Non-probabilistic robust optimization approach for flood control system design

Flood risk management in floodplain systems is a long-standing problem in water resources management. Soft strategies such as land cover change are used to mitigate damages due to flooding. In this approach one chooses the best combination of land covers such that flood damage and the investment costs are minimized. Because of the uncertain nature of the problem, former studies addressed this problem by stochastic programming models which are found to be computationally expensive. In this work, a novel non-probabilistic robust counterpart approach is proposed in which the uncertainty of the rainfall events requires a new formulation and solution algorithms. Non-probabilistic methods, developed in the field of robust optimization were shown to have advantages over classical stochastic methods in several aspects such as: tractability, non-necessity of full probabilistic information, and the ability to integrate correlation of uncertain variables without adding complexity. However, unlike former studies in the field of robust optimization, the resulting optimization model in the flood risk management problem is nonlinear and discontinuous and leads to an intractable robust counterpart model. In this work, a novel iterative linearization scheme is proposed to effectively solve nonlinear robust counterpart models. This work demonstrates the tractability and applicability of non-probabilistic robust optimization to nonlinear problems similar to the flood risk management problem. The results show considerable promise of the robust counterpart approach in terms of showing the tradeoff between flood risk and cost in an efficient manner.     

考虑双重不确定性的公交时刻表分布鲁棒优化模型

城市公交系统由于受外界干扰,其需求和运行环境在时空上呈现高度不确定性,给日常运营组织带来了巨大挑战.为增强公交系统对于客流需求和运行场景双重不确定性的应对能力,提出一种权衡服务质量和服务鲁棒性的单一线路时刻表优化方法.方法采用离散场景集刻画需求的不确定性,并以滞留人数的期望值和条件风险值最小化为目标,综合考虑多方面约束,构建多场景耦合的分布鲁棒优化模型(DRO).为方便模型求解,运用模糊集描述场景发生概率的不确定性,再借助对偶理论和常规线性化方法将原模型转化为等价的混合整数线性规划形式.最后通过实际案例对方法进行分析,结果表明:等价转换得到的线性形式可由GUROBI优化软件快速求得最优解; DRO模型所得时刻表能有效应对双重不确定性;随着不确定性的上升,分布鲁棒优化方法相较于传统随机规划方法体现出更强的鲁棒性,可以切实改善公交系统运营的稳定性.     

Model-based real-time optimization of automotive gasoline blending operations

Gasoline blending is a key process in the successful operation of most petroleum refineries and real-time optimization (RTO) of gasoline blend recipes has the potential to provide a competitive benefit for oil refiners. The trend toward the use of “running” tanks for blender feedstocks and the recent advances in measurement technology have provided the opportunity for improved blending performance using RTO. This paper provides an improved formulation for the gasoline blend optimization problem that incorporates both the blend horizon and a stochastic model of disturbances into the RTO problem. The proposed approach is illustrated with a blender simulation study.     

Using model uncertainty for robust optimization in approximate inference control

Recently, the optimization-by-inference approach has been proposed as a new means for solving high-dimensional optimization problems quickly. Approximate Inference COntrol (AICO) is one of the most successful and promising methods that implement the optimization-by-inference approach. AICO is able to solve stochastic optimal control problems and has already been successfully used in many applications. However, it is known that the iterative inference of AICO sometimes fails to converge to the optimal solution. To make the optimization more robust, in this paper, we propose to take model uncertainty into account. In AICO, the cost function to be minimized is accurate around a particular state of a given stochastic system, but the accuracy is uncertain in regions far from that state. Because using such an uncertain function is harmful to the convergence, we modify AICO, so that it does not use the function in uncertain regions. Our method is easy to implement and does not add much computational time to the original AICO. Experiments using two different scenarios show that our method substantially improves AICO in terms of the rate at which the algorithm produces convergent results.     

Commitment and dispatch of heat and power units via affinely adjustable robust optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.     

Model predictive control with robust feasibility

This paper presents a new model predictive control (MPC) method that provides robust feasibility with tractable, real-time computation. The method optimizes the closed-loop system dynamics, which involves models of the process (with parametric uncertainty) and controller at each step in the prediction horizon. Such problems are often formulated as a multi-stage stochastic program that suffers from the curse of dimensionality. This paper presents an alternative formulation that yields a bilevel stochastic optimization problem that is transformed by a series of reformulation steps into a tractable problem such that it can be solved through a limited number of second order cone programming sub-problems. The method addresses robust feasibility, manipulated saturation, state and output soft constraints, exogenous and endogenous uncertainty, and uncertainty in the state estimation in an integrated manner. Case study results demonstrate the advantages of the proposed robust MPC over nominal MPC and several other robust MPC formulations.     

电梯群的可调整鲁棒优化调度

为解决电梯群控调度(GES)中乘客交通流不确定问题, 提出基于可调整鲁棒优化的电梯群控调度方法. 基于对电梯交通流的不确定特性分析, 建立了电梯群控调度的不确定优化模型. 利用可调整鲁棒优化方法将电梯群控调度的不确定模型转化为其可调整鲁棒对等式. 在此基础上, 证明了在不确定集为椭球集直积时, 电梯群控调度模型的可调整鲁棒对等式(ARC)是可计算的. 仿真验证表明, 与其他的调度方法相比, 该方法具有较好的调度性能, 提高了调度对不同乘客交通流模式的适应性.     

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.     

LOcal Uncertainty Processing (LOUP) method for multidisciplinary robust design optimization

In this paper, we develop an easy-to-implement approximate method to take uncertainties into account during a multidisciplinary optimization. Multidisciplinary robust design usually involves setting up a full uncertainty propagation within the system, requiring major modifications in every discipline and on the shared variables. Uncertainty propagation is an expensive process, but robust solutions can be obtained more easily when the disciplines affected by uncertainties have a significant effect on the objectives of the problem. A heuristic method based on local uncertainty processing (LOUP) is presented here, allowing approximate solving of specific robust optimization problems with minor changes in the initial multidisciplinary system. Uncertainty is processed within the disciplines that it impacts directly, without propagation to the other disciplines. A criterion to verify a posteriori the applicability of the method to a given multidisciplinary system is provided. The LOUP method is applied to an aircraft preliminary design industrial test case, in which it allowed to obtain robust designs whose performance is more stable than the one of deterministic solutions, relatively to uncertain parameter variations.     

Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning

Planning infrastructure networks such as roads, pipelines, waterways, power lines and telecommunication systems, require estimations on the future demand as well as other uncertain factors such as operating costs, degradation rates, or the like. When trying to construct infrastructure that is either optimal from a social welfare or profit perspective (depending on a public or private sector focus), typically researchers treat the uncertainties in the problem by using robust optimization methods. The goal of robust optimization is to find optimal solutions that are relatively insensitive to uncertain factors. This paper presents an efficient and tractable approach for finding robust optimum solutions to linear and, more importantly, quadratic programming problems with interval uncertainty using a worst case analysis. For linear, mixed-integer linear, and mixed-integer problems with quadratic objective and constraint functions, our robust formulations have the same complexity and tractability as their deterministic counterparts. Numerous examples with differing difficulties and complexities, especially with selected ones on network planning/operations problems, have been tested to demonstrate the viability of the proposed approach. The results show that the computational effort of the proposed approach, in terms of the number of function calls, for the robust problems is comparable to or even better than that of deterministic problems in some cases.