Mixed-integer nonlinear programming techniques for the synthesis of engineering systems

Optimization of a discrete event systems including (non)linear cost in local states is mainly solved either by heuristic search methods or mathematical programming. In this paper the second approach is further elaborated, including guarantees on both optimal performance and logical correctness. An integrated algorithm is developed utilizing both Operations Research (OR) and Constraint Programming (CP). The majority of integrated approaches have up till now focused on solving linear problems. In this paper we use our integrated algorithm to optimize discrete event systems with nonlinear cost and logical constraints. We present a straightforward method to incorporate OR functionality into an existing CP algorithm such that it can process nonlinear expressions, otherwise too complex for the CP algorithm to handle. Evaluation of the algorithm's performance is done by comparison to that of state of the art Mixed Integer Nonlinear Programming (MINLP) methods. The benchmark shows that our integrated approach finds the optimal solution in roughly the same time as existing MINLP methods. However, when also proof of optimality is required, the integrated algorithm outperforms the best MINLP algorithm by roughly a factor of ten.

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.

A center-cut algorithm for quickly obtaining feasible solutions and solving convex MINLP problems

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

A non-linear mathematical farm business optimisation model, that is set within a spatial economic framework, has been developed. The model incorporates factors such as location, spatial market orientation and technology use, and identifies the business strategy that is optimal in different market and policy environments. Farm household time-use is incorporated centrally within the model, enabling it to examine how on-farm and off-farm activities compete for limited farm household human resources. The model is applied to a beef and sheep farm that can choose between selling livestock to meat processors or processing on-farm and selling direct to consumers. Model simulations reveal when it is optimal for the farm business to innovate in this way and how this decision is affected by changes in key parameters. The farm business model is solved using the GAMS/LINDOGlobal mathematical programming software package. While traditional nonlinear programming and mixed-integer nonlinear programming algorithms are guaranteed to converge only under certain convexity assumptions, GAMS/LINDOGlobal finds guaranteed globally optimal solutions to general nonlinear problems. The model and model results are discussed within the context of theoretical underpinnings, model tractability, and potential applications.

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We examine various aspects of modeling and solution via mixed-integer nonlinear programming (MINLP). MINLP has much to offer as a powerful modeling paradigm. Recently, significant advances have been made in MINLP solution software. To fully realize the power of MINLP to solve complex business optimization problems, we need to develop knowledge and expertise concerning MINLP modeling and solution methods. Some of this can be drawn from conventional wisdom of mixed-integer linear programming (MILP) and nonlinear programming (NLP), but theoretical and practical issues exist that are specific to MINLP. This paper discusses some of these, concentrating on an aspect of a classical facility location problem that is well-known in the MILP literature, although here we consider a nonlinear objective function.

Mixed-integer nonlinear programming techniques for process systems engineering

Automated design of synthetic biocircuits in the stochastic regime

This chapter helps the students to identify problems related to power systems operation. It also helps the students to link mathematical optimization models to power systems operation problems. The chapter presents four common types of mathematical optimization models: linear programming, mixed-integer linear programming, non-linear programming, and mixed-integer nonlinear programming. The chapter discusses the details of continuous models. It covers one of the most classic problems in power systems operation that is the economic and environmental dispatch of thermal units. The chapter discusses hydrothermal dispatch problems, and describes one of the most important tools for the analysis of power systems: optimal power flow. It provides the information on binary problems in power systems operation that include unit commitment and phase balancing. The chapter also discusses the real-time implementation of operation models.

We present a method based on mean field theory to cope with the mixed nonlinear integer programming, especially with optimal power flow problems involving both continuous and discrete variables, in a more exact manner. That is, we first formulate OPF as a mixed integer programming, and then derive its mean field equations as well as the annealing algorithm, by taking advantage of the characteristics of the original problems. Numerical simulations have verified effectiveness of this approach for small power systems.

Development of transportation cost functions and optimization of transportation networks for solar-aided utilization of CO2

Application of Nonlinear Optimization to Reactor Core Fuel Reloading

ABSTRACTThe main objectives in the management of energy systems are to reduce the operation costs and simultaneously increase the reliability indices. The achievement of these aims is among the key challenges that network operators encounter. To overcome this challenge, the current study presents a model in which the reliability criterion is calculated in addition to the well-established technical constraints for an energy hub. In this strategy, reliability evaluations are added to the classical model as new constraints. In other words, the energy hubs can be more appropriately and realistically operated by imposing these limitations. Moreover, in addition to the costs of different energy carriers, the objective function also includes the costs of “energy not supplied” (ENS) for different loads. This approach demonstrates a mixed-integer nonlinear programming (MINLP) technique implemented using the LINDOGlobal solver in GAMS. To examine the efficiency of the proposed method, modeling is performed on a sample energy hub, and the results assessed.

Polygeneration, a multi-input multioutput energy conversion process which typically involves the coproduction of electricity and liquid synthetic fuels, is a promising technology which offers real potential toward the reduction of excessive energy consumption and consequent greenhouse gas emissions. The optimal design of such a complex and nonlinear process system under inevitable and unpredictable future uncertainty poses great challenges in terms of both modeling and corresponding solution strategies. In this paper, we propose a stochastic programming framework for the optimal design under uncertainty of polygeneration energy systems. On the basis of a detailed mixed-integer nonlinear programming (MINLP) model, proposed in our previous work, a two-stage stochastic programming problem is formulated, which is then converted into a large-scale multiperiod MINLP problem by employing cubature based integration and sampling techniques. A decomposition algorithm is utilized for the efficient solution of the multiperiod problem, which involves iterations between a set of nonlinear subproblems of much smaller size and a master mixed-integer linear programming problem. A case study is then presented, where detailed computational results and comparisons between optimal designs obtained for both the stochastic and deterministic cases are shown.