Energy supply planning and supply chain optimization under uncertainty

In energy supply planning and supply chain design, the coupling between long-term planning decisions like capital investment and short-term operation decisions like dispatching present a challenge, waiting to be tackled by systems and control engineers. The coupling is further complicated by uncertainties, which may arise from several sources including the market, politics, and technology. This paper addresses the coupling in the context of energy supply planning and supply chain design. We first discuss a simple two-stage stochastic program formulation that addresses optimization of an energy supply chain in the presence of uncertainties. The two-stage formulation can handle problems in which all design decisions are made up front and operating parameters act as ‘recourse’ decisions that can be varied from one time period to next based on realized values of uncertain parameters. The design of a biodiesel production network in the Southeastern region of the United States is used as an illustrative example. The discussion then moves on to a more complex multi-stage, multi-scale stochastic decision problem in which periodic investment/policy decisions are made on a time scale orders of magnitude slower than that of operating decisions. The problem of energy capacity planning is introduced as an example. In the particular problem we examine, annual acquisition of energy generation capacities of various types are coupled with hourly energy production and dispatch decisions. The increasing role of renewable sources like wind and solar necessitates the use of a fine-grained time scale for accurate assessment of their values. Use of storage intended to overcome the limitations of intermittent sources puts further demand on the modeling and optimization. Numerical challenges that arise from the multi-scale nature and uncertainties are reviewed and some possible modeling and numerical solution approaches are discussed.     

Accelerating Benders stochastic decomposition for the optimization under uncertainty of the petroleum product supply chain

This paper addresses the solution of a two-stage stochastic programming model for an investment planning problem applied to the petroleum products supply chain. In this context, we present the development of acceleration techniques for the stochastic Benders decomposition that aim to strengthen the cuts generated, as well as to improve the quality of the solutions obtained during the execution of the algorithm. Computational experiments are presented for assessing the efficiency of the proposed framework. We compare the performance of the proposed algorithm with two other acceleration techniques. Results suggest that the proposed approach is able to efficiently solve the problem under consideration, achieving better performance in terms of computational times when compared to other two techniques.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

The use of metamodeling techniques for optimization under uncertainty

Metamodeling techniques have been widely used in engineering design to improve efficiency in the simulation and optimization of design systems that involve computationally expensive simulation programs. Many existing applications are restricted to deterministic optimization. Very few studies have been conducted on studying the accuracy of using metamodels for optimization under uncertainty. In this paper, using a two-bar structure system design as an example, various metamodeling techniques are tested for different formulations of optimization under uncertainty. Observations are made on the applicability and accuracy of these techniques, the impact of sample size, and the optimization performance when different formulations are used to incorporate uncertainty. Some important issues for applying metamodels to optimization under uncertainty are discussed.     

A comparative study of stochastic optimization methods in electric motor design

The efficiency of universal electric motors that are widely used in home appliances can be improved by optimizing the geometry of the rotor and the stator. Expert designers traditionally approach this task by iteratively evaluating candidate designs and improving them according to their experience. However, the existence of reliable numerical simulators and powerful stochastic optimization techniques make it possible to automate the design procedure. We present a comparative study of six stochastic optimization algorithms in designing optimal rotor and stator geometries of a universal electric motor where the primary objective is to minimize the motor power losses. We compare three methods from the domain of evolutionary computation, generational evolutionary algorithm, steady-state evolutionary algorithm and differential evolution, two particle-based methods, particle-swarm optimization and electromagnetism-like algorithm, and a recently proposed multilevel ant stigmergy algorithm. By comparing their performance, the most efficient method for solving the problem is identified and an explanation of its success is offered.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

On stochastic dynamic programming for solving large-scale planning problems under uncertainty

The stochastic dynamic programming approach outlined here, makes use of the scenario tree in a back-to-front scheme. The multi-period stochastic problems, related to the subtrees whose root nodes are the starting nodes (i.e., scenario groups), are solved at each given stage along the time horizon. Each subproblem considers the effect of the stochasticity of the uncertain parameters from the periods of the given stage, by using curves that estimate the expected future value (EFV) of the objective function. Each subproblem is solved for a set of reference levels of the variables that also have nonzero elements in any of the previous stages besides the given stage. An appropriate sensitivity analysis of the objective function for each reference level of the linking variables allows us to estimate the EFV curves applicable to the scenario groups from the previous stages, until the curves for the first stage have been computed. An application of the scheme to the problem of production planning with logical constraints is presented. The aim of the problem consists of obtaining the planning of tactical production over the scenarios along the time horizon. The expected total cost is minimized to satisfy the product demand. Some computational experience is reported. The proposed approach compares favorably with a state-of-the-art optimization engine in instances on a very large scale.     

回收不确定下WEEE逆向物流网络鲁棒优化设计

电子电器废弃物（WEEE）存在对环境和人体健康的危害,有效对其进行回收能避免此类危害和提高资源的利用率。WEEE逆向物流回收网络的设计为实现这一目标起到了关键的作用。考虑WEEE逆向物流网络运作的不确定性,引入风险偏好系数和约束背离惩罚系数,建立了WEEE逆向物流网络的鲁棒优化模型。该模型能允许决策者对系统运作的鲁棒水平进行调节,同时能允许决策者对风险偏好进行调节。仿真结果表明建立的模型能有效抑制逆向物流系统运作的不确定性,使系统具有更低的风险。     

A modified particle swarm optimization algorithm for scheduling renewable generation in a micro-grid under load uncertainty

Renewable Energy Sources (RESs) have many benefits especially when integrated in micro-grids. In this paper, the particle swarm optimization (PSO) algorithm is modified for the optimal power sharing among several RESs such as wind (WT), photovoltaic (PV), and a combined heat and power (CHP) plants within a micro-grid framework. To evaluate the proposed method, first it is utilized to optimally schedule RESs in a micro-grid with the aim of cost minimization without uncertainty. Then, it is implemented under the load uncertainty and the random nature of demand is modeled by the scenario-based stochastic programming. Finally, the proposed algorithm is verified using some benchmark functions. The proposed method is compared with some different Meta-heuristic algorithms and it presents encouraging results in the RESs scheduling and solving benchmark functions.     

Exact and fast numerical algorithms for the stochastic wave equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense.     

SearchFill: A stochastic optimization code for detecting atomic vacancies in crystalline and non-crystalline systems

We present an implementation of a stochastic optimization algorithm applied to location of atomic vacancies. Our method labels an empty point in space as a vacancy site, if the total spatial overlap of a “virtual sphere”, centered around the point, with the surrounding atoms (and other vacancies) falls below a tolerance parameter. A Metropolis-like algorithm displaces the vacancies randomly, using an “overlap temperature” parameter to allow for acceptance of moves into regions with higher overlap, thus avoiding local minima. Once the algorithm has targeted a point with low overlap, the overlap temperature is decreased, and the method works as a steepest descent optimization.Our method, with only two free parameters, is able to detect the correct number and coordinates of vacancies in a wide spectrum of condensed-matter systems, from crystals to amorphous solids, in fact in any given set of atomic coordinates, without any need of comparison with a reference initial structure.     

基于Witness的多品种批量生产系统仿真优化

针对多品种批量生产系统的复杂性,为提高其生产效率,综合考虑人、机、法、料四个方面的因素,提出了一种基于Witness的多品种批量型生产系统仿真优化方法。描述了待研究的科学问题,设计了仿真逻辑,提出了仿真模型构建的关键技术,通过仿真试验验证了所提方法的有效性。     

Hierarchical genetic optimization of a fuzzy logic system for energy flows management in microgrids

Bio-inspired algorithms like Genetic Algorithms and Fuzzy Inference Systems (FIS) are nowadays widely adopted as hybrid techniques in improving goods and services. In this paper we present an interesting application of the fuzzy-GA paradigm to the problem of energy flows management in microgrids, concerning the design, through a data driven synthesis procedure, of an Energy Management System (EMS). The main aim consists in performing decision making for power flow management tasks in the proposed microgrid model, equipped by renewable sources and an energy storage system, aiming to maximize the accounting profit in energy trading with the main-grid. In particular this study focuses on the application of a Hierarchical Genetic Algorithm (HGA) for tuning the Rule Base (RB) of a Fuzzy Inference System (FIS), trying to discover a minimal fuzzy rules set as the core inference engine of an an EMS. The HGA rationale focuses on a particular encoding scheme, based on control genes and parametric genes, applied to the optimization of the FIS parameters, allowing to perform a reduction in the structural complexity of the RB. A performance comparison is performed with a simpler approach based on a classic fuzzy-GA scheme, where both FIS parameters and rule weights are tuned, while the number of fuzzy rules is fixed in advance. Experiments shows how the fuzzy-HGA approach adopted for the synthesis of the proposed controller outperforms the classic fuzzy-GA scheme, increasing the accounting profit by 67% in the considered energy trading problem, yielding at the same time a simpler RB.     

间歇结晶过程模型和动态优化研究的进展

间歇结晶过程是一种重要的分离过程单元操作,由于机理的复杂性以及动态特性使得该过程的数学模型研究非常具有挑战性。本文从间歇结晶过程建模和动态模拟、动态优化、模型辨识以及鲁棒优化与控制等方面,介绍了间歇结晶过程数学模型的研究进展,评述了其中的关键问题和求解技术。指出对结晶过程的机理进一步深入认识,开发数值稳定、精度更高的求解算法是间歇结晶过程数学模型研究的基础。全局优化效果较好的进化算法和模型预测控制理论在结晶过程动态优化和质量控制中的应用是今后的研究方向。     

Optimizing designs and operations of a single network or multiple interdependent infrastructures under stochastic arc disruption

In this paper, we consider an infrastructure as a network with supply, transshipment, and demand nodes. A subset of potential arcs can be constructed between node pairs for conveying service flows. The paper studies two optimization models under stochastic arc disruption. Model 1 focuses on a single network with small-scale failures, and repairs arcs for quick service restoration. Model 2 considers multiple interdependent infrastructures under large-scale disruptions, and mitigates cascading failures by selectively disconnecting failed components. We formulate both models as scenario-based stochastic mixed-integer programs, in which the first-stage problem builds arcs, and the second-stage problem optimizes recourse operations for restoring service or mitigating losses. The goal is to minimize the total cost of infrastructure design and recovery operations. We develop cutting-plane algorithms and several heuristic approaches for solving the two models. Model 1 is tested on an IEEE 118-bus system. Model 2 is tested on systems consisting of the 118-bus system, a 20-node network, and/or a 50-node network, with randomly generated interdependency sets in three different topological forms (i.e., chain, tree, and cycle). The computational results demonstrate that (i) decomposition and cutting-plane algorithms effectively solve Model 1, and (ii) heuristic approaches dramatically decrease the CPU time for Model 2, but yield worse bounds when cardinalities of interdependency sets increase. Future research includes developing special algorithms for optimizing Model 2 for complex multiple infrastructures with special topological forms of system interdependency.     

Location based treatment activities for end of life products network design under uncertainty by a robust multi-objective memetic-based heuristic approach

Rapid growth in world population and recourse limitations necessitate remanufacturing of products and their parts/modules. Managing these processes requires special activities such as inspection, disassembly, and sorting activities known as treatment activities. This paper proposes a capacitated multi-echelon, multi-product reverse logistic network design with fuzzy returned products in which both locations of the treatment activities and facilities are decision variables. As the obtained nonlinear mixed integer programming model is a combinatorial problem, a memetic-based heuristic approach is presented to solve the resulted model. To validate the proposed memetic-based heuristic method, the obtained results are compared with the results of the linear approximation of the model, which is obtained by a commercial optimization package. Moreover, due to inherent uncertainty in return products, demands of these products are considered as uncertain parameters and therefore a fuzzy approach is employed to tackle this matter. In order to deal with the uncertainty, a stochastic simulation approach is employed to defuzzify the demands, where extra costs due to opening new centers or extra transportation costs may be imposed to the system. These costs are considered as penalty in the objective function. To minimize the resulting penalties during simulation's iterations, the average of penalties is added to the objective function of the deterministic model considered as the primary objective function and variance of penalties are considered as the secondary objective function to make a robust solution. The resulted bi-objective model is solved through goal programming method to minimizing the objectives, simultaneously.     

Maximum variation analysis based analytical target cascading for multidisciplinary robust design optimization under interval uncertainty

Analytical target cascading (ATC) is a generally used hierarchical method for deterministic multidisciplinary design optimization (MDO). However, uncertainty is almost inevitable in the lifecycle of a complex system. In engineering practical design, the interval information of uncertainty can be more easily obtained compared to probability information. In this paper, a maximum variation analysis based ATC (MVA-ATC) approach is developed. In this approach, all subsystems are autonomously optimized under the interval uncertainty. MVA is used to establish an outer-inner framework which is employed to find the optimal scheme of system and subsystems. All subsystems are coordinated at the system level to search the system robust optimal solution. The accuracy and validation of the presented approach are tested using a classical mathematical example, a heart dipole optimization problem, and a battery thermal management system (BTMS) design problem.     

A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty

Organizations have recently become interested in applying new approaches to reduce fuel consumptions, aiming at decreasing green house gases emission due to their harmful effects on environment and human health; however, the large difference between practical and theoretical experiments grows the concern about significant changes in the transportation environment, including fuel consumptions, carbon dioxide (CO₂) emissions cost and vehicles velocity, that it encourages researchers to design a near-reality and robust pollution routing problem. This paper addresses a new time window pickup-delivery pollution routing problem (TWPDPRP) to deal with uncertain input data for the first time in the literature. For this purpose, a new mixed integer linear programming (MILP) approach is presented under uncertainty by taking green house emissions into consideration. The objective of the model is to minimize not only the travel distance and number of available vehicles along with the capacity and aggregated route duration restrictions but also the amount of fuel consumptions and green house emissions along with their total costs. Moreover, a robust counterpart of the MILP is introduced by applying the recent robust optimization theory. Computational results for several test problems indicate the capability and suitability of the presented MILP model in saving costs and reducing green house gases concurrently for the TWPDPRP problem. Finally, both deterministic and robust mathematical programming are compared and contrasted by a number of nominal and realizations under these test problems to judge the robustness of the solution achieved by the presented robust optimization model.     

The optimization of warehouse location and resources distribution for emergency rescue under uncertainty

China is one of the countries that suffer the most natural disasters in the world. The situation of emergency response and rescue is extremely tough. Establishing the emergency warehouse is one of the important ways to cope with rapid-onset disasters. In this paper, a mixed integer programming (MIP) model based on time cost under uncertainty is proposed, which help solve the emergency warehouse location and distribution problem. Comprehensive consideration of factors such as time cost, penalty cost for lack of resources, alternative origins of resources from both suppliers and emergency warehouses, different means of transportation and multiple resources types are involved in our study. We also introduce uncertain scenarios to describe the severity of the disaster. Particle swarm optimization (PSO) and variable neighborhood search (VNS) are designed to solve the MIP model of different scales of instances. Numerous examples have been tested to compare two heuristics with commercial solver (CPLEX). Both of two algorithms can obtain the exact solution same as CPLEX in small-scale instances while show great performance on larger instances with 10 candidate warehouses, 25 disasters and 50 scenarios.