Optimization Techniques to Obtain the Best Combination of Alloy Strength and Toughness<Superscript>*</Superscript>

Mathematical tools are proposed for the optimization of chemical compositions of alloys and technological parameters of their processing during the development of new steel grades under considerable uncertainty. By reason of uncertainty, statistical models for mechanical properties of new alloys are used in optimization problems. Particularly, CVaR is used to estimate the right tail of CVN (Charpy V-Notch impact on toughness) distribution. This implies the use of nonconcave (convex) objective functions in maximization problems. Mathematical methods are proposed for solving maximization problems.     

Parallel machine scheduling in fuzzy environment with hybrid ant colony optimization including a comparison of fuzzy number ranking methods in consideration of spread of fuzziness

This paper studies parallel machine scheduling problems in consideration of real world uncertainty quantified based on fuzzy numbers. Although this study is not the first to study the subject problem, it advances this area of research in two areas: (1) Rather than arbitrarily picking a method, it chooses the most appropriate fuzzy number ranking method based on an in-depth investigation of the effect of spread of fuzziness on the performance of fuzzy ranking methods; (2) It develops the first hybrid ant colony optimization for fuzzy parallel machine scheduling. Randomly generated datasets are used to test the performance of fuzzy ranking methods as well as the proposed algorithm, i.e. hybrid ant colony optimization. The proposed hybrid ant colony optimization outperforms a hybrid particle swarm optimization published recently and two simulated annealing based algorithms modified from our previous work.     

Fuzzy bilevel programming with multiple non-cooperative followers: model,algorithm and application

In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers’ inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.     

求解模糊相关机会规划模型的混合差分进化算法

针对不确定规划领域中存在的模糊相关机会规划模型,基于群体智能的差分进化算法,设计一种新的求解模糊相关机会规划模型的混合智能算法．该算法基于粒子群优化算法对差分进化算法进行改进,并运用模糊模拟技术对模糊相关机会规划模型进行分析和数值求解,无需像传统的基于遗传算法的混合智能算法需要很长时间并经过复杂的计算才能得到合理的结果．最后,通过实例表明了所提混合智能算法的合理性和有效性．     

Computational Methods for Verification of Stochastic Hybrid Systems

Stochastic hybrid system (SHS) models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing sound computational methods for verification is challenging because of the interaction between the discrete and the continuous stochastic dynamics. In this paper, we propose a probabilistic method for verification of SHSs based on discrete approximations focusing on reachability and safety problems. We show that reachability and safety can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. We present a numerical algorithm for computing the solution based on discrete approximations that are derived using finite-difference methods. An advantage of the method is that the solution converges to the one for the original system as the discretization becomes finer. We also prove that the algorithm is polynomial in the number of states of the discrete approximation. Finally, we illustrate the approach with two benchmarks: a navigation and a room heater example, which have been proposed for hybrid system verification.     

间歇过程动态优化方法综述

间歇过程的动态优化近年来引起了广泛关注.针对近期主要的研究成果,综述了间歇过程动态优化中的数学模型、求解方法及控制架构等问题,介绍了间歇过程目前主要的操作优化方法,具体分析了含不确定性间歇过程的动态优化策略,总结了间歇过程常用的优化模拟计算工具.最后探讨了这一领域中值得进一步研究的问题和可能的发展方向.     

A hybrid approach to constrained global optimization

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.     

Topology optimization of continuum structures under hybrid uncertainties

The aim of this paper is to study the topology optimization for mechanical systems with hybrid material and geometric uncertainties. The random variations are modeled by a memory-less transformation of random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is decreased by using of sparse grids and discretization refinement that are proposed and demonstrated as well. The method is utilized in the design of minimum compliance structure. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using adaptive sparse grids method.     

An approach to fuzzy multiattribute decision making under uncertainty

It seems that there is little investigation on fuzzy multiattribute decision making (FMADM) problems under uncertainty, which are of important to scientific researches and real life applications. FMADM problems under uncertainty are investigated in this paper. Novel mathematical programming models are constructed for FMADM problems under uncertainty, and corresponding solving methods are proposed. The approach proposed in this paper may reflect both subjective judgment and objective information. Moreover, pairwise chain comparison methods for determination of relative membership degrees and weights are also proposed. Feasibility and effectiveness of the models and approach proposed in this paper are illustrated with a numerical example.     

Optimization strategies for non-linear material parameters identification in metal forming problems

The quality of Finite Element Analysis (FEM) results relies on the input data, such as the material constitutive models. In order to achieve the best material parameters for the material constitutive models assumed a priori to represent the material, parameter identification inverse problems are considered. These inverse problems attempt to lead to the most accurate results with respect to physical experiments, i.e. minimizing the difference between experimental and numerical results.In this work three constitutive models were considered, namely, a non-linear elastic–plastic hardening model, a hyperelastic model -more specifically the Ogden model- and an elasto-viscoplastic model with isotropic and kinematic work-hardening.For the determination of the best suited material parameter set, two different optimization algorithms were used: (i) the Levenberg–Marquardt algorithm, which is gradient-based and (ii) a real search-space evolutionary algorithm (EA).The robustness and efficiency of classical single-stage optimization methods can be improved with new optimization strategies. Strategies such as cascade, parallel and hybrid approaches are analysed in detail. In hybrid strategies, cascade and parallel approaches are integrated. These strategies were implemented and analysed for the material parameters determination of the above referred material constitutive models.It was observed that the developed strategies lead to better values of the objective function when compared with the single-stage optimizers.     

有色冶金过程不确定优化方法探讨

有色冶金过程受原料来源多样、工况条件波动、生产成分变化等因素的影响,存在大量的不确定性,严重影响了冶炼生产的稳定性与可靠性.鉴于此,综述不同类型不确定性优化问题的描述方法,具体包括概率不确定优化问题、模糊不确定优化问题和区间不确定优化问题.通过分析有色冶金生产过程的特点与需求,以3种典型的有色冶金过程不确定优化问题为例,探讨不同类型的有色冶金过程不确定优化方法.针对氧化铝生料浆配料过程的概率不确定优化问题,采用基于Hammersley sequence sampling(HSS)的方法实现不确定模型的确定性转换;针对湿法炼锌除铜过程的模糊不确定优化问题,采用基于模糊规则的方法进行确定性评估;针对锌电解分时供电过程的区间不确定优化问题,采用基于min-max的方法求解鲁棒解.工业运行数据均验证了上述方法的有效性.     

Real-time integrated production-scheduling and maintenance-planning in a flexible job shop with machine deterioration and condition-based maintenance

The introduction of modern technologies in manufacturing is contributing to the emergence of smart (and data-driven) manufacturing systems, known as Industry 4.0. The benefits of adopting such technologies can be fully utilized by presenting optimization models in every step of the decision-making process. This includes the optimization of maintenance plans and production schedules, which are two essential aspects of any manufacturing process. In this paper, we consider the real-time joint optimization of maintenance planning and production scheduling in smart manufacturing systems. We have considered a flexible job shop production layout and addressed several issues that usually take place in practice. The addressed issues are: new job arrivals, unexpected due date changes, machine degradation, random breakdowns, minimal repairs, and condition-based maintenance (CBM). We have proposed a real-time optimization-based system that utilizes a modified hybrid genetic algorithm, an integrated proactive-reactive optimization model, and hybrid rescheduling policies. A set of modified benchmark problems is used to test the proposed system by comparing its performance to several other optimization algorithms and methods used in practice. The results show the superiority of the proposed system for solving the problem under study. The results also emphasize the importance of the quality of the generated baseline plans (i.e., initial integrated plans), the use of hybrid rescheduling policies, and the importance of rescheduling times (i.e., reaction times) for cost savings.     

Large-scale reliability-based structural optimization

A robust and efficient methodology is presented for treating large-scale reliability-based structural optimization problems. The optimization is performed with evolution strategies, while the reliability analysis is carried out with the Monte Carlo simulation method incorporating the importance sampling technique to reduce the sample size. Efficient hybrid methods are implemented to solve the reanalysis-type problems that arise in the optimization phase with evolution strategies and in the reliability analysis with Monte Carlo simulations. These hybrid solution methods are based on the preconditioned conjugate gradient algorithm using efficient preconditioning schemes. The numerical tests presented demonstrate the computational advantages of the proposed methods, which become more pronounced for large-scale optimization problems.     

Hierarchical stochastic modeling and optimization for petroleum field development under geological uncertainty

Real-world simulation optimization (SO) problems entail complex system modeling and expensive stochastic simulation. Existing SO algorithms may not be applicable for such SO problems because they often evaluate a large number of solutions with many simulation calls. We propose an integrated solution method for practical SO problems based on a hierarchical stochastic modeling and optimization (HSMO) approach. This method models and optimizes the studied system at increasing levels of accuracy by hierarchical sampling with a selected set of principal parameters. We demonstrate the efficiency of HSMO using the example problem of Brugge oil field development under geological uncertainty.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

Global optimization in design and control of chemical process systems

This paper presents an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of Process Design and Control. The focus is on global optimization methods for (a) twice-differentiable constrained nonlinear optimization problems, (b) mixed-integer nonlinear optimization problems, and (c) locating all solutions of nonlinear systems of equations. Theoretical advances and computational studies on process design, batch design under uncertainty, phase equilibrium, location of azeotropes, stability margin, process synthesis, and parameter estimation problems are discussed.     

A Hybrid Metaheuristic for the Efficient Solution of GARCH with Trend Models

GARCH with trend models represent an efficient tool for the analysis of different commodities via testing for a linear trend in the volatilities. However, to obtain the volatility of a given time series an instance from a particular class of scalar optimization problems (SOPs) has to be solved which still represents a challenge for existing solvers. We propose here a novel algorithm for the efficient numerical solution of such global optimization problems. The algorithm, DE–N, is a hybrid of Differential Evolution and the Newton method. The latter is widely used for the treatment of GARCH related models, but cannot be used as standalone algorithm in this case as the SOPs contain many local minima. The algorithm is tested and compared to some state-of-the-art methods on a benchmark suite consisting of 42 monthtly agricultural commodities series of the Mexican Consumer Price Index basket as well as on two series related to international prices. The results indicate that DE–N is highly competitive and that it is able to reliably solve SOPs derived from GARCH with trend models.     

Optimal planning for two-stage stochastic industrial systems

We consider the optimal planning problem for a certain class of industrial systems operating under uncertainty. We construct mathematical models, define optimization problems for the planning, propose efficient algorithms for solving them. We show examples of applied problems that can be formalized in this mathematical model.     

New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

Existing collaborative optimization techniques with multiple coupled subsystems are predominantly focused on single-objective deterministic optimization. However, many engineering optimization problems have system and subsystems that can each be multi-objective, constrained and with uncertainty. The literature reports on a few deterministic Multi-objective Multi-Disciplinary Optimization (MMDO) techniques. However, these techniques in general require a large number of function calls and their computational cost can be exacerbated when uncertainty is present. In this paper, a new Approximation-Assisted Multi-objective collaborative Robust Optimization (New AA-McRO) under interval uncertainty is presented. This new AA-McRO approach uses a single-objective optimization problem to coordinate all system and subsystem multi-objective optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the system and subsystem objective functions. The new AA-McRO is able to explore the design space better and obtain optimum design solutions more efficiently. Also, the new AA-McRO obtains an estimate of Pareto optimum solutions for MMDO problems whose system-level objective and constraint functions are relatively insensitive (or robust) to input uncertainties. Another characteristic of the new AA-McRO is the use of online approximation for objective and constraint functions to perform system robustness evaluation and subsystem-level optimization. Based on the results obtained from a numerical and an engineering example, it is concluded that the new AA-McRO performs better than previously reported MMDO methods.     

Operations management issues in design and control of hybrid human-robot collaborative manufacturing systems: a survey

A manufacturing system able to perform a high variety of tasks requires different types of resources. Fully automated systems using robots possess high speed, accuracy, tirelessness, and force, but they are expensive. On the other hand, human workers are intelligent, creative, flexible, and able to work with different tools in different situations. A combination of these resources forms a human-machine/robot (hybrid) system, where humans and robots perform a variety of tasks (manual, automated, and hybrid tasks) in a shared workspace. Contrarily to the existing surveys, this study is dedicated to operations management problems (focusing on the applications and features) for human and machine/robot collaborative systems in manufacturing. This research is divided into two types of interactions between human and automated components in manufacturing and assembly systems: dual resource constrained (DRC) and human-robot collaboration (HRC) optimization problems. Moreover, different characteristics of the workforce and machines/robots such as heterogeneity, homogeneity, ergonomics, and flexibility are introduced. Finally, this paper identifies the optimization challenges and problems for hybrid systems. The existing literature on HRC focuses mainly on the robotic point of view and not on the operations management and optimization aspects. Therefore, the future research directions include the design of models and methods to optimize HRC systems in terms of ergonomics, safety, and throughput. In addition, studying flexibility and reconfigurability in hybrid systems is one of the main research avenues for future research.