Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such ...problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution.
Hybrid dynamical systems Goebel, Rafal; Sanfelice, Ricardo G; Teel, Andrew R
2012, 2012., 20120318, 2012-03-18
eBook, Book
Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, ...this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components.
Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of ...real‐world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. We present a novel deterministic mixed‐integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics‐based constraints on the first and second derivatives.
This work presents a review of the main deterministic mixed‐integer nonlinear programming (MINLP) solution methods for problems with convex and nonconvex functions. An overview for deriving MINLP ...formulations through generalized disjunctive programming (GDP), which is an alternative higher‐level representation of MINLP problems, is also presented. A review of solution methods for GDP problems is provided. Some relevant applications of MINLP and GDP in process systems engineering are described in this work.
The optimal design, planning, and scheduling of chemical processes requires the use of mixed‐integer nonlinear programming (MINLP) or generalized disjunctive programming (GDP) models to optimize discrete and continuous variables. Here, applications of MINLP and GDP are described, and a review of deterministic methods to solve these problems is provided.
Effective resource management plays a pivotal role in wireless networks, which, unfortunately, typically results in challenging mixed-integer nonlinear programming (MINLP) problems. Machine ...learning-based methods have recently emerged as a disruptive way to obtain near-optimal performance for MINLPs with affordable computational complexity. There have been some attempts in applying such methods to resource management in wireless networks, but these attempts require huge amounts of training samples and lack the capability to handle constrained problems. Furthermore, they suffer from severe performance deterioration when the network parameters change, which commonly happens and is referred to as the task mismatch problem. In this paper, to reduce the sample complexity and address the feasibility issue, we propose a framework of Learning to Optimize for Resource Management (LORM). In contrast to the end-to-end learning approach adopted in previous studies, LORM learns the optimal pruning policy in the branch-and-bound algorithm for MINLPs via a sample-efficient method, namely, imitation learning. To further address the task mismatch problem, we develop a transfer learning method via self-imitation in LORM, named LORM-TL, which can quickly adapt a pre-trained machine learning model to the new task with only a few additional unlabeled training samples. Numerical simulations demonstrate that LORM outperforms specialized state-of-the-art algorithms and achieves near-optimal performance, while providing significant speedup compared with the branch-and-bound algorithm. Moreover, LORM-TL, by relying on a few unlabeled samples, achieves comparable performance with the model trained from scratch with sufficient labeled samples.
In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on ...polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner,
i.e.
, only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set.
This study presents a probabilistic transmission expansion planning model incorporating distributed series reactors, which are aimed at improving network flexibility. Although the whole problem is a ...mixed-integer non-linear programming problem, this study proposes an approximation method to linearise it in the structure of the Benders decomposition (BD) algorithm. In the first stage of the BD algorithm, optimal number of new transmission lines and distributed series reactors are determined. In the second stage, the developed optimal power flow problem, as a linear sub-problem, is performed for different scenarios of uncertainties and a set of probable contingencies. The Benders cuts are iteratively added to the first stage problem to decrease the optimality gap below a given threshold. The proposed model utilises the Monte Carlo simulation method to take into account uncertainty of wind generations and demands. Several case studies on three test systems are presented to validate the efficacy of the proposed approach.
Peaking CO2 emissions and reaching carbon neutrality create a major role for hydrogen in the transportation field where decarbonization is difficult. Shanxi, as a microcosm of China in the systematic ...transformation of energy end-use consumption, is selected to investigate the hydrogen energy development forecast for decarbonization in the transportation sector. Multi-supply-demand integrated scenario analysis with nonlinear programming (NLP) model is established to analyze hydrogen energy deployment in varied periods and regions under minimum environmental, energy and economic objectives, to obtain CO2 emission reduction potential. Results reveal that green hydrogen contributes most to low-carbon hydrogen development strategies. In high-hydrogen demand scenarios, carbon emission reduction potential is significantly higher under environmental objectives, estimated at 297.68 × 104–848.12 × 104 tons (2025–2035). The work provides a strategy to forecast hydrogen energy deployment for transportation decarbonization, being of vital significant guide for planning of hydrogen energy transportation in other regions.
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•Hydrogen energy deployment for transportation decarbonization of Shanxi is proposed.•Multi-supply-demand integrated scenario analysis with NLP is used for H2 deployment.•Optimization of H2 deployment of Shanxi's transport under different 3E objectives.•CO2 reduction potential of Shanxi's transport within H2 deployment is analyzed.
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