An iterative numerical algorithm for modeling a class of Wiener nonlinear systems

This letter presents an iterative estimation algorithm for modeling a class of output nonlinear systems. The basic idea is to derive an estimation model and to solve an optimization problem using the gradient search. The proposed iterative numerical algorithm can estimate the parameters of a class of Wiener nonlinear systems from input–output measurement data. The proposed algorithm has faster convergence rates compared with the stochastic gradient algorithm. The numerical simulation results indicate that the proposed algorithm works well.     

Solving nonlinear multi-objective optimization problems with fuzzy relation inequality constraints regarding Archimedean triangular norm compositions

We propose an approach to solve a nonlinear multi-objective problem subject to fuzzy relation inequalities with max-Archimedean-t-norm composition by a genetic algorithm. The additive generator of Archimedean t-norms is utilized to reform the existent genetic algorithm to solve the constrained nonlinear multi-objective optimization problems. We consider thoroughly the feasible set of the fuzzy relation inequality systems in three possible cases, namely “≤”, “≥” and the combination of them. In general, their feasible sets are nonconvex which are completely determined by one vector as their maximum solution and a finite number of minimal solutions. The maximum and minimal solutions are formulated by using the additive generator. Additionally, we present some conditions for each case under which the problem can be reduced. Finally, each reduced problem is solved by the genetic algorithm and the efficiency of the proposed method is shown by some numerical examples.     

Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.     

A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements

In this paper, we consider a nonlinear switched time-delay (NSTD) system with unknown switching times and unknown system parameters, where the output measurement is uncertain. This system is the underling dynamical system for the batch process of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. The uncertain output measurement is regarded as a stochastic vector (whose components are stochastic variables) and the only information about its distribution is the first-order moment. The objective of this paper is to identify the unknown quantities of the NSTD system. For this, a distributionally robust optimization problem (a bi-level optimization problem) governed by the NSTD system is proposed, where the relative error under the environment of uncertain output measurements is involved in the cost functional. The bi-level optimization problem is transformed into a single-level optimization problem with non-smooth term through the application of duality theory in probability space. By applying the smoothing technique, the non-smooth term is approximated by a smooth term and the convergence of the approximation is established. Then, the gradients of the cost functional with respect to switching times and system parameters are derived. A hybrid optimization algorithm is developed to solve the transformed problem. Finally, we verify the obtained switching times and system parameters, as well as the effectiveness of the proposed algorithm, by solving this distributionally robust optimization problem.     

Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.     

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

In this paper, we present a multicut version of the Benders decomposition method for solving two-stage stochastic linear programming problems, including stochastic mixed-integer programs with only continuous recourse (two-stage) variables. The main idea is to add one cut per realization of uncertainty to the master problem in each iteration, that is, as many Benders cuts as the number of scenarios added to the master problem in each iteration. Two examples are presented to illustrate the application of the proposed algorithm. One involves production-transportation planning under demand uncertainty, and the other one involves multiperiod planning of global, multiproduct chemical supply chains under demand and freight rate uncertainty. Computational studies show that while both the standard and the multicut versions of the Benders decomposition method can solve large-scale stochastic programming problems with reasonable computational effort, significant savings in CPU time can be achieved by using the proposed multicut algorithm.     

Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm

This paper deals with chance constraints based reliability stochastic optimization problem in the series system. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall system reliability under chance constraints due to resources. The assumption of traditional reliability optimization problem is that the reliability of a component is known as a fixed quantity which lies in the open interval (0, 1). However, in real life situations, the reliability of an individual component may vary due to some realistic factors and it is sensible to treat this as a positive imprecise number and this imprecise number is represented by an interval valued number. In this work, we have formulated the reliability optimization problem as a chance constraints based reliability stochastic optimization problem with interval valued reliabilities of components. Then, the chance constraints of the problem are converted into the equivalent deterministic form. The transformed problem has been formulated as an unconstrained integer programming problem with interval coefficients by Big-M penalty technique. Then to solve this problem, we have developed a real coded genetic algorithm (GA) for integer variables with tournament selection, uniform crossover and one-neighborhood mutation. To illustrate the model two numerical examples have been solved by our developed GA. Finally to study the stability of our developed GA with respect to the different GA parameters, sensitivity analyses have been done graphically.     

Nonlinear programming methods in the presence of noise

The problem of minimizing a nonlinear function with nonlinear constraints when the values of the objective, the constraints and their gradients have errors, is studied. This noise may be due to the stochastic nature of the problem or to numerical error.Various previously proposed methods are reviewed. Generally, the minimization algorithms involve methods of subgradient optimization, with the constraints introduced through penalty, Lagrange, or extended Lagrange functions. Probabilistic convergence theorems are obtained. Finally, an algorithm to solve the general convex (nondifferentiable) programming problem with noise is proposed.Originally written for presentation at the 1976 Budapest Symposium on Mathematical Programming.     

基于随机规划的建筑集群冷热电联供系统优化研究

面向建筑集群的冷热电联供系统的设计和优化是实现建筑楼宇能源成本节约的重要途径。随机因素对该联供系统的优化决策,具有显著的影响。考虑建筑楼宇的能源需求为随机变量,构建随机混合整数规划模型,解决以最小化建筑楼宇总费用为目标时建筑集群冷热电联供系统的优化问题;其次,提出采用Benders多割平面方法求解多目标规划问题,从而寻找冷热电联供系统的设备配置和系统运行的Pareto最优决策;最后,通过实验验证了模型和算法的有效性。实验结果表明建筑集群在协作模式下,相比于非协作模式,具有更低的总费用。     

Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels

A great deal of research has been done on production planning and sourcing problems, most of which concern deterministic or stochastic demand and cost situations and single period systems. In this paper, we consider a new class of multi-period production planning and sourcing problem with credibility service levels, in which a manufacturer has a number of plants and subcontractors and has to meet the product demand according to the credibility service levels set by its customers. In the proposed problem, demands and costs are uncertain and assumed to be fuzzy variables with known possibility distributions. The objective of the problem is to minimize the total expected cost, including the expected value of the sum of the inventory holding and production cost in the planning horizon. Because the proposed problem is too complex to apply conventional optimization algorithms, we suggest an approximation approach (AA) to evaluate the objective function. After that, two algorithms are designed to solve the proposed production planning problem. The first is a PSO algorithm combining the AA, and the second is a hybrid PSO algorithm integrating the AA, neural network (NN) and PSO. Finally, one numerical example is provided to compare the effectiveness of the proposed two algorithms.     

The EM algorithm for ML Estimators under nonlinear inequalities restrictions on the parameters

One of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems is the EM algorithm. However, when the parameters satisfy a set of nonlinear restrictions, It is difficult to apply the EM algorithm directly. In this paper,we propose an asymptotic maximum likelihood estimation procedure under a set of nonlinear inequalities restrictions on the parameters, in which the EM algorithm can be used. Essentially this kind of estimation problem is a stochastic optimization problem in the M-step. We make use of methods in stochastic optimization to overcome the difficulty caused by nonlinearity in the given constraints.     

A genetic algorithm for a global optimization problem arising in the detection of gravitational waves

The detection of gravitational waves is a long-awaited event in modern physics and, to achieve this challenging goal, detectors with high sensitivity are being used or are under development. In order to extract gravitational signals emitted by coalescing binary systems of compact objects (neutron stars and/or black holes), from noisy data obtained by interferometric detectors, the matched filter technique is generally used. Its computational kernel is a box-constrained global optimization problem with many local solutions and a highly nonlinear and expensive objective function, whose derivatives are not available. To tackle this problem, we designed a real-coded genetic algorithm that exploits characteristic features of the problem itself; special attention was devoted to the choice of the initial population and of the recombination operator. Computational experiments showed that our algorithm is able to compute a reasonably accurate solution of the optimization problem, requiring a much smaller number of function evaluations than the grid search, which is generally used to solve this problem. Furthermore, the genetic algorithm largely outperforms other global optimization algorithms on significant instances of the problem.     

随机需求应急物流多阶段定位-路径鲁棒优化研究

为提高应急物流系统的应急反应能力,论文针对需求随机变化的应急物流定位-路径问题,利用鲁棒优化的思想将灾区物资需求量表示为区间型数据,将应急救援过程划分为多个阶段,以总救援时间和系统总成本最小为目标,构建了多物资多运输车辆应急物流定位-路径优化模型,设计了改进的遗传算法对其进行求解。实例计算结果表明,该模型和算法可以有效地解决应急物流系统中需求随机变化的定位-路径问题,为政府机构应对重大突发事件提供科学的决策参考。     

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

置换流水车间调度问题的中心引力优化算法求解

目前求解置换流水车间调度问题的智能优化算法都是随机型优化方法,存在的一个问题是解的稳定性较差。针对该问题,本文给出一种确定型智能优化算法——中心引力优化算法的求解方法。为处理基本中心引力优化算法对初始解选择要求高的问题,利用低偏差序列生成初始解,提高初始解质量;利用加速度和位置迭代方程更新解的状态;利用两位置交换排序法进行局部搜索,提高算法的优化性能。采用置换流水车间调度问题标准测试算例进行数值实验,并和基本中心引力优化算法、NEH启发式算法、微粒群优化算法和萤火虫算法进行比较。结果表明该算法不仅具有更好的解的稳定性,而且具有更高的计算精度,为置换流水车间调度问题的求解提供了一种可行有效的方法。     

A Constrained Optimization Approach for LCP

In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x,y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K-T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem. In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point, However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions: M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method.     

Computational method for optimal control of switched systems with input and state constraints

In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugate gradient algorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms.     

Stochastic dynamic lot-sizing problem using bi-level programming base on artificial intelligence techniques

Simulation is generally used to study non-deterministic problems in industry. When a simulation process finds the solution to an NP-hard problem, its efficiency is lowered, and computational costs increase. This paper proposes a stochastic dynamic lot-sizing problem with asymmetric deteriorating commodity, in which the optimal unit cost of material and unit holding cost would be determined. This problem covers a sub-problem of replenishment planning, which is NP-hard in the computational complexity theory. Therefore, this paper applies a decision system, based on an artificial neural network (ANN) and modified ant colony optimization (ACO) to solve this stochastic dynamic lot-sizing problem. In the methodology, ANN is used to learn the simulation results, followed by the application of a real-valued modified ACO algorithm to find the optimal decision variables. The test results show that the intelligent system is applicable to the proposed problem, and its performance is better than response surface methodology.     

Integral global optimization method for solution of nonlinear complementarity problems

The mapping in a nonlinear complementarity problem may be discontinuous. The integral global optimization algorithm is proposed to solve a nonlinear complementarity problem with a robust piecewise continuous mapping. Numerical examples are given to illustrate the effectiveness of the algorithm.