Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA two-stage robust optimization approach for oxygen flexible distribution under uncertainty in iron and steel plants
92
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Oxygen optimal distribution is one of the most important energy management problems in the modern iron and steel industry. Normally, the supply of the energy generation system is determined by the energy demand of manufacturing processes. However, the balance between supply and demand fluctuates frequently due to the uncertainty arising in manufacturing processes. In this paper, we developed an oxygen optimal distribution model considering uncertain demands and proposed a two-stage robust optimization (TSRO) with a budget-based uncertainty set that protects the initial distribution decisions with low conservatism. The main goal of the TSRO model is to make wait-and-see decisions maximizing production profits and make here-and-now decisions minimizing operational stability and surplus/shortage penalty. To represent the uncertainty set of energy demands, we developed a Gaussian process (GP)-based time series model to forecast the energy demands of continuous processes and a capacity-constrained scheduling model to generate multi-scenario energy demands of discrete processes. We carried out extensive computational studies on TSRO and its components using well-synthetic instances from historical data. The results of model validation and analysis are promising and demonstrate our approach is adapted to solve industrial cases under uncertainty.
rate research
Read More
This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We test this robust algorithm on real market data. The results show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns. To solve for the value function, we derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by three methods: finite difference method, Monte Carlo simulation, and Generative Adversarial Networks.
Edge computing has emerged as a key technology to reduce network traffic, improve user experience, and enable various Internet of Things applications. From the perspective of a service provider (SP), how to jointly optimize the service placement, sizing, and workload allocation decisions is an important and challenging problem, which becomes even more complicated when considering demand uncertainty. To this end, we propose a novel two-stage adaptive robust optimization framework to help the SP optimally determine the locations for installing their service (i.e., placement) and the amount of computing resource to purchase from each location (i.e., sizing). The service placement and sizing solution of the proposed model can hedge against any possible realization within the uncertainty set of traffic demand. Given the first-stage robust solution, the optimal resource and workload allocation decisions are computed in the second-stage after the uncertainty is revealed. To solve the two-stage model, in this paper, we present an iterative solution by employing the column-and-constraint generation method that decomposes the underlying problem into a master problem and a max-min subproblem associated with the second stage. Extensive numerical results are shown to illustrate the effectiveness of the proposed two-stage robust optimization model.
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following the so-called scenario optimization approach. However, when the data size is small, the sampled constraints may not statistically support a feasibility guarantee on the obtained solution. This paper studies how to leverage parametric information and the power of Monte Carlo simulation to obtain feasible solutions for small-data situations. Our approach makes use of a distributionally robust optimization (DRO) formulation that translates the data size requirement into a Monte Carlo sample size requirement drawn from what we call a generating distribution. We show that, while the optimal choice of this generating distribution is the one eliciting the data or the baseline distribution in a nonparametric divergence-based DRO, it is not necessarily so in the parametric case. Correspondingly, we develop procedures to obtain generating distributions that improve upon these basic choices. We support our findings with several numerical examples.
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and consider quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP-hard but amenable to copositive programming reformulations that give rise to tight conservative approximations. We further enhance these approximations through new piecewise decision rule schemes. Finally, we prove that our proposed approximations are tighter than the state-of-the-art schemes and demonstrate their superiority through numerical experiments.
To ensure a successful bid while maximizing of profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. So distributionally robust opti-mization (DRO) is a good choice because that it can provide an adjustable self-scheduling strategy for GENCOs in the uncertain environment, which can well balance robustness and economics compared to strategies derived from robust optimization (RO) and stochastic programming (SO). In this paper, a novel mo-ment-based DRO model with conditional value-at-risk (CVaR) is proposed to solve the self-scheduling problem under electricity price uncertainty. Such DRO models are usually translated into semi-definite programming (SDP) for solution, however, solving large-scale SDP needs a lot of computational time and resources. For this shortcoming, two effective approximate models are pro-posed: one approximate model based on vector splitting and an-other based on alternate direction multiplier method (ADMM), both can greatly reduce the calculation time and resources, and the second approximate model only needs the information of the current area in each step of the solution and thus information private is guaranteed. Simulations of three IEEE test systems are conducted to demonstrate the correctness and effectiveness of the proposed DRO model and two approximate models.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
