Qipeng P. Zheng

Optimization Models in The Natural Gas Industry

With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and has yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry, with the focus on the natural gas production, transportation, and market.

Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning

Due to the increasing demands for natural gas, it is playing a more important role in the energy system, and its system expansion planning is drawing more attentions. In this paper, we propose expansion planning models which include both natural gas transmission network expansion and LNG (Liquified Natural Gas) terminals location planning. These models take into account the uncertainties of demands and supplies in the future, which make the models stochastic mixed integer programs with discrete subproblems. Also we consider risk control in our models by including probabilistic constraints, such as a limit on CVaR (Conditional Value at Risk). In order to solve large-scale problems, especially with a large number of scenarios, we propose the embedded Benders decomposition algorithm, which applies Benders cuts in both first and second stages, to tackle the discrete subproblems. Numerical results show that our algorithm is efficient for large scale stochastic natural gas transportation system expansion planning problems.

Loss-Constrained Minimum Cost Flow under Arc Failure Uncertainty with Applications in Risk-Aware Kidney Exchange

In this article, we study a Stochastic Minimum Cost Flow (SMCF) problem under arc failure uncertainty, where an arc flow solution may correspond to multiple path flow representations. We assume that the failure of an arc will cause flow losses on all paths using that arc, and for any path carrying positive flows, the failure of any arc on the path will lose all flows carried by the path. We formulate two SMCF variants to minimize the cost of arc flows, while respectively restricting the Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of random path flow losses due to uncertain arc failure (reflected as network topological changes). We formulate a linear program to compute possible losses, yielding a mixed-integer programming formulation of SMCF-VaR and a linear programming formulation of SMCF-CVaR. We present a kidney exchange problem under uncertain match failure as an application and use the two SMCF models to maximize the utility/social welfare of pairing kidneys subject to constrained risk of utility losses. Our results show the efficacy of our approaches, the conservatism of using CVaR, and optimal flow patterns given by VaR and CVaR models on diverse instances.

Multi-level inventory matching and order planning under the hybrid Make-To-Order/Make-To-Stock production environment for steel plants via Particle Swarm Optimization

A production planning problem based on MTOMTS policy for steel plant is presented.A model which co-optimizes multi-inventory matching and order planning is proposed.An improved PSO algorithm with local search and repair strategy is proposed. This paper proposes a nonlinear integer programming model which co-optimizes the multi-level inventory matching and order planning for steel plants while combining Make-To-Order and Make-To-Stock policies. The model considers order planning and inventory matching of both finished and unfinished products. It combines multiple objectives, i.e., cost of earliness/tardiness penalty, tardiness penalty within delivery time window, production cost, inventory matching cost, and order cancelation penalty. This paper also proposes an improved Particle Swarm Optimization (PSO) method, where strategies to repair infeasible solutions and inventory-rematching scheme are introduced. Parameters of PSO and the rematching scheme are also analyzed. Three sets of real data from a steel manufacturing company are used to perform computational experiments for PSO, local search, and improved PSO. Numerical results show the validity of the model and efficacy of the improved PSO method.

Robust optimization of graph partitioning involving interval uncertainty

The graph partitioning problem consists of partitioning the vertex set of a graph into several disjoint subsets so that the sum of weights of the edges between the disjoint subsets is minimized. In this paper, robust optimization models with two decomposition algorithms are introduced to solve the graph partitioning problem with interval uncertain weights of edges. The bipartite graph partitioning problem with edge uncertainty is also presented. Throughout this paper, we make no assumption regarding the probability of the uncertain weights.

Generation Expansion Planning With Large Amounts of Wind Power via Decision-Dependent Stochastic Programming

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets’ planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of wind power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning.

On the two-stage stochastic graph partitioning problem

In this paper we introduce the two-stage stochastic graph partitioning problem and present the stochastic mixed integer programming formulation for this problem with finite explicit scenarios. For solving this problem, we present an equivalent integer linear programming formulation where some binary variables are relaxed to continuous ones. Additionally, for some specific graphs, we present a more simplified linear programming formulation. All formulations are tested on randomly generated graphs with different densities and different numbers of scenarios.

Incorporating Wind Energy in Power System Restoration Planning

Wind energy is rapidly growing. While wind brings us clean and inexpensive energy, its inherent variability and uncertainty present challenges for the power grid. In particular, employing wind energy for power system restoration is very challenging. A fast and reliable restoration plays a vital role to achieve the self-healing power grid. This paper develops a novel offline restoration planning tool for harnessing wind energy to enhance grid resilience. The wind-for-restoration problem is formulated as a stochastic mixed-integer linear programming problem with generated wind energy scenarios. The problem is then decomposed into two stages and solved with the integer L-shaped algorithm. Numerical experiments have been conducted through different case studies using the modified IEEE 57-bus system. The developed tool can provide the scheduled wind power at each restoration time. The impact of wind energy is investigated from the aspects of location and inertia capability, as well as wind penetration, fluctuation, and uncertainty. Moreover, a dynamic response validation tool is developed to validate the results of optimization problem in a dynamic simulation software. Simulation results demonstrate that the optimal wind harnessing strategy can help improve system restoration process and enhance system resilience.

A MILP formulation for generalized geometric programming using piecewise-linear approximations

Generalized geometric programming (GGP) problems are converted to mixed-integer linear programming (MILP) problems using piecewise-linear approximations. Our approach is to approximate a multiple-term log-sum function of the form log (x1 + x2 + ⋅⋅⋅ + xn) in terms of a set of linear equalities or inequalities of log x1, log x2, …, and log xn, where x1, …, xn are strictly positive. The advantage of this approach is its simplicity and readiness to implement and solve using commercial MILP solvers. While MILP problems in general are no easier than GGP problems, this approach is justified by the phenomenal progress of computing power of both personal computers and commercial MILP solvers. The limitation of this approach is discussed along with numerical tests.

Online feature importance ranking based on sensitivity analysis

Abstract Online learning is a growing branch of data mining which allows all traditional data mining techniques to be applied on a online stream of data in real time. In this paper, we present a fast and efficient online sensitivity based feature ranking method (SFR) which is updated incrementally. We take advantage of the concept of global sensitivity and rank features based on their impact on the outcome of the classification model. In the feature selection part, we use a two-stage filtering method in order to first eliminate highly correlated and redundant features and then eliminate irrelevant features in the second stage. One important advantage of our algorithm is its generality, which means the method works for correlated feature spaces without preprocessing. It can be implemented along with any single-pass online classification method with separating hyperplane such as SVMs. The proposed method is primarily developed for online tasks, however, we achieve very significant experimental results in comparison with popular batch feature ranking/selection methods. We also perform experiments to compare the method with available online feature ranking methods. Empirical results suggest that our method can be successfully implemented in batch learning or online mode.