study of semiconductor foundry

Nowadays, Six Sigma has been widely adopted in a variety of industries in the world and it has become one of the most important subjects of debate in quality management. Six Sigma is a well-structured methodology that can help a company achieve expected goal through continuous project improvement. Some challenges, however, have emerged with the execution of the Six Sigma. For examples, how are feasible projects generated? How are critical Six Sigma projects selected given the finite resources of the organization? This study aims to develop a novel approach to create critical Six Sigma projects and identify the priority of these projects. Firstly, the projects are created from two aspects, namely, organization’s business strategic policies and voice of customer. Secondly, an analytic hierarchy process (AHP) model is implemented to evaluate the benefits of each project and; a hierarchical failure mode effects analysis (FMEA) is also developed to evaluate the risk of each project; and from which the priority of Six Sigma projects can be determined. Finally, based on the project benefits and risk, projects can be defined as Green Belt, Black Belt, or others types of projects. An empirical case study of semiconductor foundry will be utilized to explore the effectiveness of our proposed approach.     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

基于决策者偏好区域的多目标粒子群算法研究*

多目标优化问题中,决策者往往只对目标空间的某一区域感兴趣,因此需要在这一特定的区域能够得到比较稠密的Pareto解,但传统的方法却找出全部的Pareto前沿,决策效率不高。针对该问题,给出了基于决策者偏好区域的多目标粒子群优化算法。它只求出与决策者偏好区域相关的部分Pareto最优集,从而减少了进化代数,加快收敛速度,有利于决策者进行更有效的决策。算法把解与偏好区域的距离作为影响引导者选择和剪枝策略的一个因素,运用格栅方法实现解在Pareto边界分布的均匀性。仿真结果表明该算法是有效的。     

Application of multiobjective optimization in aircraft control systems design

Multiobjective optimization techniques are applied in the design of an aircraft lateral control system. A large manned reentry vehicle and a fighter aircraft are considered. An algorithm suggested by Lin's Proper Inequality Constraints method, is implemented in the numerical computation of Pareto-optimal solutions. Subsequently, a trade-off analysis of several Pareto-optimal solutions is conducted.     

基于Pareto最优的PID多目标优化设计

现有的PID优化方法往往难以同时兼顾系统对时域和频域性能的要求,针对这一缺陷,提出了一种PID多目标优化方法：将动态性能指标作为优化目标,频域性能指标作为约束条件,采用基于Pareto最优的多目标优化算法对其求解。该算法采用新的拥挤距离计算方法,引入双重精英机制,进化效率高,得到的Pareto最优解集多样性好,决策者可根据当前工作需求从中选择最终的满意解。仿真结果证明了本文方法的有效性。     

A multi-objective approach to facility layout problem by genetic search algorithm and Electre method

Classical approaches to layout design problem tend to maximise the efficiency of layout, measured by the handling cost related to the interdepartmental flow and to the distance among the departments. However, the actual problem involves several conflicting objectives hence requiring a multi-objective formulation. Multi-objective approaches, recently proposed, in most cases lead to the maximisation of a weighted sum of score functions. The poor practicability of such an approach is due to the difficulty of normalising these functions and of quantifying the weights. In this paper, this difficulty is overcome by approaching the problem in two subsequent steps: in the first step, the Pareto-optimal solutions are determined by employing a multi-objective constrained genetic algorithm and the subsequent selection of the optimal solution is carried out by means of the multi-criteria decision-making procedure Electre. This procedure allows the decision maker to express his preferences on the basis of the knowledge of candidate solution set. Quantitative (handling cost) and qualitative (adjacency and distance requests between departments) objectives are considered referring to a bay structure-based layout model, that allows to take into account also practical constraints such as the aspect ratio of departments. Results obtained confirm the effectiveness of the proposed procedure as a practicable support tool for layout designers.     

A particle swarm approach for multi-objective optimization of electrical discharge machining process

This paper proposes an experimental investigation and optimization of various machining parameters for the die-sinking electrical discharge machining (EDM) process using a multi-objective particle swarm (MOPSO) algorithm. A Box–Behnken design of response surface methodology has been adopted to estimate the effect of machining parameters on the responses. The responses used in the analysis are material removal rate, electrode wear ratio, surface roughness and radial overcut. The machining parameters considered in the study are open circuit voltage, discharge current, pulse-on-time, duty factor, flushing pressure and tool material. Fifty four experimental runs are conducted using Inconel 718 super alloy as work piece material and the influence of parameters on each response is analysed. It is observed that tool material, discharge current and pulse-on-time have significant effect on machinability characteristics of Inconel 718. Finally, a novel MOPSO algorithm has been proposed for simultaneous optimization of multiple responses. Mutation operator, predominantly used in genetic algorithm, has been introduced in the MOPSO algorithm to avoid premature convergence. The Pareto-optimal solutions obtained through MOPSO have been ranked by the composite scores obtained through maximum deviation theory to avoid subjectiveness and impreciseness in the decision making. The analysis offers useful information for controlling the machining parameters to improve the accuracy of the EDMed components.     

Pareto frontier exploration in multiobjective topology optimization using adaptive weighting and point selection schemes

Topology optimization has been used in many industries and applied to a variety of design problems. In real-world engineering design problems, topology optimization problems often include a number of conflicting objective functions, such to achieve maximum stiffness and minimum mass of a design target. The existence of conflicting objective functions causes the results of the topology optimization problem to appear as a set of non-dominated solutions, called a Pareto-optimal solution set. Within such a solution set, a design engineer can easily choose the particular solution that best meets the needs of the design problem at hand. Pareto-optimal solution sets can provide useful insights that enable the structural features corresponding to a certain objective function to be isolated and explored. This paper proposes a new Pareto frontier exploration methodology for multiobjective topology optimization problems. In our methodology, a level set-based topology optimization method for a single-objective function is extended for use in multiobjective problems, using a population-based approach in which multiple points in the objective space are updated and moved to the Pareto frontier. The following two schemes are introduced so that Pareto-optimal solution sets can be efficiently obtained. First, weighting coefficients are adaptively determined considering the relative position of each point. Second, points in sparsely populated areas are selected and their neighborhoods are explored. Several numerical examples are provided to illustrate the effectiveness of the proposed method.     

Task scheduling using NSGA II with fuzzy adaptive operators for computational grids

Scheduling algorithms have an essential role in computational grids for managing jobs, and assigning them to appropriate resources. An efficient task scheduling algorithm can achieve minimum execution time and maximum resource utilization by providing the load balance between resources in the grid. The superiority of genetic algorithm in the scheduling of tasks has been proven in the literature. In this paper, we improve the famous multi-objective genetic algorithm known as NSGA-II using fuzzy operators to improve quality and performance of task scheduling in the market-based grid environment. Load balancing, Makespan and Price are three important objectives for multi-objective optimization in the task scheduling problem in the grid. Grid users do not attend load balancing in making decision, so it is desirable that all solutions have good load balancing. Thus to decrease computation and ease decision making through the users, we should consider and improve the load balancing problem in the task scheduling indirectly using the fuzzy system without implementing the third objective function. We have used fuzzy operators for this purpose and more quality and variety in Pareto-optimal solutions. Three functions are defined to generate inputs for fuzzy systems. Variance of costs, variance of frequency of involved resources in scheduling and variance of genes values are used to determine probabilities of crossover and mutation intelligently. Variance of frequency of involved resources with cooperation of Makespan objective satisfies load balancing objective indirectly. Variance of genes values and variance of costs are used in the mutation fuzzy system to improve diversity and quality of Pareto optimal front. Our method conducts the algorithm towards best and most appropriate solutions with load balancing in less iteration. The obtained results have proved that our innovative algorithm converges to Pareto-optimal solutions faster and with more quality.     

Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: An algorithm with reoptimization

This paper addresses multicriteria combinatorial optimization problems involving one cost and several bottleneck objective functions. An algorithm is developed which generates the minimal complete set of Pareto-optimal solutions. This algorithm runs in polynomial time as long as the single objective problem considering only the cost function can be solved polynomially. A reoptimization procedure is used to accelerate the convergence of the algorithm. Applications are given. Computational results on randomly generated instances and planar grid graphs concerning the minimum cost spanning tree and the shortest path problem are presented.     

Intelligent integrated plant operation system for Six Sigma

Six Sigma has been widely adopted in a variety of industries as a proven management innovation methodology to produce high-quality products and reduce the cost at all the levels of an enterprise. This paper proposes a plant operation system which can guide plant engineers and operators to pursue Six Sigma activities by providing supports for key elements of Six Sigma: measurement, analysis, improvement and control. Multivariate statistical process control (MSPC) techniques have been employed as key technologies for the system, along with the plant information systems. This paper also discusses the future research issues that should be addressed to implement the described system.